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In this special article, JYP's founder Arpan Dey discusses some of the most exciting and frequently asked questions in physics, ranging from questions on cosmology, classical physics and quantum physics to quantum gravity, chaos theory and complexity. There's definitely something in this article for you, regardless of whether you are a high-school student or a physics graduate, or just a science enthusiast. This is going to be a long read; the questions have been answered in detail, but in a simple and non-technical manner, keeping in mind that this article is aimed for young readers and the general public.
1. It's often said classical physics is wrong. Is that true? If yes, then are the present theories that seem to be correct now, actually correct, or perhaps one day we will discover even they are wrong?
-> Classical physics is wrong. It'd be better to say that classical physics is only a special case of some deeper theory. It is simply emergent from deeper and more accurate theories. It holds good enough for some limited cases. In other words, it has a limited domain of applicability, but within that domain it will always be correct. However, if we want to extend the domain, we need deeper, more fundamental theories. Classical physics works fine for a ball traveling in a straight line at 5 meters per second. This doesn’t, in my opinion, mean that classical physics is correct for the ball, but incorrect for a body traveling at light speed. A theory which is fundamentally incomplete is always incomplete, and fundamentally incorrect. Classical physics just works fine for a ball. More precisely, we can say classical physics can be assumed to be correct in a limited domain of applicability.
So, classical physics is not wrong, but incomplete. Maybe the theories we now believe to be correct will turn out to be incomplete some day in the future. The real question we face is whether there is anything final in science. Will we ever reach a final theory that is the only (or at least, the simplest) theory that explains everything and that requires no further explanation? Or will we endlessly go on discovering theories that are more accurate than the previous ones, but never truly reach a final theory? We can’t answer for sure, but it may be possible that we will discover a final, ultimate theory someday.
2. As far as I understand, Newtonian physics and electromagnetism form the two pillars of classical physics. Here’s a challenge for you! Discuss, in short, the basic concepts of Newtonian physics (both the laws of motion and Newtonian gravity) and electromagnetism, or in other words, all of classical physics.
-> Well, that’s difficult, but that’s exactly what I tried to do in the second chapter of my book Our Physics So Far. Let me do that once more. So, yeah, you're correct in saying that Newtonian physics and electromagnetism form the two pillars of classical physics. But interestingly, they are incompatible with each other, which is why theories like special relativity evolved. But anyway, coming to your question, or rather, challenge, well, yes, Newtonian mechanics. Newton developed three laws of motion, and he believed all bodies in this universe are subject to these laws. First, the law of inertia. Simply put, a body moving in a straight line will continue moving in the same straight line as long as an external force doesn’t stop it. I know that if you roll a ball, it stops after some time. But that’s because frictional force is acting between the ball and the floor on which it rolls. Inertia is simply a body’s reluctance to change its state of motion (or rest). Only when you apply a large enough force, it does. Newton’s second law relates the force acting on a body with the acceleration of the body (the acceleration is the rate of change of velocity). Force is the mass of the body multiplied by the acceleration of the body. F=ma. Force can also be defined as the rate at which the momentum of a body changes (momentum is just the mass multiplied by the velocity). Let us now discuss the law of conservation of momentum, which is a very important law in mechanics. The total momentum of a system is always conserved. Here's a simple illustration. A massive truck, moving with a high velocity, hits a stationary car. (Please note that here “massive” doesn’t mean a monster truck. In the context of physics, any body with some mass is massive.) Initially, before hitting the car, the truck had some momentum. Let us say 1000 kg m/s (the unit is kilograms multiplied by meters per second). The car had zero momentum, since the velocity of the car was zero (it was stationary). Initially, the total momentum of the truck-car system was (1000 + 0) kg m/s=1000 kg m/s. As the truck hits the car, it slows down a bit. Its velocity, and consequently momentum, decreases to (say) 800 kg m/s. The car will gain some velocity on being hit by the truck. The car already has some mass. So this time, the car will have a non-zero momentum. Can you guess what that is? Of course, 200 kg m/s. (800 + 200) kg m/s gives 1000 kg m/s. The total momentum of the truck-car system is still the same. You should keep in mind that like momentum, energy is also conserved. Energy can't be created or destroyed, just converted from one form to another. We can also state it like this: the total energy of an isolated system is constant. Anyway, back to Newton's laws. Newton’s third law can be summed up by the popular statement that every action has an equal and opposite reaction. Hit a wall at a high velocity, and you fall back. You push the wall, and the wall pushes you back. Cars move forward by pushing against the ground backward. Airplanes move forward by pushing against the air. And rockets in space move forward by using the law of conservation of momentum, because in space there's no air to push against.
Secondly, let’s come to Newtonian gravity. Let’s say you throw a ball aimed at the sky. What happens? The ball flies through the air for a few seconds and falls. Throw the ball with a higher velocity, it will fall farther away. Keep increasing the velocity. At a certain velocity the ball will start moving around the Earth. This is the orbital velocity. (If the velocity is lesser than the orbital velocity, the body will fall toward the Earth. And if the velocity is too high, the ball will fly away from the Earth. The minimum speed required to escape the Earth’s gravitational field is the escape velocity.)
Figure 1: The faster you throw a ball, the farther it will travel, until it reaches the orbital velocity when it will start orbiting the Earth (Image credit: IOPSpark)
So, in the same way, the Moon is orbiting the Earth, and the Earth orbiting the Sun, and so on. Newton gave the formula to calculate the gravitational force F between two bodies of masses M and m. If the distance between the centers of the two bodies is r, F = GMm divided by the square of r, where G is a constant. Newton’s gravitation law has been used to predict measured movements of the planets with great accuracy. Every object in the universe exerts gravitational force on every other object. Now, two balls kept on the floor don’t collide with each other. The chairs in your rooms don’t suddenly start moving toward each other. Yet, they are exerting gravitational forces on each other. Their masses are so insignificant (compared to the masses of stars and planets), this force is not enough to overcome the friction of the floor and make the chairs actually come closer to each other. Note that in physics, it is important to take into account the dominant factors and find an approximate answer. This is called the perturbative approach. For instance, as we just saw, every body exerts a gravitational force on every other body, but it is impossible to calculate the exact effects of all these bodies on the Earth. To describe the motion of Earth around the Sun, we simply take into account the dominant player: the Sun. We then get an approximate answer. To make our answer more accurate, we can then take into account the Moon's gravity and so on. Perturbation is a very important concept in science. Perturbation means you take into account the dominant factors and roughly find an answer, an approximate one. Then you take into account the finer details and modify your solution and make it more accurate. From Newton’s laws, one can derive equations for the time period of satellites, range of a projectile on an inclined plane, and the list is endless… However, Newton's theory of gravity has one serious problem. It doesn't explain what gravity is. It just explains the features of gravity. The answer to that question - what exactly is gravity - was given by Einstein in his general theory of relativity.
Now, electromagnetism. I’ll start by assuming you know that there are two kinds of charges: positive and negative, and that charge is an intrinsic property. Charge is to electromagnetism what mass is to gravity; they determine to what extent an object will respond to the force. Also keep in mind that electromagnetism is much, much stronger than gravity, yet gravity dominates the universe because most objects are neutral (they have an equal amount of positive and negative charges) and thus, don't respond to electromagnetism. All objects are massive, on the other hand, and respond to gravity. So, what's electromagnetism? Electricity is concerned with the interaction between charges. On the other hand, moving charges (or current) cause magnetism. Ampere suggested that magnetism is caused by circulating currents. The electron (which is a charged particle) is revolving around the nucleus of the atom, so it's basically just a loop of current. And there is an orbital magnetic moment associated with the moving electron. But fundamental particles like electrons also have an intrinsic magnetic moment (the spin magnetic moment). The electron is a negatively charged particle, and in fact it is the smallest charge that can exist independently. Phenomena like electricity and magnetism are studied by adopting the idea of electric and magnetic fields. You can think of a field as a physical quantity that has a value for each point in space and time. A field is the range of influence of the force. Some fields extend infinitely. So, there are electric fields and magnetic fields. A charge in rest produces an electric field, and a charge in motion produces a magnetic field in addition to an electric field. Electric field lines (an electric field line is an imaginary line drawn from a point of the field so that tangent to it, at any point, gives the direction of the electric field at that point) point away from positive charges and toward negative charges. Charges of the same type (like both positive or both negative) will repel, but unlike charges (a positive and a negative charge) will attract because the electric field lines will emanate from the positive charge and terminate at the negative charge, thus "joining" the two charges together.
Figure 2: Electric field lines point away from positive charges (+) and point toward negative charges (-); this is why like charges repel and unlike charges attract (Image credit: Brilliant)
A positive or a negative charge can exist independently, and so electric field lines can emerge out of a positive charge and spread till infinity. But in magnetism, magnetic monopoles can't exist. If there is a north pole, there must be a south pole. Or in other words, a north pole can't exist independently from a south pole. Magnetic field lines of force travel from the north to the south pole outside the magnet. Since monopoles can't exist, we see that the number of magnetic field lines entering a region must be equal to the number of field lines leaving that region. As there are no magnetic charges from which magnetic field lines emanate or at which magnetic field lines terminate, any magnetic field line entering must exit through the surface.
Magnetism was initially thought to be a completely different phenomenon from electricity. However, it was gradually discovered that electricity and magnetism aren't separate forces. They are actually the different sides of the same coin. They are both emergent from a deeper, unified force. Electromagnetism. Faraday discovered the phenomenon of electromagnetic induction. Just like a moving electric charge can produce a magnetic field, changing magnetic flux (the number of magnetic field lines passing through a given area) can produce electric current. This principle is used in generators, for instance. What Maxwell did was describe all of electromagnetism in four equations. These were not his own equations, but he did modify Ampere's law. Maxwell also found that electric fields and magnetic fields can "reinforce" each other (a varying electric field will give rise to a magnetic field, which, in turn, will give rise to another electric field and this would continue) and propagate as an electromagnetic wave even in vacuum. He also found that the speed of the electromagnetic wave is equal to the speed of light, and from this he concluded that light is an electromagnetic wave. So, that's all, I think.
3. What is Lagrangian mechanics and how is it different from Newtonian mechanics?
-> It was noticed, long back, that light follows the shortest path (the straight-line path) in a single medium. This can be called the principle of least distance. However, we know that light doesn't travel in a straight line when it moves from one medium to another (refraction). Fermat proposed that light doesn't take the shortest path, but rather the quickest path (principle of least time). And the quickest path between two media is not the straight-line path, because light travels at different speeds in the two media. (So, it makes sense to travel more distance in the medium in which the speed of light is more, instead of traveling in a straight-line path.) This has led many to wonder whether some "minimizing principle" can explain the motion of all material bodies, just like minimizing time explained the motion of light and in principle, all of optics. It was Lagrange who discovered that matter always follows the path which minimizes the difference between the kinetic and potential energies. (Kinetic energy is the energy of a moving body, like when it's in motion. Potential energy is the energy of a body by virtue of its position. Like when a ball is positioned at the top of a tower, its kinetic energy is zero since it is at rest, and the potential energy is maximum. As the ball falls, its potential energy decreases, since the potential energy depends on the height, and the kinetic energy increases due to increasing velocity. It is obvious that the sum of kinetic and potential energies remains constant for a body.) Anyway, it is the difference between the kinetic and potential energies that is minimized, and Lagrange called this action. Actually, the action is the integral over time of the difference between these two energies, and just this difference is called the Lagrange. Well, this is not the actual definition, but this can be assumed to be true for most cases, at least at this stage. So, the motion of all bodies tends to minimize the action (principle of least action). This led to the development of Lagrangian mechanics, which is much simpler and more fundamental or general than Newtonian mechanics (and they make the exact same predictions). Of course, it requires a change in perspective, but Lagrangian mechanics deals with many complex problems in a beautiful way.
4. You mentioned that Newtonian physics is incompatible with electromagnetism, which is why special relativity was developed. Could you briefly explain the basic idea behind special relativity in simple terms?
-> Sure, let me try. Einstein proposed the special theory of relativity mainly to explain the fact that light always travels at a constant speed. This was the prediction of electromagnetism. It has been verified experimentally and predicted theoretically that light always travels at its constant speed irrespective of whether an observer is stationary or moving (moving at a constant speed; or not accelerating). But, from the perspective of Newtonian mechanics, this is not intuitive. If you are chasing a car which is driving at 100 kilometers per hour at 70 kilometers per hour, then essentially, from your frame of reference, the speed of the fugitive is 30 kilometers per hour (100 - 70). But if you happen to be chasing a beam of light, even in your reference frame, the speed of light will still be the usual constant. It's as if light speeds up as you chase it. Einstein proposed to treat time as the fourth dimension, which, along with the three space dimensions, forms a spacetime continuum. Using the Lorentz transformations, he was able to show that perceptions in length and time change, according to an external observer who is moving at a constant velocity different from that of the vessel being observed. He predicted that no body, with no matter how small a rest mass, could ever reach or exceed the speed of light. This is because, as a body speeds up, its mass increases, and more energy is needed to accelerate further. This increase in mass is apparent only at near-light velocities. Mass can actually be converted into energy, and since the faster the body moves, the more will be its energy, its mass will also increase and you would need even more, actually infinite, energy to move the body faster than the speed of light.
Maxwell had already proved that light is an electromagnetic wave, or a wave with vibrating electric and magnetic fields, that travels at the constant speed of 299792458 meters per second (in a vacuum). But what happens if you chase a light beam? Intuitively, light should slow down in your reference frame. But that's not the case. Light always travels at its constant speed. Based on this result, Einstein predicted modifications to the perception of length and time. Speed depends on length and time; it is the distance/length divided by the time. So, it is obvious why keeping the speed of light constant will demand modifications on length and time. When you are in motion, your length contracts to an external observer and the flow of time in your reference frame will slow down (length contraction and time dilation). These effects become obvious only when you're moving very, very fast (at near-light speeds). But don't think these effects don't occur for cars and planes. We just don't have the technology to observe it, because the difference is tiny. And keep in mind an important point: For events occurring at the same place and same time, any perceptions of length contraction and time dilation, individually, is not possible. If two bodies collide, then no observer in this universe can see them miss one another. So if you thought that up for a sci-fi story, throw it out of your head.
And of course, the most famous result of the special theory of relativity is that mass and energy can be converted into one another and are related by the famous equation E = m multiplied with the square of c, where E is the energy, m is the mass and c the speed of light in vacuum. All this equation is saying is this very important fact (once more): mass can be converted into energy and vice versa. More precisely, a small amount of mass can be converted into a huge amount of energy, because c is a huge number, and the energy is the mass multiplied by the square of c.
So, now you may ask how does all this relate to electromagnetism? A proper answer to that question will require some technical knowledge of physics. But the basic idea is that special relativity predicts that an electric field can be viewed as a magnetic field in some other reference frame, and vice versa. This solves the problems in electromagnetism which arise when we view the same scenario from different reference frames. We learned in the previous chapter that moving charges create a magnetic field. But, why? Well, the answer is given by special relativity. Since there is relative motion between the charged particle and the observer, a magnetic field appears to exist around the particle.
5. I really can’t get my head around the idea that mass increases as we speed up. Could you help?
-> Let me try. All I ask of you, assume that the speed of light is constant in all non-accelerating reference frames. So suppose you are driving a car at x meters per second in vacuum. (Don't ever let the value of x increase too much, for it is better to lose one minute in life than to lose the life in a minute!) The light from your headlamp, to an external observer, obviously travels at the usual (3 times 10 raised to the power of 8) meters per second (299792458 meters per second, more precisely). But you are already moving at x meters per second in the same direction. So, the light should be moving away from you at x meters per second less than c. But that doesn’t happen. This means, hypothetically, the x meters per second must have been "eliminated." The speed of your car decreases, and so it takes more time to accelerate, which means that the mass of the car has somehow increased (keep in mind that mass can be converted into energy). Yes, it happens. Think of it like this: the car is moving, so it has some energy, and energy can be converted into mass, so its mass must increase. Of course, your car wouldn’t become 10 kg heavier than it was at rest for traveling at, say, 90 kilometers per hour, but your car’s and your masses actually increase by a small amount when you are moving. The faster you move, the more is the increase in the mass and thus, you can never exactly reach light speed (more mass means more energy to keep moving, meaning you'd need an infinite amount of energy to reach the speed of light). But you are never going to drive at such velocities. So, you aren’t wasting your time at the gym even if you are driving home at 90 kilometers per hour.
6. Alright, that helps! Could you illustrate length contraction and time dilation with examples?
-> Okay. Let's start with length contraction. I’m going to use the example Einstein himself used in his book Relativity: The Special And The General Theory. Suppose that lightning hits simultaneously at two points A and B, both located on a railway platform. A person standing on the midpoint of the line joining A and B will call the lightning strikes simultaneous because he sees both the lightning strikes at the same time. The distance between this person and A is the same as the distance between him and B, so the light beams from A and B reach him at the same time. But if you are in a train coming from the direction of B and moving toward A, you would find that the lightning strike at A occurred before the one at B. This is because the train, which you are using as your frame of reference, is speeding away from B and toward A, so the light from the lightning strike at A needs to travel a lesser distance to reach you than the one from B. This time, you are not just standing stationary at equal distances away from both the points. You are moving toward one and away from the other.
Figure 3: According to a person inside the moving train, the lightning strike at A occurred before the one at B, but to a person standing outside at the midpoint of the line joining A and B, they are simultaneous (Image credit: Texas Christian University)
Both the observer on the train and the stationary observer are correct in what they say. There is no objective, universal law that determines whether the lightning strikes are simultaneous or not. What we can ask is whether they appeared simultaneous to you, which depends on the state of motion of your reference body with respect to the points A and B. Perceptions of length and time vary person to person. That’s relativity.
Now, time dilation. Here's a simple thought experiment to understand time dilation. Suppose a photon of light is traveling up and down vertically between two parallel mirrors (this setup is called a light clock). One tick of this clock is equivalent to the photon traveling from the lower mirror to the upper mirror and back again. Now bring in a second light clock which is moving at a constant velocity with respect to the first light clock (the first clock is stationary). Now, the moving light clock can claim that it is at rest, and the world is moving in the opposite direction. This is an equivalent description and is, in no way, wrong. But this means, the photon should also move horizontally with the light clock in addition to moving vertically. Because if the photon moves just up and down, and the parallel mirrors are moving forward horizontally, the photon will then escape the system. And in that case, the moving clock can't claim it is stationary, because the photon has escaped it, it is no longer the same clock. But it should be. So, the photon should move both horizontally and vertically at the same time, and thus it will follow a diagonal path, which means it needs to cover a greater distance than the photon in the stationary clock. And since the speed of light is the same everywhere, traveling a greater distance will take more time, so the moving clock will tick less frequently than the stationary clock. Thus, in some sense, time flows more slowly for the moving clock.
Figure 4: Time dilation in the moving light clock (Image credit: University of Virginia)
7. How exactly do we interpret time in special relativity? What do we mean by time being the fourth dimension?
-> Consider we live in a two-dimensional world. We can move straight in direction x, in which case our velocity along direction y would be zero; we can move strictly along direction y, in which case our velocity along direction x would be zero; or we can move at an angle to both x and y, so that our velocity will be divided into two components: the x component and the y component. So, motion can be shared between two dimensions (the x and y directions). And when motion is shared between two dimensions, the speed in a single dimension will decrease. Suppose you are moving with a speed of 100 kilometers per hour strictly in the x direction. Your speed along x direction is 100 kilometers per hour and along y direction it is zero kilometers per hour. Now if you are moving with the same speed at an angle with the x (and y) directions, your speed just along the x or y directions will decrease; it is being shared between two dimensions. Einstein assumed time to be just another dimension of the universe. We are all moving through time. We can't stay fixed in time. Time is passing by. So, time's just another dimension like the three space dimensions, and Einstein called all these four dimensions together “spacetime.” Einstein assumed that all bodies in the universe are moving through spacetime, always, at the speed of light. Note that this is the speed of the body moving through all four dimensions. When a body is at rest with respect to the three space dimensions, it is moving through time at the speed of light. If it's moving through space at some finite speed, it will experience time dilation, as we've already discussed, because the velocity is being shared between the space and time dimensions. If your speed through space increases (even if by a little amount), your speed through time (or in other words, the flow of time) will have to decrease. In fact, if the body moves at the speed of light through space, its motion through the dimension of time is zero. This means light or photons do not perceive the flow of time. There is no flow of time at light speed. Time has stopped, but only in the reference frame of light.
8. So there is something called general relativity, which was discovered after special relativity. What was the need of this new theory? I mean, what was wrong with special relativity?
-> Einstein was not the type to be satisfied by the special theory of relativity. Because special relativity is incompatible with Newton's theory of gravity. In Newton's theory, the force of gravity acts instantaneously, faster than the speed of light. All Newton's theory says is gravity depends on mass (directly proportional) and the distance between the two bodies (inversely proportional to the square of the distance). It acts instantaneously. But according to Einstein, nothing (including the effects of gravity) can exceed the speed of light. After over ten years of struggle through the thickets of spacetime, Einstein found a theory of gravity compatible with special relativity. This is perhaps the best example of a theory comparable to quantum mechanics that has been developed almost single-handedly. General relativity, like quantum mechanics, remains one of the greatest theories in physics, and has been repeatedly verified experimentally as well.
Also recall that I mentioned that special relativity holds only if the observer who is in motion is moving at a constant speed. In other words, the observer is not accelerating, or his speed is not changing with time. Special relativity is not a complete theory because it doesn't work for accelerating reference frames. General relativity solves this problem as well. I mean, that's why it's called "general," it holds for all cases, not just some special cases, so it's a more general theory. It's, in some sense, an extension of special relativity to include accelerating reference frames into the picture.
9. So, what's the basic idea of the general theory of relativity?
-> General relativity, Einstein's new theory of gravity, forms the basis of modern cosmology and has provided a new interpretation of spacetime. General relativity treats gravity not as a force, but as the consequence of movement of bodies in curved spacetime. For instance, the Sun distorts or warps the spacetime continuum (spacetime is treated as a continuum in relativity, formed by the three space dimensions and one time dimension), due to which planets like Earth follow a circular path around it. The Sun is not exactly pulling the Earth.
Figure 5: The Sun, the Earth and any massive body is responsible for warping the spacetime around it (Image credit: SciTechDaily)
Have you noticed how water spirals inward toward the center, in a basin? The basin is curved inward. It appears as if a huge, invisible body has been placed on a flat surface, which, due to the body’s weight, has curved inward. The same is the case with the Sun and Earth. Imagine spacetime to be a big, flat sheet which stretches away infinitely in all directions. (This is just to make you understand, for spacetime is not actually a flat or two-dimensional sheet. It is, as we know, four-dimensional.) If you put a heavy object (the Sun) somewhere on this sheet, there will be a depression in that region. The sheet will be curved downward at that point. Now drag in another, smaller body (the Earth) into the picture. Give it a minimum velocity, and it will continue to move around this big body in circles (or in ellipses, but you get the point). The water comes closer and closer to the center since it lacks the velocity required to orbit continuously. The Earth doesn’t move closer and closer to the Sun, but moves in a fixed orbit, because it has the required velocity to orbit. Now, is the bigger body exerting a force on the smaller one to keep the latter in orbit? No! It seems true. But it’s just a consequence of the curvature of spacetime.
Note how Einstein's view of gravity is consistent with the features of Newtonian gravity. More the mass, more the curvature of spacetime, and more the effect of gravity. Also, a massive body will distort the surrounding space, but as we move farther and farther away from the body, the effect on spacetime will be less and less pronounced. So, gravity decreases with increasing distance. Also, note that Earth also curves the spacetime around it, and this is what keeps the Moon in orbit and keeps the atmosphere and us (among other things) stuck to its (Earth's) surface. And this new view of gravity solves the incompatibility of special relativity with Newton's theory of gravity. Gravitational effects are transmitted as ripples through the fabric of spacetime at the speed of light (not faster than the speed of light, not instantaneously).
So since gravity is a consequence of the curvature of spacetime, gravity can "slow down" time in addition to warping space. Clocks will tick slower in a gravitational field. This has been verified experimentally. A clock high above in space will tick slightly faster than a clock here on the Earth (within the Earth's gravitational field). But what's important is that it is technically incorrect to say that gravity slows down time. Rather, gravity is a consequence of the warping of time. Remember, time is just a fourth dimension in relativity. Gravity is a consequence of the curvature of spacetime (and not just the curvature of space). One more thing to note. We said that a massive body sinks the spacetime sheet. First, why should it sink downward? Due to gravity? Not quite. We're trying to explain gravity. When the Sun is placed in the fabric of spacetime (which, actually, is not a sheet, rather a four-dimensional continuum), spacetime responds by warping. And this warping is what gives rise to gravity.
Einstein figured out that it is impossible to distinguish between the effects caused by acceleration and gravity. He called this the equivalence principle. In special relativity, we saw that for bodies moving at constant velocities, each body's reference frame is a valid one to describe the world. Observers may disagree on perceptions of length and time, but each observer is equally correct in his frame of reference. But, what about bodies undergoing accelerated motion? General relativity solves this problem. As Greene writes in his book The Elegant Universe: "Since there is no difference between an accelerated vantage point without a gravitational field and a non-accelerated vantage point with a gravitational field, we can... declare that all observers, regardless of their state of motion, may proclaim that they are stationary and the "rest of the world is moving by them," so long as they include a suitable gravitational field in the description of their own surroundings. In this sense, through the inclusion of gravity, general relativity ensures that all possible observational vantage points are on equal footing." In other words, all reference bodies are equivalent for the description of natural phenomena, irrespective of their state of motion. This, in some sense, establishes the symmetry between all reference bodies.
Another important prediction of general relativity is that light bends under the influence of a gravitational field. How exactly did Einstein figure out that gravity bends light? Imagine the following situation. A body is accelerating upward with a person inside it. If a light is switched on outside it, and the light beam propagates in a straight line, then from the accelerating body, the light would seem to be following a bent path (a parabolic curve, to be more precise). As the body accelerates upward, with time, the light that was near the top of the body seems to have reached the bottom of the body, in addition to moving forward. And the light doesn't travel diagonally in a straight-line path because the body is not moving at a constant velocity, but is accelerating. (Try to find out why!) So, light is following a curved path in the accelerated body. And as we just learned, gravity is indistinguishable from acceleration. Thus, light must also follow a curved path under the influence of gravity (that is, in a gravitational field). Einstein reasoned that light is actually following the shortest path, which isn’t always the straight-line path. (The shortest path from country A to country B is a curved one, for instance, because the Earth is not flat.)
10. Alright. But I didn't get the part about gravity being the same as acceleration. Like, could you intuitively show why this is the case?
-> Well, sorry, I should've made it clearer. We discussed how gravity is related to the warping of time. So, intuitively, the flow of time will not be constant in the presence of gravity. And velocity is distance (more precisely, displacement) divided by time. So, velocity depends on time, and thus it will not remain constant. So, there is acceleration.
Actually, the concept of gravity (or better, gravitational fields) is just a theoretical idea. Here's why. According to what we just discussed, an observer in a closed body can’t distinguish between the effects produced by a gravitational field and those produced by an actual acceleration of the body. So (wait for it!), there are no gravitational fields. You are accelerating upward now. In curved spacetime, you must accelerate just to remain stationary. Of course, you can’t feel it, since everything around you is accelerating upward at the same rate as well. This is a possible way to describe the world. And a man who is falling downward can see this acceleration. Suppose you fall from the roof of a very high building. When you are falling through the air, you don’t feel your weight. If you drop something, it falls with you at the same rate. And you are not accelerating. You are not in any gravitational field. There is no such thing as a gravitational field. This was Einstein’s "happiest thought." Now consider a man in a spaceship in deep space, away from large masses. This man feels no acceleration. The spaceship is at rest or moving at a constant velocity. This situation is equivalent to the situation of the falling man. So anyway, the point is, Einstein didn't really explain gravity, he explained what really gives rise to the illusion of this attractive force called gravity.
11. Almost every physics lover is fascinated with black holes. When the first image of a black hole was captured by the Event Horizon Telescope, everyone was talking about how the predictions of general relativity were true. I mean, in this context, we also hear of wormholes and white holes. Could you discuss these briefly? What is the difference between black holes, white holes and wormholes?
-> We know that light bends when it comes very close to a strong gravitational field, or in other words, a deep spacetime curvature. What if this curvature is infinite? What if the strength of the gravitational field is infinite? The answer is simple. If light comes too near to such a place, which we call a black hole, even light – unstoppable light which flies through the vacuum at an alarming and constant speed of about 300000 km per second – can’t escape. In other words, the escape velocity of a black hole is greater than the speed of light.
Einstein's equations predicted that a sufficiently dense object would be surrounded by a surface where time freezes, and it sucks in light, matter and even space into a point called singularity where the gravitational field is infinite. But infinities often turn out to be "glitches" in the theory, and physicists (Einstein included) didn't believe that such objects could actually exist in reality. It was then discovered that a symmetrical, perfectly spherical and smooth ball of dust could indeed collapse into a singularity. But it was assumed that nothing in this universe is perfectly spherical or smooth. So, real objects can't collapse into singularities. Then Penrose showed that, according to general relativity, any distribution of matter, no matter how rough or unsymmetric, could form a singularity if compressed into a very small volume. There are holes in the fabric of spacetime. Penrose showed that space and time end at the singularity. Physics breaks down there. General relativity breaks down there.
Now, how does a black hole form? First, we need to know how stars are formed. Stars are born in nebulae (massive clouds of hydrogen gas gradually collapsing, to some extent, under gravity). When the nebula turns stable, it is a star, which fuses nuclei of hydrogen to form helium. But since the resulting nucleus is less heavy than the original nucleus, the remaining mass is converted to energy and this we see as light (and heat). (Note that for fusion reactions to occur, we need to bring two nuclei, both positively charged, close to each other by overcoming electrostatic repulsion. This takes a huge amount of energy. In stars like the Sun, fusion occurs even though this extra initial energy is not present, due to a phenomenon called quantum tunneling. Once the fusion reaction starts, further energy can be easily generated.) For most of their lifetime, stars fuse hydrogen into helium, but near the end of their lives, the stars can form heavier elements like carbon, oxygen and most other elements we are made of. So, basically, a star is a burning sphere of hot gases which is balanced by two forces: the gravity which tends to collapse the star, and the nuclear forces which tend to blow it up. Stars eventually run out of their "nuclear fuel" or hydrogen. Gravity will take over after some time (a really long amount of time). Now, black holes. Well, if the star has enough mass, and after going through certain stages (like a supernova explosion; as the star runs out of fuel, the core collapses and there is then a huge explosion which we call supernova, in which most of the outer matter of the star is blown away), the star may finally collapse into a black hole and its gravity would be so strong that its escape velocity will be greater than the speed of light. This is why we call them black holes, since light can’t escape the "black" holes and reach our eyes.
Now, white holes. Well, an equation can have more than one solution. The simplest example is a quadratic equation, which has two solutions. So, one of the solutions to Einstein’s equations (which, of course, are way more complicated than a quadratic equation!) predicts the existence of black holes. But the existence of a white hole – which is in a certain sense the opposite of a black hole – is equally acceptable theoretically. I mean, white holes are also predicted by a different solution of Einstein's equations. Although white holes seem to violate certain physical laws, but if they exist, they are expected to spit matter outward. Just like a black hole allows nothing to exit and sucks in everything, white holes let nothing enter and spit everything out. Some believe that a black hole can only shrink to a finite extent. Then it hits a natural limit and rebounds outward. The shrinking black hole turns into an expanding white hole and ejects all the mass the black hole had previously sucked. Also, note that white holes are expected to be short-lived since they are unstable. And interestingly, the Big Bang and the formation of our universe could potentially be the result of a white hole spewing out all the matter we observe in our universe. However, we have no conclusive evidence of the existence of white holes.
And finally, wormholes. Well, the fundamental question is whether space can tear, like a piece of cloth. According to general relativity, space is smooth and can't tear. General relativity doesn't work if there is a tear in the fabric of spacetime. But some recent theories, like string theory, predict that under certain circumstances, space can tear and even rejoin. So what's a wormhole? Suppose space at point A tears and starts stretching toward point B. The space at point B also tears and starts growing toward point A. At one point, they merge, and they create a new region of space, a shortcut between points A and B. That's a wormhole. We don't know whether they are tiny, or huge, or whether they exist at all. Note that black holes are different from wormholes. Black holes are formed due to a very intense gravitational field, and at the singularity of the black hole, we expect there is a hole in the fabric of space. Wormholes are completely different.
12. Could you briefly discuss the Big Bang theory, dark matter and dark energy, the most important ideas in cosmology?
-> Sure. I’ll try my best. For a three-dimensional isotropic universe, as Friedmann showed, Einstein’s equations produce either expanding or contracting solutions. But back then, it was believed that the universe was static. To overcome this problem, Einstein introduced the cosmological constant to his equations, basically "to keep the universe static." But then it was discovered (rather accidentally) that the universe is actually accelerating away in all directions, that is, expanding at a tremendous rate. This has been verified experimentally. For instance, the redshift of galaxies is enough to show that the galaxies are moving away. (Whenever anything moves away, it appears red shifted (red light has longer wavelength and lower energy) and whenever it comes nearer, it is blue shifted.) The cosmic microwave background also supports the idea. At the very beginning, everything existed in a plasma state, which has cooled down to eventually form atoms. The remnants of this plasma should be present far away in all directions, at the very edge of the visible universe. This has actually been detected uniformly from all sides. So if the universe is expanding, then going back in time, we see that the universe contracts and contracts till it reaches an infinitely small size. It is, thus, obvious that the universe must have formed from a single, minute, infinitely dense and huge concentration of energy. It is speculated that this state can be achieved by quantum fluctuations in the vacuum. (Quantum fluctuations are random and temporary changes in the amount of energy at a point in space. They have been detected and explained by quantum mechanics.) Anyway, this infinitely dense point started to expand (the Big Bang) and cool down, leading to the formation of the fundamental particles and atoms. Eventually, in places, the expansion slowed down and huge, rotating clouds of gases were confined by gravity to such an extent that the internuclear distances were small enough for nuclear fusion reactions to start. Thus, stars formed, and they eventually spat out clumps of matter that became the planets, which began orbiting the stars. Well, I have somewhat simplified the scenario: first galaxies were formed, then stars and planets. But the basic process is the same. Also, I say all this like it's pretty obvious, but it took a lot of effort and breakthroughs to reach these conclusions. We didn't know anything about stars initially. It was speculated long ago that the stars are just like the Sun, but only after calculating the distance of the stars (using the parallax method and inverse-square law) did we find out that the luminosity of some stars are similar to that of the Sun. Then spectroscopy was discovered, and it was found that the Sun and most stars are made of hydrogen, which was a familiar element. Spectroscopy also revealed the temperature and size of stars. Then we discovered galaxies and stuff. And the possible origins of our Solar System and so on... It should be noted that the Big Bang theory is a theory that explains the evolution of the universe, and not its origin. Also, after the Big Bang, the universe didn’t expand into space, but space itself expanded. There was simply no space and time before the Big Bang (according to many physicists, that is). It all began with the Big Bang. But maybe that's not entirely correct. Our known physics simply breaks down at the Big Bang, so likely we are missing some important parts of the picture here. Sean Carroll puts it in a better way in his book The Big Picture: "...the Big Bang doesn’t actually mark the beginning of our universe; it marks the end of our theoretical understanding."
Now, dark matter. First, we need to know about the matter density of the universe. In short, it is the average amount of matter present per unit volume of the universe. Interestingly, the value of the matter density will determine the fate of the universe. There are three possible ways the universe could end. In the "big freeze" prediction, our universe would continue expanding, but stars and galaxies would simply stop existing. Thus, planets would also be destroyed, and the universe would exist as an empty space. In the "big rip" prediction, the gravitational force can’t stop the expansion and over time, the expansion takes over, and everything is ripped apart. If the density ρ of all matter and radiation in the universe is above (10 raised to the power of -29) grams per cubic cm (i.e., the critical density ρc), the universe should re-collapse into a tiny, infinitely dense point, i.e., closed universe ("big crunch" prediction). If it is less than that, then the gravity generated will not be enough to stop the expansion, which will keep increasing, and "big rip" might indeed be the outcome (open universe). It is interesting to note that the "big crunch" prediction leaves open the possibility of a "big bounce," i.e., from that infinitely dense point, a new universe may again form... If the average density of all matter in the universe is exactly equal to the critical density, on the other hand, the universe will still expand but at a slower rate (flat universe). It is reasonably certain that the universe is actually a flat universe. So yeah, what’s dark matter? Astronomical observations of galaxies give us a clue to the actual value of the matter density because most of the matter is largely concentrated in the galaxies. However, all approximations give values that are much, much less than the required critical density. Thus, there must be some matter which can’t be perceived by us. This is the idea behind dark matter. This also solves another problem. Observations suggest that the outermost stars in many galaxies are moving too fast for the mass of the galaxy to be able to hold on to them; yet the stars don’t escape the galaxy. This can be accounted for by the dark matter present in the galaxy. Dark matter should be such a form of matter that it responds to only gravitational interaction and no other interaction. Thus, although we can't perceive it, it actually has mass, and this can help keep the matter density equal to the critical density.
However, dark matter has nothing to do with dark energy. Recent measurements of the red shifts of certain supernovas have revealed that the universe has been expanding at an accelerated rate for the last 5-6 billion years. Matter has attractive gravitational properties and should, thus, slow down the expansion. A form of matter that would exhibit repulsive gravitational property is needed to accelerate the universe’s expansion. This is called dark energy. Interestingly, Einstein’s cosmological constant, which he agreed to be the "biggest blunder" in his life and which he added to his theory to "keep the universe static," actually exhibits the properties that are required here. It provides an effective matter density to have a flat universe and also, at the same time, causes gravitational repulsion to speed up the expansion. I know terms like "gravitational repulsion" might make no sense, but we can’t discuss this in detail here. There are a lot of ideas about dark energy which you can explore, but it's something we don't fully understand yet. Alan Guth proposed that the universe went through a period of sudden, rapid expansion during the early phase (inflation). This idea is an appealing one since it solves a lot of problems in cosmology. It explains why the universe is homogeneous in all directions. It also explains the flatness problem (why the universe is flat): when a curved surface expands exponentially, it would appear flat. However, there is one common misconception about the inflation theory. It need not be true that inflation happened shortly after the Big Bang. Rather, inflation caused the "bang" in the Big Bang. It is expected that inflation will eventually end in a Big Bang, and so the Big Bang that started off our universe might not have been the beginning, but just the end of inflation in a certain region of space. I know that probably didn't make sense to you. Inflation has some assumptions that actually don't make sense at first glance. But it’s not possible to discuss inflation in detail here. I myself don’t have a very good technical understanding of inflation. But yeah, inflation solves a lot of problems in cosmology. And most physicists have accepted the idea. And there is some experimental support as well. Also, most inflation models seem to support the idea of a multiverse, or the existence of parallel universes.
13. I’ve always been interested in matter-antimatter asymmetry. Speaking of which, what exactly is symmetry and why is it such a big deal in physics? And yeah, what is the matter-antimatter asymmetry? I do know that antimatter is basically ordinary matter with the opposite charge.
-> Symmetry plays an important role in physics. Symmetry doesn’t only mean the symmetry of things, but also the symmetry of laws. By symmetry of laws, we mean that if certain properties of the particles or fields are changed in a certain manner, the laws governing those particles or fields don’t change. It is important to note that every symmetry gives rise to a conserved quantity. Noether's theorem says that for every symmetry, there is a corresponding conservation law, and it's a mathematically proven theorem. In fact, the conservation laws in physics (like the laws of conservation of momentum and energy) emerge from certain fundamental symmetries. Now, as per conservation laws, the Big Bang should have created equal amounts of matter and antimatter. But if that was so, complete annihilation would occur, and the universe wouldn’t be as it is. Antimatter is essentially similar to matter, except that, as you say, it is oppositely charged (there are a few more things as well, but as of now this knowledge will suffice). When matter and antimatter collide, they vanish in an explosion and release of energy, which we call annihilation. But it is clear that matter does exist in the universe, and everything we see around us is made of matter, which means there was initially more matter than antimatter and this extra matter didn’t annihilate. This is the problem of asymmetry, and perhaps one of the most debated topics in modern science. A possible solution could be that our universe originated from a neutral parent universe where there were equal amounts of matter and antimatter separated (so they don’t annihilate). This universe spat out our universe and it may be the case that our universe originated from the part of this universe where matter density was greater, and hence the asymmetry. Another solution says that the Big Bang actually gave rise to two universes which are mirror images of each other, and in the other universe, there is more antimatter than matter just as there is more matter than antimatter in our universe. There are basically three conditions for creation of matter and antimatter at different rates (baryogenesis), so that there will be an asymmetry between the amount of matter and antimatter. You can look it up if you’re interested.
14. You have mentioned nuclear fusion and stuff a few times. So tell me the basics about nuclear reactions. How do nuclear bombs work? What are your views on this?
-> It is all based on the fact that mass can be converted into energy and vice versa. The second world war saw the development of nuclear weapons. Einstein warned America that Germany could be secretly developing nuclear weapons. After the bombings of Hiroshima and Nagasaki, Einstein struggled for world peace. The impact of the bombs affected him greatly. And not just him, many other scientists who worked in the Manhattan Project. They didn’t want so many people to die, since the defeat of Japan was, in any case, imminent. And also, contrary to common misconception, Einstein's mass-energy equation did not tell us how to build a nuclear bomb. It was known long before that the nucleus contains huge amounts of energy.
So, how does a nuclear bomb work? To start with, nuclear reactions can be of two types: a fission reaction (where a fissile nucleus is split apart by a bombarded neutron and energy is released) or a fusion reaction (where two lighter nuclei fuse together to form a heavier nucleus, resulting in the release of energy). It all comes down to radioactivity, or the phenomena of the decay of unstable nuclei. In alpha decay, the nucleus is spontaneously reduced to a lighter nucleus by fission. In beta decay, there is either an excess of neutrons or protons within the nucleus, and these protons and neutrons transform into each other. Gamma decay means when the nucleus emits a gamma ray or simply light.
To achieve nuclear fission, a neutron is fired at the nucleus of an atom of a heavy radioactive element. The unstable radioactive nucleus collapses, releasing the neutrons and protons in it, and the neutrons again each collapse other nuclei of other atoms, releasing yet more neutrons which again collapse nuclei of yet other atoms (chain reaction). Keep in mind that neutrons, being chargeless, are not repelled by the nucleus and hence it is easy to break unstable nuclei by bombarding neutrons at them. The mass of the sum of all the particles of a nucleus and the original nucleus are different, the former being less. This missing mass is converted into energy according to Einstein’s equation and the accumulation of energy from the chain reaction results in the destructive atomic explosion. However, nuclear fission (unlike fusion) can be controlled and used for harnessing useful energy as well. Controlled fission reactions take place in the presence of boron control rods, as boron can absorb the liberated neutrons. In case of uncontrolled fission reactions (that is, atomic bombs), a huge amount of energy is released as m is multiplied with the square of c, and the speed of light is a huge number.
Now, nuclear fusion. In fusion reactions, initially a lot of energy is required to fuse nuclei despite the fact that, being positively charged, nuclei repel each other. These nuclei are fused into a nucleus of a heavier element. After the reaction, some mass is lost, which is turned into energy. And the energy released in a fusion reaction is much more than that released in a fission reaction. So anyway, the plan now is to build nuclear fusion reactors, to harness nuclear energy without radioactive wastes (since radioactive wastes are formed after a fission reaction but not after a fusion reaction). Although it has been possible to successfully build nuclear power plants based on fission, it has been impossible to control the much stronger fusion reactions. Scientists are trying to use confinement techniques to achieve this feat. In these approaches, a strong magnetic field is used to confine the plasma. Plasma is a state of free electrons and ions. Fusion reactions need so much initial energy that they take place only in plasma state.
And yeah, you asked about my views on nuclear weapons. Well, interestingly, I was born on 6th August, the date Hiroshima was bombed. It is difficult to forget how the creation of so many scientists was unnecessarily used to wipe out so many innocent lives on the 6th and 9th of August 1945. That’s the problem, actually. The ultimate power doesn’t rest with science. Science just does its work. And a class of people always find ways to use science to their benefit and to exploit the lower classes of people.
15. Okay, now let's come to quantum mechanics. First, what's the nature of light? What exactly do we mean when we say light is both a particle and wave? And why does quantum physics say that everything has dual nature?
-> The nature of light has been controversial for ages. Waves or particles? On one hand, we have particles, which form a notion of distinctness. If a particle occupies a position, no other particle can simultaneously occupy that same position. On the other hand, waves form a notion of continuity. And we know that more than one wave can exist at the same point. Both the wave and particle theories of light explained certain phenomena.
Newton believed that light is made up of "corpuscles." However, the particle nature of light failed to explain interference and diffraction. Also, it was found that two light beams could pass through each other. If light is made of particles, they should collide, but that does not happen. When Huygens put forward the wave theory of light and derived the laws of reflection and refraction using wave optics, in addition to explaining interference and diffraction, it was accepted that light has wave nature (longitudinal wave nature, according to Huygen). Then Maxwell found out that an electromagnetic wave propagating in vacuum has the exact same velocity as that of light in vacuum, it was accepted that light is an electromagnetic wave and has transverse wave nature. But Einstein reintroduced the idea of the particle nature of light by proposing the idea of discrete quanta of light, photons, to explain the photoelectric effect.
Ultimately, as per modern quantum mechanics, light has dual nature. It's technically incorrect to say light is both a particle and a wave. Rather, light is neither a particle nor a wave. Light has neither particle nature nor wave nature. Light can act like both particles and waves. Bohr believed that it all comes down to whether we are using a wave detector or a particle detector. This is the basic idea behind complementarity, which formed an integral part of Bohr’s philosophy.
Anyway, so de Broglie then proposed the idea that everything must have a particle as well as a wave character. Just like light (initially thought to be waves) has a particle nature, matter (initially thought to be of particle nature) should also have a wave nature. Think of it this way. According to Einstein, matter can be converted into energy. According to Planck, energy is related to the frequency (which is a wave concept). So, although this isn't a rigorous proof, maybe matter has wave-like properties. de Broglie gave a relation: h/p=λ, where h is Planck’s constant, p is the linear momentum of the particle and λ is the de Broglie wavelength associated with the particle. de Broglie’s relation is a simple, yet extremely important relation in quantum theory. de Broglie's equation holds for all particles. In general, all particles (microscopic and macroscopic) must exhibit dual nature, although this dual nature is not prominent for macroscopic objects. For macroscopic objects (with larger mass), the particle nature is prominent. For macroscopic objects, the wavelength is negligibly small to give rise to any perceptible wavelike phenomena. In other words, the wavelength is so small that we don't have sensitive enough instruments to detect it. The wavelength is small because, from h/p=λ, we see that the wavelength is inversely proportional to the momentum, p=mv, and if the mass m increases, λ decreases. You can also think of it this way: large objects have more mass, and so more energy. And energy is directly proportional to frequency from E=hf (Planck's equation). But f=c/λ, so energy is inversely proportional to wavelength. The more the energy, the shorter the wavelength.
The double-slit experiment using electrons (and also electron diffraction experiments) provides evidence in support of de Broglie's hypothesis. In the double-slit experiment, a beam of electrons is passed through two slits and a larger screen is placed behind. Though it seems obvious that the most probable location for finding the electrons would be the areas on the larger screen directly behind the two slits (though some electrons may get deflected through an angle), this is not the case with electrons. Although this holds true for macroscopic objects, this doesn’t hold true for microscopic objects like electrons. The electrons behave like waves and interfere!
Figure 6: The double-slit experiment with electrons (Image credit: Wikipedia)
Imagine a wave passing through these two slits. On the other side of the screen with the slits, there will be two smaller waves emanating from the slits. And they will interfere. What I mean by this is that in some regions, the crest (or the peak) of one wave will overlap with the crest of the other wave, and thus they will reinforce each other and result in a higher crest. In some regions, troughs (depressions or valleys) will overlap with troughs and result in a lower trough. And in some regions, the crest of one wave overlaps with the trough of the other wave, and they cancel each other out. Now, imagine this is a light wave. Some regions will be bright (where crests overlap with crests and troughs with troughs) and some regions will be dark (where crests and troughs cancel out) and we get a pattern, alternate bright and dark bands. This is the interference pattern. In the case of electrons, we have alternate regions where the electrons are found (say, bright bands), and where they are not found (dark bands).
Figure 7: Interference of waves after passing through two slits (Image credit: Physics World)
Incidentally, this very experiment with light (where light is used instead of electrons) revealed the wave nature of light. If light had a particle nature, we would find two bright bands directly behind the two slits. But on actually carrying out the experiment, we get the interference pattern. This is how the wave theory of light gained support.
And also, coming back to the double-slit experiment with electrons, it's not that the electron is a point particle, but when many electrons are fired at the double-slit, it gives rise to wave-like behavior just like water is made of water molecules but water shows wave-like behavior. No, it is not that. If you fire the electrons slowly, that is, one electron passes through the slits at a time, you still get the interference pattern. This is because this electron interferes with itself! Think of the electron not as a point particle, but as a wave spread out in space. However, interestingly, if we attach a detector to the slit(s), or in other words the electrons are observed, the wave function collapses, and we don’t get the interference pattern. The electrons start behaving like particles then. It doesn't necessarily mean that a human or a conscious being has to do the observation. Observation simply means that information about the electron has been recorded.
16. What’s Heisenberg’s uncertainty principle? Like I know this thing about not being able to know both the position and the momentum of a particle accurately at the same time. But what was the motivation behind the uncertainty principle, and what does it really mean?
-> Long back, the world was satisfied by the Newtonian explanation of the universe. Some people, like Laplace, were seized by the dream of an absolutely certain universe. Laplace believed that, if the positions and momenta of all the particles of the universe are known, then, in principle, it becomes possible to predict the states of these particles at any time, in the past or future. This is the idea of classical determinism. However, Heisenberg’s uncertainty principle, which stems from the fact that everything has a particle as well as wave nature, has proved that it is impossible to determine, with a hundred percent certainty, both the position and momenta of even a single particle, leave alone all the particles of the universe. Here's a simple explanation. To determine the position of a particle (consider a microscopic particle, here), one must shine light on it. To locate a microscopic particle (like an electron) accurately, we need a high energy (that is, low wavelength) light, so that it can interact with the particle and locate it. But high energy light will change the momentum of the particle. So if we want to measure the position accurately, the momentum of the particle will be uncertain (it can't be measured accurately), and the converse is also true. Yes, light does bounce off trees and houses and cars, but these are huge things compared to photons, so the effect is not noticeable. And also, it's not the case that in the absence of light, an electron has a well-defined position and momentum. Even when the electron is left to itself, its velocity and position changes unpredictably from one moment to the next. That, according to quantum mechanics, is a basic feature of the universe. And also, just like the errors in position and momentum, both the errors in energy and time also can’t be simultaneously known for a particle. This means, to measure the energy precisely, you need to carry out the measurement for a longer amount of time. This also implies that a particle can "borrow" energy for a short amount of time. The more energy you borrow, the sooner you must return it. The error in position multiplied with the error in momentum must always be greater than or equal to a constant (ℏ/2, where ℏ is the reduced Planck constant). And the same holds for the product of the errors in energy and time. And this uncertainty is inherent, it's not due to some technological limitation. This is not to be confused with the errors in experiments that can be addressed using statistical methods of error analysis.
17. What did Feynman mean when he said no one understands quantum mechanics? And yeah, what is quantum mechanics?
-> Feynman famously remarked that anyone who claims to understand quantum mechanics actually understands nothing of it. This quote has been hailed by many people to justify incorrect claims. What Feynman meant, in my opinion, is that although physicists know how to use quantum mechanics, they don’t understand exactly what quantum mechanics is telling us about the fundamental nature of reality. You can use the computer, but it is very likely that you don’t exactly understand everything about how the computer works. Quantum mechanics is used everywhere, yet nobody understands what it is actually telling us about the fundamental nature of reality.
Quantum mechanics, simply put, is the mechanics of tiny particles. At the atomic scale. And beyond. Deeper. Now, one of the greatest misconceptions about quantum mechanics is that it is the science of only the subatomic world. We often forget that classical mechanics is only a rough approximation of quantum mechanics. Yes, you can derive all of classical mechanics from quantum mechanics. In fact, you can derive all of the older theories of physics either from quantum mechanics or general relativity. However, these two theories have not yet been reconciled to a single theory which would reproduce all known physics. So anyway, the basic principles of quantum mechanics are applicable even to the macroscopic world, and classical mechanics only produces an approximation of the results obtained by using quantum mechanics. For example, we don’t perceive the wave nature of a macroscopic object since the associated wavelength is so small (due to the large mass) that we can’t detect and perceive it. But wave-particle duality holds for macroscopic objects just as well as for microscopic objects.
So, basically, according to quantum mechanics, the subatomic world is inherently random and unpredictable. It is not possible to exactly predict the behavior of a quantum particle. But we do make predictions about the macroscopic world around us by using classical physics. At this point, you may ask how a predictable world can be made of particles that are random and unpredictable. Well, the answer might lie in the law of large numbers. You can't predict the outcome of the toss of a single coin. It's 50% heads and 50% tails. You can't predict whether it'll be a head or tail. But if you toss a coin a thousand times, you'll see that the number of heads will be around 500, and the number of tails around 500 as well. It's very unlikely, for instance, that you'll get 900 heads and 100 tails. So, although you can't make predictions about a single coin flip (or a single particle), you actually can make predictions about a large number of coin flips (or a large group of particles). Toss ten coins, it's likely you'll get 5 heads, or 4 heads, but very unlikely that you'll get no heads. Toss it even more times, and the head:tail ratio will settle down at or near 1:1. And everything in the macroscopic world is made up of a huge, really huge number of quantum particles.
18. Wow, that's really great! Could you briefly talk about the history of quantum mechanics, and also, what are the major findings of quantum mechanics?
-> When Einstein was busy fighting his battle in the thickets of spacetime, other physicists were developing a new and revolutionary theory: quantum mechanics. Well, Einstein himself also played an important role in the development of quantum mechanics, although he later refused to accept quantum mechanics as a complete theory. So anyway, quantum theory was born when Planck showed that energy can't be radiated continuously, but in discrete packets called quanta. This was an essential step in resolving the ultraviolet catastrophe. Planck showed that the energy is directly proportional to the frequency, and thus is equal to a constant multiplied with the frequency. This constant is what we call Planck's constant. It was Einstein's insight that to explain the photoelectric effect, we must think of light as a stream of discrete quanta, called photons. Einstein reintroduced the particle nature of light, and it was necessary. Today, we say that light has dual nature: the wave theory explains some phenomena while you need the particle theory for some other phenomena. Then we had de Broglie's great idea that everything has dual nature (a particle nature as well as a wave nature). Then Heisenberg showed that it was impossible to determine both the position and momentum of a particle simultaneously. There is a certain amount of uncertainty in Nature. Then came Schrödinger's equation. There was the interpretation of the wave function as a function the square of which gives the probability of finding the particle in the given region. The basic idea is, only on observing the particle, does the wave function collapse to a distinct value, and we observe the particle in a distinct location. Before observation, the particle has a non-zero probability of existing everywhere, even in distant galaxies. And, roughly speaking, Nature tries out all possibilities, so if we wait long enough, we can observe the effect of quantum tunneling: the particle can instantaneously disappear from here and appear at a distant location. Quantum mechanics disproved all commonsense notions about reality. In this new world, a particle can simultaneously pass through two slits, you have a certain probability of tunneling to a distant galaxy (although not in your lifetime, such extremely rare events will occur after a long, really long time) and so on. There is a certain amount of randomness in Nature, and everything is reduced to probability, in some sense. Some physicists accepted this revolution, while others were not so happy about this. Oh, one more thing. Did I say there is a certain amount of randomness in Nature? That’s not entirely true. More appropriately, according to quantum mechanics, either the outcomes of quantum events are entirely random, or the outcomes of quantum events are actually deterministic deep down, and we perceive them to be random due to our limitations. This last point is a very important point.
19. What is quantum entanglement and the EPR paradox?
-> Entanglement is basically lack of independence. What does that mean? Well, if two systems are entangled, they will be dependent on each other, and if we know the state of one system, we can predict the state of the other system without observing it. There will be some connection or correlation between the two systems.
Einstein, Podolsky and Rosen (EPR) put forward a thought experiment that, according to them, proves that quantum mechanics is incomplete. Consider an atom which is about to decay, and which produces two particles of the same mass. The particles initially have zero momentum, so by the law of conservation of momentum, the total momentum of the two particles must remain zero. This means they must have equal and opposite momentums, which means they will move away from the atom in opposite directions with the same speed (they have the same mass, and momentum is mass times velocity, so they must have the same magnitude of velocity, but in opposite directions, so that the total result is zero). Now, we know that the speed (or velocity) of the particle(s) is not uniquely defined, because these are quantum particles. Suppose we measure the speed of one of the particles when it has already reached far, far away from the other particle. We find the velocity to be say 200 miles per second in direction x. Immediately, we know that the velocity of the other particle, which is a long distance apart, is 200 miles per second in direction -x. So, we can reveal the velocity of the other particle without going near it! These particles are entangled. Is some information passing between the particles instantaneously, faster than the speed of light, violating relativity? Well, in reality, relativity is not violated. Because no information is actually transferred between the particles at a speed faster than the speed of light. There is actually no paradox at all. There is some correlation between the entangled particles, but no information is transferred between them faster than the speed of light. You can't, for instance, use entanglement to send a signal faster than the speed of light.
20. Einstein was not the only one to come up with a so-called paradox in quantum mechanics. I read a bit about the famous Schrodinger’s cat paradox, and what I’ve been able to gather is basically that the cat exists in superposition - a combination of two states. It is, in some sense, both dead and alive before it is observed. But I also read somewhere that all this is true only at the quantum level, for microscopic particles. My question is, why can’t large objects exist in superposition?
-> The reason is simple. You can't isolate a large object from its surroundings. Isolating means no photon should collide with the object. Because if a collision occurs, the path information of the object has been recorded, and it is possible for someone to deduce this information by studying the path of the photons. Also, the object must not emit photons as well, so we need to cool it to near absolute zero. We need to eliminate the effects of gravity on the object and so on. So, macroscopic objects are impossible to isolate informationally from the environment, which is why they don't exist in a superposition of all possible states. This is technically called quantum decoherence, or loss of quantum coherence. Yes, large molecules have been experimentally put in superposition in some recent experiments. But it is true that large, really large objects can't be informationally separated from their environment. So the chances of them existing in superposition are pretty slim.
21. Einstein refused to accept quantum mechanics as a complete theory. He famously remarked “God doesn’t play dice with the world,” to which Bohr replied, “Stop telling God what to do.” What are your views on the Bohr-Einstein debates?
-> Amid the chaos of the second world war and the then-new quantum mechanics "heresy," Einstein would remain engaged in a futile attempt to unify gravitation with electromagnetism. He would keep this up for over thirty years until his death. He couldn’t bring himself to truly accept the strange, bizarre ideas of quantum mechanics. He believed in a perfectly ordered and deterministic universe, putting up his famous mantra against quantum randomness – “God does not play dice with the world.” Bohr, however, retorted with “Stop telling God what to do!”
Einstein believed in an objective reality. A reality which would exist even in absence of an observer. Does the Moon exist because a mouse looks at it? Some people believe that the world exists independent of our observations; while others say that observation collapses the wave function from a superposition of all possible states to a distinct, perceptible state and it is even possible that the reality is subjective, and the outside world is an illusion (solipsism). Yes, all we can account for is the existence of our subjective reality. We can’t get out of our consciousness to see if there is an objective reality out there. In fact, there is probably no way to prove that reality is not just ideas in our minds. And a subjective reality can create the illusion of an objective world, and vice versa. So maybe, there is no definite answer to the question of whether reality is subjective or objective. Now, I don't believe in solipsism because even if it is true, it would lead us nowhere. We can't prove or disprove it. So it is best not to think about it. To some people, it is a pleasure. I am the only one who exists. I am everything. Others end up feeling lonely and depressed about it. I, to be perfectly honest, have no difficulty in accepting solipsism as a possibility, but still, I would say it is a pointless concept. And in the end, I prefer to believe in an objective reality out there which doesn't depend on our existence. We can't prove everything, but we should believe things worth believing and not think about things not worth believing. It would be no good doubting an objective reality, or in other words, believing in solipsism. But of course, what you believe is up to you. And here's the thing: to the best of my knowledge, quantum mechanics doesn't disprove the existence of an objective reality (just that, this reality is stranger than we had imagined, but we have no concrete evidence that suggests this reality is not objective). Whatever you have heard about quantum mechanics requiring a subjective reality is utter nonsense. Don't get me wrong, reality may be subjective, but quantum mechanics doesn't prove (or disprove) that. And again, in the end, I prefer to believe in an objective reality. I’ve reached this conclusion after several years of thought. Also, the debate between Einstein and Bohr was not exactly one of realism and solipsism, but rather revolved around the question of whether quantum mechanics is a complete theory (Einstein's answer was no, although Bohr didn't find Einstein's arguments convincing). I think it would be too premature to support either Einstein’s views or Bohr’s, based on our current knowledge. But personally, I can relate with Einstein. But yeah, even though Einstein might be correct in saying that quantum mechanics is incomplete, and we need a deeper theory for a better understanding of Nature, it is worth pointing out that quantum mechanics can’t be wrong. Quantum mechanics has survived many stringent tests. And it works surprisingly well. However strange and bizarre it may be, it still works. Thus, it can be the case that quantum mechanics and its extensions like quantum field theory are incomplete, in the sense that they don't explain everything, like the force of gravity, yet. But it can never be just plain wrong. To quote Daniel Greenberger, “Einstein said that if quantum mechanics was correct then the world would be crazy. Einstein was right, the world is crazy.”
22. You mention Wheeler's interpretation of quantum mechanics in some of your writings. What exactly is Wheeler’s negative twenty questions thought experiment, and his interpretation of quantum mechanics, in simple terms?
-> According to Wheeler, our questions create reality. We participate in the creation of the present, future as well as the past. In this view, the universe is a "work in progress." To explain how our questions can create the world, we consider the negative twenty questions thought experiment. Suppose you think of something, it could be anything. And I am allowed to ask questions whose answers can be either yes or no. I will be asking questions like "Is it living?" and "Is it bigger than an elephant?" to narrow down the possibilities until I arrive at the object which you thought of. But here's the twist. Suppose you didn't think of anything in the first place. I ask you these yes/no questions, and you answer them randomly, or maybe according to some pattern (for example, yes-no-yes-no etc.). After you answer a lot of questions, you actually narrow down the possibilities and close in on something particular (although you didn't think of it initially). So, in some sense, my questions brought this object into existence. Note that the order of questioning is important. Suppose you have decided to first answer yes and then no. If I first ask you whether it is living, and you say yes, and then I ask you if it's big, and you say no, then the answer may be an ant (of course, I need to ask many more questions before forming a conclusion). If I first ask you if it is big, and you say yes, and then I ask you if it is living, and you say no, then the answer could be a house, which is very different from an ant. It would be technically incorrect to say that my questions are affecting the past (rather, affecting what you thought of in the past), because you didn't think of anything. My questions are creating reality. According to Wheeler, the reality we live in is the only reality which is consistent with our questioning. (If you want to learn more, I recommend reading Wheeler's paper Information, Physics, Quantum: The Search For Links.)
23. There are many ways to interpret quantum mechanics, like the CopenHagen interpretation and the many-worlds interpretation. What’s your favorite interpretation of quantum mechanics and why?
-> First, let me tell you about a different possibility you probably haven't considered. Take a less fundamental subject like psychology. Open a psychology book and count the number of equations you find throughout the book and the number of words. Then take the ratio of the number of equations to the number of words. This number would approach zero. Take a textbook of a more fundamental science like physical chemistry, this number would be slightly larger, because there are way more equations (and way less words) in a textbook of physical chemistry as compared to a psychology textbook. Now come to an even more fundamental science, physics. For physics, this number would be still larger. Open any good physics textbook, it is full of equations. The point is, it might be the case that as we go down deeper and deeper, words lose the ability to describe what's really going on. Language is a human construct, and it is foolish to assume language to be capable of describing everything. (I don't believe that mathematics exists objectively and fundamentally, so in my opinion mathematics is also a human construct, but it is different from language, and it does a better job describing what's going on fundamentally; but I always assert that we will not be able to answer every question. If the universe were just math, then it would have been possible to completely understand it. Math can take us very far, but I believe even math can't fully describe the universe. We will never completely understand the universe. And we humans are preprogrammed to easily understand language and not easily understand math because our early ancestors needed a language to communicate, and not math. Math wouldn't have given them any survival advantage. We have been speaking for way longer than we have been doing math, but that doesn't make language superior to math in describing the universe.) Anyway, coming back to the question, well, my second favorite interpretation of quantum mechanics is the "shut-up-and-calculate" interpretation. Quantum mechanics is a successful theory, it makes extremely accurate predictions. And it is mathematically well-defined. We know how to use quantum mechanics pretty well. So maybe we should just use quantum mechanics to calculate different properties of fundamental particles and investigate fundamental particles and forces. But any attempt to describe in language what's really going on deep down is doomed to fail and is a waste of time. That's just a possibility, and as I have already said, that's my second favorite interpretation of quantum mechanics. The favorite interpretation is of course the many-worlds interpretation. Again, many will say that it is speculative and not testable. The very idea of parallel universes cannot be called a scientific idea. However, this is a completely deterministic and elegant interpretation of quantum mechanics. There are a lot of other interpretations, some of which I really like, some not so much and some I don't even properly understand. But from my knowledge, I would vote for the many-worlds interpretation. I would give superdeterminism the third place. And, although this was not asked in the question, the CopenHagen interpretation is my least favorite interpretation of quantum mechanics.
24. Okay. So could you briefly discuss the CopenHagen and the many-worlds interpretations?
-> According to the Copenhagen interpretation, before a measurement or observation is made, an object exists in a superposition of all possible states, and in multiple places at the same time. Only on observation does it collapse to a distinct state. And it is not possible to describe what happens between observations. It is just the observations that are real. While it is not clear whether this observation requires consciousness, it is believed that measurement must be made for things to exist in a distinct state. Note that it is not at all necessary that consciousness should be involved in the wave function collapse. We have seen that even a single photon bouncing off a ball can destroy the ball's superposition. So, please don't mix up quantum mechanics and consciousness. So anyway, it is obvious that the Copenhagen interpretation lacks mathematical rigor. And there are other problems as well. Also, what you must keep in mind is that the wave function of a system, described by Schrödinger's equation, is completely deterministic. The relation between the wave function and the observable properties (in other words, the wave function collapse) seems probabilistic and random. You know the probabilities of getting this or that state as an outcome, but you can't predict it. But, as we have already discussed, when a large number of particles get involved, things become predictable.
The many-worlds interpretation, proposed by Everett, says that the wave function never collapses. So, nothing is random. This interpretation is deterministic. All the possibilities take place in parallel worlds. Maybe new worlds are being created with every observation! It may be the case that parallel realities coexist in the same space and at the same time, but completely out of phase with each other. So, you can only perceive a single world, the world you're in-phase with. But parallel worlds may exist in the same space and at the same time as your world! Crazy, isn't it? It may be the case that these alternate possibilities take place in parallel universes. I decide to pursue physics here, but my counterpart in a parallel universe decides to pursue evolutionary biology. And it is meaningless to ask who the real Arpan is, the one who chooses physics or the one who chooses evolutionary biology. Both these Arpans are real in their respective worlds. Also, some pretty successful theories like inflation in cosmology predict the existence of parallel universes, and if you accept a theory, you've to accept all its predictions.
25. What is Feynman’s sum-over-paths formulation of quantum mechanics, in simple words?
-> According to this formulation, on moving from a point A to another point B, a particle considers all possible ways to reach from A to B, including paths that might take you from A to Jupiter and from there to B, or even paths that go backward in time. It turned out that the probabilities of the particle actually taking the bizarre paths is nearly zero for macroscopic objects (that is, these paths cancel one another out). Ultimately, we get the expected path, as in Newtonian mechanics, that is the shortest path (or rather, the path with the least action). Quantum fluctuations basically represent those paths that generally cancel out in real-life situations. The Newtonian path doesn’t cancel out and has the maximum probability. Thus, our commonsense notion of reality is just the most probable state among an infinite number of states. The concept of sum over paths is perhaps the greatest generalization in physics. And of course, that the probability of each compulsory path being taken, varies. Paths with greater probability amplitudes have a greater contribution to the final sum of paths.
26. What is quantum field theory, and what is the new quantum-field-theoretic idea of force?
-> A force is something which tends to change the state of rest or state of motion, or size, shape, the direction of motion of a body, etc. A better definition of forces is that forces are something that are required to exist to maintain some particular symmetries. This is true for all the four forces. As an example, the existence of gravity is required to maintain the symmetry between all observers, regardless of their state of motion (recall the equivalence principle in general relativity). So yeah, there are many different forces, but often many forces are just different forms of the same fundamental force. Over the years, physicists have come to the conclusion that there are four fundamental forces: gravitational, electromagnetic, strong nuclear and weak nuclear forces. These forces are responsible for all possible interactions that can take place in this universe, from planets orbiting a star to electrons repelling each other.
So what really gives rise to forces? Particles called bosons. More appropriately, bosons are particles the exchange of which gives rise to forces. Bosons, along with the fermions (which make up matter), are referred to as the elementary particles. But what are these bosons? They are excitations of their respective quantum fields. All forces, according to quantum field theory, result from the quantum field. Each particle has a field associated with it, and all these quantum fields can interact with one another. If two electrons are present near one another, there are many things that can happen. Electron A can emit a virtual photon which can be absorbed by electron B; electron A can emit a virtual photon, which can turn into an electron-positron pair, which can further annihilate into a virtual photon, which can then be absorbed by electron B; A and B can exchange two virtual photons, and so on. The electron field interacts with the photon field in all possible manners, but when all these possibilities are taken into consideration, we see that the electrons move away from each other almost always (recall that like charges repel).
In quantum mechanics, energy can be temporarily "borrowed" from a particle. As per Heisenberg’s uncertainty principle, the greater the amount of energy you "borrow," the sooner you must return it. The exchange of photons gives rise to electromagnetic forces (or in other words, the photon is the boson for the electromagnetic interaction). Virtual photons can pop out of nowhere around an electron, by "borrowing" some of the electron’s energy. (Note that although photons are massless, these virtual photons can have mass.) If there is another electron near the virtual photon, it will absorb the photon. Thus, essentially, some energy and momentum is exchanged between the electrons, causing them to repel each other, since the second electron, on gaining energy, will move away from the first one. Note that in the above case, the exchange of the photon gave rise to the force of repulsion between the two electrons. Thus, the photon is a boson and electrons, both being negatively charged (like charged), repel each other. A photon can also materialize into an electron and its antiparticle, the positron. This process is called pair production. Here, electromagnetic energy is converted into matter. (We already know that energy can be converted into matter.)
One of the most important predictions of quantum field theory is that vacuum is not an entirely empty space. The amount of energy is randomly and temporarily changing at every point in space. Or in other words, what we call vacuum is teeming with particle-antiparticle pairs (called virtual particles) that pop up, and after a very short amount of time, annihilate one another and just vanish. They pop up by borrowing energy from vacuum, and as per the uncertainty principle, they must vanish after a short period of time. These particle-antiparticle pairs emerge spontaneously in vacuum, and this phenomenon is called vacuum fluctuation. The quantum fields (there is an underlying field for every particle) are randomly fluctuating, and this is what gives rise to these virtual particles. And the existence of virtual particles, although not directly perceptible, gives rise to certain interesting effects (like the Casimir effect), and such effects have been observed. And interestingly, these virtual particles carry energy, and it has been proposed that these vacuum fluctuations might explain the accelerated expansion of the universe.
27. From where did the idea arise that particles are disturbances or vibrations in a field?
-> Let’s say we have an electron here on Earth, and another electron in a distant planet in some different galaxy. They both are the same, right? Electrons are electrons. This suggests that electrons (and any particle) are emergent from a deeper field, which is present throughout the universe. The underlying field is the same, and so are the electrons, wherever they are.
28. What is the Standard Model? Is it really the most successful theory ever?
-> The Standard Model can be regarded as currently the most successful theory which explains all the three forces of Nature, except gravity. It is mainly based on two principles: gauge principles (which have unified all the three forces except gravity) and spontaneous symmetry breaking (which explains the difference between these forces). In the Standard Model, there are three generations of fermions (or the particles that make up the matter). No one knows why Nature has created exactly three generations of particles (that is, fermions). That’s a problem with the theory. There are also other problems with the Standard Model. For instance, according to theory, neutrinos should be massless. But they do have a very little mass. Although we can modify the Standard Model to get around this problem, there are a lot of arbitrary constants in the Standard Model, and we don't know the origin of these constants. That's a big problem. Then there have been recent developments like the muon g-2 experiment, which might point at the existence of new particles beyond the Standard Model. So yeah, physicists are in search of physics beyond the Standard Model. The Standard Model is successful in the sense that it has explained a lot of features of the world, but it is not really a fundamental and complete theory. So, there’s more to come.
Figure 8: The Standard Model of elementary particles (Image credit: Wikipedia)
29. What’s the problem with gravity? Isn't there a boson for gravity, like the other three forces?
-> There are four fundamental forces: the gravitational, the electromagnetic, the weak nuclear and the strong nuclear forces. Gravity here is the odd one out, because all the other forces can be explained in terms of exchange of bosons. But we haven’t discovered such a particle for gravity (yet). Recent discoveries, like gravitational waves from two colliding black holes, hint at the existence of gravitons (the boson for gravity). Some physicists believe that gravitons must exist, and we've not observed them simply because gravity is the weakest force, gravitons interact weakly with other fields.
General relativity allows the idea of gravitational waves (disturbances in the curvature of spacetime). It’s possible that these waves are made up of gravitons (in much the same way light waves are made of photons). Gravitons, if they exist, would be massless, but contain energy, and a graviton can create more gravitons. In fact, when confined to a small space, a graviton can go on producing an infinite number of gravitons. This means gravitons are not renormalizable, which is a bad thing. Interestingly, string theory treats these gravitons not as point particles but as strings; and we know that strings can’t be effectively confined. So, in this way, we can make gravitons renormalizable. A possible explanation as to why we haven’t been able to find the graviton yet is that gravitons may exist in other higher dimensions. And not just the graviton, it is predicted that there may be heavier versions of the standard particles recurring at higher and higher energies as they navigate smaller dimensions.
30. Could you please discuss the concept of the Higgs boson, also dubbed the "God particle"?
-> A classical physicist would say that mass is an intrinsic and fundamental property: it is the amount of matter contained within a body. But in modern physics, mass is no more treated as a fundamental property. It is a consequence of a particle’s interaction with the Higgs field. (This made me wonder if charge is also not a fundamental property, and there exists a field interaction with which gives rise to the property of charge in particles. However, in case you're thinking along similar lines, charge is mostly treated as a fundamental quantity in most quantum field theories.) So, the omnipresent Higgs field (a field that is present everywhere in the universe) is the field by interacting with which particles get their mass. The excitation of this Higgs field creates a particle called the Higgs boson (also dubbed the God particle). It is interesting to note that the Higgs boson also has some mass, and it gets it by interacting with the Higgs field, just like the other particles. The Higgs boson is not really a force-carrier, but it is responsible for generating the masses of the particles (it's a scalar boson). The idea is that this Higgs field exerts something like a drag force on the particles which are moving through it, and this is what we perceive as mass. As particles react with the Higgs field, mass is "transferred" to them. Symmetry is broken in this manner. Before interacting with the Higgs field, the particles remain massless, and thus, are symmetric in some sense. All the particles get their respective masses from the Higgs field due to this symmetry breaking. Different particles interact differently with the Higgs field. If it was not for this symmetry breaking, all particles (I mean, all fermions) would be massless. But the concept of the Higgs field alone can’t explain why less fundamental particles like protons have mass, for the sum of the masses of the constituent quarks (which are the particles present in a proton) is unable to account for much of the proton’s actual mass. This extra mass can be accounted for by the fact that, when quarks are confined in a tiny region, they contain much more energy. This energy is expressed as the extra mass. This is because, when the quarks are confined in a small region, the uncertainty in their position is less, consequently increasing the uncertainty in momentum. (Always remember that mass can be converted to energy and vice versa.)
31. We know that the Higgs boson has been discovered. The discovery of the Higgs boson is arguably one of the biggest achievements of the Large Hadron Collider till date. So, how was the Higgs boson discovered?
-> So the Higgs boson was expected to be quite heavy, and its presence might be inferred if an elementary particle is found in numbers greater than expected when two particles collide at high velocities. This would indicate that the massive Higgs boson has decayed into these particles. However, it can’t be conclusively assumed that such an excess of fundamental particles can occur only due to a Higgs boson decay.
Now, yeah, how exactly was the Higgs boson discovered? More generally, how do scientists look for elementary particles? I mean, you can’t see them with a microscope, of course. Well, we need to collide two particles at extremely high velocities. Then, we need to analyze the particles that were emitted as a result of this collision. Then we search for evidence of elementary particles. Huge machines called particle accelerators are employed to detect elementary particles like the Higgs boson. The simplest particle accelerator is the cyclotron. In a cyclotron, particles are made to move in a spiral path in the presence of an electric and a magnetic field, thus accelerating the particle to high velocities. On reaching high velocities, the particle can be thrown at a target to disintegrate it for further investigations on its inner structure. The Large Hadron Collider (LHC), which you mentioned, is a huge particle accelerator built by the European orgNon for Nuclear Research (CERN). The LHC is located in Switzerland. It accelerates two particles to near-light velocities and collides them. The particles ejected due to the collision are then studied. The Higgs boson was initially discovered as a new particle in 2012, based on collisions in the LHC, and the new particle was subsequently confirmed to match the expected properties of a Higgs boson over the following years.
32. I read this term so much: “entropy.” And as far as I understand, it’s some measure of disorder. But what exactly is entropy?
-> Entropy can be defined as the number of ways a particular state can be achieved. More technically, entropy is the number of ways a state can be achieved, by taking into account spatial configurations, velocity configurations, and energy distributions. In our universe, it is clear that entropy increases with time. It seems reasonable to assume that entropy is a measure of disorder but that is not exactly so. Some people will tell you if you have an untidy room, it's in a high entropy state, whereas a neat and clean room will have a low entropy. That's true, but that's not a very accurate description of the concept of entropy. The following example might be more helpful. If we have five differently colored balls and two jars, then the lowest entropy state would be achieved if we keep all five balls in one jar and thus, no balls in the other. This state is not an equilibrium configuration, obviously, for the concentration of the balls is more on one side. (An equilibrium state can’t be achieved in this case, since that would require each jar to have 2.5 balls in it!) If we decide to keep two balls in one jar and three in the other, by taking into account the five different colors, there are many different ways we could achieve this state. Thus, in this case, the entropy of the system is more than in the previous case, when there were only two possible ways to achieve our state (that is, either put all the balls in the first jar or in the second jar, while keeping the other jar empty). And in this case, a near-equilibrium is attained (which means this is a more stable state). Everything in this universe tends to remain stable, and entropy increases in our universe. Think about it. It is not possible for entropy to decrease in an expanding universe, because as the universe expands, more and more space and thus, possible spatial configurations are created. Entropy always increases with time in this universe. For instance, even if we try to compress some atoms in a smaller space so that the number of possible spatial arrangements decreases, the energy of the atoms will increase, increasing the total number of possible arrangements.
33. What’s the link between entropy and information?
-> What exactly do we mean by information in physics? In some sense, information is responsible for the existence of the different objects in the universe. For instance, it is information of the arrangement of electrons and number of protons and neutrons in an atom that defines whether the atom is a hydrogen atom or a carbon atom (etc.). Different arrangements of these atoms will give rise to different forms of the same element. For instance, carbon can exist in two main forms: graphite or diamond. As a friend of mine put it in a Medium article she wrote, "The only difference between the tip of a pencil and your mother’s wedding ring (if your father wasn’t stingy) is the order of its constituent carbon atoms." Well, anyway, you can think of information in terms of reduction of uncertainty. If someone is about to send you a message, you are uncertain about what the message would say. But once you read it, the information in the message reduces your uncertainty. The information (I) in the message can be defined as the logarithm, to the base two, of the total number of messages that might possibly have been sent (M). The logarithm is taken to the base two, since according to the model we're discussing here, one gets information by asking questions that can have two answers: true or false (yes or no). If the answer to a question can be either true or false, then the answer can be assumed to contain one bit of information. For answers that can’t be defined using just true and false, we may assume that the information associated with it is just the number of questions one needs to ask whose answer can be either true or false, to have enough data to make a successful guess at the answer. For example, the answer to "What is your name?" can't be true or false. In such cases, we ask questions whose answers are yes/no, like "Does your name start with A?," "Is your name five-lettered?" etc., and information, as we just discussed, is the number of such questions we need to ask so that we can narrow down the possibilities and make a successful guess at the answer (in this case, the name).
The more different the objects you are trying to describe are, the more the amount of information you need to completely describe the objects. For example, suppose A and B are similar in all respects except one. Then, you need to only describe either A or B and mention this one difference. If A and B are different in two aspects, you need more information to describe A and B, and so on. 11111111 and 0000000 contain less information than 01100011111111011100000000101. You can describe 11111111 as “eight ones.” This is not possible for 01100011111111011100000000101.
Now, do you see how entropy is related to information? Entropy is directly proportional to the number of possible ways the system under consideration can be assembled, which is basically nothing but the information about the system.
34. So, that’s what we mean by information in physics. You have written an article about the information paradox, a topic about which I know almost nothing. Would it be possible to explain what exactly is paradoxical about information, assuming the “information” in “information paradox” is the same information we discussed?
-> Yes, they are the same thing. So the information paradox. Or better, the black hole information paradox. Recall that particle-antiparticle pairs can pop up in vacuum. However, they must soon annihilate each other. Now consider that a particle A and its antipartner B emerges near the event horizon (the border, roughly speaking) of a black hole in such a manner that A falls inside the black hole, while B remains outside the black hole. Now, before the particles have a chance to annihilate each other, A is sucked in by the black hole. But then, who annihilates B? Who accounts for the energy of B? Doesn’t that violate the law of conservation of energy? Hawking concluded that the black hole contributes part of its own energy. The black hole emits a radiation: the Hawking radiation. After a very long amount of time, the black hole evaporates away completely. So, information, in some sense, helps us tell things apart. On the other hand, black holes suck in things and crush them into the singularity. Or in other words, the difference between a pen and a pencil, as they fall into a black hole, is lost in the sense that inside a black hole, we have no means to differentiate a pen and a pencil. As far as we know, there is no way to retrieve information from a black hole. If you fall through a black hole, your existence is simply "deleted." This means that the information associated with you is lost. So what exactly is paradoxical about all these? Well, information can’t be destroyed. This is a fundamental law. The information associated with a particle can’t be destroyed. Every object in the universe is composed of particles with unique quantum properties. And no matter how much we try to destroy these objects, the quantum information related to them can never be entirely deleted. In theory, it is even possible to recreate the object. (Like in quantum teleportation, you can, in theory, transfer all the quantum information about an object to a different place, where it can be reassembled.) But it seems that we can't retrieve information from a black hole. However, the information must be present somewhere. Oh well, maybe we can’t perceive this information. But it exists inside the black hole alright. After all, no one has ever been inside a black hole. But once we learn that even black holes are not permanent, they radiate energy, the possibility of the information resting peacefully in there gets ruled out, too. And the Hawking radiation seemed to contain no information about the objects that fell into the black hole. So where does the information go? This is the information paradox.
35. What is the current status of this paradox? Have we made progress toward a solution?
-> Some early speculative proposals were that perhaps black holes pass on the information to “baby universes,” which store the information, or maybe the information is contained in the Hawking radiation in such a manner that we can’t perceive it.
According to classical physics, black holes are simple objects. According to recent research, however, black holes are more complex than we originally thought. The "lost" information is likely to be present in the gravitational field of the black hole at the quantum level (quantum hair). Objects falling into a black hole will leave a mark in its gravitational field, and the info36.rmation is not lost. Black holes of the same mass and same radius, but which sucked in different objects, will have very slight differences in their gravitational fields. The information, thus, is preserved. However, this only shows that it is possible to retrieve some of the apparently lost information. It is still not clear whether this can be considered a complete solution to the paradox.
36. Another related term I often hear is the holographic principle. What’s that?
-> Okay, let’s start with the black hole information paradox. Bekenstein proposed that black holes must have some entropy. If a black hole sucks everything inside, the surrounding entropy definitely decreases. But the total entropy must increase. Bekenstein, from this, concluded that the black hole has some entropy which increases as it sucks in matter.
Anyway, so maybe the event horizon of the black hole contains this entropy, and so the information. ’tHooft demonstrated that particles falling into black holes cause gravitational deformation and "bumps" on the event horizon. This can contain the information of the particle.
So essentially, the black hole can be treated as a hologram. This is because the information of the three-dimensional object falling into the black hole is stored on a two-dimensional surface: the event horizon. Similarly, the universe can also be considered to be a hologram. Thus, we can consider gravity as nothing but a projection of quantum mechanics in a higher dimension. This is the holographic principle.
Holography can explain and link two entirely different kinds of theories in physics. Holographic duality is also referred to as AdS/CFT correspondence, where AdS refers to Anti de-Sitter spaces (AdS are spaces with negative curvature), while CFT refers to Conformal Field Theory. All this is technical, but the concept is really simple. Imagine a sphere. CFT is related to the boundary, while the AdS space sits inside the sphere. Everything in the AdS space has a counterpart in the CFT boundary. It is crucial to understand that a hologram is two dimensional, but it can contain all the information about all three dimensions of the object it represents.
The idea is that a three-dimensional universe contains black holes and strings (in the context of string theory) governed solely by gravity, whereas the two-dimensional boundary of this three-dimensional universe contains ordinary particles governed solely by standard quantum field theory. This means it is possible to relate gravity to a quantum field theory which has no gravity, and this may prove to be of great help when trying to reconcile general relativity and quantum field theory. And the AdS/CFT correspondence can somewhat resolve the black hole information paradox. The information is contained in the two-dimensional event horizon of the black hole. But the holographic principle is much more than just a possible solution to the information paradox. It holds a key for a deeper understanding of quantum gravity. It is arguably one of the, if not the best insights in modern theoretical physics.
37. Does gravity decrease entropy? What’s the relation between gravity, entropy, symmetry and equilibrium?
-> With increasing distances, gravity decreases. However, the more the distance increases, the more is the increase in entropy. However, this does not mean that gravity decreases entropy. With increasing distances, and increasing entropy, a system approaches equilibrium state. However, this state is, of course, not the most ordered state and thus, lacks symmetry. Bring in gravity, and everything collapses to a symmetric point. So, very roughly speaking, it seems that gravity and symmetry form one side of the coin, whereas entropy and equilibrium form the other side. That's the basic concept, and you can play with it if you like: you might come up with something. In the end, research can demand radical revisions to existing theories, or maybe the solution is simple and lurking just around the corner. Only time will reveal the truth.
38. Now, the holy grail of physics. The theory of everything, or the unified field theory. Einstein spent the last three decades of life hunting for it. My question is, what exactly is the motivation behind the idea that such a theory might exist?
-> Humans have always strived to make sense of the world around them. We have discovered that there is some regularity in the world. For instance, certain experiments always produce the same results, or in other words, they are repeatable. To explain these experiments, we have strived to discover some laws: universal, fundamental laws that would explain a wide range of experiments or phenomena. This is what science does. From Newton’s days to the present, science has built up our view of the universe, using the convenient language of mathematics. So now, the question of whether we will ever successfully formulate a final theory inevitably comes up.
What do we mean by a final theory? A final theory would explain all the interactions that can take place between all possible kinds of elementary particles in this universe, and it would probably also allow us to investigate phenomena like dark matter and singularity, about which we currently understand very little, in a better way. A final theory would unite the four forces of Nature, explain them all in a single theoretical framework and possibly even lay the groundwork for the other, less fundamental sciences.
It is easy to see why physicists think there is a single theoretical framework describing all the forces. The idea of unification is a fundamental philosophy in physics. For instance, with the discovery of atoms, ice, water, and water vapor have been, in some sense, unified into water. All three are made up of water molecules. Today we have some brilliant insights about unifying the strong, weak and electromagnetic forces. But it has been particularly difficult to unify gravity with the quantum-field-theoretic description of the electromagnetic, weak nuclear, and strong nuclear forces. When things are massive as well as tiny, both general relativity and quantum mechanics must be taken into account, but they are incompatible. If we try to unify them, we get infinities and other nonsensical results like a probability greater than one, which just can't be true. So perhaps, we need a deeper theory, provided it exists, to find out what's really going on.
Spacetime is supposed to be smooth. But if we zoom in, really deep, we will see what has been called the quantum foam. We will reach a point where the familiar notions of space and time simply don't work. It should be noted that general relativity works fine for large distances and massive objects, and quantum mechanics works fine at small scales. So you may wonder why we should try to unify these two theories, instead of just applying them to places where they work. Well, the answer is simple. It seems to me that two fundamental theories in physics can't be incompatible. The apparent incompatibility means that our current understanding of the universe is flawed or incomplete. There very likely is a missing piece, a deeper theory that explains what really goes on deep down. Yeah, it is also possible that there is no unifying theory. Maybe our love for unification isn't shared by Nature. However, I don't think this is the case. I believe there is some unifying principle. Whether (or how soon) we are going to find it is another matter.
39. So, the best candidate theory for such a final theory is string theory. What is string theory all about?
-> Yes, today, the best candidate we have for a theory of everything is, perhaps, string theory. String theory proposes that there are vibrating one dimensional loops dubbed "strings" deep down every particle, and the different modes of vibrations of these strings correspond to the different particles. All forces and particles can be explained in string theory by assuming strings propagate in a fixed background in such a way so as to minimize the area covered. Forces in string theory arise from the joining and breaking of strings.
Replacing the concept of point particles with strings proved to be the crucial step to solve the conflict between general relativity and quantum mechanics. Roughly speaking, there is a smallest possible distance, distances smaller than which can't be probed and don't exist (in some sense). Strings are not point particles, they are smeared out, and by putting a lower limit to the distances that can be probed, we can avoid the conflict between general relativity and quantum mechanics, which arises when we magnify spacetime to very small scales.
Also, as you have probably heard already, string theory works in ten dimensions. Actually, string theory, in certain calculations, yielded negative probabilities, which is, of course, rubbish. After a lot of effort, physicists found that if the string is assumed to be moving in all these extra dimensions, the negative probabilities cancel out and the results obtained are sensible. These extra dimensions fundamentally affect the properties of particles like mass and charge, since the particles are emergent from vibrating strings, and these strings are vibrating in, and thus are affected by the extra dimensions. The explanation of why we don't see these extra dimensions is that these dimensions are curled up to such small lengths that they are not perceivable.
40. Okay, alright. I don’t understand how extra dimensions can be curled up to small lengths. I mean, what exactly do we mean by “extra dimensions”? Why exactly are they not perceivable?
-> Here's a simple (and common, so you might've heard of it before) analogy. Think of a thin pipe. From a long distance, it would appear that this pipe is just a straight line, that is, one-dimensional. You can specify the position of an ant on the pipe just by using a single number: the distance of the ant from either the left or the right end of the pipe. But zoom in, and you see that in addition to moving forward or backward, the ant can also move around the pipe in a clockwise or anticlockwise direction. So the pipe is really two-dimensional. If you cut along the pipe and unfold it open, you get a two-dimensional sheet.
Figure 9: A thin pipe appears one-dimensional from a distance, but if you zoom in you will find that it has a second, curled-up dimension in addition to the extended dimension.
The dimension we can see, the one along the length of the pipe, is stretched and easy to see, while the other dimension is curled up, and difficult to see from a distance. Similarly, in addition to the stretched, easy-to-see dimensions around us, it is possible to have smaller dimensions which are curled up and very difficult to detect, even using our present technology. And it is important to note that this curled up dimension is present everywhere, at each point in space. The important thing to keep in mind is that, as Michio Kaku said, the fundamental laws of physics are simpler and easier to deal with in higher dimensions.
41. Okay. Now, string theory is a controversial topic. It receives a lot of criticism. What exactly is the problem with string theory?
-> A serious problem with string theory is that it is background dependent. We describe strings moving in a fixed background, in fixed space and time. Quantum mechanics also treats the background as fixed, and is, thus, background dependent. But general relativity is background independent. The background (spacetime) isn't fixed in general relativity, but directly takes part in the theory. And it seems a final theory must also be background independent. String theorists assume the background to be almost fixed with small disturbances and use perturbation techniques to account for these disturbances. Speaking of perturbations, there are also non-perturbative approaches to string theory, but a detailed discussion of them is beyond the scope of this article.
Then, of course, there is the problem that string theory has not been verified experimentally. In science, no theory is acceptable until it is repeatedly verified by experiment. String theory has made no unique and viable prediction. The predictions of string theory, if proved to be true, will not conclusively prove that string theory is true. And even if these predictions are false, string theory might still be true. However, we should understand that maybe it is too early to expect experimental support, because after all we understand so little about these theories.
Also, before you ask, there are a few alternatives to string theory, the most notable of which is loop quantum gravity (I am not aware of the other alternatives, sorry). Loop Quantum Gravity attempts to apply the principles of quantum mechanics to gravity. LQG isn’t a unifying theory, it just explains the gravitational field in a quantum-mechanically acceptable manner. General relativity, as we know, describes gravity as a consequence of the curved geometry of spacetime. LQG, however, suggests that space itself is discrete and quantized (not continuous). It assumes that space is emergent from discrete building blocks. And although LQG makes some testable predictions, is mathematically well-defined and background independent, there are problems with this theory as well, the main problem being that the “experiments” suggested to test LQG are not at all viable using present technology. For instance, one proposed method to test loop quantum gravity uses evaporating black holes. But yeah, I think LQG is somewhat underrepresented in the physics community, as compared to string theory.
42. What’s the current state of string theory and in general, the elusive “theory of everything”? I mean, consider string theory. How much do we really understand about string theory? Is it likely to be correct? Also, do you think, as some physicists have suggested, we should focus more on empirical physics rather than speculative theories like string theory?
-> String theory involves so complicated mathematics that we don't even know what the exact equations of the theory are. We know only approximations, which have been partially solved. Some physicists believe that they are on the right track. But, at the same time it is important to remain skeptical. A good friend of mine once asked what the basic idea behind string theory is. I think the reason behind her asking is that I used to be obsessed with string theory in those days (I still am). After I filled her in for about twenty minutes, she remarked that such a beautiful theory, which explains so much and unites the four forces, must be true, regardless of whether we can verify it by experiment or not. She went further, claiming that we shouldn't bother with experiments always.
I admit that I used to think like her, at one point of time. And I have always been more interested in theoretical physics, and not experimental physics. But although string theory is beautiful and promising, we shouldn't accept it as an established scientific theory until and unless we have enough experimental support. Experimental support is important. That’s the way science works. Keep in mind that what makes a statement scientific is that it could have been false, but is shown to be true according to experiments. Experiments are crucial to tell us if the scientific statements we have discovered are true in our world.
So even if I chose to answer your question - is it [string theory] likely to be correct - it would be nothing more than speculation. We really don’t know enough right now. The best we can do is to train ourselves and become researchers in this field, and try our best to find out, and in the meantime, wait for developments.
As for the last question, well, I have talked with a lot of professors and science communicators about this. Many of them believe physics should be an empirical science. Theories like string theory do not qualify as physics, because they make no testable prediction, and we have no way to verify that they are actually true. But I don't think that string theory is entirely nonsense and that we should stop working on it. Because if a theory is mathematically elegant and answers a lot of theoretical questions, it could be true. We understand very little about string theory, so maybe it's too early to expect experimental support. If you don't know the details of the theory, how can you figure out an experiment to test the theory? And I admit it is all math and speculation and maybe a bit too radical, but can you suggest a better theory that will answer (or at least give possible answers to) all the questions?
The problem today is that theoretical physics has advanced much, much faster than experimental physics, which is why we can't bridge the two. But that doesn't necessarily mean modern theoretical physics is wrong, philosophy, speculation and all that. String theorists didn't make up the story of strings and extra dimensions, they were led to those conclusions by some well-defined mathematics. But yeah, it may be true that there is no unifying theory, and even if there is such a theory, the approach the majority of physicists take to discover such a theory is not the correct one. Like maybe some of our preconceived notions are incorrect. We need to consider each and every possibility. We should look for alternatives to string theory and loop quantum gravity. We shouldn't get stuck on these theories.
43. You are also very interested in chaos theory. What exactly is chaos theory?
-> Chaos theory is the study of the underlying rules and order in chaotic (roughly speaking, unpredictable), and apparently random systems. So chaos theory is not really a theory of chaos. It is the study of the rules and order underlying complex systems that appear chaotic to us. Now, some people use the words “complex” and “chaotic” interchangeably. But a complex system is not necessarily chaotic, and the reverse is also true. A chaotic system need not be complex. A simple system can give rise to chaos.
Anyway, so although chaos theory is the science of unpredictability, the rules of complexity are universal, and apply to all dynamical systems, regardless of their constituents. Chaotic dynamics essentially depend on two things: expansion and recurrence. Most systems which show expansion and recurrence will show chaotic behavior. Complexity arises when, roughly speaking, there are competing effects. Like gravity trying to crush everything down, the expansion of the universe trying to blow everything apart.
One of the most important predictions of chaos theory is that systems with slightly different initial conditions give rise to hugely different results. Technically, this is called sensitivity toward initial conditions. The most popular example is the butterfly effect. A butterfly flapping its wings can give rise to a chain of events which might end up creating a thunderstorm in some distant place. This is only an example, and this idea applies to everything in our universe. Tiny changes in the initial conditions produce results that are very different from each other and are, thus, practically unpredictable.
44. What are some applications of chaos theory?
-> Chaos theory has a lot of applications. I really don’t know in detail about these applications, but I can tell you that chaos theory is used to understand turbulence in physics, study the motion of galaxies, animal population, evolution etc. It is used in economics and market research, then in the study of social behavior. It is used in Artificial Intelligence research; especially chaos theory comes in handy when you are trying to build an AI or maybe even a robot that can respond to unpredictable changes. Then, chaos theory has numerous applications in medicine. The idea is that mathematical tools can help biologists and physiologists understand the complex systems of the human body, without a thorough knowledge of local detail. Chaos theory has successfully explained the sudden, aperiodic and chaotic behavior of the heart, called ventricular fibrillation. According to chaos theory, the fibrillation is the result of disorder of a complex system, like the human heart. Though all individual parts of the heart seem to work perfectly, yet the whole system becomes chaotic, and fatal for human life. Ventricular fibrillation is not a behavior that returns to stable conditions on its own; rather this fibrillating state is itself "stable chaos."
45. Okay. My next question is: what exactly are these strange patterns called fractals, which are often discussed alongside chaos theory?
-> Fractals are intricate and complex patterns, some of which repeat endlessly. You can see fractal patterns everywhere in Nature. And all of these patterns arise from some underlying rules, which are often simple. One of the most important and counterintuitive predictions of chaos theory is that a simple set of rules can give rise to complexity and chaos. Most people find it difficult to accept this fact. If you are still not convinced that complexity can emerge from a set of simple rules, let's discuss an example. It's called the game of life. It's basically a cellular automaton. This game is played on a grid, where each cell is either alive (say white) or dead (black). And each cell can be surrounded by a maximum of eight cells (neighbor cells). There are some rules: alive cells with no or one alive neighbor die (solitude), alive cells with more than four alive neighbors also die (overpopulation), alive cells with two or three alive neighbors survive and dead cells with three alive neighbors become alive. If you play the game by following these simple rules, you get some very complex, interesting patterns, sometimes which can even self-replicate. So, we actually shouldn't be surprised about the complexity in our universe. To quote Carroll, "If interesting complex structures can arise in a computer simulation with nothing more than white dots and black dots, it’s not surprising that they arise in something as multifaceted as the expanding universe."
So anyway, a fractal, roughly speaking, is a complex pattern which has a measure of roughness. Two famous examples of fractals are coastlines and snowflakes. On zooming in a coastline (which appears relatively simple on the globe), we see that more and more complexity is revealed, and length of the coastline curve goes on increasing. And here’s how to generate a snowflake-like pattern: Start with an equilateral triangle. The sides of the triangle are trisected (divided into three equal parts) and the middle part is removed from each side. With the removed portion as an invisible side of it, another equilateral triangle is constructed, which is again treated similarly. On continuing this process infinitely, a fractal is formed, which resembles a snowflake.
Figure 10: The process of generating a Koch snowflake (Image credit: Wikipedia)
Though this fractal has a finite area, it actually has an infinite length (since you are going on increasing the number of sides of the pattern, and in theory, you are doing it an infinite number of times, to get a pattern resembling a snowflake). So, intuitively, its dimension should be a number greater than 1 (since it has an infinite length, it is more than just a one-dimensional pattern) but less than 2. Yes, fractals can have fractional dimensions. The fractal dimension of the Koch snowflake is 1.2618, a number which lies between 1 and 2, as expected.
46. Could you elaborate how exactly something can have a fractional dimension? Maybe with an example?
-> Okay, so there’s a fractal called the Sierpiński triangle. How to generate it? Well, by playing the chaos game. Start with three non-collinear points (say, A, B and C), such that they form an equilateral triangle. A random starting point (say, P) is chosen anywhere on the plane. The game proceeds by following certain simple rules. A die is rolled. If the outcome is 1 or 2, the point halfway between the points P and A, is marked. Similarly, if the outcome is 3 or 4, the midpoint of the line segment joining the points P and B is marked. For outcomes 5 or 6, the midpoint of the line segment joining the points P and C is marked. As the game continues, the midpoint of the line segment joining the point last obtained, with A, B or C (depending on the outcome), is marked. If this is continued for long enough, the collection of all the marked points resembles a beautiful fractal called the Sierpiński triangle.
Figure 11: The Sierpiński triangle (Image credit: Wikipedia)
The Sierpiński triangle has an infinite length, because the fractal continues infinitely. However, the area tends to zero, since most of it is just empty space and there is no solid surface. Now, interestingly, this process is not sensitive to initial conditions. This is because, no matter wherever we choose the starting point to be, we will always get back the same pattern, provided we plot points as per the rules of the chaos game.
Now, dimension. Intuitively, this fractal, with an infinite length, is "more" than a one-dimensional pattern, but "less" than a two-dimensional figure, since its area tends to zero. So the fractal dimension of the Sierpiński triangle lies between 1 and 2.
If a one-dimensional line is broken into two equal halves, that is, if it is scaled by one half; its mass is also scaled down by one half, since two such halves will reproduce the original line. Similarly, if we scale the side of a square by one half, its mass is scaled by one fourth, since it takes four squares (each of a length one half the length of the original square) to reconstruct the original square. One fourth is just one half raised to the power of two, and this number is the dimension of the square, which is two. Similarly, just as a line is one dimensional and a square two dimensional, a cube is three dimensional because if a side of the cube is scaled by one half, the mass is scaled down by one eighth (or one half raised to the third power), and it takes eight copies of the smaller cube to generate the original cube.
For a Sierpiński triangle, on scaling it by one half, we get a similar, but smaller pattern, three of which, when arranged in the right pattern, give back the original triangle. Thus, the mass has been scaled by one-third. Following the above line of reasoning, this means that one half raised to the power of (say) x, should equal one third. This x is the dimension of the Sierpiński triangle. Some simple mathematics reveals that x is 1.585, which is the fractal dimension of a Sierpiński triangle.
47. Alright. That’s really interesting. Now, I’ve heard fractals have a lot of applications in the fields of biology and medicine as well. Could you give some examples?
-> Yes, fractals are found everywhere in Nature. One example is the structures found in different living organisms. Fractals are self-similar patterns. There’s just one simple part with which you initially start, and which repeats endlessly, and then you apply two or three simple rules again and again to generate the fractal. Although the fractal is complex and will take up a lot of space if you want to store it in a computer as it is, you can also store it by storing the simple information about the repeating part and the rules. This takes up a lot less space. However, if you do the latter, you’ve to give some time to the computer to generate the fractal from this information. So, you either compromise on time or on the storage space. Anyway, the thing is, different structures grow in different life forms in a similar way, or in other words, recursively. But there’s one crucial difference. If you generate a fractal on the computer, you’ll get a perfect fractal. The same thing is repeated again and again. However, the fractal (or rather, fractal-like) structures found in living organisms aren’t perfect. There are slight variations and imperfections. This allows the organism to modify certain parts of it to better adapt to its environment and evolve, without having to redesign the entire body from scratch (since it works recursively).
Let me give some more examples of the applications of fractal geometry in biology and medicine. Fractal geometry allows the formation of bounded curves of great lengths, and that is how the lungs manage to accommodate so large a surface area inside so small a volume, which in turn, increases the efficiency of the respiratory system. Fractal geometry has also been used to model the dynamics of the HIV virus, which is responsible for the AIDS disease. Bone fractures are fractal and even the surface structures of cancer cells display fractal properties, and perhaps this property can be manipulated to detect cancerous cells at an early stage. Fractal patterns exist throughout the body – from the tissues to the way blood vessels branch.
48. Okay, so this might not seem relevant, but this is a question I’ve always wanted to ask. I’ve always been fascinated by the idea of time travel. I mean, who isn’t? From a physics perspective, what are your views on the idea of time travel?
-> Time travel? Well, what’s time? We don’t know. And I don’t want to discuss the different (mostly metaphysical) theories of what time is here. The most likely answer, from a scientific perspective, is the block universe idea. We’ve actually already discussed this, while discussing special relativity. Time is just a fourth dimension. And here’s something we haven’t explicitly stated then: the flow of time is an illusion. Quoting Tegmark from his book Our Mathematical Universe, "Einstein's work suggests that change is an illusion, time being merely the fourth dimension of an unchanging spacetime that just is, never created and never destroyed, containing our cosmic history as a DVD contains a movie." To quote Einstein himself, "The distinction between past, present, and future is only a stubbornly persistent illusion." And I think the block universe is the best theory of time we have, as of now. But there are some issues with this view as well, and not everyone agrees with it.
So, is time travel possible? At least theoretically? That is to say, time travel at a rate faster or slower than one second per second? Well, it may be possible theoretically. But to answer whether it really is, we first need to understand the nature of time. You can find solutions to general relativity that allow traveling to the past. The Alcubierre drive proposes to manipulate the surrounding spacetime to travel faster than light and into the past. (When a signal travels faster than light, it is received before it is sent, in all reference frames. So, in some sense, it has traveled back in time.) But the Alcubierre drive needs negative energy density and is not at all a feasible idea. And it may be theoretically impossible as well. General relativity is not complete. If we find a so-called “theory of everything,” it would probably eliminate these particular solutions of general relativity. Wormholes could serve as a gateway between parallel universes and might allow time travel. But it would, again, need negative energy, and we don't know if that's possible. We don’t know for sure whether wormholes exist in the first place.
According to Hawking's chronology protection conjecture, the laws of physics fundamentally don't allow time travel. The idea of time travel is, in itself, bizarre and paradoxical. For instance, if time travel was possible, one could go back to the past and kill his grandfather before the latter married the former’s grandmother (the grandfather paradox). This means, he would not even exist in the future, which contradicts the fact that he actually visited the past. Some people believe that the history can’t be changed, and if you were to kill your grandfather (say with a gun), something must happen (say, the gun doesn’t fire, or someone comes in between) that prevents the death of your grandfather. Your grandfather would perhaps tell you about the incident. Some unknown person attempted to shoot him, and another man died instead. Only if he knew that it was his grandson! So basically, you go back to the past to fulfill what has already occurred. You are not changing history. Simply because you can’t. Also, if we assume that by traveling in time (of course, at a rate other than one second per second), we simply enter different timelines, then paradoxes like the grandfather paradox can be resolved.
Some critics, including Hawking, have pointed out that if time travel was possible, time travelers from the future should be contacting us right now. Of course, this is not conclusive evidence that time travel is not possible. However, personally I still think it is not possible. Also, time travel violates the law of conservation of energy since if you travel to the past, you are an extra there. Your mass, for instance, needs to be accounted for. Thus, if it is not that your visit from the future was already recorded in the past, you can’t actually travel in time. Also, you can’t just go and visit the past and not be able to interact with anything. Even to be able to see, you must interact with the environment.
49. Do you believe in simulation theory?
-> The simulation theory is a popular argument, although a very controversial one at the same time. According to the simulation theory, we are living in a simulation, run by a computer. It is likely that everything in our universe follows certain mathematical laws. So, why can't an advanced civilization actually run a simulation of our world on a computer? What if we are already living in a simulation? Some scientists have started devising experiments to test the simulation hypothesis. It can be the case that as a simulation runs, over time there are certain errors or glitches. And the simulators could slightly adjust the fundamental constants of Nature to take care of such glitches. So, maybe we can look for such slight changes, but such changes will be extremely hard to detect, because we are talking about small, really small changes. Such experiments, if they succeed, can have a lot of explanations, and don't conclusively prove that we are living in a simulation.
Well, yeah, we actually have no way to conclusively prove that we are not living in a simulated reality. Some would argue that no computer simulation can produce so complex a reality, and so complex a thing as consciousness. However, maybe it is not so complex after all. Maybe all that matters is the mind, and it is being simulated to create the illusion of the complex reality.
Another interesting thing to keep in mind is that if simulation theory is correct, space and time are not continuous. Why? Because if space and time are continuous, they are infinite (in the sense that they can be divided infinitely) and no finite computing power (no matter how large) can simulate infinity.
So, that’s all I know about simulation theory. I really haven’t reached a firm conclusion on whether simulation theory is true or not. You are free to form your own opinion.
50. Recently, you confirmed that although you were interested in metaphysics at one point of time, you now believe that physics is much better than metaphysics. Why?
-> Well, first of all I’d like to point out that “better” is probably not a very good choice of word in this context. What I believe is that physics is more useful than metaphysics. Physics is about the real world. Metaphysics is just speculation. Of course, we don't know how "real" the physical world is, or what goes on deep down, or what happened at the very beginning and so on. But still, physics has proven its worth countless times, and ultimately, physics works. Physics builds a model which best explains the world. And it allows us to find the underlying laws of the physical world and make predictions. You can't deny that studying the physical world has given rise to a lot of important sciences, and they, in general, improve the quality of our lives. Speculating about the fundamental nature of reality from a metaphysical perspective, while tempting to some, will not really help us find a cure for cancer or solve the energy crisis. This is why physics (and science) is more important. This is why I chose physics over metaphysics. And while I don't say metaphysics is completely useless, I still say that physics is more important.
51. This one might not qualify as a physics question, but I'm sure this is a question every physics lover can relate with. You’ve written an article Did Einstein Believe In God? In general, as a physics student, what are your views on Einstein?
-> Einstein. Well, the most interesting figure during the revolution of quantum mechanics. I also refer to him as the best man during the marriage of the law of constancy of the speed of light in vacuum with the principle of relativity in the restricted sense. Well, we’ve actually already discussed these when we were talking about special relativity, although I didn’t mention the phrase “the principle of relativity in the restricted sense.” Anyway, special relativity brought with it a hitherto-unknown, young man into the physics community. And my views on Einstein can be summed up in one word: genius. One single thought, that of chasing a light beam, transformed a young man into a revolutionary physicist who attempted to come closer than most people to the ultimate truth. And even today, at least to me, it is surprising how that young man took over his shoulders the insurmountable task of writing the equations for the behavior of matter in curved spacetime. In light of all he has done, it is indeed obvious why the term "genius" will always be inextricably linked with the wild-haired, casually dressed physicist. Of course, I acknowledge Einstein’s limitations, and I also admit that people who say he’s a bit overrated have got a point. I mean, of course he was talented, but he was also a bit lucky. And there were a lot of physicists who deserved much more recognition for their works than they actually got. Some of their contributions are, by no means, any less important than Einstein’s. But still, Einstein is Einstein. The only person who probably had a greater impact on the field of physics than Einstein is, in my opinion, Newton. Newton established physics as a proper science, while Einstein just revolutionized modern physics. Most of the groundwork of Einstein’s theories were laid down a long time ago. Einstein’s genius is that he challenged the conventional beliefs and connected the dots in the right way to create an entirely new picture of the universe.
52. Again, this might not qualify as a physics question, but as a science student, what are your views on religion and God? Why did the idea of God emerge in the first place?
-> There is nothing wrong in believing in a particular religion, as long as you don’t justify incorrect actions on the basis of that. But physics (or in general, science) is much more fundamental than religion. This is easily settled. Physics all around the world is the same. It isn’t the case that an Indian physicist and a German physicist discover different fundamental laws. In all countries, the study of physics has evolved independently; and we have all reached the same conclusions (mostly). And in science (physics), everything is subject to change. No matter how good and revered a theory is, if we find something in contradiction with the theory, we reject it. That clearly isn’t the case with religion. Religious teachings are based on ancient beliefs, and they hardly change. All the religions of the world, also, don’t converge to a single explanation. People bend religion to their wills. Indeed, I tend to agree with Weinberg that: “With or without religion, you would have good people doing good things and evil people doing evil things. But for good people to do evil things, that takes religion.”
Now, God. I don’t believe in God, but rather in a naturalistic worldview. I argue that God is an unnecessary and illogical hypothesis to explain the origin and nature of the universe. God is not only a bad explanation for the universe, but also a bad idea for humanity. In fact, sometimes it seems to me that God is the source of all evil, suffering, and injustice in the world. God is the ultimate tyrant, who demands absolute obedience and worship, and threatens eternal punishment for those who disobey or question him. God is the enemy of reason, science, and progress. I think it is time to reject this monstrous fiction, and embrace the truth of Nature. It is time to free ourselves from the shackles of religion and live by the light of reason. It is time to be human, and nothing more.
Now, why do we even believe in God? I have a scientific answer to that. Our hunter-gatherer ancestors believed that the night arrived when God became angry and prayed, believing that the next day to be a result of their prayers! It might be a natural tendency of humans to avoid taking responsibilities of any sort, accepting unknown powers. There is a theory about religion. From the point of view of evolution, we have evolved to get better at survival. But evolving humans also learned to ask questions; they were intelligent. During early times, humans lived in groups in jungles, with a leader. The members might not always agree with the leader. However, this might cause a clash and that member might be isolated from the group which would harm his chances of survival. So, there was a need that our ancestors should follow someone unquestioningly. These hereditary feelings show in us in our tendency to believe in God.
One more way to think about it is this. Early philosophers reasoned that God must exist. The order and complexity of the world requires some creator, just like a watch requires a watchmaker. If you see a watch lying on the road, you will not assume that it has been there for eternity. It was made by someone. It's the same thing, according to these arguments, with the human body: it requires a creator. But I personally believe that, as I have said many times, ordered complexity is a fortunate product of random processes. And also note, even if we choose to believe in these arguments in favor of the existence of God, they don't refer to any religious God.
53. I’m studying physics, and it seems to me that it’s just math. I mean, I expected there to be some theory as well. Is physics fully mathematics? Do we draw all conclusions in physics from our equations?
-> Well, I’d say, no. Maybe the problem lies in the way physics is taught. Yeah, it’s true that to make sense of the exciting physics theories you read about in popular science books, and to work on these ideas, you first need to have rigorous mathematical training. But still, physics is more than just mathematics and calculations. Revolutionary physics theories start with some wild idea, some intuition, and then we of course need math to develop the theory. This reminds me of something, which might be relevant. I think I have discussed this with my audience previously as well. Anyway, here it is.
The pressure at a point inside a fluid at a depth of h units is given by P + hρg where P is the atmospheric pressure, ρ is the density of the fluid and g is the acceleration due to gravity. So, the pressure depends only on the height (the other terms are constant). Now, imagine a container containing some fluid which is very narrow near the bottom but wide near the top. Like a “V.” Imagine another container shaped like an “A,” narrow near the top while wide near the bottom. The pressure at a point A at a depth of h units in the first container is the same as the pressure at a point B at a depth of h units in the second container. The pressure doesn’t depend on the shape of the container. But look at the containers closely. The volume of the fluid above A is much more than that of the fluid above B. So shouldn’t the pressure at A be greater?
Figure 12: The pressure at point A is the same as the pressure at point B; the pressure depends just on the height and not on the shape of the container.
When our physics teacher was teaching this in a class, a student stood up and said that in physics, intuitions are not to be trusted. Only equations are to be trusted. (The equation clearly shows that the pressure depends only on the height. P(A) = P + hρg and P(B) = P + hρg. So, P(A) = P(B).) I disagree. This doesn’t mean intuitions are not to be trusted. Some of the greatest discoveries in physics were possible because physicists have had the right intuition. The right intuition. You must train your mind to have the right intuition. Some people fail to get the right intuition for the above example. But that doesn’t mean intuitions are not to be trusted. It was clear to me that P(A) = P(B), and I didn’t use the equation (believe me). I figured out that the pressure on A is due to the column of water just above it. And the same for B. It is immediately clear that these two cylindrical columns of water above A and B are the same since the height is equal. So the pressures at A and B should of course be equal. Looking at the shape of the container and the volume of fluid above the point is not the right thing to do in the first place. Just look at the columns of water immediately above the points A and B. They are just like lines (the radius of the cylindrical column is infinitely small since A and B are points).
54. What are your views on free will? What does physics say about free will?
-> To start with, there is no way to conclusively prove that free will exists, even if it actually does exist. So this is a question which is resistant to scientific analysis. It's not a scientific question. Anyway, I suspect free will could be an emergent property of human consciousness, but I think it is more likely that there is no free will. After all, we are nothing more than machines. Yes, we are machines of flesh and blood, not machines of metal. But we are made of the same fundamental particles that follow the same laws of physics; so fundamentally that makes no difference. Free will is just a dream of the machine, which probably can be explained by studying the physical state of the machine and the way its parts are arranged and interact. But free will does not have a fundamental existence. That’s one way to think about it, anyway, and personally I find this view appealing. Also, some people argue that since quantum mechanics proves that the universe is random, it shows that free will must exist. This argument makes no sense. Even if I accept that the outcome of a quantum experiment is random and can't be predicted, it still doesn't mean our consciousness can influence this outcome. Determinism ruled out is not equal to free will verified. I believe that deep down, the universe is perfectly deterministic and ordered, just as Einstein believed, and that the apparent randomness is indicative of our incomplete knowledge. The reason I say the universe might be deterministic is that even randomness can be deterministic. There are laws that apply to random systems; random doesn’t mean it can’t be studied or understood. All I mean by deterministic is that the universe functions according to some universal laws. So anyway, I think free will is an illusion, and human actions are determined by the laws of physics and the physical state of the brain. Neuroscience shows that human decisions are influenced by subconscious processes and environmental factors, and that the conscious mind is often unaware of the true causes and motives of its actions. Well, free will may be a useful and pragmatic concept, but I think it's not a fundamental scientific truth. Free will is a product of human perception and cognition, and it’s important because it serves as a basis for morality, responsibility, and agency.
55. Okay, final question. So you believe there’s no free will. However, you say that ordered complexity is a fortunate product of random processes. How do you reconcile this with your belief that the universe might be deterministic deep down? Also, what exactly do you mean by that statement?
-> I just answered that in the previous answer. Well, kind of. Let me quote myself: "Randomness can be deterministic. There are laws that apply to random systems; random doesn’t mean it can’t be studied or understood." When I say ordered complexity is a fortunate product of random processes, I simply mean that everything happened spontaneously and not because of some greater power or God. But I don’t think this rules out the possibility of a deterministic universe. Notice the phrase “ordered complexity.” Ordered implies that certain rules are being followed, and thus determinism may hold. But there is some randomness in the system as well. I think we can say with reasonable certainty that ordered complexity may arise from randomness plus some rules. One example that comes to my mind is the Sierpiński triangle, it is generated according to some simple rules, but there is some randomness built in the rules (as we've seen, we start with a random point and the subsequent steps depend on the outcomes we get after rolling the die). And after a huge number of iterations based on these rules, we always get this same fractal called the Sierpiński triangle. So the process is not sensitive to initial conditions, the outcome is fully deterministic, even though there is an element of randomness in the process. One more example is random Boolean networks, which have been used to explain self-organization in complex systems. In this case also, there are some local rules and some randomness in the system, and what we get in the end is a complex, self-organized system.
Actually, I should say ordered complexity is a process of seemingly random processes. The complex and ordered structures that we see in Nature, such as living organisms, are the result of seemingly random processes, such as mutations, natural selection, and environmental fluctuations. These processes are currently known to be completely random. As of now, it seems there is no order or design behind the emergence of complexity, rather it is a lucky outcome of randomness. And keep in mind that this complexity is not a static or fixed state, but a dynamic and adaptive one that changes and evolves over time. However, we don't really know whether this is randomness, in the true sense. This randomness could be considered deterministic in some sense. It is entirely possible that the universe is deterministic deep down, and it just appears random to us. As I've said, deterministic just means that the universe functions according to some universal laws, although there can be some (apparent?) randomness built into these laws. However, whatever be the case, to me it seems unlikely that we are going to completely understand every aspect of the universe any time soon. In fact, there are several reasons why we may never find a complete theory of the universe, such as the limitations of our observations, the incompleteness of our mathematics, the complexity of our models, the unpredictability of our experiments, and the uncertainty of our interpretations.
Thanks for reading! Also, just like Wheeler's participatory universe, this article is a work in progress! If you have any physics questions (try to avoid questions involving topics like consciousness and/or metaphysics) that are not included in this article, please send your questions to this email address (make sure the subject of your email is "Physics questions for Arpan Dey, JYP"), and if the questions are suitable, they will be answered and added to this article.