Home > Physics > The speed of light – Part 2/2

The speed of light – Part 2/2

This post is about two aspects of the universe, wherein the rule of the upper limit of the speed of light seems to be violated, but actually isn’t. But before that, I have something to say about my previous post. In that post, we tried to understand one of the radical consequences of Einstein’s theory of relativity, which was that time is not universal and that it depends on the relative velocity of the two observers involved. I thought I should add 2 brief points to that. Firstly, It is not just that time changes when you travel. Do you remember I mentioned that speed=distance/time? So it is not just that time varies. Distances also vary with speed. This too is confusing, but I don’t know much about it to even attempt explaining it. What I can do is to point you to this wikipedia link, so that you can pull your hair out if you feel so. I have just picked up a book by Albert Einstein from Connemara public library in which he tries to explain his Special and General relativity theories to an ordinary non-scientific reader. If I get through the whole book, I will come back and make an attempt to explain how distances also vary. I am skeptical about completing it, since Einstein himself says in the preface (that is how far I have gone in the book), that one needs patience to read the book through. The second point I wanted to make about the previous post is that, even though time slows down for someone travelling at high speeds, she will not realise it on her own. To her, it will seem that time is flowing as usual and she will not notice any change till she compares her clock with somebody’s who is moving faster or slower relative to her velocity. This is fairly obvious, but I just wanted to make it clear. Thinking about it after writing the post, I thought someone might try to imagine it as if, at high speeds, their life will start running slowly similar to a slow motion movie. But that is definitely not so. To her, time will be normal. It is only on comparison that the change can be noticed.

Expanding universe: Coming back to this post, the first instance where the rule of “nothing can travel faster than speed of light” seems to be violated, comes from the expansion of our universe. If you did not know before, the universe we are living in, is expanding at an accelerated rate. The most common way that this is explained is to visualise the universe like the surface of an expanding balloon with the galaxies represented by coins stuck on the balloon. There are a couple of important reasons why this analogy suits so well to explain the phenomenon of expansion. You need to note that galaxies are not represented by paintings on the balloon but by coins stuck on the balloon. Thus as the universe (balloon) expands, the galaxies don’t increase in size. The galaxies only move farther away from each other. So it is not as if all the objects in the universe are expanding. Before explaining the second important point of the analogy, I need to make one thing clear. When the universe is compared to the surface of a balloon, you must realise that the universe is in 3 dimensions, where as the surface of the balloon is only in 2 dimensions. Asking what the balloon’s inside corresponds to in the universe is meaningless, since the analogy breaks there. All of the universe is represented by the surface of the balloon. Now, the second point of the analogy. It is that the expansion is not centered at any point. From any point in the universe, it seems to be expanding in exactly the same way as at any other point in the universe. Imagine you are sitting on one of the coins. You will see coins flying away from you in all directions. The important thing to note is that, no matter which coin you are sitting on, the way the rest of the universe appears to be flying away from you would be the same.

As mentioned before, this flying away happens in an accelerated manner. Which means that if there are three galaxies O, A and B and that A is farther from O than B is from O. Then the speed with which A is flying away from O will be greater than the speed with which B is flying away from O. That is, speed increases with distance. So if a galaxy is sufficiently farther away from another galaxy, then it can travel at very high speed, which can exceed the speed of light. Thus there are cases where galaxies are moving at a relative speed greater than that of the speed of light (let your mind chew on this fact a bit). This means that the speed of light limit is violated, right? But here is where the key is. The explanation to this seeming violation is that the speed of light limit applies only for objects moving through space. In this case of the expansion of universe, the space itself is expanding. So it is not that galaxies are moving through space, but that galaxies are moving along with the expansion of space itself, and hence the rule is not violated. Thus it is better to state the rule as “No object can move through space at a speed greater than speed of light”.

If that sounded like a cheap play of words, let me make an attempt to make it better for you. In that balloon analogy, the surface of the balloon represents all of the universe. So it is not as if the universe (represented by the balloon) exists in space. The surface of the balloon is the space. There is nothing else. Though it is hard to imagine otherwise, if we imagine the universe to exist in some big dark space in which it is expanding, it is wrong. It is space itself that is expanding and not the universe present in space. This is crucial. Thus in an expanding universe, galaxies move away from each other at speeds greater than the speed of light, but since that movement is not through space, it does not violate the rule.

Quantum Entanglement: Quantum mechanics (QM) is an area of Physics which deals with subatomic particles. Thus it deals with particles at extremely small scales. It is from this field of physics, that the idea of the possibility of there being an infinite number of universes, other than the one that we are in, came up. Some of the ideas were so weird, that Einstein himself, refused to accept that the theory was the last word on such small scales. Here again there is a scenario where the speed of light seems to be violated, but actually isn’t.

The basic problem that Einstein had with Quantum theory was that the theory postulated that particles don’t have a single value for a property. For example, take the property to be the position of the particle. QM says that till the time you see/measure the position of the particle, the particle does not exist in one place. It could have existed anywhere in the universe, and in one sense, it does exist everywhere, but once you detect it, it will choose one of those many places to exist in. This is like saying that suppose you have a book on your bookshelf. You have locked your house and gone for a vacation. So now, nobody is there to see that the book is on the shelf. But this does not mean that the book is not there. If anybody asks you where the book is, you will confidently answer that the book is in your house on the bookshelf. So the location of the book, which is its property, has a definite value (your bedroom shelf of your house which is at a specific address), even if nobody is checking that. But quantum mechanics says, that till you see it, the book cannot be said to exist anywhere. Rather the only thing you can say about it is the probability or chance of it existing at each point in the universe. Something like, right now, this probability that it exists on earth is 99%, and that it exists in andromeda galaxy is .001%, that it exists in Milky Way but outside the earth is .2% and so on. That is, till you measure it, the particle does not exist anywhere but in some kind of “quantum limbo”, and chooses one of the possible positions, when you measure it. Yes, it sounds weird. It was not for nothing that Einstein tried to disprove it. Of course, this does not apply to objects the size of books but only to particles at very small scales.

In fact, the scenario I am going to describe here, was formulated by Einstein and 2 other scientists Podolsky and Rosen, to disprove  a particular interpretation of Quantum Mechanics. This is called EPR paradox after the initials of the 3 scientists who came up with it. Einstein said something like “See, if your theory is correct, then this particular thing has to happen. But since this cannot happen, your theory is wrong”. But what he said cannot happen, was actually proved to happen. I will explain this more specifically a little further down.

Quantum entanglement is the phenomenon wherein two sub-atomic particles are linked together and act in synchronisation even if they are extremely far away from each other. This does not sound strange at first. Consider the case where a pair of shoes are split up and sent to different places. One of the pair is sent to a person X and another is sent to Y. But nobody knows who has been sent what. Assume that the splitting up and sending was done in a random fashion by a computer. When the boxes containing the individual shoes reach X and Y, X sees that he has received the left shoe, he can immediately conclude that Y has received the right shoe. No matter how much distance is between them. This is perfectly obvious since at the time of splitting itself, the decision of which shoe is going where has been made, though nobody knew what the decision was. Since it was randomly done, X has 50% chance of receiving the left shoe and 50% chance of receiving the right shoe. Vice-versa for Y.

Something similar has been observed in quantum mechanics. There are situations where 2 particles are entangled in the sense that, if  the particles are measured after they travel very far away from each other from the point where they had split, their properties would be in sync. That is, if you measure the property of one particle, the other particle will have the exact opposite value for the property. This again is not surprising. Like, in the case of a pair of shoes, at the time of splitting, the particles could have been endowed with opposite properties which is what we are measuring after they have travelled very far away from each other. That is, the decision of which particle has which value, has been decided at the time of splitting itself, and hence though nobody knew of that decision (nobody measured the particles at the time of splitting), their properties were decided beforehand. This is what we tend to think.
But here comes in quantum mechanics. In the previous paragraph, I had explained Einstein’s gripe with QM was that it postulated that the particle cannot be said to have any value till you measure it. Which means that till the time of measurement, no decision has been made as to which particle has which value for the property. This is different from saying that the decision has been made, but is not known, which is what we would think happens. QM says that the decision is not made at all till the time of measurement.

What this means is that, till the time of measurement, either particle could have taken up either of the values for the property (in the case of shoes, the property is orientation and the values are Left or Right). But the moment you measure one particle, the observation that two particles are synchronised means that at the same moment the other particle is “forced” to take the opposite value of the property. It is something like, the moment you see a shoe, and it turns out to be Left, then it “forces” the other shoe to be Right and this happens only at the time of measurement. The point is the time of decision. Quantum mechanics says that the decision is made only at the time of measurement, whereas we tend to think that the decision is made at the time of splitting itself. This is a somewhat subtle point, and so please make sure you understand what the difference is.

So quantum mechanics says that once the property of one particle is determined, the other particle is made to take the opposite value only at that moment, and till that time either could have taken any value. Also, this forcing happens instantaneously. This seems to imply that once you measure one particle, this somehow informs the other particle “I have taken this value up, now you must take the opposite value, ok?” and the other particle complies. Remember that QM implies that this kind of “communication” since it says that the decision of the value is not made till the time of measurement. And this point is where Einstein objected.

The EPR paradox was this. Assume two entangled particles p and q. They are say a thousand light years apart. Which means, for a light particle to travel from p to q, it would take 1000 years. Remember that nothing can travel faster than speed of light, and so any information to be transmitted between them will also take a minimum of 1000 years. But quantum entanglement says that even for such particles which are so far away, the properties are in sync instantaneously. This can happen only if the properties are already decided while splitting (like the left and right shoes) or to concede that these particles are communicating instantaneously at speeds far greater than the speed of light which is impossible. If you say that the values are not pre-decided, the only option left is to agree that the speed limit of light is violated, which is not possible. Hence this theory is not complete. That was the argument, the three scientists put forward.

Let none of the above description make you think, that quantum mechanics, is not very dependable. Quantum mechanics’ predictions are extremely accurate and have been tested repeatedly. In fact, even in the above EPR paradox, the fact that the value of the property is not already decided (like that of the shoe’s orientation) has been proved by John Bell with the help of elementary probability. (I will try to explain that some other time, it is one of those beautiful explanations of Science, that made my eyes moist with the happiness of having understood something so elegant). So it is now true that particles indeed randomly decide on their value at the time of measurement, and yes, till the time you measure the value, the property cannot be said to have any particular value. With that established, it seems to follow that the properties that are not pre-decided, but being in sync clearly implies violation of the speed of light since the only other option left for them is to communicate instantaneously, at speeds greater than the speed of light. But the problem of entanglement violating the speed of light rule, can be solved as follows.

Though there is no doubt, that there are no pre-decided values that are with the particles (as shown by John Bell. Such pre-decided values are also called hidden variables), the entanglement fails an important test, for it to violate the speed of light maxim. The test for whether something can travel faster than speed of light, is to see whether information can be sent via such channels. In this case, though you can measure the value of a particle and see that its pair particle is giving an exactly complementary value on measurement, there is no way you can force a particle’s property here in a way that you can force the particle;s property there. That is, you can passively observe the value of a property of the particle here, but you cannot actively “set” its value to something, so that somebody measuring its pair particle 1000 light years away, can “read” the value. That cannot be done. Thus, even though entangled particles do synchronise instantaneously, there is no way information can travel faster than the speed of light. And therein, entanglement fails to violate the upper limit of the speed of light.

Thus the test of whether something is indeed exceeding the speed of light, is to see whether such a mechanism can be used to transmit information. If information cannot be transmitted faster than light, then it cannot be considered to violate the speed of light.

You might still have the nagging question of how the particles are in sync. That is something that is not yet clear. but what is clear is that that synchronisation indeed happens, and that the values are not pre-decided (thanks to John Bell). How that happens is still not clear. We need to wait to find out if there is something out there that is still beyond our understanding. This post ends with that tantalising question still somewhat hanging in the air.

PS 1: I would like to point out here again that whatever little I learnt about QM comes from Brian Greene’s book, The fabric of the cosmos.

PS2: I know this and the last post have been a bit heavy. I will move away from Physics for my next post. That is a promise.

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