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The speed of light – Part 2/2

October 30, 2010 Leave a comment

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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The speed of light – Part 1/2

October 16, 2010 4 comments

First of all, let neither the topic nor the length of the post put you off. It is a very simple post, and can be understood with little effort. If it gives you even a fraction of the thrill that I get from reading Brian Greene’s “The fabric of the cosmos”, I would be happy. It is a terrific book, in that it assumes the reader to be a complete layperson, but still explains advanced Physics. Many of the discoveries are completely counter intuitive and almost unreal. I strongly recommend this book. Penguin has come out with a low cost edition costing only 200 rupees but I would have spent even 2000 for it. Most of this material is from the book, though I have elaborated a bit on the examples.

Suppose you are walking at a speed of 4 KMs per hour (KMPH) on top of a train which is travelling at, say, 100 KMPH. To somebody standing on the ground who is watching, you would be travelling at 104 KMPH. This is straightforward addition, and is also obvious. In one hour the train will take you 100 kms, but as you are also walking on the train, you would walk an extra 4 kms in the same time (assume for the moment that the train is indeed 4 kms long).

Similarly suppose you are walking by the side of the train at 4 KMPH, and the train is rushing past you at 100 KMPH, a person standing would see the train as going at 100 KMPH, but you would see the train as moving at 96 KMPH. This too is straightforward and is understandable. So speed is always dependent on the relative motion of the observer and the observed. So far everything is simple.

The speed of light has been calculated to be 300,000 KMs per second. Which means, that light will travel at 1,080,000,000 KMPH (1.08 billion KMPH). Now suppose a light particle is travelling at its speed of 1,080,000,000 KMPH,  and you are walking alongside the particle at 4 KMPH, it makes complete sense to us to assume that, the light particle would seem to you to be travelling at 1,079,999,996 KMPH (1.08 billion – 4) as was seen in the last paragraph. But Einstein said no. He said that no matter how fast you are travelling with respect to light, your observed speed of light will always remain the same at 1.08 billion KMPH.

If that did not sound weird, imagine the consequence. If you are travelling at the speed of light, and a light particle is also travelling, then common sense tells us that, to you, the light particle must appear to be stationary. But Einstein says that is not right. I am not going to explain why Einstein is right and common sense is wrong. But I am going to tell you what its consequence is, and it is stunning.

Let us go back to the example of a person A, travelling close to the speed of light, and a light particle travelling alongside. Now B, who is A’s friend, is watching this whole thing. He sees that light is travelling at 1.08 billion KMPH, his friend is travelling at 1 billion KMPH, and hence says that light was speeding away from his friend A at the speed of of .08 billion KMPH (1.08 – 1). But A, who has been travelling, comes back and tells B that whenever he measured the speed of light on his journey, he always found its speed to be 1.08 billion KMPH only.

How do we explain this difference? The answer that Einstein gave to this was, simple to see mathematically, but almost impossible to imagine. What do we know about speed. We know speed = distance/time. But both A and B used the same equation to measure the speed of light relative to A and got different answers. But if both their results were different, it could have happened only if both the friends measured distance and time differently, since that is what determines speed.

Now this is not possible. How can A and B measure different distances and times? If A has a watch and B also has a watch which showed the same time before the experiment, that would have been enough to ensure that they both measure the same amount of time. But the strange part is that after the experiment, A and B notice that their clocks are now out of sync. B’s watch has moved faster while A’s watch is running slow. It is not that the watches need repair. It was our understanding of time that needed repair, and Einstein provided that.

Thus, one of the staggering outcomes of his theory was that time is not universal, the time measured by somebody travelling, would be different from the time measured by somebody who is stationary. To bring home how completely this throws into disarray all our understanding of time, imagine this scenario, as was depicted by Carl Sagan in his classic video series Cosmos. A couple of twins are playing with their friends. One of them suddenly takes a bike and rides off at a speed comparable to the speed of light. When he comes back a little later to the playing ground, he would see his twin has become old and sitting there with a walking stick, while he himself has remained young.

Now, this is NOT a fantasy. This is completely true and real. As true as 1+1 equals 2. If you indeed start travelling at speeds comparable to the speed of light, your time starts running slowly, compared to how time flows for those who are stationary. For that matter, even while you walk slowly, your time does indeed run slow, but the difference will be so insignificant that you cannot notice it. That this theory is true has been confirmed by experiments on atomic particles and measuring how they decay.

To easily visualise what is happening, Brian Greene gives an example, which I have illustrated here with a couple of pictures below.

 

 

Understanding how travelling along one direction, slows down travelling on the other.

 

Suppose the person at the bottom wants to reach the beach on the North on a bike which has a maximum speed of say 50 KMPH. If he chooses path 1, which is travelling North throughout, he would reach the beach quickly. But suppose, he uses path 2, which goes somewhat in a north easterly direction, he would be slightly delayed, since some of his motion is now diverted to travelling east, but he eventually reaches the beach. Note that he cannot compensate for this eastern travel by going faster, since his bike has a maximum speed of 50 KMPH. Path 3, would mean even more delay, since his eastward motion has now increased even further and is using up more of his quota of 50KMPH speed. But Path 4 would mean he would never reach at all, since now the whole 50 KMPH is being eaten up by eastward travel. This is an easily understandable example.

The way to imagine how Einstein’s theory works in reality is this. Consider a similar example, but with one important difference, as shown in the picture below. In this case one direction is time, and the other direction is space (instead of North and East). If you are sitting idly  (scenario 1), then you are travelling through time in full speed, that is you go from 9 AM to 10 AM quickly. The moment, you start walking slowly (scenario 2), which means you are travelling through space, your time starts running slowly. This is similar to our previous example of how if the person starts moving a bit towards east (path 2) his motion towards North slows down. So if you increase your speed further more, say you go on a jet, then your time will run even more slowly (scenario 3). And if you start travelling at speeds very close to that of light (scenario 4), your time almost stops running. Thus when combining space and time, there is a speed limit, which is the speed of light (which is the analog of the upper limit of 50 KMPH speed of the bike in the previous example). If you use too much of it travelling through space, then your travel through time slows down.

 

Understanding the overall speed of light limit while travelling through spacetime

 

As mentioned before the effects of this is so small for the speeds of objects that we encounter in daily life, and hence you cannot experience it directly. But the mere fact that time varies depending on your speed is a fascinating thought and so thoroughly changes our way of thinking. And this is a surefire way of travelling into the future, though there is, so far, no way to come back. There is another problem too. So far, there have been no spacecrafts which can move at speeds comparable to the speed of light. So till then, our dreams of time travel will remain just that. But imagine what would happen if scientific advances reach a stage where we can travel close to the speed of light. And imagine how the experimenters will be. They start travelling now, and will return after say 10 years or even 100 years. But for them only a fraction of the time would have elapsed. Who would not want to be on such a spacecraft? Though I personally would board it only if I can take all my family and friends with me.

I intend to add a form, wherein given a speed and the duration for which you travelled at that speed, it will give an idea of how much you have gained in time when compared to those who have remained stationary. But meanwhile, you can have a look at this link, which does something like that.

In the second part of this post, I will talk about 2 other areas of physics where it seems that this upper limit of the speed of light is violated, though it actually is not. They are equally, if not more, mind boggling, and will surely leave you exhilarated. But first, let this sink in.

Solar Eclipse

October 2, 2010 Leave a comment

There are different types of Solar Eclipses. Annular, Total and Partial.

Total Solar Eclipses are those wherein the Moon completely covers the sun. For those who have not heard the word “Annular”, it means ring-shaped. Thus Annular Solar Eclipses are those where the Sun is not fully covered, and hence you can see the sun like a ring around the Moon. Partial solar eclipses are those where the the Moon neither completely covers the sun, nor is completely “inside” the sun. Here are pictures to help you visualise.

 

Different Types of Eclipses

 

 

Any planet which has a moon will have solar eclipses. But not every planet has a Total Solar Eclipse. Did you know that we are lucky to have total solar eclipses at all?

The question is not how a body as big as the sun, can be blocked by an object that is 400 times smaller, our moon? That is easy. It can be done in the same way that we can use a small coin to block the sun from our eyes by appropriately positioning the coin. If you keep it too far away from the eye, you can see that the apparent size of the coin is not big enough to cover the sun, and so you will keep bringing it closer till the Sun is fully covered.

But the catch here is that the position of the coin can be changed as you like. But what about the moon? You cannot move the moon around to your liking. At least, not yet. And this is where we are lucky, because there is an interesting coincidence here. Though the sun is 400 times bigger than the moon, the sun is also almost 400 times farther from the earth than the moon. That means, the moon is positioned almost perfectly for it to block the sun completely from our view. It is this bit of coincidence that causes total solar eclipse on Earth.

But then if the Moon and sun’s sizes are in the same ratio as their distances from the earth, why are there both Annular and Total eclipses. Should we not expect only total solar eclipses? The answer lies in the fact that the orbit of the Moon around the earth is elliptical. Hence the Moon is not always at the same distance from the earth. Sometimes it is closer and sometimes it is farther. Thus if the eclipse occurs when the Moon is farther from the earth, the apparent size of the Moon as seen from the earth reduces, and hence it wont be able to cover the sun completely. Then you get an Annular eclipse. But if the eclipse occurs when the Moon is close to the earth, it is sufficiently big enough to block out the sun and hence we get a total solar eclipse. As my wife asked, the earth’s orbit is also elliptic, which means the sun should also be at varying distance from the earth during different times of the year. But this variation does not affect the totality and annularity as much as the elliptic nature of the Moon’s orbit.

To understand when eclipses are caused, see the picture below. Of course, the sizes of neither the orbits, nor the objects are in scale. As explained before the ratio of the diameters of the Sun to the Moon is 400:1, which means if I have to draw it in proportion, you would not see the Moon :-).

 

Top view (As if looking from above the orbit of the Earth)

 

 

But if you think about the picture a bit, a question that could come up is this. The Moon revolves around the earth every 28 days. So every 28 days there should be at least 1 day, when the sun, the Moon and the earth are aligned. Then why are we not experiencing an eclipse every month?

To understand that, we need to picturise the previous situation from a different angle. The previous picture showed the top view of orbit of the earth. See the picture below. This gives the side-on view. Here you can see that the Moon’s orbit is not on the same plane as the earth’s orbit. It is tilted relative to the earth’s orbit. Hence what you saw above will not cause an eclipse since when you see the situation side on, you realise that the three objects are actually not aligned. This scenario occurs every month but does not cause an eclipse.

 

Looking at the previous scenario but edge-on

 

So when do we actually experience an eclipse. For that, look at the picture below.

 

Another edge-on view. But this time a Solar Eclipse

 

This is the time when the the sun, the earth and the Moon are actually aligned. And this is when we see solar eclipses. Similarly another 6 months from this position, the Earth will be at the opposite side, and then again we can experience eclipses. There are more details to it, but for now, this understanding will do.