## The speed of light – Part 1/2

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.

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.

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.

Nice one !

Nice post da Madhav. I like watching Astrophysics Programs on NATGEO/DISC channels. I like to dwell on some of those topics after watching on TV. I got the same thrill and exitment after reading your post. Keep posting my friend!

Hey Suresh. Long time. Feels good to know you enjoyed the post. That encouraging comment might just egg me on to write my second part of this post by this weekend rather than waiting for the one after that 🙂