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Friday, 11 November 2011

The Irregularity of Time <1/2>

Time is the same for anyone and everyone...Isn't it??

How weird would it be if, when someone ran past you, that time for them would be going slower than it was for you, on your watch it says 12:15, but for them its only 12:10? Its seems ridiculous right? Yeh...but it is totally and utterly possible...Ok, to be honest on that scale it won't happen, but as soon as you start launching satellites into space, the difference is huge.
You see, time isn't as constant as we like to think. Of course, if you're sitting on a park bench with your friend, they won't suddenly start turning into Gandalf in front of your eyes. It requires certain conditions and the change is measurable. The way we know this is through The Theory of Relativity, which I will be taking two blog posts to explain very briefly. I will warn you, this is a big and complicated subject, I'm only scratching the surface of what relativity is. This is Einstein's paper on only the first half of it...yes, I know...But please, read on, I think it will really interest you.

Oh good, you have chosen to continue, now we will get into the real stuff. Relativity is split into two types, Special Relativity and General Relativity. Today I'm going to be talking about the former, a theory put forward in 1905 by Einstein in his aforementioned paper, "On the Electrodynamics of Moving Bodies" and don't worry about the other yet. One of the things that Special Relativity proves is that for an object moving at a high speed, the time within that object is slower than that of the time within a object traveling at a different speed, or that is stationary.
Special Relativity relies on two main axioms, or assumptions. The first axiom is that:
The laws of physics are the same for all observers in uniform motion relative to one another (principle of relativity).
As Wikipedia so fantastically puts it, but to make it simpler, the same laws of physics apply to two things moving at a constant velocity relative to one another. It would be extremely weird if when your friend got up from the bench and walked about, a different force of gravity worked on them.
The second axiom is a lot more counter intuitive and this is where all the strange results we get from Special Relativity comes from. It is:
The speed of light in a vacuum is the same for all observers, regardless of their relative motion or of the motion of the source of the light.
Another remarkable description from Wikipedia but to put it simpler: A beam of light will always be calculated to be at the speed of light, no matter the direction or velocity of the observer or the source of the light. Now, this seems ridiculous, "If I'm traveling at a speed near the speed of light and a light-wave passes me, it must appear to be going slower, mustn't it?". And that is where a huge amount of complexity lies, its not logical, or at all observable to someone without state of art equipment, so it is very difficult to believe this axiom. But equations using the axiom have been proven true and it is widely accepted as true throughout the scientific community so you may just have to accept it and see the wondrous results.

Ok, now we get to the good part, this is why time runs slower in a fast moving object.

So, the easiest way to explain this is through an example, a train passes through a station, with one person sitting in the end of train (S) and the other on the platform (S'):
The train is moving incredibly quickly, otherwise the effect is not really noticeable. Inside the train,S is holding a torch and on the opposite wall to them is a mirror. He turns on the torch and times the time it takes for the light to return back to him.
In the diagram "d" is the distance from S to the mirror. To work out the time taken we apply the equation Time=DistanceSpeed and from that we can work out that the time taken for the light to travel to the mirror and back is t=2dc with c being the speed of light. Now we are going to look at the same event but from the perspective of S' sitting on the platform. For them, the torch is turned on in the same place as for S but when it reaches the mirror the train has moved:

This continues for the whole journey and the track of the light ends up looking like this:
As you can tell, the distance to the mirror is longer than for S, we will call this distance d'. Of course, there is nothing remarkable about that, its very logical really, but the next step is both the incredible and the illogical. We have to use Time=DistanceSpeed and equation we find is t=2d'c, because, due to the second axiom, the speed of light is a constant for any observers, irrelevant to the speed on the source of the light. This shows that the time it took for the light to travel from S to the mirror and back to S, is different from within the train and from outside of the train. Time for S if running slower than it is for S', although S won't notice, it isn't like he will suddenly be moving in slow-mo, S will just have elapsed less time than S'.
This is the measurements without the train:
You can use Pythagoras' theorem in order to find in what way these values connect. In the diagram, t is the time to light ray takes to get to the mirror, but not back, or dc:
Now using a2+b2=c2 to for an equation:

c2t2 = (c2-v2)t'2
t2= = (1-  v2  )t'
c2
t=t'√(1-  v2  )
c2
and then:
t'=t√(1-  v2  )
c2
This means that the closer the velocity of the moving object is to the speed of light, the slower the time goes inside the object relative to a stationary object.

The thing is, all this seems ridiculous. In no way does this make sense but sadly, there is no to make it any other way. It is nonsensical and illogical but it works. Both the two axioms have been tested and confirmed, and experiments have been done to prove the overall concept. For example, muons are particles that breakdown into an electron and two neutrinos in two milliseconds. An experiment was done at CERN in Switzerland, they shot some muons around a fourteen meter diameter loop at a velocity of 0.9994c, the results were both remarkable and, based on our previous calculations, totally logical: the average lifetime of one these muons was measured to be 29.3 times longer than that of a stationary one.

I hope you enjoyed this post, it took me a while to complete but I'm very happy with it now. I'm only scratching the surface of an immensely huge subject, but I find it incredibly interesting, and I hope that i have at least shown to you just how much lies beneath the basic physics we know instinctively and how, sometimes, our instinct is wrong...
You can read the second and third posts now!

Main source for this and the other articles based around relativity is the book about relativity here. It goes into more detail on all these subjects and the other books they do are brilliant too, I recommend a lot.

1 comment:

  1. can I have the permission to translate this post into Arabic ?
    I'll definitely provide a link to your blog

    ReplyDelete