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I don't understand how time can be relative to different observers, and I think my confusion is around how I understand what time is.

I have always been told (and thought) that time is basically a measurement we use to keep track of long it has been since an objects inception.

If that is even somewhat true, how can time be relative? If I have a rate of decay of X and you are somehow able to observe that (such as watching me age) how could I age at a different rate to 2 observers?

If time slows down the faster you go, does that mean you age slower? Or do you age at the same rate, only it seems like it takes longer? If a second is currently defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom at 0K, how can that change at higher speeds? Assuming the temperature stays the same, shouldn't the measurement be the same?

Moving faster surely can't cause cells to decay slower, or atoms to radiate slower...can it?

Can someone explain, in the simplest of terms, how time can be relative?

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"Moving faster surely can't cause cells to decay slower, or atoms to radiate slower... can it?" sure it can, that is exactly what happens. in the reference frame of the atoms they would decay at the same rate always.. but that rate will be different in other frames –  lurscher Apr 3 '12 at 18:00
    
Related: physics.stackexchange.com/q/15371/2451 –  Qmechanic Apr 3 '12 at 18:02
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You are thinking of perceptual time, which is computational and "felt internally" in your brain, while physicists deal with physicist time, which is a coordinate of space. The two are only obliquely related, and this leads to many questions here. –  Ron Maimon Jul 20 '12 at 19:26

2 Answers 2

up vote 9 down vote accepted

Intuition and perception (or the lack of there of) can be a big problem when you're trying to comprehend the implications of special/general relativity. You must understand that in everyday life which fuels our intuition is pretty slow. Most people don't move faster than $900 km/h$ or $250 m/s$. And that's a luxury for most, to travel by a fast jet.

The speed of light is a staggering $299 792 458 m/s$. That is a million times faster from anything we have today. Just because time seems to be relatively absolute (pun intended) from our standpoint because our stage is rather small, the time it takes light to propagate from one point to another is so small, it doesn't mean that time is indeed invariant.

The interesting bit is that while Michelson & Morley were working on their amazing interferometer to measure Earth's speed in relation to the "magical aether", a man by the name of Hendrik Antoon Lorentz made a fascinating discovery about the nature of things, especially the nature of electrons. The direction-of-motion parts of the interferometer contracted as they moved and thus prevented any relative motion or interference to be detected. The two light signals always came at the same time because of the length contraction in the direction of movement.

Michelson couldn't accept this. It went against his life's work. Lorentz did the mathematical foundation as an explanation to the problem, but he did little to analyze the result. Einstein came to the same equations by following a different train of thought, this time involving the nature of Galilei-Newton relativity (which troubled him), the problem of light and all the evidence that was pointing that propagation through spacetime is constricted by a velocity limit. $299792458 m/s$.

So, Einstein "took the bone" nature was throwing him. The speed of light is constant for ALL observers. No matter if they're sitting, falling, running, flying, sleeping. A light signal is exactly $c$ at all times. No matter how fast you're moving relative to others.

If that is true, then something else must bend. Space and time become intertwined to accomodate the nature of our existence, to allow light to travel at $c$ for all observers. From these simple postulates, which include the inability to differentiate intertial frames of reference, comes the death of simultaneity and of absolute time.

A simple proof involves a moving light clock which passes exactly time $t$ in his up-down trip. When it begins to move with someone, a second observer - you on the ground will notice that its path elongates relative to you. Therefore, the time it takes to go up and down increases to $t_1$. All the while, the man on the moving platform sees the light perfectly in sync, up and down, because he's moving with it. Therefore, for him, you're the one who is slowed down in time (the $t_1$).

That's special relativity, but the one who really experiences slower decay or the relativistic effects is the man who is accelerating. So, yeah, time is relative to protect the constancy of the speed of light.

Hope it helps. And give it time. It has been proven many times over and a lot of scientific work today relies on relativistic effects of time dilation.

ADDENDUM:

It's exactly the repercussion of this. Decay is the passage of time. The biological processes are the same, but if he is moving really fast (and let's say uniformally), to every other observer the time slows down for the man onboard (lightclock thought experiment, proved with satellite sync and plane/atomic clock experiments). Also, to every other observer the ship contracts. To the man onboard, he feels nothing. The passage of time is the same and the ship dimensions are the same. To protect relativity, he sees that others are slowed down in time and contracted. But he is the one who accelerated, therefore, he is experiencing the time dilation.

And thus, time dilation implies slower time passage for the man onboard relative to other stationary observers. He feels normal, relative to him, time runs "nicely", but when he comes back, the relativistic effects will have done their part based on the famous $\gamma^{-1} = \sqrt{1−(v/c)^2}$. This has not yet been proven directly, but it is inferred from various experiments done by planes and atomic clocks and also the need to sync up satellites after a while because of the gravitational differential. Why? Time goes slower, decay is dependent on time, slower decay.

The final and most important point would be that time passes for everyone in the same manner (you can't feel a change). But it is the relativity (comparing to someone else) which enables us to detect time passage differences. Just like you can't know how it feels to be a rabbit, because you've never had a chance to be one to make the comparison. A blunt, but accurate comparison. Just like you can't imagine a different kind of existence because you can't compare to an another Universe (we've never been in it). That's the gist of relativity. Everything we know is relative. That's "how" we know.

But the beauty of the human mind and the triumph of all science lies in the fact that we can contemplate this, our own limitations, our ways of thinking. And by doing so, we find a way to overcome them or to make the most of them.

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this is fantastic and helps greatly. I have one more question. I imagine I am asking you to to fit years of study into 500 characters, but what makes the decay of the traveling man slower? That is where my hangup is right now. Is it just one of those things I should accept that I will never understand, or is there a simple answer? –  Joe Apr 3 '12 at 20:24
    
I've written an addendum in an attempt to explain, hope it helps. –  Domagoj Pandža Apr 3 '12 at 21:17
    
thanks so much! –  Joe Apr 3 '12 at 21:40
    
No problem, enjoy physics! –  Domagoj Pandža Apr 3 '12 at 21:44
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Those are modern facts, in the time of Einstein, it was measured at around $186350$ miles per second, a little over today's precise measurement. Today's iterations of the MichelsonMorley experiment give a million times more precise results. What was important for Einstein is the fact that all the evidence pointed towards the constancy of light. The specific value isn't even important, you could express velocity as a percentage of the speed of light for the sake of argument and it would still work. But yes, it's not entirely historically accurate, it would take a book to write that out. –  Domagoj Pandža Apr 4 '12 at 0:09

You're "understanding of time" is perfectly okay. What you are missing is the relation between space and time. If you (an observer) are sitting (flying) there, looking just at your clocks -- then you will never notice any time dilation.

Relativistic effects appear when we have different observers in different points of space. Moving around, observing, sending signals, e.t.c. And when this observers try to make a coherent picture of their observations, they arrive at the conclusion that one cannot extend his local "understanding of time" to the "understanding of time" for the whole space.

Actually space and time turn out to be very strongly interwoven, so we usually prefer to use the term spacetime.

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