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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

4 Answers 4

up vote 14 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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So, here's the deal. "Time is relative" means a lot of different things to a lot of different people. In order to make a solid step forward, Einstein and company basically needed to clarify what they were trying to say.

What they were trying to say looks something like this: "if you see a train passing by you, you're going to see things happen in slightly "fast motion" when it's at a distance coming toward you, and in slightly "slow motion" when it's at a distance moving away from you. This is no surprise; when you hear the train blow its horn it sounds higher-pitched as it approaches and lower-pitched as it leaves. BUT, when you successfully correct for this 'Doppler effect,' as the speed of the train gets closer to the speed of light, you will find that actually, in your coordinates, the train and things happening inside of it appear to happen in uniformly "slow motion", slowed down by the factor $1/\sqrt{1 - v^2/c^2}$."

As you can imagine, this effect is a little hard to observe! It really comes from "adding up" a lot of little effects that happened when the train accelerated to this massive speed.

The most obvious little effect is that when you accelerate in the $x$-direction, changing your speed by a small amount $\delta v$, your sense of space coordinates changes to $x \rightarrow x' = x - t ~ \delta v$. That is, a wall that you used to think was a constant "5 feet away" (in the x-direction) is now going to start off being "5 feet away" but after a little time it might be "4 feet away", then "3 feet away", then "2 feet away", and so on. This is very obvious and was known to Galileo and Newton.

But there's a subtle effect, too, about time. Suppose you have clocks on two walls, one is $x = +5$ feet away, and one is $x = -5$ feet away. This effect says that they go out of sync a little bit, $t \rightarrow t' = t - x ~ \delta v / c^2$. The $c^2$ is a huge number that historically made this property of acceleration totally ignorable. But we can't ignore it so much these days, not with high-velocity particles that we have to calculate.

Now it turns out that you have to break apart what's happening into little intervals of time when you're accelerating, but if you add this little change up, many times over, then it says both that stuff happening in your train appears to be in slow motion relative to people outside the train, but also that stuff happening outside the train appears to be in slow motion relative to what's happening in the train. So it's because time has this little "we start to disagree on the simultaneity of remote events" property, that we eventually build up a larger "we start to disagree on how big things are and how fast their clocks are ticking" discrepancy. And the great part about it is: you're both correct. Both of you have perfectly valid coordinates which perfectly describe the world.

In fact, many contemporaries of Einstein thought that the newer "electrodynamics" science which was implying these things was fundamentally broken. Before Einstein, people knew about these problems due to a guy named Lorentz, but didn't tend to take his work too seriously. Einstein's 1905 paper said, effectively, "we have to take him seriously."

One reason that we can now appreciate is: we now know that the mathematics is totally self-consistent. Nobody ever disagrees on the order of events and nobody can use these weird "de-synching clock" effects to travel in time, unless they somehow find a way to move faster than the speed of light. There is another reason why we think that nobody can move faster than the speed of light, which has to do with the key fact about these de-synching clocks: they coordinate together with the change in your spatial coordinates to ensure that once you stop accelerating, you still think that light moves every direction at constant speed $c$, even in your new $(x', t')$ coordinates. This means that if you challenge someone to race a beam of light, and they start moving at speed $c/2$ relative to you, the light is not moving at $c/2$ away from them in their coordinates, but at speed $c$ away from them. So there's a real Zeno Paradox here guaranteeing that nobody can ever outrun light.

The most obvious paradox which turns out to not be a big deal is, "if I think that the people on the train are moving in slow motion, and they see me in slow motion, can't I just call one of them up and we'll see who's faster and who's slower on the phone call?. And the answer to that is, yes, if a phone could transmit information instantaneously, then nature would have to establish one of these people as correct and one of them as incorrect. But, of course, real phones are also bound to transmit energy no faster than the speed of light -- and this gives the precise ambiguity that you need to make sure that both of them are perfectly correct and neither one can claim supremacy over the other.

So that's what we mean by "time is relative": someone on the street, after correcting for Doppler effects, still thinks that people on the train are moving "in slow motion" and thus aging slower than people on the ground. People in the train of course see themselves just fine, but after correcting for Doppler effects think that people on the ground are moving "in slow motion" and thus aging slower than the people on the train. Both groups have valid coordinates, and we cannot choose between them. Whenever you find an experiment which actually seems to test it, like "Well we'll stop the train and get out and check their ages," those coordinate shifts invariably balance everything out so that there is no paradox: usually the person who is accelerating becomes "wrong", so if we speed up to jump on the train we see the people on the train moving in fast-motion until they appear to be older than us, and it turns out that the "train was right"; but when the train slows down to check on the ages of the people on the ground, all those people move in fast-motion until they appear to be older than the people on the train, hence the "ground was right." Neither was really absolutely right, but there is a consistent math where remote clocks which seemed in-sync suddenly get a little out-of-sync, causing systematic disagreements about how fast clocks are ticking in general.

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If you think about time as we know it does not actually exist/flow - it is our mental manifestations of the world around us that we think of as time. For example, what we see is not actually there how we view it. Whatever the object is sends us light-waves (only a small portion possibily of what the object really is), our eyes then have to decode the light waves and our brain must decoded the neuronal signal from our eyes. Therefore, there are many levels of filtering that go on when we try to understand the universe.

That filtering makes it difficult to understand the passage of time. Time doesn't actually pass. Time doesn't actually exist and it definitely doesn't flow or pass. What time is - is just the change of particles relative to other particles. Our brain makes sense of the changing environment by the passage of time causing things to change, but really the rate at which things change relative to other things is making our brain conscious of time.

To that end, we must think about the particles - when there are a lot of particles close together in a confined space they slow down because they can't move anywhere and other forces prevent them from changing shape as fast as they would otherwise. Therefore, a mass heavy object is moving slower relative to other objects because the particles aren't changing as fast relative to particles external to the object. This is essentially what Einstein was saying: objects with great mass move slower than objects with less mass. Einstein also understood that at some threshold the energy expended in making particles change shape also can be converted to energy that causes particles to move (E=MC2). Therefore, a particle moving is expending more energy than another particle of equal mass at a standstill and thus is moving through time faster as well. Therefore, masses being equal between two objects the one moving faster will be moving faster through time to the other object.

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This is mostly (self-contradictory) nonsense and complete misunderstandings of a famous formula. –  Kyle Kanos 23 hours ago
    
im not sure how its self-contradictory –  Dan 20 hours ago
    
For one you claim "Time doesn't exist" and "Time is the change of particles relative to other particles" at different points (how can something not exist but be something at the same time). –  Kyle Kanos 20 hours ago

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