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#1
Dec2912, 07:37 AM

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I would like to know why it is called time DILATION and not time CONTRACTION?



#2
Dec2912, 07:48 AM

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#3
Dec3012, 07:27 AM

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I think it's just a matter of perspective. When some particle is accelerated at the LHC, the scientists who observe the particle will see time "slowing down" for that particle, whereas the particle (if it had a brain) would see time "contracting" for those scientists.



#4
Dec3012, 07:30 AM

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Why time DILATION?



#5
Dec3012, 10:24 PM

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A specific guy on the train sees the time changing more rapidly on the sequence of clocks he passes along the ground than the time on his own clock (i.e., that he carries along with him). This is why it is called time dilation.



#6
Dec3012, 11:04 PM

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If you look at this from the perspective of the traveling twin (or LHC particle), you could call what is happening to the stationary twin as 'time contraction' from that perspective. The terminology is not in common use however. 


#7
Dec3112, 01:01 AM

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Why don't both age the same relative to each other? 


#8
Dec3112, 01:21 AM

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This is how SR works. 


#9
Dec3112, 01:57 AM

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arindamsinha, it sounds like there might be some confusion in your understanding of twin paradox. The moving twin still observes a time dilation. Whether an observer has accelerated in the past or is going to accelerate in the future does not change the current description of physics. And so as a particle drifts along a chamber in accelerator at constant speed, relative to it, it's the scientists who are timedilated.



#10
Dec3112, 02:45 AM

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I am not talking about the 'observed' time dilation, which would be true based even on classical (Newtonian) Doppler effect. I am talking about differential aging, i.e. real clock time dilation. The moving twin always has the real clock time dilation, never mind who observes what. Same applies to the particle in the accelerator. No matter what it sees, it is living longer than expected by the scientists' clocks, and this is aymmetric differential aging (i.e. the scientists do not live longer by the particles clock, they live shorter, leaving aside any observations based on Doppler effect). 


#11
Dec3112, 03:33 PM

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There is no "moving" twin. They are both moving relative to each other. There is no absolute frame. You cannot say who is standing still.
The only time it makes sense to distinguish between the two is if one twin left and then came back. After he came back, we can compare the net aging of the two. But while in transit, SR applies to both. The twin that stayed behind is aging slower from perspective of the twin that left. A particle coasting through accelerator is in an inertial frame. There is nothing special about that frame with respect to the laboratory frame. 


#12
Dec3112, 07:30 PM

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However, when one of the twins accelerates and then reaches a steady velocity, that makes him the clearly "moving" twin. He has differential slower aging throughout the journey, not at certain arbitrary parts. There is no necessity for the traveling twin to come back to the origin and compare clocks for differential aging or relative time dilation to happen. I believe this is well demonstrated by the velocity time dilation of GPS satellites. Even though they never come back, we know clearly that their clocks slow down compared to Earthbased ones (ignoring gravitational time dilation). You may contend that they are never in an inertial frame, but I believe they are in a good enough approximation of an inertial frame for us to apply SR for the velocity part. 


#13
Dec3112, 09:57 PM

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Lets forget twins for a moment. Lets focus on particles. Now, you might think that asking about the age of particle is silly, I mean, it's not like it celebrates birthdays, or anything, but there is a special case. Radioactive particles. They are ideal time keepers. We know that halflife of radioactive particles in accelerator increases as a direct confirmation of special relativity. Of course, that's perfectly consistent with your point of view. We accelerated a particle, so it ages slower, and we should expect a longer halflife. Good so far. Picture the following thought experiment. We have a big chunk of radioactive material with a long halflife. We need long halflife so that the number of radioactive atoms remains roughly constant. That gives us a constant rate of radioactive decay events. So we can set up a detector nearby, connect it to a light, and the light will flash, on average, a constant number of flashes per unit time. Say, N times per second. Now rather than accelerate all of this mess, which we agree on predictions for, lets say a ship with scientists accelerates towards it. They speed up for a while, reach constant velocity v ~ c and then drift towards the sample with the flashing light. Suppose, this drifting ship recorded flashes for some time t in frame of the device. Naturally, during that time the crew aged t/γ. Again, simple time dilation you agree with. How many flashes did the team record? Well, there are the Nt flashes generated in that time, plus the flashes that were emitted earlier and were located in that space the ship covered. So the total is Nt + N(vt/c) = Nt(1+v/c). Of course, the researchers only aged t/γ, so the rate they record is Nγ(1+v/c). But these researchers aren't stupid. They know the source of flashes is traveling at them at v. They know they'll see flashes more frequently than they are actually emitted. So, you have an object coming at you at v, and you receive flashes from it at the rate of Nγ(1+v/c). What is the actual rate according to you? Well, if it emits a signal every T seconds, the second pulse has vT less to travel than the first one. So you get it with a vT/c shorter delay. In other words, the time between pulses you see becomes T(v/c). So to get the actual rate, you need to divide what you measure by v/c. So according to the researchers, the light signals are emitted at a rate of Nγ(1+v/c)/(v/c) = Nγ/γ² = N/γ. (Check all the algebra as an exercise.) So the rate of radioactive decay appears lower! And by the same factor γ. Despite the fact that it's the researchers that were accelerated and not the particles. The halflife of the particles is longer in either scenario! This is a very important result in Special Relativity and is the crux of the entire matter. Two observers traveling with respect to each other would observe the other being timedilated, regardless of which one had to accelerate to get them to the current state. This also makes sense physically. How should the particle know which of the two accelerated? It has no memory. Theory that suggests otherwise would be very suspicious. So in order for the twin paradox to manifest, one of the twins has to leave and come back. Only afterwards can we talk about which of the two really aged. Not so with circular motion. An object traveling around the source can have high velocity and experience no Doppler effect. This lets you synchronize the clocks. This means that in flat spacetime, an object traveling in a circle around you must not experience any time dilation at all. So the acceleration effect is canceling the effect due to the velocity. So you can never claim this effect negligible. Of course, in case of a satellite, you are also looking at time dilation due to gravity, and things get a lot more interesting. But that's General Relativity. 


#14
Dec3112, 10:33 PM

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#15
Jan113, 01:05 AM

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But differential aging does happen. In a setup like this, only one of the participants is moving (the one who accelerated) and the other is at rest. Otherwise you would never have measurable differential aging. Over the years this has been tacitly recognized based on experiments. A traveling body doesn't have to come back to the origin for establishing this. Where do you draw the line anyway? If your twin has traveled and come back to within 100m, you still can't be sure who aged more? Or is it 10m? Or is it when your clocks are touching each other? In other words, at what stage does the magic of "differentially aging" suddenly materialize? I think it is more reasonable to accept what SR is saying  the actual differential aging happens throughout the journey at a predictable rate (depending on velocity), and what the twins compare when they meet is the "cumulative differential aging". If you can answer the following simple twinbased thought experiment, it will help establish what we are discussing more clearly: Thought Experiment: Two twins on Earth syncronize clocks. One twin stays on Earth. Another twin travels at almost light speed for a certain distance (say 10 seconds on the Earth clock, reaching a distance of 10 light seconds) and then stops. (Assume the acceleration and deceleration periods are negligible). At exactly half the distance (i.e. 5 light seconds from Earth), we have previously placed a device that can send a light signal simultaneously to both twins. This signal is activated when the twin who left Earth stops, and sends a signal to the device, saying "I've stopped". Once the twins receive the device light signal, each twin immediately sends their "current clock readings" to their other twin. (They can subsequently communicate and establish whether there was a difference in their clocks, and if so, how much. Since they are now mutally at rest, there's no complex hanky panky about this.) Now, tell me which of the following possibilities is correct: 1) The twin who left Earth has his clock behind the Earth twin's (about 10s or so) 2) The twin who left Earth has his clock ahead of the Earth twin's (about 10s or so) 3) There is no difference between the clock readings of the two twins 4) We cannot predict the outcome without actually doing an experiment Once you have answered this, you will probably understand what I am saying, or we can discuss further. 


#16
Jan113, 03:04 AM

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I really chose a horrible example. This problem behaves exactly as arindamsinha expects, since the acceleration of the frame of the circling source results in accelerated time for the central source. That's still the point. The acceleration of the second source is responsible for the effect, but it's a bad example to use with somebody who is confused on inertial case. You can read Einstein's original works, and he derives time dilation exactly the same way, via exchange of clock pulses using light beams. In every frame, the other's clock appears to run slow. 


#17
Jan113, 04:42 AM

P: 181

BTW, who is this 'somebody' who is confused on inertial case? Me? It would be nice not to have such patronizing statements in a civilized discussion. While I may not have your expertise in relativity, I may possibly understand it just a wee little bit better than you think. (a) In Section 4, on what basis does he conclude that 'the clock moved from A to B lags behind the other'? By your logic, the clock not moved also has a symmetrically equal motion w.r.t. the moving clock, so in the end there is no 'relative time dilation'. Why do experiments show relative time dilation? (b) Note that he also takes an example of a clock traveling in 'a closed curve with constant velocity until it returns to [the origin]', and says that such a moving clock will be slower. This is exactly what the GPS satellite is showing. Einstein doesn't bring into picture any acceleration for this. It is all about the velocity here. Why don't you answer the thought experiment I mentioned, and see where we go from there? It is a very simple question after all. 


#18
Jan113, 05:36 AM

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Perhaps, a slightly better illustration is choice of rotating coordinate system. In a rotating coordinate system there is a definite center. Points away from center experience a centrifugal force which arises due to the choice of an accelerated reference frame. (Ref for clarity, if needed.) So unlike linear, unaccelerated motion, where we cannot say which is moving and which is still, in case of rotation, we can clearly state which one is rotating. That breaks the symmetry of SR and introduces a difference. Indeed, in the rotating frame, since both objects are static, time dilation is computed from the tt term of the metric tensor. This term unambiguously tells us that the object undergoing centripetal acceleration is the one that will age slower by the factor 1/γ. Which, of course, agrees with prediction from the inertial frame. With gravity things get slightly more complicated. Satellite isn't actually accelerating. It follows a geodesic. So now to understand the clock differences we have to consider the curvature that actually causes it to go around in circles. Schwarzschild metric describes it, and it does give you a time dilation effect which does depend on your altitude. Of course, in Scwarzschild metric, the satellite is also moving, so you have both the gravitational time dilation and the time dilation due to satellite's velocity. Again, none of this is terribly complex, so long as you take Scwarzschild metric on faith and accept the satellite velocity at given radius as given. If you want to actually verify the former and compute the later, it is going to involve some tensor calculus. b) Yes. Einstein, being quite a bit smarter than myself, didn't make the same mistake of confusing oneself with accelerated systems. If you have a clock that travels along an accelerated curve, you can still describe it from an inertial frame. In inertial frame, you can use SR and consider time dilation of an accelerating object. There is no problem with that. Lorentz factor will simply be a function of time rather than a constant. No big deal. It's only when you decide to try and describe that inertial observer from perspective of an accelerating clock that you run into a headache. All inertial frames, on the other hand, are equivalent under SR. So time dilation formula applies exactly the same way, regardless of whether you are looking at source flying towards the rocket or if you are looking at a rocket flying towards the source. So long as both of these are traveling at uniform velocity, both can use time dilation formula under assumption of self being static. 


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