The word dilation means stretching out or lengthening, which is just what is observed. Moving clocks run slow (in the observing frame), thus 1 second on the moving clock appears longer (dilated) from the observing frame.
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.
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.
Yes, there is a bit of terminology issue here. What you are talking about is 'differential aging', as in the Twin paradox. The term 'time dilation' seems to be reserved for slow down only, though it is certainly related to differential aging. 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.
If the first twin (who ventures on a space journey) is moving away from the second one, the second one is also moving away from the first one. Why don't both age the same relative to each other?
The twin who is moving away has to accelerate, putting him/her in a non-inertial frame of reference for some time (and breaking the symmetry of the situation). After the acceleration stops, he/she is in another inertial frame, but in this frame time is dilated compared to the twin who never moved. This is how SR works.
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 time-dilated.
I think you misunderstood me. 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).
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.
I do not think that is a correct interpretation of SR. If the movement of the "twins" was symmetrical in every way, there could never be a "differential aging" between them. 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 Earth-based 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.
Ok, that's a fairly jumbled mess you've got there. Don't take it as criticism, but try to bear with me, and we'll sort it out. 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 half-life 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 half-life. Good so far. Picture the following thought experiment. We have a big chunk of radioactive material with a long half-life. We need long half-life 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 half-life 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 time-dilated, 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. First of all, GPS satellites do have to take gravitational time dilation into consideration. It is a significant enough factor. Second point is more philosophical. A lot of SR results with time dilation follow from the fact that you cannot be moving with respect to a source and still remain at the same distance. If you are moving, you will experience Doppler effect, and you have to correct for it. As you can see from above, it makes all the difference. 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 space-time, 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.
I'm not sure I get your meaning here. If you have a radioactive source traveling rapidly in a circle around another radioactive source in flat spacetime (gravity ignorable), then the central one detects the circling source decaying slower; and the circling source detects the central source decaying faster. (For simplicity, assume each source sends a spherical light pulse every N of its decays, so there is no concern about direction particles are emitted).
PAllen, you have crisply summarized the point I am trying to make. Yes K^2, I am aware. I meant we ignore that gravitational time dilation part for the sake of isolating the velocity time dilation, which is the part under discussion. This has been one of the key issues with SR interpretations. Contrary to your initial premise, you have changed frames and now you are saying the other body is coming towards you at a certain velocity v instead of being at rest, and therefore need to divide/compute etc. etc. If you looked at things this way, there would never be any relative time dilation this way. All is 'observation', none of it is real 'differential aging' 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. Again, very good point from the original SR derivations, but experiments suggest otherwise. Whether a particle has memory or otherwise, it is the moving one if it has "felt" acceleration. 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 twin-based 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.
Sorry, yes. That's right. I got myself confused there for a bit. The moving one is still time-dilated. But not the static one. Got that mixed up. I should have written down the metric tensor right away. Though, it's really obvious in the retrospect. 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. RELATIVITY. You can't say A is moving and B is static. The whole POINT is shifting frames. The whole POINT is that we can look at it from A's rest frame or the B's rest frame. In both frames the OTHER is dilated. 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. Precisely. STOPS. They now have the same rest frame. We are talking about a particle that's still moving. Situation where two observers have different rest frames.
Can you square the above statement with your post #11 where you say 'There is no "moving" twin'. They are both moving relative to each other.'? Huh?!! Can you please explain this part further? You mean the acceleration of the GPS satellite is responsible for its velocity time dilation? Can you please explain a little better? 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. In other words, everything is symmetrical, and therefore, there is no question of 'relative time dilation' or 'differential aging'? Let me refer to one of Einstein's original works here: http://www.fourmilab.ch/etexts/einstein/specrel/www/. (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. No, we are not splitting hairs about whether a moving object has 'stopped' or is 'still moving'. We are talking about 'when' and 'where' the relative time dilation or differential aging occurs between two entities, whatever the stage when we inspect them (stopped or still moving). 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.
I'm not trying to say this is too complex for you to understand, or anything. And I am explaining some of these things less than well, which is entirely my fault. But there is a definite flaw in your understanding of SR. If I try to explain it to you, a certain degree of patronization is necessary. If I'm overstepping the necessity, and am more patronizing than absolutely necessary, I apologize. It is not my intention. Absolutely. A bit of it is sloppy language on my part, but it is fairly common usage. While the motion is still relative, the acceleration in GR, and to the best of our knowledge in general, is absolute. So there is no ambiguity in deciding which object is going around in circles around which. 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. Hopefully, the above already helps. If you aren't afraid of metric tensors, I can write out the GR treatment of this in a rotating frame. Because in the rotating frame nothing is moving, it is extremely simple, and you really don't need to understand anything about curvature of manifolds or differential geometry, or any of the other stuff that usually scares people away from GR. Depends on choice of coordinate system. If you look at it from perspective of the satellite itself, yes! I mean, from perspective of satellite itself, it's not moving. Yet (ignoring gravity) the Earth's clocks run fast. The only explanation to that is the fact that the satellite is accelerating. 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. Everything is symmetrical, so the time dilation is too. Observer A claims that B's clock runs slow, and observer B claims that A's clock runs slow. They are in a disagreement, but they cannot find a contradiction by simply exchanging light signals. a) On the contrary. I've taken that from radioactive source's perspective the ship is time-dilated as a given. Since it accelerated, and you seem to accept that fact. I then derived the identical time dilation of the source from perspective of the ship. It's in perfect agreement with the section. 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. It's not splitting hairs. It's precisely where all of the Special Relativity is. What happens to the twin that accelerated and then decelerated by the same amount is absolutely clear to both of us. We are in agreement on that. The question is, who's clock runs slow relative to whom in between. We aren't talking about the fact that the clocks themselves are already in disagreement by this point. We are talking about the rates at which each clock runs at this point. The twins can communicate while in relative motion. And they can correct for Doppler Effect quite easily, because they both know that speed of light is always c. And after they correct for Doppler effect and compare their clocks, they still find that the other twin's clock is running slow. Not in terms of absolute difference. But in terms of the rate at which the clocks advance.
There is a nuance here that I am not sure has been addressed adequately (I admit I haven't read the whole thread). Imagine the turnaround twin deriving the rate of the distant clock as described. Assume, for simplicity, instant turnaround. Then, throughout the trip they consider the stay at home clock running slow. For example, from 1 pm (when they separate) to 2 pm on their clock the see a redshifted clock going from e.g. 1 pm to 1:15 pm, and they figure it is slow (but by less than visual after correction for 'pure doppler'). Then, from 2 pm to 3 pm (at which point they re-unite), they see the stay at home clock advance uniformly from 1:15 pm to e.g. 3:15 pm. Correcting for doppler, it is considered to run slow during this whole time - yet advances more than their own clock. Obviously, the resolution, is that to use this standard approach for removing Doppler, they must also accept the standard approach to simultaneity, which says that much of the blueshifted history occurred before the turnaround, even though seen after and indistinguishable from the period they consider the distant clock running slow (this is unsurprising, due to finite light speed). With a non-instant turnaround, you would consider this to be delayed reception of the remote clock running fast during the turnaround. The key point is that for a significant period after turnaround (even for non-instant turnaround), after the turnaround twin is inertial, they must interpret the signals they receive in a way that is cognizant of the fact of their turnaround - if they want to avoid a logical contradiction, while still using the standard removal of doppler convention. Personally, I prefer to give much less emphasis the uniqueness, let alone, objective reality of this interpretation. I consider that time dilation is a coordinate dependent, non-observable quantity whose character is a matter of convention - the choice of coordinates.
OK, I feel there has been a disconnect in what you and I are saying. As per my posts in threads #9 and #11 where this discussion started, I was specifically referring to the disagreement or difference in age between the two clocks at any point in the journey, should that be periodically measured. My contention is that a periodic measurement will prove that the traveling clock is ticking at a slower rate throughout the journey, and that there is no need for it to come back to the other clock for such 'relative time dilation' or 'differential aging' to be proven. It happens throughout the journey at an uniform rate given an uniform velocity. You are talking about how they would 'appear' to each other from a distance. Let me know if that is a correct interpretation of what you are saying. I understand the standard approach you mentioned. However, my preference is to consider that this is objective reality - the traveling clock always ticks slower at a specific predictable rate, compared to the stationary one, throughout the journey. Moreover, the materialization of such relative time dilation does not depend on the traveling clock returning to the stationary clock's location for a face-to-face comparison. (@PAllen - I realize you have not referred to this, but I have seen that in many posts) Let me explain why I am partial to this way of thinking. Refering back to Einstein's paper http://www.fourmilab.ch/etexts/einstein/specrel/www/, I see in Section 4: - He writes "A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by ^{1}/_{2} tv^{2}/c^{2}" - He does not state that the clock stationary at B could similarly be considered slower by the moving clock A in its own rest frame (which is strange since he does say that about length contraction earlier). I am not saying he meant it would not happen, just that he does not stress that part - Nevertheless, he then goes on to talk about one clock at the equator and another at a pole of Earth, and concludes that the equator one "must go more slowly, by a very small amount". This last part to me implies a clear objective reality. He seems to tacitly state that in any real situation the stationary and moving clocks would become clear, the situation will be aymmetric, and real relative time dilation will show up between the clocks (unless the conditions of both clocks are really completely symmetrical). Moreover, such difference between the clocks is an ongoing and predictable amount at any point of the journey of the moving clock. Also, the equator/pole relative time dilation happens even though the two clocks never get together at a location. Would you say my thinking is correct, or is there something wrong with it?