On 3/4/07, Stephen A. Lawrence <[EMAIL PROTECTED]> wrote:
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OK so far? (Note that we didn't need gamma for anything here -- I
just used the metric to find the proper distances.)
I think we can stick to thought experiments and dump equations. Einstein said he didn't understand his theory once the mathematicians were done with it. To really understand the issues you can't use equations which are there to shortcut real comprehension.
If you introduce FTL communication you also must introduce a preferred reference frame.
Yup, and that's NOT SR! You are dancing around the problem by pointing out difficulties with the model of a train (among various other side issues), yet you could easily choose to not have each cabin mechanically connected to each other. I can easily counter all of your argument but it will be pointless and long. So let's get to the heart of the twin paradox. Basically SR states that the faster you travel the more time slows down, and yet it tries to do this without specifying 'Relative to what', because that's why it's called Relativity of course, all frames are equal, it's relative to each observer. This is of course impossible because each observer demands a different reality, but SR basically says 'Prove it'. Because communicating in real time between 2 different frames can seem challenging it might seem there is a point, however this is just an illusion. First it's not really about communicating, but rather knowing the rate that time flows for a different reference frame and instantaneous communication is merely something that would allow gaining such knowledge which is admitted to destroy SR if possible, if you can observe what the true rate of time is in the other reference frames and they can know your true rate of time then you will either see that time does not slow down or both will agree as to which frame time is moving the fastest (which frame is the most preferred or 'still'). Neither of these results would agree with SR, so the issue comes down to just how possible it might be to measure the rate of time in another reference frame. Now it is actually very easy and straight forward to measure the rate of time in another frame, the only thing that can seem to make it difficult is the Doppler effect, each moment each twin is further apart (or closer together on the return) causing the viewer to observe that time is moving more slowly or faster on the other ship than their own time. There are a few ways around this, one is that the moving twin could instead by orbiting the other twin (or simply spinning really fast while standing next to the other twin, or vibrating). Another is that the moving twin could be doing a flyby, this give a chance to measure both sides of the Doppler effect and a moment where they can share true instantaneous communication right as they pass. However the simplest way is to simply to have one twin hop in a space ship, accelerate to full speed in the blink of an eye and hold radio communications between the twins. Sure these communications will be strained by the Doppler effect, but if each twin tells the other twin the apparent rate of time (based on the transmission) relative to their own then they can compare numbers, if both see the other as say 23% slower (or 23% faster) then obviously neither are undergoing time dilation, it is all Doppler effect. (this could also be calculated and be found equal to the expected Doppler shift) If however they get different values then they can establish which twin is in the more preferred or still frame. SR couldn't really accept either event because is is based on ignorance of the rate of time in another frame. SR simply can't work because there is no way to truly stop someone from knowing the rate of time in another frame. Ok, now I'll answer some of your objections. You have big, big problems in this scenario, which you have not fully
worked out. Work out all the details and the timekeeping problems go away, but the details are a mess. First of all a long object cannot accelerate simultaneously along its length,
Incorrect, it is trivial to sychronize the clocks and each cabin has it's own means of propulsion as I said, the only thing you could claim would be that it would break into sections so naturally each cabin would be either unconnected or connected with something that can strech as required. The interesting problem you will have then is that if in a millisecond the entire train accelerates to .999 C then if you were in such a train you would notice the front of the train and the and caboose get further away because as far as you are concerned your cabin didn't shrink but rather gaps just appeared between cabins because the the who train stretched out at faster than C. because as soon as it starts to accelerate its parts
(stretched out along its length) no longer share a single inertial frame.
Furthermore, the whole thing must shrink due to Fitzgerald
contraction, which means that either different parts accelerate at different rates or the thing breaks up into pieces (this is related to Bell's paradox, which has two accelerating space ships, one in front of the other, connected by a long string -- if they both acclerate at the same rate, eventually the string must break). The longer it is, the less it can accelerate without breaking up; if it accelerates at 1g, for instance, and it's more than 1 light year long, the back end will break off no matter how hard it tries to keep up: there's what's called a Rindler horizon about 1 ly behind someone accelerating at 1g. In general, if a very long train tries to start "simultaneously" along its length it will break up as all the cars shrink -- but that's just what the people on the platform see. The people on the train see something entirely different.
Yes, they see in an instant the cars separate at faster than C. In that FOR the train doesn't shrink,
of course. Instead, they see that as soon as it starts to move the clocks go out of sync,
Only due to the the Doppler effect which is just a transmission delay and can be accounted for to arrive at the real answer that all clocks are in sync. and as far as anyone on the train can
determine, the locomotive started up before the caboose and hence broke the train apart.
If the front (I'll call it the front as it doesn't apply the power) and the caboose emitted a pulse of light when started, obviously yes you are right, those in middle cabbins would see the light pulse from the front first, but only because they have moved toward the front. If you just want to find the durations each party experiences , just find the proper distances as I did, above, for the twins. Proper
distance is a Lorentz invariant, so you'll get the same answer no matter what frame you work the problem in. If you want to determine exactly what everybody actually sees at each moment you have a lot more work to do. > There is another way however, you can have one twin stay on earth > and the other twin orbit the earth at near light speed. You see the > twin paradox always assume the twins are moving away from each other No it doesn't. In fact the original "paradox" had one fly away and then come back, so half the time they were moving toward each other.
I knew that naturally, I actually meant 'away or toward' as these are effected by Doppler distortions.
but in the case of orbit where they can constantly communicate or > for that matter merely flying by where they get a moment to observe > the rate of time the other experience and communicate without > Doppler distortion. The distant orbiting astronaut situation is very cool. See, for instance: http://www.physicsinsights.org/revolving_astronaut.html Dig that clock going backwards. Note that there's a Rindler horizon in there somewhere which keeps anyone from ever actually _seeing_ a clock go backwards. Counter-orbiting twins are entertaining too, and tricky to work out: http://www.physicsinsights.org/revolving_twins.html The simple question of what you "see" when you accelerate is pretty nifty, too. This came up recently on this list; I mentioned then that I had done up a rather elementary page on it, here: http://www.physicsinsights.org/porthole_view_1.html Sorry for the rerun. > There are yet more problems. I haven't seen any real problems in what you've described so far. Surprising results, yes. Counterintuitive, yes. Contradictory? No. > Let's say we now have 3 parallel close trains with open beds, we'd > better put them on earth so no one suffocates. > > We will have 2 flash bulbs of each train, each a set distance apart > and an observees on each train positioned in the middle of the 2 > flash bulbs, if the bulbs go off at the same time the short sharp > photon pulse reach the observes and he sees a single bright flash. This is one common starting point for deriving the Lorentz transforms. > Now let the middle train not move, let the bulbs flash at 12:00 and > at 12:01 (it's slow light ok ;) You mean the flash is at 12:00, the arrival is at 12:01, I think. Right?
Yes
the observer on that train see a bright flash from each bulb > simultaneously. However at 12:00 as the bulbs go off the train to > the right was moving down the track, at that exact moment the > observer on the right train passes the observer on the middle > stationary train. > > The observer on the right train expects to see the bulbs flashes > simultaneously because he was in the middle when they went off NO HE WAS NOT!
YES HE WAS ;) Sorry for shouting.
You have neglected relativity of simultaneity. In the moving observer's FOR, the bulbs did _NOT_ flash at the same time, and he was _NOT_ in the middle "when they flashed". The term "when they flashed" is FRAME RELATIVE.
No I'm not, It's all bunk...
(and if there were a bunch of censors along the right train they > would demand to see the pulses from each bulb advance from detector > detector and hence must meet in the middle). So what do they see? Don't just wave your hands, work it out.
Sure, well SR is wrong so they will all see a very sensible results due to the fact that light travels in the earth entrained aether. Indeed not a single experiment disagrees with the aether yet many disagree with SR. Use the Lorentz transforms, that's what they're there for. Don't try
to "intuit" this one, it won't work. > Furthermore in case you are unsure I'm not. Been there, done that, this is a standard example, almost identical to Einstein's two lightning flashes beside the train tracks. He does that in "Relativity: The special and general theories" IIRC. > you could have (different > colour?) bulbs on the moving right train that go off simultaneously > and right next to the bulbs on the middle train, obviously the > observer on the right train would insist on seeing the bulbs on it's > own train similtaniously. OK, let's work the darn thing out (just one bulb color, sorry). I'll pick some distances, and I'm just going to do it in one moving train with one set of stationary observers. C=1. We'll have the bulbs go off at +/- 1 on the X axis, at time 0 in the stationary frame. Coordinate (0,0) matches in the two frames, and that's when the bulbs go off in the stationary frame. So far so good? Train is moving in the +x direction at velocity "v". What time is it, according to riders on the train (who all have synchronized watches), when the flashes go off? For this I'll need gamma, g=1/sqrt(1-v^2). If the train is the prime frame, the track is unprimed, then the transforms from the track to the train are t' = g*(t - x*v) x' = g*(x - v*t) In our particular case the events are at x=+/-1, time t=0, so we have t' = +/- g*v x' = +/- g*x The flashes are equidistant from the origin, **BUT** they didn't take place at time 0, **AND** they didn't take place at the same time. The time lag between the flashes, according to the clocks on the train, is 2*g*v. Again, simultaneity is frame-relative in SR. > Now here is the really tricky part, if that didn't convince you SR > is flawed It convinced me that you don't understand relativity of simultaneity, and you don't understand relativistic clock skew. > as it require the same pulses to pass each other multiple > times, in different places depending on the reference frame. No it doesn't. You only think that because you didn't realize that the flashes are only simultaneous in ONE of the reference frames. In the frame where they're not simultaneous the moving observer who was in the middle when the flashes went off (according to the stationary observers) doesn't see them in the middle
That is totally untrue. The moving trains frame does not effect distance. You might be talking about the Doppler effect again where when approaching something it will appear longer and shorter when it recedes (this is because the age of the light for a space ship is not simultaneous, the light from the front is newer where it is closer but the light from the rear is older due to the difference in transmission time hence this could seem to effect simultaneity and length but in reality clearly it is neither, this again is not a real effect. The observer in the center train was in the middle at 12:00 (and stayed there), he passed the observer in the moving train. You have not been able to argue the twin experiment in space trains (other than point out the need foe elastic) because in that case the 2 frames are effectively in real-time communication. But I'll drop that one for the simple situation of two observers passing (possibly at a distance as that offers more time for communication that is not Doppler distorted). You can't explain the train without making use of Doppler distortions so that make things neither the middle nor simultaneous despite the fact that it is known that that is the middle regardless of Doppler distorted optical illusions. So ok, no more complex models but how about the simple truth. That SR is based on ignorance, it is based on Doppler distortions which not only are clearly not real but are not always present, when they aren't (as with passing by or orbit) the true rate of time can be easily detected. Here is something I found which tries to explain the reason for the twin paradox, do you agree with it? There are two key points about the twin paradox. The first point is that when Alice turns around she knows the moment that she turns and all incoming data changes at this instant. Bob cannot detect that a turn has occurred until x/c seconds later. The situation is highly ASYMMETRIC. It is not a symmetrical problem such as would occur if both Bob and Alice turned at a prearranged moment. This is clearly again treating the Doppler effect as if it were real time distortion. The reason this doesn't happen in reality is simple, light isn't C (it is impossible to have Doppler shifting the frequency of EM and yet light be C). Even so it is treating the Doppler effect as the cause of slowing down of time which is absolutely wrong.
