Is symetry across inertial frames purely theoretical?

Aaron_Shaw

Hi. If the twin paradox, etc, is not really a paradox because one twin experiences acceleration, then is the idea of recipricol time dilation etc due to symetry across inertial frames purely theoretical?

What I mean is that could we ever find two inertial frames moving relatively to each other in reality? At least one of them must have experienced some acceleration in order to produce the relative motion in the first place, right?

Edit* I know i just explained that incorrectly. Of course we can have to inertial frames. What I mean is that because one of them must have experienced acceleration, then we will always have a "stationary" frame, and a "moving frame".

Ich

The acceleration history of an object is completely irrelevant for time dilatation.
When people mention acceleration they do so to emphasize that the rocket frame is not an inertial frame. Hence you can't claim that SR predicts reciprocal time dilatation in the twin "paradox": SR predicts nothing for noninertial frames, as it is not applicable to them.

Whenever you have two frames that are inertial during the experiment, there is reciprocal time dilatation, no matter what accelerations happened in the past.
And in every inertial frame, you can correctly calculate proper times by applying the appropriate time dilatation (1/gamma) to each segment of the motion of the interesting object.

Aaron_Shaw

Ok. Thanks for the answer. So based on the assumption that time dilation IS recipricol across two inertial frames, then is it the relativity of simultaneity that will prevent the twins, while still in inertial frames, to agree on their ages?

If so, then i assume that when the rocket suddenly stops, something happens during that non-inertial period that changes the experience of time for the twins? The reason i say this is that after the stop (at the halfway point), both twins are now stationary and could agree on each other's ages by sending their ages and calculating the time it would have taken to recieve those age messages. There's no relativity of simultaneity here to nullify the paradox, so presumably the act of decelerating to a stop altered the rocket man's perception of earth time? (like it speeds up?)

yuiop

Try this. Imagine two space stations S1 and S2 equidistant from Earth but on opposite sides. A rocket observer R1 is passing S1 and another rocket observer R2 is passing the Earth (simultaneously from the Earth frame POV). Both rockets are heading in the S2 direction with equal velocity (0.866c and a time dilation factor of 2). The clocks in the S1-E-S2 frame are synchronised with each other and the clocks in the R1-R2 frame are synchronised with each other.
After 20 years Earth time, R2 arrives at S2 and R1 arrives at Earth (but they have not yet decelerated)

and the respective times on the various clocks looks like this in the Earth frame.

Now the rockets decellerate very rapidly (almost instantaneously) and land. This changes the elapsed time very little. Now the rockets have to synchronise their clocks again with each other. If they choose R2 as the master clock then the situation looks like this:

and they agree more time has passed in the Earth frame than in their own frame. If they choose R1 as the master clock then the situation looks like this:

Now it looks like less time elapsed in the Earth frame. It is obvious that their perception of how much time has ellapsed on the Earth clock relative to R2 is very much dependent on the arbitrary choice of master clock.

Ich

Without relativity of simultaneity, time dilatation could hardly be reciprocal.
You measure the time between two events. And you measure the twin's time between two events that are simultaneous (your simultanteity) to yours.
Nothing really happens, except for some coordinate adjustments.


Look here for some graphics and explanation.
Let's take 8 years earth time, 4 years twin time, so turnaround is after 4 years earth time / 2 years twin time.
After 4 years earth time, 2 years passed for the twin.
After 2 years twin time, 1 year passed for earth.
See, reciprocal - if I take the twin's line of simultaneity.
All that happens at turnaround is that the twins line of simultaneity shifts. That has nothing to do with the twin's perception; all events on this "line" are totally unobservable for him at that time. That's more a bookkeeping procedure, which you can verify after the experiment is over and data has been exchanged.
So, for the outbound twin, the first earth year is simultaneous to his two years.
For the inbound twin, it's the last earth year.
All reciprocal, but somehow 6 earth years have been forgotten.

The reason why - after reunification - earth is older is a very simple geometric one: earth's path through spacetime is longer than the twin's path, and proper time = path length.
Just like, in ordinary euclidean geometry, two sides of a triangle are larger than the third. In relativity's spacetime, the two sides are always shorter than the straight path, but otherwise, the twin paradox is nothing but a "triangle paradox".
http://www.phys.ncku.edu.tw/mirrors/...spacetime.html

Aaron_Shaw

So.. lets imagine that the turnaround was not instant, but fairly swift, and that this whole journey was being recorded by the travelling twin. Then when he gets home he plugs it into a computer which can adit it to account for calculating dopplet effect.

The sumultaneity of it al look slike this:



So when the travelling twin watches the video am i right in thinking that he'd see time passing on earth very slowly on the outward journey, and then it would start to speed up and go very fast during decelleration to the point where there is no relative motion (horizontal simultaneity line) and then earth time would appear to start slowing down again as the twin had accelerated back in the opposite direction. At this point the video would be showing earth in the future (compared to the travelling twin at that point of the journey), but as earth time is now passing slowly again, the video will show rocket time running faster and the travelling twin's present catching up with that of earth. ?

I'll ignore the part where the rocket stops in order to edit the video recording.

Ich

No.
You can't see things that happen simultaneously somewhere else.
If you could, relativity would be absurd.
What you see is plotted in the diagram above the one you cited. Information is relayed maximally at the speed of light. The red lines connect what you see with what happened - much earlier - on earth.
Obviously, you can't see the future of earth at turnaround.

It is a common misconception that these blue lines are somehow directly physically important. They aren't. Nothing changes for the travelling twin if the blue lines change. Nothing outside the twin's light cone at that time can possibly have anything to do with her. These blue lines are out of reach per definition. They have nothing to do with what the twin sees.

Aaron_Shaw

I was thinking though that if you take the diagram showing the doppler shifting:



and run the calculations, based on distance and a constant speed of light, to transform the diagram into showing where the rocket WOULD have been when the light was emmitted from earth you'd see the second, blue lined, simultaneity diagram?

If that is true then what i was trying to suggest is that simultaneous events, during turnaround, are occuring over a larger span of earth time than rocket time (longer section of the CT axis).

The recording of the video, and editing it based on those calculations, was a way of observing those simultaneous events occuring in 2 frames, in one single frame. ie, the video will run for the same duration as the rocket trip, but the frames (video frames) displayed will render earth in slow motion, then fast-forward during turnaround, and back to slow motion at the end of the tape.

Hence, seeing the earth in the 'calculated' future, based on a calculated rendition of the trip rather than an actual observed trip.

I wonder if that makes more sense?

Ich

These lines don't transform. They show all the events that, in a so-called "momentarily comoving" inertial frame, would be considered simultaneous at some time.
Or, simpler, what - for the rocket - happens at a certain time anywhere in the world. The diagram itself is plotted in earth coordinates, you can directly read off where the rocket is at any instant -according to earth. There, simultaneous events are on horizontal lines.
It is most importan that simultaneity means different things for different observers.


Simultaneous according to the rocket! These events aren't simultaneous acoording to earth.
I think so, especially as it makes clear how artificial this generated "experience" is.

Aaron_Shaw

Thanks alot for the help. Rather than trying to depict the 'reality' of events, i was trying to conjur a scenario that i could use in order to verify that the diagrams represented what I thought they did.