Change of frames in relativity

[yuiop]

... Basically, what happens during acceleration or the change of frames, so that one observer can get from one position of simultaneity defining to another?

Please see the diagram and explanation I posted in a related thread here: https://www.physicsforums.com/showpost.php?p=4688465&postcount=10
I hope it might be helpful to you.

 

[ghwellsjr]

Please see the diagram and explanation I posted in a related thread here: https://www.physicsforums.com/showpost.php?p=4688465&postcount=10
I hope it might be helpful to you.

I can't see a diagram in that link. Maybe you are having the same problem I continually run into where I can see a diagram that I uploaded but if the thumbnail disappears, that means no one else will be able to see the diagram (or the thumbnail). If this happens, then I have to re-upload the diagram and re-link to it.

 

[yuiop]

I can't see a diagram in that link. Maybe you are having the same problem I continually run into where I can see a diagram that I uploaded but if the thumbnail disappears, that means no one else will be able to see the diagram (or the thumbnail). If this happens, then I have to re-upload the diagram and re-link to it.

It was post #10 of this thread https://www.physicsforums.com/showthread.php?t=742905

I posted that a few days ago so it is too late to edit it. Here is the diagram uploaded again here:

This is the text that accompanied the diagram in the other thread:

I have created this diagram to help illustrate some of the concepts that are being discussed here:

A and B are initially at rest in frame S in the year 2014. The line of simultaneity is represented by the horizontal blue line connecting A and B at events e1 and e3. By prior agreement they both instantaneously accelerate to high speed to the right simultaneously in 2014 as measured in S. The line of simultaneity is now represented by the tilted red line connecting events e1 and e2 in the new rest frame of A and B.

By a naive interpretation, from A's point of view in A's new reference frame, B has shot into the future of frame S and is "now" (by A's new definition of now) in the year 2021 of the old reference frame S. However it is not as straight forward as that simple interpretation suggests. When an extended objects accelerates to a new reference frame the clocks do not automatically synchronise themselves. B had to wind his clock back by 3 years at the acceleration event (e3) so that his clock would be re-synchronised with A in the new reference frame. B had to wait a further 3 years of his own proper time to arrive at the event (e2) that A called "now" when A accelerated in 2014. There was no magical leap into the future as far as B was concerned and B had to manually adjust his clock. While A assumes that B was at event e2 immediately after the acceleration event, A does not see where B actually was, until the light from that event (the light blue line) arrives back at A in the year 2018 of the new reference frame or the year 2023 in the old reference frame and anything could have happened to B in the intervening years to prove A was wrong in his assumption of where B was in his new concept of "now" in the year 2014.

In the year 2018 of the new reference frame, A can look back and have real information about the events e1, e2 and e3 as they are all in his past light cone and can now say with some objectivity that B was at event e2 when A started accelerating at event e1 in the year 2014, but from the point of view of his new reference frame, B started accelerated to the new reference frame, 3 years earlier than A. This is a perfectly valid interpretation of past events, but at no time does A or B have information about the future before it happens beyond an educated guess. To me, the unpleasant aspect of the spacetime loaf concept, (which I believe is closely related to the block universe idea), is that it implies the future is predetermined.

 

[ghwellsjr]

It was post #10 of this thread https://www.physicsforums.com/showthread.php?t=742905

I posted that a few days ago so it is too late to edit it...

Why don't you just add another duplicate post on the other thread with the diagram intact and then report #10 as obsolete and ask the moderators to delete it.

I think you should add the comments on this thread so that we don't have to jump back and forth between two threads to see the diagram and read the comments.

 

[WannabeNewton]

So I'll ask again, before and after acceleration, if we use the standard textbook 'lines of simultaneity' in those two different frames, there is no contradiction if the lines of simultaneity overlap between those two observers.

It's not a contradiction. This is what happens if one uses the simultaneity surfaces of the momentarily comoving inertial frames of an accelerating observer. This simultaneity convention for non-inertial observers will only be well-behaved if one restricts the domains of the simultaneity surfaces of each instantaneous rest frame.

 

[yuiop]

I think you should add the comments on this thread so that we don't have to jump back and forth between two threads to see the diagram and read the comments.

I have edited the post to include the quoted comments with the diagram. Hopefully the context won't be confusing.

 

[grav-universe]

So we have two observers on Earth mutually at rest and at rest wrt Andromeda. Their clocks are in sync so they agree on simultaneity.

One of them starts to move away from Andromeda, and from the other observer that stays in the same inertial frame. He accelerates and the starts to move away inertially, and therefore he should consider the present of Andromeda the past of what the stationary observer considers to be present. So my question is how? If we consider the time to flow 'normally' in the reference frame of the stationary observer, and by that I mean that the clock on Andromeda ticks at the same rate as his, how is it possible that the 'moving-away' observer saves a day of time, or more, during the short acceleration period? How do the two simultaneity 'surfaces' compare?

This is true when using the standard Einstein simultaneity convention. Observers in each inertial frame synchronize their clocks so that light travels isotropically at c. The clocks at the front and rear of the ship will then be considered synchronized. But when changing frames, the clocks become out of sync, no longer measuring c, so they must be re-synchronized to measure c again in the new inertial frame. This can be performed by setting the clock at the rear of the ship back some so that c is now measured in the new frame when traveling away from Andromeda. Let's say that the back of the ship extends all the way to Andromeda. The further the distance, the more the rear clock will have to be set back. So in the new inertial frame, the event will now be said to occur in the past according to that coordinate system.