Change of frames in relativity

[johnny_bohnny]

It seems that I'm getting opinions from you guys that aren't similar, there is no convention.
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.

And regarding differences between radar coordinates and standard textbook lines, I still didn't understand what is the difference between those two conventions. I know we can use both of them, but how can they be identical if they have different lines of simultaneity? That makes no sense.

 

[ghwellsjr]

@Ghwellsjr, thank you very much for the diagrams, I've understood them quite well, I think. The only problem with this is that they don't quite follow the scenario I was talking about.

I gave you a full answer that does follow your scenario completely in post #5 but you said in post #10 that my diagrams were "very complicated" and that you "don't really understand them". So in my previous post, I was trying to break it down into smaller chunks that you could understand and now you say you do understand them as well as other aspects so now I would like you to take another look at post #5.

In the scenario that I'm seeking the answer for, the blue observer in some kind of way becomes the black observer.

Yes, and that is what I showed you at the end of post #5. You also said (in post #16) that you understand the paper that DaleSpam linked to in post #14. If that is the case, then you should be able to understand post #5 because it uses the method described in that paper.

I'll again describe it. We have two observers on Earth which are at rest wrt Andromeda and they agree on simultaneity. Suddenly, one starts accelerating to move away from Andromeda and this should shift his simultaneity hyperplane in some kind of way so that after he finishes acceleration and starts to move inertially, his 'now' of the Andromeda should be the event of Andromeda which happens before the event that the stationary observer considers to be present. So how does this happen? If the observer didn't start to accelerate he would keep on agreeing with the second one about what's happening on Andromeda. The one that didn't accelerate continues to have his definition of simultaneity, while the first one changes frames, and what does he get as a result?

This is the third time you have described your scenario. I understood it the first time. No need to keep repeating.

Please study post #5 and if at any point you don't understand, please explain your point of confusion. It is a direct answer to your questions. It shows how the observer who changes his inertial state can construct his own non-inertial rest frame in a seamless manner that has no discontinuities or overlapping events and uses exactly the same convention for the inertial regions as for the non-inertial region. In other words, he doesn't have to be aware of his own acceleration, he just continues to apply his same convention all along.

Please don't be concerned about the fact that this convention differs from the one in your textbook. After you understand this convention, you can describe for us the convention that your textbook is promoting and we'll be able to comment on it.

 

[ghwellsjr]

It seems that I'm getting opinions from you guys that aren't similar, there is no convention.
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.

And regarding differences between radar coordinates and standard textbook lines, I still didn't understand what is the difference between those two conventions. I know we can use both of them, but how can they be identical if they have different lines of simultaneity? That makes no sense.

I doubt that there is any difference between those two conventions except in how the textbook applies it.

The blue inertial observer (Earth) uses the radar method to establish his coordinates:

The black inertial observer (traveler) uses the same radar method to establish his coordinates:

The blue-black non-inertial observer uses the exact same radar method to establish his coordinates:

They all get different coordinates because they all have different rest states.

I'm going to guess that your textbook takes portions of the first two diagrams and combines them into a third diagram without actually showing how the blue-black observer would have done it.

EDIT: I have made a new diagram for the traveler showing the Proper Times for easier comparison with the other two diagrams. I also made the transitions between the two inertial states more realistic.

 

[Dale]

What is the difference between this method and the textbook method, can they both be considered standard conventions for inertial observers?

The radar time method reduces to the standard convention for inertial observers and the Rindler convention (not "standard" but well known) for uniformly accelerating observers. Dolby and Gull mention this explicitly in the paper on pages 5 and 6.

 

[Dale]

It seems that I'm getting opinions from you guys that aren't similar, there is no convention.

This is troubling that you believe this. The replies you have received are very similar. What specifically do you think is a different opinion. It would help if you would quote rather than just make broad statements of a disagreement that I (for one) don't see.

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.

There is no contradiction because they are two different frames. Different coordinate charts are allowed to disagree. Did you not understand the geometric analogy I posted above?

And regarding differences between radar coordinates and standard textbook lines, I still didn't understand what is the difference between those two conventions. I know we can use both of them, but how can they be identical if they have different lines of simultaneity? That makes no sense.

They are identical only for the special case of inertial observers. For non-inertial observers the standard convention does not even apply.

 

[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.