by jaumzaum
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P: 15,573
 Quote by bobc2 I think that Minkowski diagrams are pretty well established and understood in the field of special relativity, as is the concept of simultaneous spaces.
Yes, but apparently not by everyone. Particularly since we get many novices and students, it is a point that bears mentioning and you didn't so I did.
P: 1,162
 Quote by bobc2 Hi, Austin0. What I think (if I haven't messed up) is that I've used the Lorentz transformations to develop a Minkowski diagram for the twin's outgoing trip (up to the point of the turnaround) and then, picking up the travelling twin's trip after completion of turnaround, showing the diagram for the return trip. The diagram shows the intersection of the simultaneous space of the outgoing X1 axis with the 2nd Red worldline right at the start of the outgoing trip. And then it shows the intersection of the outgoing X1 axis with the 2nd Red worldline right after the turnaround is complete. If one would like to nit-pick, they could point to the round off of the total round trip time given as 10 years for the traveling twin (the small turnaround time was not included, which would add some decimal value to the total 10 year number). `
Well I don't think you "messed up" as this is a perfectly standard chart for an instant turnaround. While I am sure all agree this is an accurate charting of two separate inertial frames the question at hand is how this relates to a single extended accelerated frame, yes?

 The diagram shows the intersection of the simultaneous space of the outgoing X1 axis with the 2nd Red worldline right at the start of the outgoing trip. And then it shows the intersection of the outgoing X1 axis with the 2nd Red worldline right after the turnaround is complete.
Yes this is self evident but does not address my simple explicit question.

Given a single extended accelerated physical system of clocks and rulers do you think that right after turnaround this system would be congruent with x1 intersecting event A?
Would there, or not, be a traveler at A with a clock reading of t'=5+(a hair)??
P: 846
 Quote by Austin0 Well I don't think you "messed up" as this is a perfectly standard chart for an instant turnaround. While I am sure all agree this is an accurate charting of two separate inertial frames the question at hand is how this relates to a single extended accelerated frame, yes?
You miss the point here. I explicitly indicated that this is not a chart for an instant turnaround. I emphasized that the curved path portion is so small on this scale that I couldn't represent it with the limited chart space. The Lorentz frames with the simultaneous spaces indicated actually occur before the turnaround and then after the turnaround.

If you don't get this sketch, I could easily select simultaneous spaces much farther away from the start of the trip and from the turnaround. I didn't think this would be such a problem. I'm not showing an accelerated frame at all, so that's not relevant here.

 Quote by Austin0 Yes this is self evident but does not address my simple explicit question. Given a single extended accelerated physical system of clocks and rulers do you think that right after turnaround this system would be congruent with x1 intersecting event A? Would there, or not, be a traveler at A with a clock reading of t'=5+(a hair)??
I'm not talking about a single accelerated physical system here. In an earlier post, I analyzed the turnaround using a sequence of incremental inertial frames. We got tangled up with straw men, so now I've simplified the discussion to avoid arguing over single accelerated systems. And the fundamental point illustrated using two frames (outgoing and returning) which are clearly not accelerated is still the same as what I was trying to illustrate all along--just the fundamental concept of simultaneity and the interesting feature of events A, B, and C. Again, those features do not have to be interesting to you or anyone else. It was just a comment in the event anyone else might be intrested.
P: 846
 Quote by DaleSpam Yes, but apparently not by everyone. Particularly since we get many novices and students, it is a point that bears mentioning and you didn't so I did.
Do you have a problem with Minkowski space-time diagrams in general? Or, is it just when someone refers to the "simultaneous spaces" that show up in the space-time diagrams?
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P: 15,573
 Quote by bobc2 Do you have a problem with Minkowski space-time diagrams in general? Or, is it just when someone refers to the "simultaneous spaces" that show up in the space-time diagrams?
Neither. I have a problem when people make mathematically invalid statements and persist in doing so when their error is pointed out to them.

A "sequence of simultaneous spaces" is a simultaneity convention, in this case a non-inertial one. You may try to disguise it all you like, but that is what you are doing. Inventing new terms like "3D worlds" and "simultaneous spaces" doesn't change what it is.
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P: 15,573
 Quote by bobc2 And the fundamental point illustrated using two frames (outgoing and returning) which are clearly not accelerated is still the same as what I was trying to illustrate all along--just the fundamental concept of simultaneity and the interesting feature of events A, B, and C.
In neither of those frames does B come before A nor C before B.
P: 846
 Quote by DaleSpam In neither of those frames does B come before A nor C before B.
We may not be talking about the same thing. I've made it clear before that in the 2nd Red guy's frame, as the Red guy moves along his worldline, he encounters event A first, then event B, then event C.

However, as the blue guy moves along his worldline, the event B is presented to his outgoing simlultaneous space first (right at the start of the outgoing trip). Then. event A is presented to blue's simultaneous space just after blue completes his turnaround.

Also, just before blue enters his turnaround path, event C is presented to blue's simlultaneous space. Then, event A is not presented to the blue simultaneous space until after the turnaround is complete.
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P: 15,573
 Quote by bobc2 We may not be talking about the same thing. I've made it clear before that in the 2nd Red guy's frame, as the Red guy moves along his worldline, he encounters event A first, then event B, then event C.
Not just the red guys frame, but all inertial frames.

 Quote by bobc2 However, as the blue guy moves along his worldline, the event B is presented to his outgoing simlultaneous space first (right at the start of the outgoing trip). Then. event A is presented to blue's simultaneous space just after blue completes his turnaround. Also, just before blue enters his turnaround path, event C is presented to blue's simlultaneous space. Then, event A is not presented to the blue simultaneous space until after the turnaround is complete.
And here you go with your non inertial frame.

A sequence of simultaneous spaces is a simultaneity convention. And I have already told you that the naive simultaneity convention used here cannot cover the red worldline because it violates the few mathematical requirements of a coordinate system.

Your statement is mathematically invalid, as I pointed out well over 100 posts ago. I don't know why you persist in it.
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I would like to bring up this earlier comment. I am trying to understand bobc2's position.
 Quote by bobc2 You should understand that most forum members here would insist that the Andromeda Paradox does not represent anything about physical reality. It could be taken as a pedagogical illustration to help graphically visualize aspects of the mathematics of special relativity. They consider that there are other equally valid interpretations of special relativity, such as the Lorentz Aether theory, that are in conflict with any notion that the Andromeda Paradox illustrates something about reality--thus, in that view, the block universe is not to be taken as a true characterization of external physical reality.
Paradoxes do not represent reality. Paradox reveals contradiction and we do not allow idea that reality could be self contradictory. Only models of reality can be self contradictory (and therefore flawed).

So I would ask in what model Andromeda Paradox is supposed to appear.
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P: 4,463
 Quote by bobc2 However, as the blue guy moves along his worldline, the event B is presented to his outgoing simlultaneous space first (right at the start of the outgoing trip). Then. event A is presented to blue's simultaneous space just after blue completes his turnaround. Also, just before blue enters his turnaround path, event C is presented to blue's simlultaneous space. Then, event A is not presented to the blue simultaneous space until after the turnaround is complete.
And this is the core of disagreement. You speak of blue's simultaneous space as if it has some physical meaning. Further, since blue, after turnaround, has a different past than the past of the post turnaround inertial frame, any physical procedure defining simultaneity will come out different for the blue observer than for an observer always at rest in the post turnaround inertial frame. Finally, even as a mathematical convention, talking about blue's simultaneous spaces does imply an overall simultaneity convention for the blue world line. For this, there are mathematical requirements - any region where a proposed simultaneity convention for blue has intersecting surfaces is outside the domain of that convention. If you want to talk about a blue simultaneity for such a region, you must adopt a different convention that does not have intersecting surfaces - of which there are many.
P: 1,162
Quote by Austin0

 Well I don't think you "messed up" as this is a perfectly standard chart for an instant turnaround. While I am sure all agree this is an accurate charting of two separate inertial frames the question at hand is how this relates to a single extended accelerated frame, yes?
 Quote by bobc2 You miss the point here. I explicitly indicated that this is not a chart for an instant turnaround. I emphasized that the curved path portion is so small on this scale that I couldn't represent it with the limited chart space. The Lorentz frames with the simultaneous spaces indicated actually occur before the turnaround and then after the turnaround. If you don't get this sketch, I could easily select simultaneous spaces much farther away from the start of the trip and from the turnaround. I didn't think this would be such a problem. I'm not showing an accelerated frame at all, so that's not relevant here.
yes of course ,instant turnaround is a convenient idealization,
it was understood that this depicted inertial phases before and after turnaround.
When you attribute the x 1 axis to the traveler you are implicitly applying it to an accelerated frame. I.e. there is no turnaround without acceleration. So whether the traveler frame is accelerating at that time is not relevant , In the context of the overall trip it is non-inertial.
Quote by Austin0

 Yes this is self evident but does not address my simple explicit question. Given a single extended [edit out-accelerated] co-moving physical system of clocks and rulers do you think that right after turnaround this system would be congruent with x1 intersecting event A? Would there, or not, be a traveler at A with a clock reading of t'=5+(a hair)??
 Quote by bobc2 I'm not talking about a single accelerated physical system here. In an earlier post, I analyzed the turnaround using a sequence of incremental inertial frames. We got tangled up with straw men, so now I've simplified the discussion to avoid arguing over single accelerated systems. And the fundamental point illustrated using two frames (outgoing and returning) which are clearly not accelerated is still the same as what I was trying to illustrate all along--just the fundamental concept of simultaneity and the interesting feature of events A, B, and C. Again, those features do not have to be interesting to you or anyone else. It was just a comment in the event anyone else might be interested.
Well you have completely avoided answering my question again.
Whether or not you are talking about a single accelerated system I am asking your thought regarding the x1 axis as it would apply to such a system (with the edit above).

If there was such a co-moving system at that time after turnaround (inertial) would it correspond (be congruent) to the x1 axis in your chart?
Would there, or not, be a traveler at A with a clock reading of t'=5+(a hair)??
 PF Patron P: 1,366 When we speak about reality, do we mean only single moment of space or do we include all past and all future? I believe that with reality we mean single slice of spacetime i.e. we do not include all past and all future.
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 Quote by zonde When we speak about reality, do we mean only single moment of space or do we include all past and all future? I believe that with reality we mean single slice of spacetime i.e. we do not include all past and all future.
I value my past and future possibilities perhaps more than you More seriously what slice? Through a given event (e.g. me hitting submit for this post), there are uncountably infinite spacelike slices.
 P: 846 You folks still seem to be troubled by the approximaty of the simultaneous spaces to the accelerated turnaround point in my sketches. So, here is a sketch where we consider the simultaneous spaces far far removed (years and millions of miles) from the turnaround neighborhood. We still have the same interesting feature about the order of events. Event A occurs before event B in the 2nd Black's rest frame. However, for the travelling twin moving along his worldline, event B is presented to his return trip simultaneous space before it is presented to his outgoing simultaneous space. To emphasize the distinction between the outgoing frame and the return trip frame (not a single acceleration frame), I've colored the outgoing frame blue and the return frame red. The stay-at-home twin has the worldline along the black X4 axis.
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P: 15,573
 Quote by bobc2 However, for the travelling twin moving along his worldline, event B is presented to his return trip simultaneous space before it is presented to his outgoing simultaneous space.
Again, as we have already covered over and over again and again, your comments about simultaneous spaces are defining a simultaneity convention, and that convention is non-inertial. All of my previous comments hold. This approach violates the mathematical requirements in the region of the 2nd (now) black observer, so it is not a valid simultaneity convention for that region. If my many posts on this topic were not sufficiently clear, then please read PeterDonis' post 190, which is very well written.

You seem to think that I am having difficulty understanding your point. I understand your point quite clearly. Your point is not unclear, it is wrong.

 Quote by bobc2 To emphasize the distinction between the outgoing frame and the return trip frame (not a single acceleration frame), I've colored the outgoing frame blue and the return frame red. The stay-at-home twin has the worldline along the black X4 axis.
In neither the blue frame nor in the red frame does B come before A.

EDIT: oops, it is PAllen's post 190
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 Quote by bobc2 You folks still seem to be troubled by the approximaty of the simultaneous spaces to the accelerated turnaround point in my sketches....We still have the same interesting feature about the order of events.
Bobc2, a while back you did say that this "reversal of time" was just an interesting feature, nothing more. But now you appear to be saying that it *is* more; that there is some genuine physical meaning to the "interesting feature". And the pushback you are getting is because of the obvious paradoxical consequences of such a claim. So which is it?
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P: 4,463
 Quote by bobc2 You folks still seem to be troubled by the approximaty of the simultaneous spaces to the accelerated turnaround point in my sketches. So, here is a sketch where we consider the simultaneous spaces far far removed (years and millions of miles) from the turnaround neighborhood. We still have the same interesting feature about the order of events. Event A occurs before event B in the 2nd Black's rest frame. However, for the travelling twin moving along his worldline, event B is presented to his return trip simultaneous space before it is presented to his outgoing simultaneous space. To emphasize the distinction between the outgoing frame and the return trip frame (not a single acceleration frame), I've colored the outgoing frame blue and the return frame red. The stay-at-home twin has the worldline along the black X4 axis.
The question is the occurrence of this 'interesting feature' is part of the definition of the applicability of this simultaneity convention to the non-inertial observer. That is, the maximal spacetime region in which this simultaneity convention is applicable is the region in which there are no intersections of simultaneity surfaces. I could describe additional, physical plausibility criteria as well, but it is at least mathematically valid to use such a convention for the non-inertial observer as long as you don't try to cover a region of spacetime including such intersections.

Of course, I remain convinced that, even where applicable, making such statements as 'this is where the distant clock really runs faster than mine' are physically meaningless and conceptually grossly misleading.
P: 846
 Quote by DaleSpam Again, as we have already covered over and over again and again, your comments about simultaneous spaces are defining a simultaneity convention, and that convention is non-inertial. All of my previous comments hold.
We will just have to agree to disagree. You concept of non-inertial simply does not apply to the two separate blue and red inertial frames in the above sketch.

 Quote by DaleSpam This approach violates the mathematical requirements in the region of the 2nd (now) black observer, so it is not a valid simultaneity convention for that region
Neither of the separate individual frames violates the mathematical requirements. If I had been talking about a single non-inertial coordinates, I might have tried using Rindler coordinates or something, but then I would have to explain the Rindler horizen, etc. But, we are confronted with no such situation here.

 Quote by DaleSpam If my many posts on this topic were not sufficiently clear, then please read PeterDonis' post 190, which is very well written.
There is no PeterDonis post no. 190.

 Quote by DaleSpam You seem to think that I am having difficulty understanding your point. I understand your point quite clearly. Your point is not unclear, it is wrong.
In that case, your point is also clear--it is just wrong.

 Quote by DaleSpam In neither the blue frame nor in the red frame does B come before A.
Just look at the space-time diagram. The intersections of the blue and red simultaneous spaces with the 2nd black worldline are there to see. There can be no mistaken about where the intersections are.

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