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Suppose we have three frames of reference, A and B, and a lab frame. Taking the lab proper time as the coordinate time, we can draw worldlines for A and B. B is stationary in the lab frame, so its worldline is a straight line at $x = x_B$. A initially moves at a constant speed $u$ until time $t=t_A$, at which point it instantaneously halts. We can let its worldline start at $t = 0$ and $x = x_0$, and the point where A halts be at $t = t_A$ and $x=x_A$ such that $x_0 < x_A < x_B$.

An observer traveling along the worldline of A will measure simultaneity with events along worldline B by seeing if the are parallel to his x-axis. But there is something that happens when A abruptly halts. The x-axis shifts from being positive sloping to being horizontal, shifting which events an observer in A sees happened simultaneously to ones that occurred further back on B's worldline, which observer A had already seen.

Would observer A see a younger version of frame B again?

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    $\begingroup$ Like with the twin paradox, if you account for the time it takes for light pulses to fly between these two points, there will be no problems - no discontinuous shift in the image that observer A sees from observer B $\endgroup$
    – AXensen
    Apr 6, 2023 at 20:34
  • $\begingroup$ Are you talking about a Minkowski diagram? A horizontal line in the diagram is not physical for all I know. A stationary world line is vertical and all physics happens within the light cone. $\endgroup$ Apr 6, 2023 at 20:35
  • $\begingroup$ I was saying that the x-axis will become horizontal when frame A abruptly changes frames, not that any worldline itself is horizontal. $\endgroup$
    – NX37B
    Apr 6, 2023 at 20:38
  • $\begingroup$ I think I see why the image would be continuous, but does that mean that it it ok for observer A to 'see' events along worldline B that it already saw before it changed frames (I know I am stretching the definition of 'see' here). $\endgroup$
    – NX37B
    Apr 6, 2023 at 20:42
  • $\begingroup$ A single event is only visible once, no matter where you are, unless somebody installs a mirror for you somewhere else. Then you can see the event and its image in the mirror. $\endgroup$ Apr 6, 2023 at 21:04

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It depends on you definition of "see". If it's observe light, then of course: no.

If it's the thought experiment definition: what does your infinite lattice of clocks and rulers measure, then: yes. (If you have the sign right).

If the observer in question changes speed such the the rate of separation from the observed is suddenly greater (and the separation is not zero), then the new lattice of clocks has a basis at the observed that is before the prior one.

Of course this does not mean the observed has gone backwards in time, since:

"That no inherent meaning can be assigned to the simultaneity of distant events is the single most important lesson to be learned from relativity."

— David Mermin, It’s About Time

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  • $\begingroup$ Exactly right. Spot on answer. $\endgroup$ Apr 7, 2023 at 9:06

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