Curved simultaneity lines while at rest due to future motion?

This is an amazing spacetime diagram of a round-tripper with acceleration.

Note that when the round-tripper is at rest in the pink area before the journey, the horizontal simultaneity lines outside the pink area are CURVED DUE TO THE MOTION IN THE FUTURE!

I think this is overlooked evidence for the block universe because motion in the future apparently affects the simultaneous events in the past.

• What is your definition of simultaneous? Nov 9, 2020 at 23:36

I think what David Mermin thinks:

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

Also: at any point in spacetime (e.g., at and event), any other event that is outside the light cone could be in the past, present, or future depending on how you move, locally.

Since this is feature of special relativity is called the Andromeda Paradox (https://en.wikipedia.org/wiki/Rietdijk–Putnam_argument), and Andromeda is very neatly 2.5 million light years away and approaching us at $$v=c/1000$$, it is very easy to calculate that right now, on a planet in Andromeda Galaxy, it is:

$$2020{\rm AD} + 0.001\,{\rm ly/yr}(2.5\times 10^6\,{\rm ly}) = 4520{\rm AD}$$

right here on Earth, now, ...., over there. Frankly, that disturbs me more than a squiggly line on a Minkowski diagram...though they are equivalent.

I'd say it is necessary that simultaneity is affected by the future, simply because of how simultaneity is defined. The definition of simultaneity isn't anything like "two events are simultaneous if they really happen at the same time". How would one even work with that definition?

This is the simplest, workable way to define simultaneity: "Let $$\mathcal{O}$$ be an inertial* observer. An event $$A$$ that happens outside of the worldline of $$\mathcal{O}$$ is simultaneous (from $$\mathcal{O}$$'s perspective) with an event $$O$$ that happens on $$\mathcal{O}$$'s worldline if

$$\tau_0=\frac{\tau^+ +\tau^-}{2} ,$$

where:

• $$\tau_0$$ is the proper time at which $$O$$ happens, measured by $$\mathcal{O}$$.
• $$\tau^-$$ is the proper time at which $$\mathcal{O}$$ would need to send a light pulse to reach $$A$$
• $$\tau^+$$ is the proper time at which $$\mathcal{O}$$ recieves a light pulse sent from $$A$$

In these conditions, we say that $$\tau_0$$ is the time coordinate that $$\mathcal{O}$$ assigns to the event $$A$$"

In other words:

Of course it depends on the future! If $$\mathcal{O}$$ starts moving after what in this diagram is $$\tau_0$$, then that same $$\tau_0$$ won't be the time coordinate of $$A$$ anymore! And that's fine! It's simply a result of defining simultaneity in a pragmatic way.

*If the observer is not inertial, it can of course follow the same procedure. It's just not as clear that that's what we should call simultaneity. Nevertheless, this seems to be what the graph you presented uses.