[MikeFontenot (OP)]

One of the issues that remains controversial in special relativity is whether or not simultaneity at a distance has any meaning. In other words, when the traveling twin (he) in the twin paradox says that the home twin's (her) current age "right now" is such-and-such, is his conclusion true, real, and meaningful?

Personally, I've always thought (purely for philosophical reasons) that the answer is "yes": his conclusion about her current age IS "meaningful", "real", and "true". I base that on my belief that she doesn't cease to exist just because they are separated by a vast distance. And if she DOES currently EXIST, then she must currently be DOING something specific. And if she is currently doing something specific, her brain must currently be in a specific and unique state, which implies that she is currently some specific age.

But I THINK I may have discovered a proof that his conclusion about her current age is meaningless. If that proof is valid, that is obviously very disturbing to me (because of the above philosophical argument).

I discovered the proof while investigating a possible new simultaneity method (different from the one that I wrote about some months ago). In the new method, I decided to assume a much stronger version of the causality principle than I had been using. The weaker causality principle that I had been using just says that how the traveling twin chooses to accelerate in the future can't influence the home twin's current age "right now". Under that (weak) causality principle, both my previous simultaneity method, and the CMIF simultaneity method, are (weakly) causal, but the Dolby and Gull method, and Minguizzi's method, are NOT (weakly) causal.

The strong causality principle that I've decided to impose says that the home twin's (her) current rate of ageing (relative to the traveling twin's (his) rate of ageing) can't change for some period of time after he changes his velocity. Specifically, when he changes his velocity, he immediately sends a light pulse to her, and strong causality says that her relative rate of ageing can't change before that light pulse reaches her. I.e., strong causality says that his velocity change can't cause his conclusion about her current relative ageing rate to instantaneously change.

So I took a specific twin paradox example, and constructed an age correspondence diagram (ACD), using the above reasoning. The outbound portion of the trip before his velocity change, as usual, gives a slope of 1/gamma for the first segment of the ACD ... he says she is ageing gamma times slower that he is. But, because of strong causality, that slope continues for a while after he changes his velocity. Then finally, after his transmitted pulse reaches her, the slope of the ACD changes to a value greater than one (and just enough to make her age be the required value at their reunion).

The trouble is, when I tried to do that, I found that his age at the beginning of the steep segment is GREATER than his known age at their reunion, which is of course nonsense. There can be no doubt about the correctness of the outcome of the twin paradox at the reunion, and the strong causality assumption is inconsistent with that outcome. Therefore strong causality can't be correct.

IF his conclusion about her current age is meaningful, real, and true, that would seem to me to REQUIRE that suddenly changing his velocity COULDN'T instantly change her current relative rate of ageing. Specifically, her current relative rate of ageing CAN'T change before the pulse reaches her. So meaningfulness REQUIRES that the strong causality principle be obeyed. But strong causality ISN'T obeyed in the (correct) twin paradox reunion outcome. Therefore his conclusion about her current age isn't meaningful, real, or true.

[Halc]

For the record, the OP is a word for word copy of a post made earlier on another site, which is a violation of this site's terms of service. I'm responding anyway, but I want it noted.

One of the issues that remains controversial in special relativity is whether or not simultaneity at a distance has any meaning.

The meaning of simultaneity at a distance is quite clear in SR, and this controversy you're trying to invent seems to be instead a controversy with all these various causality principles you keep pushing. The 'proof' here seems to be an argument against these principles, and not against the meaningfullness of simultaneity at a distance as discussed in SR theory.

In other words, when the traveling twin (he) in the twin paradox says that the home twin's (her) current age "right now" is such-and-such, is his conclusion true, real, and meaningful?

This statement, as worded, is completely ambiguous, and thus the truth value of it is meaningless.
If it is meant to say something like "Under SR, given a pair of continuous worldlines, can there be a meaningful method mapping each event on one worldline to a unique event on the other worldline?".  The answer to that is yes of course. There are several such methods, although some require the worldlines not to have discontinuities in it or its derivatives.  It doesn't work in GR mind you, but you are restricting yourself to SR here.

I base that on my belief that she doesn't cease to exist just because they are separated by a vast distance.

Depends on your coordinate system of choice.  If accelerating Bob decides to partition up spacetime according to say Rindler coordinates, then she may well not exist at all in spacetime.  Yes, this is still SR.

And if she DOES currently EXIST, then she must currently be DOING something specific. And if she is currently doing something specific, her brain must currently be in a specific and unique state, which implies that she is currently some specific age.

You're rambling. If her clock reads a particular value, that's enough. What her brain is doing, or the fact that there's a live person at either end of the stick is entirely irrelevant, which is why my rewording above referenced only worldlines instead of observers.  SR does not depend on anything being observed by humans.

But I THINK I may have discovered a proof that his conclusion about her current age is meaningless. If that proof is valid, that is obviously very disturbing to me (because of the above philosophical argument).

Your above philosophical argument boils down to the fact that you have a gut feel about the ability to do what you describe, and no actual argument as to why that ability must exist.

I discovered the proof while investigating a possible new simultaneity method

Demonstrating a given method to not be viable just discards that one method. It doesn't in any way prove that there isn't another method any more than my finding a white swan doesn't prove that there are no black ones.

The strong causality principle that I've decided to impose says that the home twin's (her) current rate of ageing (relative to the traveling twin's (his) rate of ageing) can't change for some period of time after he changes his velocity.

Terms are poorly defined here, and assumptions are not stated.  OK, so Alice's rate of aging is X and must remain X for at least time T (measured by something unspecified).  Bob does something that brings him into the presence of Alice before time T expires, and tells Alice her age is such and such, and Alice's clock says otherwise.  No contradiction unless you have an assumption that Alice's age must match her clock when in her presence. If that assumption is made, then you've doomed your new principle, but have not disproved the existence of a principle that works.

Therefore strong causality can't be correct.

Last I checked, my current age has nothing to do with the actions of somebody else, so I tend to agree that your causality (strong or otherwise) is pretty hokey.

Therefore his conclusion about her current age isn't meaningful, real, or true.

No, because he's using a faulty strong-causality method. That's not a problem with SR, just a problem with that particular method.

[MikeFontenot (OP)]

Happily, I discovered an error in my above post. When she receives his message, he is NOT older than his age at the reunion. That should have been obvious to me, because that would require that he beats the pulse home. His speed is 0.57735, and the pulse's speed is 1.0, so obviously the pulse is going to win that race. So the strong causality principle in NOT inconsistent with the known outcome of the twin paradox, and I don't have to conclude that simultaneity at a distance is meaningless. I'm very relieved.

Here are the corrected calculations:

Immediately before his turnaround, she says their separation is

(0.57735)(40) = 23.094 ly.

He says their separation then is

(23.094)/gamma = (23.094)/(1.2247) = 18.857 ly.

So he says he will age 18.857 years during the transit of the pulse. He is 32.66 years old when he sends the pulse, so he is

32.66 + 18.86 = 51.52 years old

when she receives the pulse, and he is

(18.875)(0.57735) = 10.8871 ly

from the turnaround then. So when she receives the pulse, he says he is

18.857 - 10.8871 = 7.970 ly

from her then. How old does he say she is then? He says she has been ageing gamma times slower than he has. So he says she has aged a total of

51.52 / 1.2247 = 42.067 years

when she receives the pulse ... i.e., she is 42.067 years old then. So we have the coordinates for the point where the steep section of the ACD starts: according to him, he is 51.52 years old then, and she is 42.o67 years old then. So the slope of the final segment of the ACD is

S = (80 - 42.067)/(65.32 - 51.52) = 37.933/13.80 = 2.749.

So the ACD consists of just two segments. The first segment starts at the beginning of the trip (when they are both zero years old), and continues until she receives his pulse (well after his turnaround). That first segment has a slope of

1/gamma = 0.8165,

so he says she is ageing more slowly than he is during that whole segment.

The second (and final) segment has a slope of 2.749, which continues until their reunion. During that segment, he says she is aging much faster than he is ... just enough so that they both agree about their final ages at the reunion (as they of course must).

[CPT ArkAngel]

Imagine that the universe is made of only two identical twins. To simplify, the two twins are represented by two identical and perfectly symmetrical spherical balls. 

The two twins start together and then each of them pushes the other with perfect symmetrical forces. The interaction is local and symmetrical. Then, each twin sees the other aging asymmetrically. But if an observer is in the middle, he will see both aging at the same rate, but differently than his own aging. This is similar to the cosmological expansion without the middle observer. The thing is it makes sense in an absolute present. The cosmological expansion makes sense in the absolute present, in an extension of our mind of the now. This is where the symmetry is conserved. This is why it is considered an expansion of space.

In the case of the two balls, if the forces were weak enough, gravity will slow down the balls and then they will fall into each other in a perfect symmetry. When they will meet, they will find no difference in aging. Doesn't this imply that the present is kind of real?

What about entanglement? I don't see anyway to solve the problem within the speed of light. But Einstein's law may be respected if what breaks the speed of light is not matter or spacetime but... space, a basic space which is only an observable in quantum entanglement, which includes black holes. It is probably an observable as a flat universe also and condensed matter.