A Possible Proof that Simultaneity at a Distance is Meaningless

M

Mike_Fontenot

Registered Senior Member
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.
 
Try this thought experiment:

Give both him and her a selfie video camera, a clock and a room.
Kit-bash his video camera so that, for any acceleration of his room, the camera on him slows down its recording rate by an amount determined by relativity.
Do the same for her camera.

Essentially they are each keeping a clock that corresponds to the other's time passage, as predicted by their own accelerations.

When they come back together, you should be able to match up the two recordings side-by-side, and see that, for every moment in her timeline, there is a corresponding moment in his.

Now, that is not much use in real-time but it ought to show, after-the-fact, the correspondence between their time frames.

I think that would work. Gotta give it more thought.
 
Mike,

I hope you have abandoned your idea that SR deals exclusively with perpetually-inertial reference frames. If not, then I would rather not give my input to your current idea. If you are ready to talk about SR on the basis that all inertial frames are equally valid, then please let me know, and I will try to contribute to this thread.
 
Mike_Fontenot said:
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.
Click to expand...
You need to start by defining the phrase "the home twin's current rate of aging relative to the travelling twin's rate of aging" in a precise way. It seems to me that you haven't done that, which makes the rest of your proposal too vague to allow discussion.
 
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).
 
MIke;

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".
Click to expand...

The motion of either twin cannot influence the age of the other twin. Their clocks, mechanical and biological, operate independently of each other.

The aging depends on accumulated time, not clock rates. A comparison of clocks can only occur after the motions during separation are completed.

When the plane flies toward the horizon, it seems to disappear. That's perception for the observer, but not reality for the plane. The images of the plane get smaller, to the point of exceeding the resolution of vision. We can only be certain it's still flying vs crashing, via communication with the plane, ATC, eye witnesses, etc. The plane could still crash following that communication, putting us back to square one, unaware of the plane's status.

Put something valuable in a box with a cover. Leave the house for a period of time and return. Can you be certain the valuable is in the box, without looking, or any other form of inspection? No, since you are missing part of the history of the box.

The idea of simultaneous knowledge of distant locations is prohibited, with the revelation of finite light speed, resulting from the astronomical work of Cassini and Romer in the 1600's, before 'relativity'.
 
My monograph on "A New Simultaneity Method for Accelerated Observers in Special Relativity" is available on Amazon for $5.00. You can find it by searching on "simultaneity method".
 
You should
Mike_Fontenot said:
My monograph on "A New Simultaneity Method for Accelerated Observers in Special Relativity" is available on Amazon for $5.00. You can find it by searching on "simultaneity method".
Click to expand...
You should get an 'A' for perseverance!
 
Neddy Bate said:
Mike,

I hope you have abandoned your idea that SR deals exclusively with perpetually-inertial reference frames. If not, then I would rather not give my input to your current idea. If you are ready to talk about SR on the basis that all inertial frames are equally valid, then please let me know, and I will try to contribute to this thread.
Click to expand...
Nobody wants to hear information they might not agree with.

even if it is for their own benefit.

just advice.
 
Mike_Fontenot said:
My monograph on "A New Simultaneity Method for Accelerated Observers in Special Relativity" is available on Amazon for $5.00. You can find it by searching on "simultaneity method".
Click to expand...
How many copies have been bought so far?
 
Mike_Fontenot said:
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.
Click to expand...
the only difference between the two is that one is under a constant velocity field and one is under a constant acceleration field. the motion is faster on earth than that is in the free space.
 
Ethernos 1997 said:
the only difference between the two is that one is under a constant velocity field and one is under a constant acceleration field. the motion is faster on earth than that is in the free space.
Click to expand...

After I posted the original post in this thread (that you quoted in your post), I posted a followup (post #5) that showed that my original proof (that simultaneity at a distance is meaningless) was incorrect. And I then showed what the correct age correspondence diagram (ACD) is for this scenario. So I'm back to believing that simultaneity at a distance is fully meaningful.
 
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