# Is Simultaneity "Real"?

#### MikeFontenot

In my paper,

"Accelerated Observers in Special Relativity", PHYSICS ESSAYS, December 1999, p629

I gave a proof that (in regards to the well-known twin "paradox"), the current age of the home twin (she), according to the traveler (he), as given by the CADO reference frame (which is completely equivalent to the better-known "co-moving inertial frames montage"), AGREES with what he can determine himself, using ONLY his own elementary observations, combined with his own elementary calculations. I first show how the traveler could do that if he were perpetually inertial. Then, I show how he can do that during his unaccelerated inertial periods. And finally I prove (by using a "counter-factual" argument, combined with a causality argument) that the same result holds even during each instant of his accelerating periods. IF my proof is valid, then it is NOT true, as is commonly believed, that simultaneity conventions are arbitrary and meaningless: there is only ONE valid definition of simultaneity, and simultaneity IS meaningful and "real". All of this is discussed in Section 10 of my webpage,

https://sites.google.com/site/cadoequation/cado-reference-frame

and to a greater extent (and more rigorously) in my paper.

So is my proof valid? No one has ever contacted me (in the 20 years since that paper was published) and told me that they had found a flaw in my proof. And several times over the years, I have looked again carefully at my proof, and I have never spotted an error in it. If anyone reading this believes they have found an error in my proof, I would like to hear from them. Email me at (Adminstrative comment: PM him for his e-mail address.)

___________

Michael L. Fontenot

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#### Woody

I admit I have not yet looked at your link,
I will try to find some time to study it soon.

However, one thing that strikes me in your post is:
same result holds even during each instant of his accelerating periods
This sounds like some of the "pseudo-static" approximations I used to make in a 6DOF motion simulation.
For example the mass and inertia at each time step included the changes due fuel being used,
but the effects of the rate of change of mass and inertia were ignored.

So looking at each instant, the calculations were correct for the static situation pertaining to that instant;
but they excluded certain terms relating to the dynamic situation.

For my simulations, the missing terms were small (so I could get away with the simplification).
However, care has to be taken ,when looking at these instantaneous snapshots, to remember that it is snapshot of a dynamic process.

As I say I haven't (yet) looked at your link,
so perhaps my diatribe is totally off the mark...

2 people

#### neila9876

I have not yet read the whole content either. One excuse might be that it's not an easy job for me to read English. haha...
But I want to say something simple. I don't know why some people consider that the story of twin is a "paradox"? I doubt if I am not able to understand that word exactly in English.

#### MikeFontenot

I have not yet read the whole content either. One excuse might be that it's not an easy job for me to read English. haha...
But I want to say something simple. I don't know why some people consider that the story of twin is a "paradox"? I doubt if I am not able to understand that word exactly in English.
The twin "paradox" is not actually an inconsistency. It "appears" to be inconsistent, but it is not.

It SEEMS inconsistent, because the time-dilation result says that each twin, while they are not accelerating, concludes that the other twin is ageing gamma times slower. So the home twin (she), who never accelerates, can use the time-dilation result for the entire trip, so she concludes that he will be younger than her at the reunion (which is correct). Similarly, the traveler (he) doesn't accelerate during his outbound leg, or during his inbound leg. So during each of those portions of the trip, he concludes that she is ageing gamma times slower than he is. The "paradox" arises when he incorrectly assumes that, since his turnaround is instantaneous, nothing can happen to her age during that single instant at the turnaround. So he expects her to be the younger twin when they are reunited. But they can't both think the other is younger at the reunion, because they are standing there looking at each other. Thus the apparent paradox.

The resolution of the paradox is that, during that instantaneous turnaround, he must conclude that she instantaneously ages by a large amount, just enough so that her age at their reunion will be greater than his, and they will thus agree with each other at the reunion.

#### Woody

The "twin paradox" has been knocking around for decades
It basically says that if one twin travels at high speed relative to the other twin
"he" will end up older than "her"

The issues arise when one tries to "simplify" the problem with "instantaneous" accelerations.
These (obviously) lead to unrealistic situations (like one twin aging instantaneously).
However if one considers a realistic model, with one twin in a non-inertial (accelerating) reference frame and the other in a non-accelerating (inertial) reference frame,
then the unrealistic instantaneous issues go away.

Everyone can calculate the age of everyone relative to everyone else,
and everyone will agree that the accelerating twin is aging slower than the inertial twin.

#### MikeFontenot

[...]
The issues arise when one tries to "simplify" the problem with "instantaneous" accelerations.
These (obviously) lead to unrealistic situations (like one twin aging instantaneously).
The instantaneous velocity change scenario is of course not realizable in practice, but it IS possible to do the analysis for a 1g acceleration that lasts for a couple of years. When you do that, the results are qualitatively VERY similar to the instantaneous velocity change scenario: the home twin rapidly ages by 60 years (according to the traveler) during the two years that the traveler accelerates. So the instantaneous velocity change scenario DOES capture the essence of what is happening in the twin "paradox".

#### topsquark

Forum Staff
The instantaneous velocity change scenario is of course not realizable in practice, but it IS possible to do the analysis for a 1g acceleration that lasts for a couple of years. When you do that, the results are qualitatively VERY similar to the instantaneous velocity change scenario: the home twin rapidly ages by 60 years (according to the traveler) during the two years that the traveler accelerates. So the instantaneous velocity change scenario DOES capture the essence of what is happening in the twin "paradox".
I have heard of this method (possibly from your own posts a few years ago) and it does seem to give identical results to the standard programme. But I'm certainly not an expert in SR (or even GR) so I can't really help you with any support and say if the method is good in general.

My question: Since you are getting the same results as others, why are you posting here? Are you trying to garner interest in the mechanics of your system or have us help you proof-read something? I'm not sure why you are posting here.

-Dan

#### MikeFontenot

My question: Since you are getting the same results as others, why are you posting here? Are you trying to garner interest in the mechanics of your system or have us help you proof-read something? I'm not sure why you are posting here.
I'm not certain that I understand your question here. But I'll elaborate a bit on my original posting when I created this thread.

The results I get by using my CADO equation are the same results that other physicists get with the "momentarily co-moving inertial frames montage" approach. That is not surprising, because the "CADO reference frame" is no different from the co-moving montage ... it just uses some different terminology that is intended to reduce careless mistakes and misunderstandings, and it uses the CADO equation to make the whole process easier and faster.

But I should add that not all physicists agree that the "co-moving inertial frames montage" is the correct way to define simultaneity for an accelerating observer. Other definitions are possible, and there is still controversy about simultaneity, even 100 years after Einstein discovered special relativity.

But even though my basic results (like the assertion that the home twin's age will instantaneously increase by a large amount, according to the traveler, when the traveler reverses his velocity at the turnaround) are the same as what some other physicists have said, there ARE some results in my published paper which are new, and which have not previously been shown by other physicists (as far as I am aware, at least). The most important of those new results is my proof that, even for an observer who is in the midst of accelerating, it is possible for him to deduce the current age of the home twin (according to him) just from his own elementary observations, combined with his own elementary calculations. The first part of that proof is the easy part: showing explicitly how a perpetually-inertial observer could do it with only elementary observations and elementary calculations. I suspect other physics have done that exercise themselves, but I'm not sure. Then, I extend that to include the traveler doing it during his unaccelerated inbound trip, AFTER he has accelerated recently. That's still fairly straightforward. But the last part of the proof is more complex, and I doubt it has ever been done before: I use a counter-factual argument, combined with a causality argument, to show that the result applies even when the traveler is in the midst of accelerating.

IF that proof is correct, it shows that physicists who contend that simultaneity can be defined in multiple ways, and that physicists who contend that simultaneity is meaningless, are wrong, and that the "co-moving inertial montage" definition (which is equivalent to the CADO reference frame definition) is the ONLY valid definition of simultaneity, and that simultaneity is thus "real".

If my proof is valid, that's a big deal, because it can end the present controversy about simultaneity. But if there is a mistake in my proof, I'd like to know it. So I'm asking anyone who thinks they've found an error in my proof to contact me.

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