# Minguizzi's Simultaneity Method

#### Mike_Fontenot

Registered Senior Member
Is anyone of this forum familiar with the Minguizzi simultaneity method (for the resolution of the twin paradox)?

You describe it on your website. Why, are you unfamiliar with it now?
I don't think there is any use to it or any other method. No 'method' is needed since the twins scenario is not paradoxical.

I read this paper:

https://arxiv.org/pdf/gr-qc/0506127.pdf

In it, Minguizzi concludes that using their convention, the simultaneity of a rotating platform turns out to be the same as that of the inertial frame in which the platform is only rotating and not translating.

I don't think that is very controversial. If we make the path of the traveler (he) a polygon, and put the stay-home (she) at the center of the polygon, then he would say that she is aging at the slower rate (factor of 1/gamma) than himself only during the straight parts of the path, and then as soon as he changes direction at the corner of the polygon, he would consider her to be older than himself by a factor of gamma, because of relativity of simultaneity.

As the number of sides of the polygon increases without bound, the number of times he finds her to be older than himself grows greater, to the point where eventually he finds her to be older than himself at almost all times. In the limit, the path becomes indistinguishable from a circle, and so it seems he could say that she is older than him for the whole journey.

That is because his direction changes have to be taken into consideration. Relativity does not say that only motion in one direction results in time dilation. But it does says that by convention the axes of the two systems are oriented with the x & x' axes in the direction of relative motion. So every time he turns a corner, the orientation of the axes needs to be re-worked, and because she is located at the center of the polygon, he and she always end up with practically the same x & x' coordinates (for a polygon with a sufficiently large number of sides). But the accumulation of the times when she got older than him by a factor of gamma have to be retained no matter how many times the axes are re-worked.

You describe it on your website. Why, are you unfamiliar with it now?

I'm not. But I've been corresponding with someone who disagrees with my interpretation of how Minguizzi was using his imaginary twin to define the current age of the home twin, according to the traveling twin. I was hoping to get some other opinions on that issue.

But I've been corresponding with someone who disagrees with my interpretation of how Minguizzi was using his imaginary twin to define the current age of the home twin, according to the traveling twin.
What you write on your site (but not your subsequent disagreement with it) seems to make sense, but Minguizzi's method seems to require exactly one arbitrary anchor event rather than an arbitrary reference frame. In most practical situations, that anchor event doesn't exist, or there are multiple events each resulting in different answers.
The method objectively orders only events within the light cones of the anchor event, and thus isn't useful in the general case.

I'm not sure how you're interpreting the method. As I said, I disagree with your analysis of it on your web page. It doesn't violate any principle of causality as far as I can tell.

I'm not sure how you're interpreting the method. As I said, I disagree with your analysis of it on your web page. It doesn't violate any principle of causality as far as I can tell.

My understanding of what Minguizzi said is that when the imaginary twin is momentarily co-located with the traveler, the home twin has the same age as the imaginary twin at that instant. So that defines Minguizzi's simultaneity at a distance.

Here's a specific numerical example:

Take the case where gamma = 2.0, corresponding to v_1 = 0.866 ly/y. And take the case where the traveling twin is 20 years old at the instant in his life immediately before he instantaneously reverses his velocity. Suppose the imaginary twin reaches him at that instant. What is the imaginary twin's age then, and how old is the home twin then (according to the traveling twin)?

What is your answer to those two questions?

My understanding of what Minguizzi said is that when the imaginary twin is momentarily co-located with the traveler, the home twin has the same age as the imaginary twin at that instant. So that defines Minguizzi's simultaneity at a distance.
Right. But that only orders certain events, not all of them like other methods do.

Take the case where gamma = 2.0, corresponding to v_1 = 0.866 ly/y. And take the case where the traveling twin is 20 years old at the instant in his life immediately before he instantaneously reverses his velocity. Suppose the imaginary twin reaches him at that instant. What is the imaginary twin's age then, and how old is the home twin then (according to the traveling twin)?
What is your answer to those two questions?
A quiz now eh? The imaginary twin has been with him the whole time in that case since he's been inertial since the 'anchor' event (my term, not his). All 3 twins are 20 years old at that event, according to Minguizzi's method, and thus according to the travelling twin if he's using that method.

All 3 twins are 20 years old at that event, according to Minguizzi's method, and thus according to the travelling twin if he's using that method.

That's exactly what I got. But note that that result violates the principle of causality, because the traveler COULD choose NOT to change his velocity after that instant. In that latter case, the traveler SHOULD conclude that the home twin is ageing half as fast as he himself is. So Minguizzi's solution violates causality because he says her ageing depends on what happens in the future.

Also, I'm told that Minguizzi now says that his paper says NOTHING about simultaneity at a distance.

That's exactly what I got. But note that that result violates the principle of causality, because the traveler COULD choose NOT to change his velocity after that instant.
The result has nothing to do with what the traveler plans to do in future events. He'll be older in all those events (according to this method) regardless of if he turns around or not.

I don't see any cause and effect going on at all in this scenario, so I have no idea how you think the principle comes into play, let alone gets violated by this.

In that latter case, the traveler SHOULD conclude that the home twin is ageing half as fast as he himself is.
Not if he's using Minguizzi's method.
So Minguizzi's solution violates causality because he says her ageing depends on what happens in the future.
Nonsense. It depends on where he is at that event, and not at all on his future actions. It depends only on the two events, and not on what path through spacetime is taken, what velocity anybody is going, or what reference frame is used. It is a method using a reference event instead of a reference frame.

Also, I'm told that Minguizzi now says that his paper says NOTHING about simultaneity at a distance.
I've already noted that it only orders events within the light cone of the reference event (what I call the anchor event), which is when all 3 twins are born in this case. Those events always have time-like separation and thus cannot be simultaneous with the reference event. The method indeed says nothing about the simultaneity of events separated from the reference event in a space-like manner.

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Suppose the two twins are perpetually inertial. Then each says the other is ageing more slowly. So the traveler (he) says that the home twin (she) is 5 when he is 10, and that she is 10 when he is 20, and that she is 20 when he is 40, etc. This is true regardless of which simultaneity method is being assumed (including Minguizzi's), because there is no acceleration involved in this scenario. The time dilation equation rules in this scenario. So Minguizzi says that, in THIS scenario, when he is 10, she is 5.

BUT, if he decides instead to reverse his velocity when he is 20, then Minguizzi then says that she is ageing at the SAME rate as he is, during the ENTIRE outbound leg. Minguizzi now says she is 10 when he is 10. So in Minguizzi's method, her age when he is 10 depends on what he decides to do in the future, when he is 20. That violates the principle of causality ... causality says that an effect can't precede its cause.

Suppose the two twins are perpetually inertial. Then each says the other is ageing more slowly.
If you're going to start a thread about Minguizzi's method, then I have to assume you are using that method unless you state otherwise.
So no, both twins, if inertial since birth, have the same age under that method.

So the traveler (he) says that the home twin (she) is 5 when he is 10, and that she is 10 when he is 20, and that she is 20 when he is 40, etc. This is true regardless of which simultaneity method is being assumed (including Minguizzi's), because there is no acceleration involved in this scenario.
This is not true under Minguizzi's method. We both computed it above as 20 years, and now you're saying something else.

The time dilation equation rules in this scenario. So Minguizzi says that, in THIS scenario, when he is 10, she is 5.
You don't understand his method then. You're referencing an inertial frame in making that calculation, and Minguizzi's method doesn't reference them at all. He referenes an event and the temporal distance from that event to any event within the causal cones of the reference events. That is a frame independent calculation. It has nothing to do with observers or twins, but twins are often used since their definition implies an obvious reference event, their mutual and presumed simultaneious birth. I'll bet mom loved squeezing them both out side-by-side like that.

BUT, if he decides instead to reverse his velocity when he is 20, then Minguizzi then says that she is ageing at the SAME rate as he is, during the ENTIRE outbound leg. Minguizzi now says she is 10 when he is 10.[/QUOTE]Correct, but you're contradicting what you said just above when you say Minguizzi's method computes her age as 5 when he's 10. The latter figure (5) is using a different method, so your assertion about this being true regardless of method used is demonstrably wrong.

So in Minguizzi's method, her age when he is 10 depends on what he decides to do in the future, when he is 20.
There is nothing in his method that takes future intent into consideration. So this statement is wrong as well. The paragraph above gives some wrong statements, and you somehow conclude from those wrong statements that Minguizzi's method is dependent on future intent or future action from when he is 10.

That violates the principle of causality ... causality says that an effect can't precede its cause.
I suppose it would if your argument was valid, but it is full of errors.

If you're going to start a thread about Minguizzi's method, then I have to assume you are using that method unless you state otherwise.

Yes, I'm exclusively talking about that method.

So no, both twins, if inertial since birth, have the same age under that method.

No. That's true in the Minguzzi method ONLY if the traveler changes his velocity at some point. In the above scenario, he doesn't.

This is not true under Minguizzi's method. We both computed it above as 20 years, and now you're saying something else.

We both computed that, for the scenario when he changes his velocity during the trip. The above is a different scenario ... there is NEVER any velocity change in the revised scenario. ALL simultaneity methods use the time dilation equation when there is no velocity change during the traveler's entire trip.

No. That's true in the Minguzzi method ONLY if the traveler changes his velocity at some point. In the above scenario, he doesn't.
We both agreed in the computation of 20 above, so you're contradicting yourself now. For this situation, said imaginary twin is present with the traveling twin the entire time, and that means all 3 twins are the same age. His method doesn't work differently if anybody has accelerated. The past worldline of the traveling twin is not in any way figured into the computation.

We both computed that, for the scenario when he changes his velocity during the trip.
He had not changed his velocity. This is the part you're getting wrong then. You said he's doing the computation just before changing velocity, so he's inertial up to that point.

The above is a different scenario
It is eventually, but at the time of the computation, the two scenarios are still identical, so the computed age is the same. The twins are the same age for inertial twins, but it doesn't stay the same.

There is an inconsistency in the method, but you're not finding it. You're insisting on using a different method, and then asserting that it doesn't matter despite the fact that you've pointed out that the two methods compute different values for the same situation.

So in Minguizzi's method, her age when he is 10 depends on what he decides to do in the future, when he is 20. That violates the principle of causality ... causality says that an effect can't precede its cause.
I take my answer back. This would not violate the PoC even if the first statement was true, which it isn't.
On a second note, the PoC has never been proven, although I personally have a preference for it.

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We're now GUESSING what Minguzzi would say, if asked whether his instructions should be followed even in the case of the traveling twin NEVER changing his velocity. (His "instructions" being: to use the imaginary twin's age when"it" is co-located with the traveler as the current age of the home twin (according to the traveler)).

The problem right now with Minguzzi is that he now says that his paper has NOTHING to do with simultaneity at a distance! That's obviously nonsense, because the imaginary twin serves no purpose other than defining a method of determining simultaneity at a distance.

Feel free to ask him about the no-acceleration scenario ... his email address is given in that arXiv paper. But he's never answered my emails. Someone else that I've been corresponding with HAS gotten recent responses from him, so you might have better luck with him than I've had.

We're now GUESSING what Minguzzi would say, if asked whether his instructions should be followed even in the case of the traveling twin NEVER changing his velocity. (His "instructions" being: to use the imaginary twin's age when"it" is co-located with the traveler as the current age of the home twin (according to the traveler)).
You're really going with this line?
You quoted the instructions. There is no 'if' in there. At any point in the trip, use the imaginary twin's age when"it" is co-located with the traveler as the current age of the other twin. That BTW makes both twins the same age at all times, regardless of what they do, and regardless of if they meet again once or many times, and this is Minguizzi's resolution of what he apparently found to be paradoxical.
The problem right now with Minguzzi is that he now says that his paper has NOTHING to do with simultaneity at a distance!
Well, it does, I mean the twins are always simultaneously the same age, even when they're 'at a distance'. The problem is that it doesn't order all events, so it only tells you the age of an event with an imaginary spacetime interval relative to the reference event. It is mute for events with real intervals. It is impossible for any twin to be present at one, so it doesn't bother the twins scenario.

At any point in the trip, use the imaginary twin's age when"it" is co-located with the traveler as the current age of the other twin. That BTW makes both twins the same age at all times, [...]

That last line is incorrect. All three of them ARE the same age on the outbound leg (before the velocity change), but after that, the traveler and the home twin AREN'T the same age (she is older than him after that). On the outbound leg, there is only one imaginary twin, and "it" is always co-located with the traveling twin. But after that, the traveler and the imaginary twin who passes him when he's asking his question AREN'T the same age when they are momentarily co-located. After the velocity change, there is a DIFFERENT imaginary twin for each instant in the traveler's life. All of the imaginary twins are zero years old when they leave the home twin (when she is zero years old).

What's REALLY funny about this conversation is that Minguzzi (if he were here now) would tell us that his method has NOTHING to do with imaginary twins (in spite of what's in his paper), and NOTHING to do with simultaneity at a distance (in spite of what's in his paper)! What a bizarre situation.

I'm going to TRY to attach a jpeg to this message. OK it worked! That is the age correspondence diagram (ACD) that my simultaneity method produces. By comparison, the CMIF ACD would have the same first segment that mine has, but then would have a VERTICAL line segment going upward when he is 20, and intersecting the extension of my third line segment (of slope 1/2). The Dolby and Gull ACD would look somewhat like mine, except that it would begin the steep middle line segment WELL BEFORE the velocity change. And the Minguzzi ACD would have a slope of 1.0 for the first segment (until he is 20), and then a curved line going upward to the right, first with an increasing slope, and then with a decreasing slope. Note that the ACD diagram shows her age versus his age, ACCORDING TO HIM. Her age versus his age, ACCORDING TO HER, is just a single straight line, going upward to the right, with a constant slope of 2.0.

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At any point in the trip, use the imaginary twin's age when"it" is co-located with the traveler as the current age of the other twin. That BTW makes both twins the same age at all times, regardless of what they do, and regardless of if they meet again once or many times, and this is Minguizzi's resolution of what he apparently found to be paradoxical.

Are you saying that Minguzzi uses an imaginary twin co-moving with the traveling twin, and from that concludes that the resolution to the twin 'paradox' is that they are both the same age upon being reunited?

By the way, here is the link I found after Googling Mike_Fontenot's 0411233v1 reference:
https://arxiv.org/abs/physics/0411233

I don't see where any imaginary twins are mentioned, and I don't understand anything the paper is trying to say. To me it looks like someone pulling every mathematical trick in the book to try to get something published. But what do I know.