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?
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.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'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.
Right. But that only orders certain events, not all of them like other methods do.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.
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.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?
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.
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.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.
Not if he's using Minguizzi's method.In that latter case, the traveler SHOULD conclude that the home twin is ageing half as fast as he himself is.
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.So Minguizzi's solution violates causality because he says her ageing depends on what happens in the future.
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.Also, I'm told that Minguizzi now says that his paper says NOTHING about simultaneity at a distance.
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.Suppose the two twins are perpetually inertial. Then each says the other is ageing more slowly.
This is not true under Minguizzi's method. We both computed it above as 20 years, and now you're saying something else.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.
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.The time dilation equation rules in this scenario. So Minguizzi says that, in THIS scenario, when he is 10, she is 5.
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.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.
I suppose it would if your argument was valid, but it is full of errors.That violates the principle of causality ... causality says that an effect can't precede its cause.
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.
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 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.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.
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.We both computed that, for the scenario when he changes his velocity during the trip.
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.The above is a different scenario
I take my answer back. This would not violate the PoC even if the first statement was true, which it isn't.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.
You're really going with this line?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)).
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.The problem right now with Minguzzi is that he now says that his paper has NOTHING to do with simultaneity at a distance!
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, [...]
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.