According to the CMIF (Co-Moving-Inertial Frames) simultaneity method,
an observer (he) who accelerates in the direction away from a distant
person (she) will conclude that she rapidly gets YOUNGER during his
acceleration. But I think I may have found a counterexample that shows
that doesn't happen.

It is well-known that two stationary clocks at different positions in a
gravitational field will run at different rates. The clock that is
closer to the source of the gravitational field will run slower than the
clock that is farther from the source of the field.

Because of the equivalence principle, it is also true that if two clocks
that are separated by a fixed distance "d" ly are both accelerated with
a constant equal acceleration of "A" ly/y/y, the trailing clock runs
slower than the leading clock, by the factor exp(Ad).

So consider the following scenario:

At some instant, the perpetually-inertial "home twin" (she) is 20 years
old, and is holding a display that always shows her current age. Facing
her is the "helper friend" (the "HF") of an observer (he) who is "d" ly
away to her right. Both the HF and he are also 20 years old, and are
stationary wrt her at that instant. Like her, he and the HF are each
holding a display that always shows their current ages.

Now, suppose that he and his helper then both start accelerating at a
constant "A" ly/y/y toward the right. He knows that his helper friend
(the HF) is then ageing at a constant rate that is slower than his own
rate of ageing, by the factor exp(Ad).

An instant later, his display shows the time 20 + epsilon_1, where
epsilon_1 is a very small positive number. He knows that HF's display
shows the time 20 + epsilon_2, where epsilon_2 = epsilon_1 / exp(Ad).
She can still see HF's display (because HF has only moved an
infinitesimal distance away from her, to her right). She will see that
HF's display reads 20 + epsilon_1 / exp(Ad). And likewise, HF can still
see her display. What does HF see on her display? Does HF see that she
is now slightly younger than 20? No! It would clearly be absurd for
someone essentially co-located with her to see her get younger. HF would
see her display reporting that she was some very small amount epsilon_3
OLDER that she was at the instant before the acceleration. HF then sends
a message to him, telling him that she was 20 + epsilon_3 right then.
When he receives that message, he then knows that her current age, when
he was 20 + epsilon_1, was 20 + epsilon_3. So he KNOWS that she didn't
get younger when he accelerated away from her. That contradicts what
CMIF simultaneity says.

On Sunday, June 13, 2021 at 7:23:10 AM UTC-7, Mike_Fontenot wrote:
> According to the CMIF (Co-Moving-Inertial Frames) simultaneity method,
> an observer (he) who accelerates in the direction away from a distant
> person (she) will conclude that she rapidly gets YOUNGER during his
> acceleration.

No, that's a garbled and inaccurate statement. First, special relativity is not a subjectivist theory, so it is not about different people "concluding" different things. It provides a single coherent representation of the objective facts, which can, of course, be described differently in terms of different systems of coordinates. Second, no one ever "gets younger" (and no one ever "concludes" that anyone "gets younger"). What you are trying to express is that, based on the mapping between the events on the worldlines of two separate objects provided by the slices of constant t of the sequence of inertia-based coordinate systems in which one of the objects is instantaneously at rest, we can have can have negative dtau1/dtau2 for sufficiently high acceleration of that object. This does not imply that either object is "getting younger", it just represents a characteristic of the mapping.

> I think I may have found a counterexample that shows that doesn't happen.

That depends on what "that" you are referring to. If you are referring to someone "concluding" that someone else is "getting younger", then of course that doesn't happen. On the other hand, if you are claiming that for sufficiently high acceleration and separation we do not have negative dtau1/dtau2 for the mapping given by the sequence of temporal foliations of the instantaneously co-moving inertial coordinate systems, then you are mistaken. It is simple algebra, which you can learn about in any good book on relativity.

> Because of the equivalence principle, it is also true that if two clocks
> that are separated by a fixed distance ... are both accelerated

You need to distinguish between a fixed distance in terms of some system of inertial coordinates or a fixed distance in terms of the momentarily co-moving system of inertial coordinates of one or the other object. In other words, you need to specify if you are talking about Born rigid motion - which can't be applied to arbitrarily far separated entities, or to accelerating objects at fixed coordinate distance, which then introduces variations in the "proper" distance.

> with a constant equal acceleration...

You need to specify whether it is constant coordinate acceleration or constant proper acceleration. Whatever you specify, you cannot defeat simple algebra. There are infinitely many possible mappings between the events of two separate worldlines, and some of those mappings have dtau1/dtau2 negative. You cannot disprove this, because it is trivially true, but (again) it does not signify that anyone is "getting younger".

On 6/13/21 11:55 AM, Arthur Adler wrote:
> On Sunday, June 13, 2021 at 7:23:10 AM UTC-7, Mike_Fontenot wrote:
>> According to the CMIF (Co-Moving-Inertial Frames) simultaneity
>> method, an observer (he) who accelerates in the direction away
>> from a distant person (she) will conclude that she rapidly gets
>> YOUNGER during his acceleration.
>
> No, that's a garbled and inaccurate statement. First, special
> relativity is not a subjectivist theory, so it is not about different
> people "concluding" different things. It provides a single coherent
> representation of the objective facts, which can, of course, be
> described differently in terms of different systems of coordinates.
> Second, no one ever "gets younger" (and no one ever "concludes" that
> anyone "gets younger"). What you are trying to express is that,
> based on the mapping between the events on the worldlines of two
> separate objects provided by the slices of constant t of the sequence
> of inertia-based coordinate systems in which one of the objects is
> instantaneously at rest, we can have can have negative dtau1/dtau2
> for sufficiently high acceleration of that object. This does not
> imply that either object is "getting younger", it just represents a
> characteristic of the mapping.

Yes. I had not thought of it in precisely those terms, but this is
clearly correct.

> [... requests that Fontenot be more precise]

Yes. Lack of precision in thought and word is a common problem around here.

Tom Roberrs

On 6/13/21 9:23 AM, Mike Fontenot wrote:
> It is well-known that two stationary clocks at different positions
> in a gravitational field will run at different rates.

No it is not! That is a claim from an oversimplified pop-sci approach to
GR that is not actually correct. In GR, clocks ALWAYS run at their usual
rate [#], but when COMPARED VIA SIGNALS, the way those signals are
measured makes them compare with different rates. The clocks are not
affected in any way by their motion or their position in a gravitational
field.

[#] I.e. advancing 1 second for every second of their
elapsed proper time. IOW: the time displayed by a clock
(any clock anywhere or anywhen) is modeled by the integral
of the metric over its trajectory through spacetime.

Modern physics is both complicated and subtle; precision in thought and
word is required. Such wishy-washy and incorrect claims just serve to
confuse you and your readers.

Tom Roberts

On 6/13/21 8:23 AM, Mike Fontenot wrote:
>
> So consider the following scenario:
>
> At some instant, the perpetually-inertial "home twin" (she) is 20 years
> old, and is holding a display that always shows her current age. Facing
> her is the "helper friend" (the "HF") of an observer (he) who is "d" ly
> away to her right. Both the HF and he are also 20 years old, and are
> stationary wrt her at that instant. Like her, he and the HF are each
> holding a display that always shows their current ages.
>
> Now, suppose that he and his helper then both start accelerating at a
> constant "A" ly/y/y toward the right. He knows that his helper friend
> (the HF) is then ageing at a constant rate that is slower than his own
> rate of ageing, by the factor exp(Ad).
>
> An instant later, his display shows the time 20 + epsilon_1, where
> epsilon_1 is a very small positive number. He knows that HF's display
> shows the time 20 + epsilon_2, where epsilon_2 = epsilon_1 / exp(Ad).
> She can still see HF's display (because HF has only moved an
> infinitesimal distance away from her, to her right). She will see that
> HF's display reads 20 + epsilon_1 / exp(Ad). And likewise, HF can still
> see her display. What does HF see on her display? Does HF see that she
> is now slightly younger than 20? No! It would clearly be absurd for
> someone essentially co-located with her to see her get younger. HF would
> see her display reporting that she was some very small amount epsilon_3
> OLDER that she was at the instant before the acceleration. HF then sends
> a message to him, telling him that she was 20 + epsilon_3 right then.
> When he receives that message, he then knows that her current age, when
> he was 20 + epsilon_1, was 20 + epsilon_3. So he KNOWS that she didn't
> get younger when he accelerated away from her. That contradicts what
> CMIF simultaneity says.
>

In the above, I asked

"What does HF see on her display?".

And I answered

"HF would see her display reporting that she was some very small
amount epsilon_3 OLDER that she was at the instant before the acceleration."

Since the above argument makes use of very small (unspecified)
quantities, it could be argued that time delays due to the speed of
light might also need to be taken into account when describing what the
HF sees on her display.
But I think any such concerns can be addressed by pointing out that the
separation "d" between him and her can be made arbitrarily large, and
CMIF simultaneity says that the amount of negative ageing that occurs is
proportional to their separation. Since the errors involved due to the
finite speed of light between her and the HF are independent of the
distance "d", those errors become negligible for sufficiently large "d".

On Sunday, June 13, 2021 at 7:23:10 AM UTC-7, Mike_Fontenot wrote:
> According to the CMIF (Co-Moving-Inertial Frames) simultaneity method,
> an observer (he) who accelerates in the direction away from a distant
> person (she) will conclude that she rapidly gets YOUNGER during his
> acceleration. But I think I may have found a counterexample that shows
> that doesn't happen.

In relativity all considerations of this type are certain properties of
the chosen accounting method. Physically, according to the relativistic
model, there is no such thing as simultaneity at a distance.

--
Jan

On Tuesday, 15 June 2021 at 07:14:20 UTC+2, JanPB wrote:
> On Sunday, June 13, 2021 at 7:23:10 AM UTC-7, Mike_Fontenot wrote:
> > According to the CMIF (Co-Moving-Inertial Frames) simultaneity method,
> > an observer (he) who accelerates in the direction away from a distant
> > person (she) will conclude that she rapidly gets YOUNGER during his
> > acceleration. But I think I may have found a counterexample that shows
> > that doesn't happen.
> In relativity all considerations of this type are certain properties of
> the chosen accounting method. Physically, according to the relativistic
> model, there is no such thing as simultaneity at a distance.

For sure, your Shit has been completely lost in its own mumble
and has no ability of providung basic tools to model anything.

On 6/14/21 11:14 PM, JanPB wrote:
> On Sunday, June 13, 2021 at 7:23:10 AM UTC-7, Mike_Fontenot wrote:
>> According to the CMIF (Co-Moving-Inertial Frames) simultaneity method,
>> an observer (he) who accelerates in the direction away from a distant
>> person (she) will conclude that she rapidly gets YOUNGER during his
>> acceleration. But I think I may have found a counterexample that shows
>> that doesn't happen.
>
> In relativity all considerations of this type are certain properties of
> the chosen accounting method. Physically, according to the relativistic
> model, there is no such thing as simultaneity at a distance.
>
> --
> Jan
>

Simultaneity at a distance is certainly well defined in the case of a
perpetually-inertial observer. Einstein showed very clearly how an
array of clocks can be synchronized in that case, and those clocks then
clearly specify simultaneity in that perpetually-inertial reference
frame, and the question "How old is that distant person, right now,
according to the perpetually-inertial person" has a definite, and
meaningful, answer.

When the observer ISN'T perpetually inertial, he still can ask the same
question, and I think he still deserves a meaningful answer. And I
think there IS a correct answer. But what IS that correct answer?
There isn't universal agreement about that. Some do say that
simultaneity at a distance is meaningless for an accelerating observer.
Others say that the CMIF simultaneity method gives the correct answer.
But CMIF simultaneity says that the distant person will get YOUNGER if
the accelerating observer accelerates in the direction AWAY from the
distant person. The proof that I've recently posted says that that
negative ageing DOESN'T occur. If my proof is valid, then the CMIF
simultaneity method isn't correct.

On Wednesday, June 16, 2021 at 8:55:00 AM UTC-7, Mike_Fontenot wrote:
> Simultaneity at a distance is certainly well defined in the case of a
> perpetually-inertial observer.

Correction: Inertial simultaneity is well-defined for any given (local) system of inertial coordinates, but simultaneity need not be based on inertial isotropy for a given frame, it can be based on other physical considerations, so there is no unique simultaneity, i.e., no unique mapping between the events and proper times of two separate objects.

> Einstein showed very clearly how an array of clocks can be synchronized in that case...

He described more than one method for synchronizing clocks, and explained the physical meaning and significance of each of the methods. You unfortunately just focused on one of them, and concluded that it was the only possible (or physically meaningful) one. You are simply mistaken, and you should have read more carefully.

> When the observer ISN'T perpetually inertial, he still can ask the same
> question, and I think he still deserves a meaningful answer.

Again, there are many meaningful answers that one can give. For example, at every location in the universe there is a cosmological time, which is the time that would appear on an ideal clock that has been continuously at rest in terms of the local inertial coordinates in which the CMBR is maximally isotropic at that location, and that was set to zero at the energy-matter decoupling event (initiation of the CMBR). This gives a well-defined temporal foliation that every object could use in order to correlate their events with the events of some distant object. You could label this the universal now.

Of course, this cosmological measure of time may not appeal to you (Mike), and you may prefer a more parochial and fragmented convention (non-transitive, non-reflexive, etc.), but that's just your preference. You cannot deny that the cosmological time is a perfectly meaningful and indeed universal way of defining a common time coordinate for all objects, and it is transitive and reflexive. To prove that you have found "the" unique and true sense of "now", different from cosmological time, you will need to prove that cosmological time cannot be regarded as a viable and physically meaningful measure of time. You obviously cannot prove that, because it's not true. Do you see the problem?

> Some do say that simultaneity at a distance is meaningless for an accelerating observer.

No competent scientist says that. What we say is that simultaneity means "at the same value of the time coordinate", and since there are infinitely many different physically meaningful coordinate systems, there is no unique simultaneity, i.e., no unique mapping between the events of two separate objects. This is true whether they are accelerating or not.

> Others say that the CMIF simultaneity method gives the correct answer.

No competent scientist says that. A coordinate system comprised of the time slices of successive inertial coordinate systems in which a given object is successively at rest is a peculiarity that clearly does not inherit the useful properties of the individual inertial coordinate systems, not even providing a one-to-one mapping between events and coordinates.

> But CMIF simultaneity says that the distant person will get YOUNGER if
> the accelerating observer accelerates in the direction AWAY from the
> distant person.

No it does not. Your mistake has been explained to you many times before. Remember?

> The proof that I've recently posted says that that negative ageing DOESN'T occur.

Well, no object "gets younger", but it is nevertheless true that for sufficiently great acceleration we have negative dtau1/dtau2, so you cannot disprove that we get negative values of the derivative using the time slices of successive inertial coordinate systems.

> If my proof is valid, then the CMIF simultaneity method isn't correct.

That sentence is overflowing with false premises, misunderstandings, and confusions. First, it is well known that co-moving inertial slices don't constitute a very useful, let alone uniquely correct, system of coordinates. Second, you cannot prove that dtau1/dtau2 is never negative, because it manifestly is negative for sufficient acceleration. Third, the fact that this derivative can be negative does not imply that anyone gets younger. Fourth... well, suffice it to say that you are just totally confused.

On 6/16/21 3:27 PM, Arthur Adler wrote:
> On Wednesday, June 16, 2021 at 8:55:00 AM UTC-7, Mike_Fontenot wrote:
>>
>> But CMIF simultaneity says that the distant person will get YOUNGER if
>> the accelerating observer accelerates in the direction AWAY from the
>> distant person.
>
> No it does not. Your mistake has been explained to you many times before. Remember?
>

The famous physicist Brian Greene disagrees with you:

Skip to the 23:15 point on this link:

https://www.pbs.org/wgbh/nova/video/the-fabric-of-the-cosmos-the-illusion-of-time/

On Wednesday, June 16, 2021 at 3:26:52 PM UTC-7, Mike_Fontenot wrote:
> >> But CMIF simultaneity says that the distant person will get YOUNGER if
> >> the accelerating observer accelerates in the direction AWAY from the
> >> distant person.
> >
> > No it does not. Your mistake has been explained to you many times before. Remember?
> >
> The famous physicist Brian Greene disagrees with you:
> Skip to the 23:15 point on this link:
> https://www.pbs.org/wgbh/nova/video/the-fabric-of-the-cosmos-the-illusion-of-time/

As explained to you before, with verbatim quotes, that video does not say what you claim it says. It says the slice of [inertial] simultaneity swings back, but this does not signify (and the video does not say) that anyone ever "gets younger". One of the pre-requisites for scientific study is honesty. This includes not willfully mis-quoting people. Appeals to authority are never a good idea, and they are particularly bad when your authority actually doesn't say what you claim they said.

Another pre-requisite for scientific thought is to actually engage with criticism of your ideas. I invite you to actually respond to the substantive criticisms below:

> Simultaneity at a distance is certainly well defined in the case of a
> perpetually-inertial observer.

Correction: Inertial simultaneity is well-defined for any given (local) system of inertial coordinates, but simultaneity need not be based on inertial isotropy for a given frame, it can be based on other physical considerations, so there's no unique simultaneity, i.e., no unique mapping between the events and proper times of two separate objects.

> Einstein showed very clearly how an array of clocks can be synchronized in that case...

He described more than one method for synchronizing clocks, and explained the physical meaning and significance of each method. You unfortunately just focused on one of them, and concluded that it was the only possible (or physically meaningful) one. You are simply mistaken, and you should have read more carefully.

> When the observer ISN'T perpetually inertial, he still can ask the same
> question, and I think he still deserves a meaningful answer.

Again, there are many meaningful answers that one can give. For example, at every location in the universe there is a cosmological time, which is the time that would appear on an ideal clock that has been continuously at rest in terms of the local inertial coordinates in which the CMBR is maximally isotropic at that location, and that was set to zero at the energy-matter decoupling event (initiation of the CMBR). This gives a well-defined temporal foliation that every object could use to correlate their events with the events of some distant object. You could label this the universal now.

Of course, this cosmological measure of time may not appeal to you (Mike), and you may prefer a more parochial and fragmented convention -- even at the expense of transitivity and reflexivity -- but that's just your preference. You cannot deny that the cosmological time is a perfectly meaningful and indeed universal way of defining a common time coordinate for all objects, and it is transitive and reflexive. To prove that you have found "the" unique and true sense of "now", different from cosmological time, you will need to prove that cosmological time cannot be regarded as a viable and physically meaningful measure of time. You obviously cannot prove that, because it's not true. Do you see the problem?

> Some do say that simultaneity at a distance is meaningless for an accelerating observer.

No competent scientist says that. We say simultaneity means "at the same value of the time coordinate", and since there are infinitely many different physically meaningful coordinate systems, there is no unique simultaneity, i.e., no unique mapping between the events of two separate objects. This is true whether they are accelerating or not.

> Others say that the CMIF simultaneity method gives the correct answer.

No competent scientist says that. A coordinate system comprised of the time slices of successive inertial coordinate systems, in which a given object is successively at rest, is a peculiarity that clearly does not inherit the useful properties of the individual inertial coordinate systems, and does not even provide a one-to-one mapping between events and coordinates.

> But CMIF simultaneity says that the distant person will get YOUNGER if
> the accelerating observer accelerates in the direction AWAY from the
> distant person.

No it doesn't. Your mistake has been explained to you many times before. Remember? Abstractly associating different sequences of events does not cause any physical object to "get younger".

> The proof that I've recently posted says that that negative ageing DOESN'T occur.

Well, no object "gets younger", but it's nevertheless true that for sufficiently great acceleration we have negative dtau1/dtau2, so you cannot disprove that we get negative values of the derivative using the time slices of successive inertial coordinate systems.

> If my proof is valid, then the CMIF simultaneity method isn't correct.

That sentence is overflowing with false premises, misunderstandings, and confusions. First, it is well known that co-moving inertial slices don't constitute a very useful, let alone uniquely correct, system of coordinates. Second, you cannot prove that dtau1/dtau2 is never negative, because it manifestly is negative for sufficient acceleration. Third, the fact that this derivative can be negative does not imply that anyone gets younger. Fourth... well, suffice it to say that you are just totally confused.

On 6/16/21 10:54 AM, Mike Fontenot wrote:
> Simultaneity at a distance is certainly well defined in the case of a
> perpetually-inertial observer. [...]

Yes, if that inertial observer chooses to use the definition of their
rest frame. They could, of course, choose otherwise....

> When the observer ISN'T perpetually inertial, he still can ask ["how
> old is that distant person"], and I think he still deserves a
> meaningful answer.

This is just you attempting to impose your personal hopes and dreams
onto the universe. THAT'S HOPELESS.

> [...] CMIF simultaneity says that the distant person will get
> YOUNGER if the accelerating observer accelerates in the direction
> AWAY from the distant person.

No. Not even close.

You REALLY need to learn that physics is complicated and subtle, and
requires precision in thought and word.

What "CMIF simultaneity" actually says is that as the observer
accelerates away from the distant person, the successive 3-surfaces
labeled by increasing proper time of the observer intersect the
worldline of the distant person at successively earlier proper times of
that worldline. This says NOTHING AT ALL about how that distant person
is ageing, and indeed we know that the advancing proper time along their
worldline is how they are ageing (i.e. their worldline is timelike and
future directed).

So yes, that distant person never experiences "negative ageing", even
though the accelerated observer's "CMIF simultaneity" selects
successively earlier points along their worldline. The previous
paragraph also shows that the details of the distant person's worldline
matter -- that paragraph shared your implicit assumption that the
distant person is moving inertially; if that person (worldline) is
not inertial, a much more complicated analysis is required.

Tom Roberts

On Wednesday, June 16, 2021 at 8:55:00 AM UTC-7, Mike_Fontenot wrote:
> On 6/14/21 11:14 PM, JanPB wrote:
> > On Sunday, June 13, 2021 at 7:23:10 AM UTC-7, Mike_Fontenot wrote:
> >> According to the CMIF (Co-Moving-Inertial Frames) simultaneity method,
> >> an observer (he) who accelerates in the direction away from a distant
> >> person (she) will conclude that she rapidly gets YOUNGER during his
> >> acceleration. But I think I may have found a counterexample that shows
> >> that doesn't happen.
> >
> > In relativity all considerations of this type are certain properties of
> > the chosen accounting method. Physically, according to the relativistic
> > model, there is no such thing as simultaneity at a distance.
> >
> > --
> > Jan
> >
> Simultaneity at a distance is certainly well defined in the case of a
> perpetually-inertial observer.

Only as a coordinate-accounting method designed to mimic
Newtonian mechanics in the slow speed limit. Not in any
absolute sense.

> Einstein showed very clearly how an
> array of clocks can be synchronized in that case,

Sure

> and those clocks then
> clearly specify simultaneity in that perpetually-inertial reference
> frame, and the question "How old is that distant person, right now,
> according to the perpetually-inertial person" has a definite, and
> meaningful, answer.

Only in the sense of a certain man-made accounting method designed
to mimic everyday experience (i.e., Newtonian mechanics).

There is no intrinsic meaning to simultaneity (at a distance) in relativity.

--
Jan

On 6/16/21 4:44 PM, Arthur Adler wrote:
>
> As explained to you before, with verbatim quotes, that video does not say what you claim it says. It says the slice of [inertial] simultaneity swings back, but this does not signify (and the video does not say) that anyone ever "gets younger".
>

A distant person gets younger, ACCORDING to the observer who accelerates
in the direction away from the distant person. That's what Brian Greene
and I believe.

On Thursday, June 17, 2021 at 8:20:51 AM UTC-7, Mike_Fontenot wrote:
> > As explained to you before, with verbatim quotes, that video does not say what you claim it says. It says the slice of [inertial] simultaneity swings back, but this does not signify (and the video does not say) that anyone ever "gets younger".
> >
> A distant person gets younger, ACCORDING to the observer who accelerates
> in the direction away from the distant person. That's what Brian Greene
> and I believe.

Nope, you need to stop lying. Brian does not believe (and his popularizing video does not say) that anyone "gets younger" according to anyone else. Appeals to "authority" are never a good idea, and they are especially bad when your "authority" doesn't actually agree with you, as in this case. He makes the bland statement that the slices of [inertial] simultaneity swing backwards and forwards when the bicycle changes speed, intersecting with earlier or later times on earth. He does not say that anyone "gets younger".

Just as bad as your inability to make that distinction and your falsified appeals to "authority" is your persistent refusal to engage with any criticism of your ideas, which is a pre-requisite for scientific thought. I invite you to actually respond to the substantive criticisms below:

> Simultaneity at a distance is certainly well defined in the case of a
> perpetually-inertial observer.

Correction: Inertial simultaneity is well-defined for any given (local) system of inertial coordinates, but simultaneity need not be based on inertial isotropy for a given frame, it can be based on other physical considerations, so there's no unique simultaneity, i.e., no unique mapping between the events and proper times of two separate objects.

> Einstein showed very clearly how an array of clocks can be synchronized in that case...

He described more than one method for synchronizing clocks, and explained the physical meaning and significance of each method. You unfortunately just focused on one of them, and concluded that it was the only possible (or physically meaningful) one. You are simply mistaken, and you should have read more carefully.

> When the observer ISN'T perpetually inertial, he still can ask the same
> question, and I think he still deserves a meaningful answer.

Again, there are many meaningful answers that one can give. For example, at every location in the universe there is a cosmological time, which is the time that would appear on an ideal clock that has been continuously at rest in terms of the local inertial coordinates in which the CMBR is maximally isotropic at that location, and that was set to zero at the energy-matter decoupling event (initiation of the CMBR). This gives a well-defined temporal foliation that every object could use to correlate their events with the events of some distant object. You could label this the universal now.

Of course, this cosmological measure of time may not appeal to you (Mike), and you may prefer a more parochial and fragmented convention -- even at the expense of transitivity and reflexivity -- but that's just your preference. You cannot deny that the cosmological time is a perfectly meaningful and indeed universal way of defining a common time coordinate for all objects, and it is transitive and reflexive. To prove that you have found "the" unique and true sense of "now", different from cosmological time, you will need to prove that cosmological time cannot be regarded as a viable and physically meaningful measure of time. You obviously cannot prove that, because it's not true. Do you see the problem?

> Some do say that simultaneity at a distance is meaningless for an accelerating observer.

No competent scientist says that. We say simultaneity means "at the same value of the time coordinate", and since there are infinitely many different physically meaningful coordinate systems, there is no unique simultaneity, i.e., no unique mapping between the events of two separate objects. This is true whether they are accelerating or not.

> Others say that the CMIF simultaneity method gives the correct answer.

No competent scientist says that. A coordinate system comprised of the time slices of successive inertial coordinate systems, in which a given object is successively at rest, is a peculiarity that clearly does not inherit the useful properties of the individual inertial coordinate systems, and does not even provide a one-to-one mapping between events and coordinates.

> But CMIF simultaneity says that the distant person will get YOUNGER if
> the accelerating observer accelerates in the direction AWAY from the
> distant person.

No it doesn't. Your mistake has been explained to you many times before. Remember? Abstractly associating different sequences of events does not cause any physical object to "get younger".

> The proof that I've recently posted says that that negative ageing DOESN'T occur.

Well, no object "gets younger", but it's nevertheless true that for sufficiently great acceleration we have negative dtau1/dtau2, so you cannot disprove that we get negative values of the derivative using the time slices of successive inertial coordinate systems.

On 6/17/21 10:20 AM, Mike Fontenot wrote:
> A distant person gets younger, ACCORDING to the observer who accelerates
> in the direction away from the distant person.

There isn't any "getting" here. It's just that in flat spacetime, the
successive surfaces of simultaneity to that observer, using their
successive instantaneously co-moving inertial frames, intersect the
worldline of that (inertial) distant person at successively earlier
points. This says NOTHING AT ALL about ageing, it's just a curious
geometrical fact about this physical situation.

Tom Roberts

Tom Roberts <tjroberts137@sbcglobal.net> wrote:
> On 6/17/21 10:20 AM, Mike Fontenot wrote:
>> A distant person gets younger, ACCORDING to the observer who accelerates
>> in the direction away from the distant person.
>
> There isn't any "getting" here. It's just that in flat spacetime, the
> successive surfaces of simultaneity to that observer, using their
> successive instantaneously co-moving inertial frames, intersect the
> worldline of that (inertial) distant person at successively earlier
> points. This says NOTHING AT ALL about ageing, it's just a curious
> geometrical fact about this physical situation.
>
> Tom Roberts
>

As an illustration by analogy, there is a surveyor who is surveying the
heights of shoreline trees from a boat. There is a water-filled pool in the
boat and his surveying level floats on a raft on the water in this pool. He
sights the tops of the trees through this surveying level, counting on the
fact that the water in the pool is horizontal.

Now the boat accelerates away from shore. Of course, the surveyor doesn’t
account for the fact that in an accelerating boat, “horizontal” as defined
by the plane of the water in the pool has changed meaning. And looking
through his sight, he is shocked to find that the trees on the shore some
distance away now suddenly look much shorter. “They have gotten younger by
a decade!” is his cry.

What distresses him more is when the boat coasts to a stop and then
accelerates toward the shore. Again looking through his sights, he is even
more shocked to find that the trees on the shore are now measured to be
much taller. “What? They have now advanced in age by at least two decades!”

--
Odd Bodkin -- maker of fine toys, tools, tables

On 6/18/21 9:15 AM, Tom Roberts wrote:
> On 6/17/21 10:20 AM, Mike Fontenot wrote:
>> A distant person gets younger, ACCORDING to the observer who
>> accelerates in the direction away from the distant person.
>
> There isn't any "getting" here. It's just that in flat spacetime, the
> successive surfaces of simultaneity to that observer, using their
> successive instantaneously co-moving inertial frames, intersect the
> worldline of that (inertial) distant person at successively earlier
> points. This says NOTHING AT ALL about ageing, it's just a curious
> geometrical fact about this physical situation.
>
> Tom Roberts

Two perpetually-inertial observers (he and she), who are moving in one
common spatial dimension at some constant relative velocity, can each
construct for themselves an array of clocks that are stationary with
respect to themselves. And each of them can synchronize their own array
of clocks, using the fact that they know what the speed of light is, and
that it is constant when it travels between their clocks.

At any instant "t" in his life, one of his clocks will happen to be
momentarily co-located with her. The "helper person" ("HP") permanently
stationary and permanently co-located with that clock can directly
ascertain her age "tau" at that instant. The HP can send a message to
him, telling him what her age was when he (and the HP) were age "t".
When he gets that message, he then knows she was "tau" years old when he
was "t" years old.

OR, he can use the Lorentz equations, and/or the time-dilation equation
(TDE) to immediately give him that same result when he is age "t" ...
he'll get the same answer he'll eventually get from the HP, without
having to wait.

That result he gets, for her age "tau" when he is age "t", is the ONLY
answer that is consistent with what his array of clocks (and HP's) tell
him. He can't choose to use some other age for her (for example, like
what SHE says about the correspondence between their ages) without
violating his own measurements.

The answer he got from his HP about her current age when he was "t"
years old is completely meaningful to him.

Given that her current age "tau" is completely meaningful to him IF he
is perpetually inertial, the important question is this:

"Does her current age cease to be meaningful to him if he decides to
accelerate?"

I think a "yes" answer to that question would be absurd.

On 6/18/21 2:22 PM, Mike Fontenot wrote:
> [for a female moving inertially and a male about to accelerate away
> from her] "Does her current age cease to be meaningful to him if he
> decides to accelerate?" I think a "yes" answer to that question
> would be absurd.

Then the universe of SR is "absurd" to you.

Here's why: consider your initial setup:
> Two perpetually-inertial observers (he and she), who are moving in
> one common spatial dimension at some constant relative velocity, can
> each construct for themselves an array of clocks that are stationary
> with respect to themselves. And each of them can synchronize their
> own array of clocks [...]

That array of co-moving clocks gives each of them a sensible way to
measure the other's current age: to measure her age at his proper
time t, he can pre-arrange one of his clocks to be co-located with her
when it indicates t, and record the clock she carries at that instant.
The array of his clocks physically implements simultaneity in his rest
frame. Similarly for her measuring his current age.

Imagine setting that up for an observer with proper acceleration a. The
clocks must clearly perform Born rigid motion, which FAILS for clocks
more than c^2/a behind the observer -- they would need infinite
acceleration, would have to travel faster than the local speed of light,
and would have to tick infinitely fast.

So the observer's "now" is cannot be measured or implemented for
distances more than c^2/a behind him; his "now" and her "current" age
are therefore MEANINGLESS.

[Note c^2/a is where a Rindler horizon appears to a
perpetually accelerating observer. If the observer
ever stops accelerating the horizon never arises.
But the problem described above remains.]

Tom Roberts

On Friday, June 18, 2021 at 12:22:11 PM UTC-7, Mike_Fontenot wrote:
> Simultaneity at a distance is certainly well defined in the case of a
> perpetually-inertial observer.

Correction: *Inertial* simultaneity is well-defined for any given (local) system of inertial coordinates, but simultaneity need not be based on inertial isotropy for a given frame, it can be based on other physical considerations, so there's no unique simultaneity, i.e., no unique mapping between the events and proper times of two separate objects.

> Einstein showed very clearly how an array of clocks can be synchronized in that case...

He described more than one method for synchronizing clocks, and explained the physical meaning and significance of each method. You unfortunately just focused on one of them (the one he said was "more practical" for inertial frames), and concluded that it was the only possible (or physically meaningful) one. You're mistaken, and should have read more carefully.

> When the observer ISN'T perpetually inertial, he still can ask the same
> question, and I think he still deserves a meaningful answer.

Again, there are many meaningful answers that one can give. For example, at every location in the universe there is a cosmological time, which is the time that would appear on an ideal clock that has been continuously at rest in terms of the local inertial coordinates in which the CMBR is maximally isotropic at that location, and that was set to zero at the energy-matter decoupling event (initiation of the CMBR). This gives a well-defined temporal foliation, which every object could use to correlate their events with the events of some distant object. You could label this the universal now.

Of course, this cosmological measure of time may not appeal to you, and you may prefer a more parochial and fragmented convention -- even at the expense of transitivity and reflexivity -- but that's just your preference. You cannot deny that the cosmological time is a perfectly meaningful and indeed universal way of defining a common time coordinate for all objects, and it is transitive and reflexive. To prove that you have found "the" unique and true sense of "now", different from cosmological time, you will need to prove that cosmological time cannot be regarded as a viable and physically meaningful measure of time. You obviously cannot prove that, because it's not true. Do you see the problem?

> Some do say that simultaneity at a distance is meaningless for an accelerating observer.

No competent scientist says that. We say simultaneity means "at the same value of the time coordinate", and since there are infinitely many different physically meaningful coordinate systems, there's no unique simultaneity, i..e., no unique mapping between the events of two separate objects. This is true whether they are accelerating or not.

> Others say that the CMIF simultaneity method gives the correct answer.

No competent scientist says that. A coordinate system comprised of the time slices of successive inertial coordinate systems, in which a given object is successively at rest, is a peculiarity that clearly does not inherit the useful properties of the individual inertial coordinate systems, and generally doesn't even provide a one-to-one mapping between events and coordinates.

> But CMIF simultaneity says that the distant person will get YOUNGER if
> the accelerating observer accelerates in the direction AWAY from the
> distant person.

No it doesn't. Your mistake has been explained to you many times before. Abstractly associating different sequences of events does not cause any physical object to "get younger". (No, the web video you watched does not say otherwise.)

> The proof that I've recently posted says that that negative ageing DOESN'T occur.

Well, no object "gets younger", but it is nevertheless true that for sufficiently great acceleration we have negative dtau1/dtau2, so you cannot disprove that we get negative values of the derivative using the time slices of successive inertial coordinate systems.

I've put my possible proof that there is no negative ageing (and thus
that the CMIF simultaneity method can't be correct) on the viXra repository:

http://viXra.org/abs/2106.0142

There is another argument that shows that the HF ("Helper Friend") can't
conclude that the home twin (she) is less than 20 years old when the HF
is 20 + epsilon_2. We can require that she transmits NO light messages
to him when she is 20 years old or younger. Suppose the HF receives a
light message from her when he is 20 + epsilon_2 years old. By the
requirement, she must have been older than 20 years old when she sent
that message. When the HF receives that message, he knows that she must
be older than when she sent the message, so she must definitely be older
than 20 years old when the HF is 20+epsilon_2. Therefore, she did NOT
get younger, according to him, when he accelerated away from her.

A still simpler argument is that, if the HF ever concluded that she got
younger when he accelerated away from her, he would be concluding that
she was less than 20 years old at that instant of his acceleration. But
the HF was co-located with her when she was less than 20, and he
couldn't be two places a that same instant.

It seems to me that, once the distant accelerating observer has a way to
set up an array of clocks (with attending observers) that he can use to
define his concept of "NOW" (analogous to how Einstein did it for
perpetually-inertial observers), it becomes impossible for the home twin
to age negatively, according to the distant accelerating observer. It's
true that those clocks aren't synchronized as they are in the
perpetually-inertial case, but they don't have to be, since the distant
accelerating observer knows exactly how the rates of those clocks
compare to his own clock.

I suspect that the same type of argument can be used to show that the
essentially instantaneous (positive) ageing of the home twin (according
to the traveler who instantaneously changes his velocity) also cannot
occur. If these arguments are correct, then the commonly-used CMIF
(Co-Moving Inertial Frames) simultaneity method can't be correct.

On 8/3/21 3:09 PM, Mike Fontenot wrote:
>
> It seems to me that, once the distant accelerating observer has a way to
> set up an array of clocks (with attending observers) that he can use to
> define his concept of "NOW" (analogous to how Einstein did it for
> perpetually-inertial observers), it becomes impossible for the home twin
> to age negatively, according to the distant accelerating observer.  It's
> true that those clocks aren't synchronized as they are in the
> perpetually-inertial case, but they don't have to be, since the distant
> accelerating observer knows exactly how the rates of those clocks
> compare to his own clock.
>
> I suspect that the same type of argument can be used to show that the
> essentially instantaneous (positive) ageing of the home twin (according
> to the traveler who instantaneously changes his velocity) also cannot
> occur.  If these arguments are correct, then the commonly-used CMIF
> (Co-Moving Inertial Frames) simultaneity method can't be correct.
>

It's now looking like to me that Einstein's 1907 method of defining an
array of clocks for an accelerating observer agrees completely with the
CMIF method. If so, that means that CMIF is the law of the land, no
further assumptions required. I can also now see what the error in my
proof (that negative ageing doesn't occur) was. Details to follow.

On Friday, July 23, 2021 at 9:41:58 AM UTC-7, Mike_Fontenot wrote:
> I've put my possible proof that there is no negative ageing (and thus
> that the CMIF simultaneity method can't be correct) on the viXra repository:
>
> http://viXra.org/abs/2106.0142
No one gives a shit about your crankeries.

slow in space is fast in time...
change position slow in dimension is for faster temporal order.

Mitchell Raemsch