The material that we've been discussing recently (involving people
stationary in inertial frames) is elementary. Much more interesting is
what special relativity says about the conclusions of separated people
who are undergoing identical (as confirmed by accelerometers)
simultaneous finite accelerations along the same straight line. The
answer is that the person on the trailing rocket will conclude that the
leading rocket maintains a constant separation ahead of the trailing rocket.

Many people still believe that the separation INCREASES in that
scenario, according to the person on the trailing rocket. That belief
comes from mutually-contradictory statements in Bell's Spaceship
paradox, as given in the webpage:

https://en.wikipedia.org/wiki/Bell%27s_spaceship_paradox .

That webpage makes two mutually-contradictory claims:

First, that the two rockets maintain the same separation, according to
the initial inertial observers, and secondly,
that the two rockets are identically constructed, and thus produce the
same thrust and acceleration when ignited, according to the people on
the trailing rocket. Those two statements can't both be simultaneously
true. If the first statement is true, then the second statement is
false: the two accelerometers can't have the same reading. The leading
rocket will be accelerating faster than trailing rocket, according to
the person on the trailing rocket.

I've written eleven papers (on viXra) on this subject, the first two
fairly long, and the latter ones fairly short. You can find them on viXra:

https://vixra.org

by searching on my full name: "Michael Leon Fontenot". They can be
downloaded (in PDF form) at no charge.

You can also get the two long papers separately on Amazon, and a third
paper on Amazon that contains all of the short papers. They aren't
free, but only cost about $7 (not counting shipping and taxes, etc.) ...
that's just a dollar or so more than printing costs. To find them, you
can just search on Amazon for my full name. (The fourth monograph
returned in that search, "A New Simultaneity Method for Accelerated
Observers in Special Relativity", is now known to be incorrect ... it's
only value is in providing some comfort to those people who can't
tolerate the instantaneous ageing of the home twin, according to the
traveling twin when he instantaneously reverses course in the twin paradox).

The titles of the first two long monographs are

"An Inconsistency Between the Gravitational Time Dilation Equation and
the Twin Paradox"

and

"A New Gravitational Time Dilation Equation".

The third Amazon monograph is titled

"An Accelerated Array of Clocks in Special Relativity: A Meaningful
"NOW-at-a Distance” ",

and contains all the short papers.

If you have any questions, I can be reached at:

PhysicsFiddler@gmail.com

On 12/17/23 6:46 PM, Mike Fontenot wrote:
> the two rockets are identically constructed, and thus produce the
> same thrust and acceleration when ignited, according to the people on
> the trailing rocket.

NO. Their thrust and acceleration are the same TO OBSERVERS IN EACH
ROCKET. That is, their proper accelerations are equal. Identical
construction MUST yield equal proper accelerations (in an idealized
gedanken like this).

Just think about the symmetry. Singling out the trailing rocket is
unwarranted and WRONG.

You keep screwing this up and writing nonsense.

Tom Roberts

On 2023-12-18 00:46:33 +0000, Mike Fontenot said:

> Many people still believe that the separation INCREASES in that
> scenario, according to the person on the trailing rocket.

You belive otherwise but cannot support your belief with correct
mathematics. That your reasoning is faulty is shown many times
both in sci.physics.relativity and on comments on vixra pages.

Mikko

You are forgetting the length contraction equation (LCE) of special
relativity. If a yardstick is moving away from an inertial observer,
the inertial observer will conclude that the yardstick is getting
shorter by the factor gamma. And if you run the experiment again, but
this time you remove the middle 34 inches of the yardstick, leaving only
the outer two inches, the LCE tells you that the two one-inch pieces of
the original yardstick will still get closer, by the same factor gamma.
And the two separated rockets (with accelerometers showing the same
constant readings) are like the two outer inches of what was once the
yardstick: the two rockets will likewise will get closer together. So,
in the Bell scenario, where the initial inertial observers, by
definition, say the separation of the rockets is CONSTANT, that means
that the people on the trailing rocket will say that the leading rocket
is getting farther away, and the accelerometers do NOT show the same
reading.

So the Bell scenario IS different from my scenario, in which the
accelerometers show the same reading, and the separation between the
rockets is constant.

On December 19, Mike Fontenot wrote:
> You are forgetting the length contraction equation (LCE) of special
> relativity. If a yardstick is moving away from an inertial observer,
> the inertial observer will conclude that the yardstick is getting
> shorter by the factor gamma.
> And if you run the experiment again, but this time you remove the
> middle 34 inches of the yardstick, leaving only the outer two inches,
> the LCE tells you that the two one-inch pieces of the original yardstick
> will still get closer, by the same factor gamma.

Replace the yardstick with a steel disc. Punch a hole in the middle of
the disc, and attach a flame heater below.

The disc flies away at relativistic speed. Does the hole expand or contract?
--
Rich

On December 17, Mike Fontenot wrote:
> The answer is that the person on the trailing rocket will conclude that the
> leading rocket maintains a constant separation ahead of the trailing rocket.

The wrong answer -
> Many people still believe that the separation INCREASES in that
> scenario, according to the person on the trailing rocket.
> That belief comes from mutually-contradictory statements in Bell's Spaceship
> paradox, as given in the webpage:
> https://en.wikipedia.org/wiki/Bell%27s_spaceship_paradox .
> First, that the two rockets maintain the same separation, according to
> the initial inertial observers,

Correct, BY STIPULATION, not 'conclusion'.
Do you understand the difference?
Never mind, rhetorical question -

> and secondly, that the two rockets are identically constructed, and thus produce the
> same thrust and acceleration when ignited.
> Those two statements can't both be simultaneously true. If the first statement
> is true, then the second statement is alse: the two accelerometers can't have
> the same reading. The leading rocket will be accelerating faster than trailing
> rocket, according to the person on the trailing rocket.

They accelerate with identical profiles, but the trailer starts AFTER A DELAY,
in his frame. Obviously, relative simultaneity constitutes a mental block you
will never overcome. Give up and cut your losses -

> I've written eleven papers (on viXra) on this subject,

Kudos, you have a perfect track record on those papers -

--
Rich

RichD wrote:

> The wrong answer -
>
>> Many people still believe that the separation INCREASES in that
>> scenario, according to the person on the trailing rocket.
>> That belief comes from mutually-contradictory statements in Bell's
>> Spaceship paradox, as given in the webpage:
>> https://en.wikipedia.org/wiki/Bell%27s_spaceship_paradox .
>> First, that the two rockets maintain the same separation, according to
>> the initial inertial observers,
>
> Correct, BY STIPULATION, not 'conclusion'.
> Do you understand the difference? Never mind, rhetorical question -

not sure you do. Please make sure you know what speed you are
differentiating. The one contracted or the other, uncontracted.

𝗠𝗲𝗿𝗿𝘆_𝗖𝗵𝗿𝗶𝘀𝘁𝗺𝗮𝘀_𝗳𝗿𝗼𝗺_𝗼𝘂𝗿_𝗦𝘂𝗽𝗿𝗲𝗺𝗲_𝗟𝗲𝗮𝗱𝗲𝗿_𝗡𝗮𝘇𝗶_𝗞𝗹𝗮𝘂𝘀_𝗦𝗰𝗵𝘄𝗮𝗯_𝗳𝗿𝗼𝗺_𝘁𝗵𝗲_𝗪𝗼𝗿𝗹𝗱_𝗘𝗰𝗼𝗻𝗼𝗺𝗶𝗰_𝗙𝗼𝗿𝘂𝗺
https://bi%74%63hute.com/video/F5ZdaGyJIEcf

On 12/19/23 6:46 PM, RichD wrote:
> On December 17, Mike Fontenot wrote:
>> The answer is that the person on the trailing rocket will conclude
>> that the leading rocket maintains a constant separation ahead of
>> the trailing rocket.
>
> The wrong answer -

Yes, Fontenot keeps insisting on his WRONG answer.

Assuming the person on the trailing rocket measures the separation
simultaneously in their successive instantaneously co-moving inertial
frames, that separation MUST successively increase.

>> Many people still believe that the separation INCREASES in that
>> scenario, according to the person on the trailing rocket. That
>> belief comes from mutually-contradictory statements in Bell's
>> Spaceship paradox, as given in the webpage:
>> https://en.wikipedia.org/wiki/Bell%27s_spaceship_paradox . First,
>> that the two rockets maintain the same separation, according to
>> the initial inertial observers,

This has nothing to do with Fontenot's misreading of that page. It has
to do with simple calculus.

> Correct, BY STIPULATION, not 'conclusion'.

No. The stipulations are:
a) the rockets have identical proper accelerations as a
function of their proper times since starting
and
b) they start accelerating simultaneously in their initial
inertial frame.

One CONCLUSION is that they maintain a constant separation when measured
simultaneously in their initial inertial frame. This is CONCLUDED from
simple calculus: the first integral of their accelerations shows that
their speeds relative to that inertial frame are always equal when
measured simultaneously in that frame. Integrate their speeds and one
concludes that their separation is constant when measured simultaneously
in that frame. Both integrals are with respect to the time coordinates
of that inertial frame.

I do not know why Fontenot keeps getting this simple calculus wrong. Or
why he keeps ignoring me when I tell him this. He has been obsessing
over this scenario for many years, and refuses to THINK about it.

THINK 1: If the rockets have identical proper accelerations and
start simultaneously in their initial inertial frame, then their
trajectories MUST be congruent in the frame, differing only by their
initial offset. That is, their separation measured in that frame must be
constant.

THINK 2: Since their separation is constant in the initial inertial
frame, then in their successive instantaneously co-moving inertial
frames their separation MUST successively increase, as the "length
contraction" factor successively increases with increasing speed
relative to the initial frame.

> and secondly, that the two rockets are identically constructed, and
> thus produce the
>> same thrust and acceleration when ignited.

Yes -- that is identical proper accelerations as a function of their
proper times.

>> Those two statements can't both be simultaneously true.

Sure they can.

>> I've written eleven papers (on viXra) on this subject,

Fontenot's claims are wrong. Repeat them eleven times and they are still
wrong.

Tom Roberts

On 12/20/23 11:44 AM, Tom Roberts wrote:
>
> Assuming the person on the trailing rocket measures the separation
> simultaneously in their successive instantaneously co-moving inertial
> frames, that separation MUST successively increase.
>

That's NOT the way person on the trailing rocket measures the
separation! He measures the separation with a tape measure, and THAT
shows the separation is constant.

On 12/20/23 1:06 PM, Mike Fontenot wrote:
> On 12/20/23 11:44 AM, Tom Roberts wrote:
>> Assuming the person on the trailing rocket measures the separation
>> simultaneously in their successive instantaneously co-moving
>> inertial frames, that separation MUST successively increase.
>
> That's NOT the way person on the trailing rocket measures the
> separation! He measures the separation with a tape measure, and
> THAT shows the separation is constant.

WHAT tape measure? -- none is specified in the problem.

Add one and you're still wrong:
To qualify as a tape measure, it must execute Born rigid motion, nailed
down only at the trailing rocket -- this makes it always be at rest in
the instantaneously co-moving inertial frame of the trailing rocket, so
this is no different from what I said above. Born rigid motion requires
the leading end of the tape measure to have a smaller proper
acceleration than the trailing rocket, with the difference evenly spread
out along its length. Note the two rockets do not execute Born rigid
motion, because they have equal proper accelerations; the leading rocket
has a larger proper acceleration than the leading end of the tape
measure, and thus pulls away from it. So the tape measure shows the
separation is increasing. This is no different from what I said above.

I do not know why Fontenot keeps getting this wrong. Or why he keeps
ignoring me when I tell him this. Or why he ignores the voluminous
literature on this. He has been obsessing over this scenario for many
years, gets it wrong, and refuses to THINK about it -- see THINK 1 and
THINK 2 of my previous message for a very simple demonstration of my
claims.

Tom Roberts

On 12/20/23 10:29 PM, Tom Roberts wrote:

>> On 12/20/23 11:44 AM, Tom Roberts wrote:
>>> Assuming the person on the trailing rocket measures the separation
>>>  simultaneously in their successive instantaneously co-moving
>>> inertial frames, that separation MUST successively increase.

I (Mike Fontenot) respond:

The person on the trailing rocket would want NOTHING to do with the
momentarily co-moving inertial person (the MCMIP) or what the MCMIP says
about the separation of the rockets: that person says that the rockets
started their engines at different times ... the accelerating trailing
person says the rockets were fired at the same instant.

And then I (MLF) said:

>>
>> That's NOT the way person on the trailing rocket measures the
>> separation!  He measures the separation with a tape measure, and
>> THAT shows the separation is constant.

And Tom Roberts (TR) responded:
>
> WHAT tape measure? -- none is specified in the problem.
>

If the two people on the two rockets want to run a tape measure between
their rockets, they can do it. Since I'm interested in the trailing
person's conclusions about their separation, I'll assume that the end of
the tape is attached to the tail-end of leading rocket, and that the
CASE of the measuring tape is attached to the front-end of the trailing
rocket, so that the tape is free to slide in or out of the case.

Tom wrote:

> the leading rocket
> has a larger proper acceleration than the leading end of the tape
> measure, and thus pulls away from it.

And I (Mike) responded:

That's ridiculous. The spring tension inside the case of the tape
measure is small, and certainly doesn't pull the end of the tape away
from the leading rocket, where it is firmly attached.

Then Tom said:

> So the tape measure shows the
> separation is increasing.

And I (Mike) respond:

No, it doesn't. The accelerometers on the two rockets show the same
(constant) readings, and that results in the separation between the
rockets being constant, and the tape measure showing a constant reading.

Then Tom said:

> Or why he (Mike) ignores the voluminous
> literature on this.

The primary relevant literature for this discussion is the Wiki page on
Bell's Spaceship Paradox, and that webpage is a great example of "too
many cooks spoiling the broth" ... it's a collection of multiple
statements that are mutually inconsistent. For example, they say that
the initial inertial observers will observe the separation of the
accelerating rockets to be constant. The length contraction equation
(LCE) says that if a yardstick is moving away from an inertial observer,
the inertial observer will conclude that the length of the yardstick has
gotten smaller at any instant by the factor gamma (where gamma is a
function of speed, and increases with speed). So that means that if the
initial inertial observers say the rocket separation is constant, then
the two rockets must actually be getting farther apart (as measured in
the frame of the person on the trailing rocket). And THAT means that
the two accelerometers CAN'T be showing the same readings: the leading
rocket is accelerating faster than the trailing rocket. So when the Wiki
article claims that the initial inertial observers say the separation is
constant, AND that the accelerometers show the same readings (i.e., that
the rockets "are identical"), they are being inconsistent. If the
initial inertial observers say the separation of the rockets is
constant, then the separation of the rockets, according to the people on
the trailing rocket, is increasing, and the leading accelerometer will
read higher that the trailing accelerometer.

On 2023-12-21 05:29:31 +0000, Tom Roberts said:

> I do not know why Fontenot keeps getting this wrong.

Maybe he just wants to disagree. That is easier if he gets
sometihnig wrong and keeps getting it (rather than some
other thing) wrong.

Mikko

On 12/20/2023 11:29 PM, Tom Roberts wrote:
> On 12/20/23 1:06 PM, Mike Fontenot wrote:
>> On 12/20/23 11:44 AM, Tom Roberts wrote:
>>> Assuming the person on the trailing rocket measures the separation
>>>  simultaneously in their successive instantaneously co-moving
>>> inertial frames, that separation MUST successively increase.
>>
>> That's NOT the way person on the trailing rocket measures the
>> separation!  He measures the separation with a tape measure, and
>> THAT shows the separation is constant.
>
> WHAT tape measure? -- none is specified in the problem.
>
> Add one and you're still wrong:
> To qualify as a tape measure, it must execute Born rigid motion, nailed
> down only at the trailing rocket -- this makes it always be at rest in
> the instantaneously co-moving inertial frame of the trailing rocket, so
> this is no different from what I said above. Born rigid motion requires
> the leading end of the tape measure to have a smaller proper
> acceleration than the trailing rocket, with the difference evenly spread
> out along its length. Note the two rockets do not execute Born rigid
> motion, because they have equal proper accelerations; the leading rocket
> has a larger proper acceleration than the leading end of the tape
> measure, and thus pulls away from it. So the tape measure shows the
> separation is increasing. This is no different from what I said above.
>
> I do not know why Fontenot keeps getting this wrong. Or why he keeps
> ignoring me when I tell him this. Or why he ignores the voluminous
> literature on this. He has been obsessing over this scenario for many
> years, gets it wrong, and refuses to THINK about it -- see THINK 1 and
> THINK 2 of my previous message for a very simple demonstration of my
> claims.
>
> Tom Roberts

Wasting your time. But then it is yours to waste.

You need to completely re-think this, because your claims are wrong. You
MUST learn what Born rigid motion [#] is. And isn't. And you MUST learn
to always specify which frame you are talking about. EVERY TIME.

On 12/21/23 1:48 PM, Mike Fontenot wrote:
> The person on the trailing rocket would want NOTHING to do with the
> momentarily co-moving inertial person (the MCMIP) or what the MCMIP
> says about the separation of the rockets:

That's very strange coming from you, as that is how you insist an
accelerated observer determines the "current age of a distant person".

> The accelerometers on the two rockets show the same (constant)
> readings, and that results in the separation between the rockets
> being constant,

You keep saying stuff like this, WITHOUT SPECIFYING WHICH INERTIAL
FRAMES ARE INVOLVED. The separation is constant IN THE INITIAL INERTIAL
FRAME. But not in any instantaneously co-moving inertial frame of either
rocket.

> and the tape measure showing a constant reading.

No, it doesn't. See below.

First, let me show that the separation is constant in the initial
inertial frame:

*** Since they have equal proper accelerations [@], their
*** trajectories relative to the initial inertial frame
*** are identical, except for their initial offset. Their
*** separation therefore remains constant when measured
*** simultaneously in that frame.

[@] aka identical rockets or equal values displayed
by onboard accelerometers.

And you already know that being constant in the initial frame means
increasing separation in the successive instantaneously co-moving
inertial frames of either rocket:

> [...] if the initial inertial observers say the rocket separation is
> constant, then the two rockets must actually be getting farther apart
> (as measured in the frame of the person on the trailing rocket).

BEWARE: your "actually" is completely misplaced. You CANNOT talk like
that in relativity. There is no "actual", there are just values measured
in different inertial frames. This may be the core of your confusions.

Let's see how a tape measure is applied between rockets. Note the tape
measure must extend between the rockets on its own, and can be attached
to just one rocket, so the position of the other rocket can be read on
the tape. Any spring in the tape case is irrelevant.

To qualify as a tape measure it must execute Born rigid motion [#]. If
you affix the tape to the trailing rocket, to show what the trailing
observer measures (with an assistant at the leading rocket to read the
tape), then the leading rocket has a larger proper acceleration than the
leading end of the tape, and the tape measure shows the rockets have
increasing separation. If you affix the tape to the leading rocket, to
show what the leading observer measures (with an assistant at the
trailing rocket to read the tape), then the trailing rocket has a
smaller proper acceleration than the trailing end of the tape, and the
tape measure shows the rockets have increasing separation.

[#] Born rigid motion is specified as an object
maintaining constant proper length. For an
acceleration along an axis, the object's leading
end must have a smaller proper acceleration than
its trailing end.

Bottom line: the two rockets do NOT execute Born rigid motion, because
their proper accelerations are equal and they are separated along their
direction of acceleration. The tape measure, however, MUST execute Born
rigid motion, or it is not a tape measure.

> [... more confusion due to not specifying which frames are involved]

You need to completely re-think this, because your claims are wrong. You
MUST learn what Born rigid motion is [#]. And isn't. And you MUST learn
to always specify which frame you are talking about. EVERY TIME.

Tom Roberts

Tom says:
>
> That's very strange coming from you, as that is how you insist an
> accelerated observer determines the "current age of a distant person".

No, that is not at all how I say an accelerating observer determines the
current age of a distant
person ... it involves NO inertial observers at all.

An accelerating observer (him, the AO) determines the current age of a
distant person (her, the DP) by asking the helper person, the HP, who is
moving along the same line as the AO, and accelerating with the same
acceleration as the AO, and who happens to be momentarily co-located
with her at that instant.

The details are explained in my Amazon monograph:

An Accelerated Array of Clocks in Special Relativity: A Meaningful
"NOW-at-a-Distance".

On Amazon, you can search on my full name (Michael Leon Fontenot), and
it will pop up all three of my monographs, plus an older one which is no
longer of any value. You can also get the same thing on viXra for free,
by searching on my full name there, and it will list all of my viXra
papers. That's more complicated, though, because there are a LOT of
them ... the Amazon one with the "Accelerated Array ... " title is an
easier way to get the collection. The two other monographs on Amazon
are the first one, which shows an error that Einstein made in his1907
gravitational time dilation equation [and its equivalent acceleration
version], and the second one where I give the corrected acceleration
version].

_______________________________________

Here are some additional responses to your last post:

In the current situation, of interest to me, (with finite, and constant,
accelerations), the person on the trailing rocket knows that his
accelerometer shows the same constant value that the accelerometer shows
on the leading rocket, and so he knows that the separation between the
two rockets is constant. And he doesn't care what any inertial observers
say about anything! In that scenario, the initial inertial observers
will say that the separation between the rockets is decreasing,
according to the length contraction equation (applied at each instant).

The scenario in the Bell Paradox is DIFFERENT! There, the initial
inertial observers say that the separation between the two rockets is
constant. In that case, (in spite of what some of the authors of the
Wiki page on the Bell Paradox say), the accelerometers on the two
rockets will show different accelerations (the leading rocket's
accelerometer will show a greater acceleration the reading on the
trailing rocket's accelerometer), and the separation between the two
rockets, according to the people on the rockets, will be increasing.

On 12/23/23 6:13 PM, Mike Fontenot wrote:
> In [the Bell paradox scenario], [...] the accelerometers on the two
> rockets will show different accelerations

This is JUST PLAIN WRONG. Equal proper accelerations is stipulated in
the setup. (IOW: the rockets are identical.)

Please explain how, in the initial inertial frame, two identical rockets
can have differently-shaped trajectories simply because they are started
at different locations. You are claiming they do have differently-shaped
trajectories, which is ABSURD. (See the "***" paragraph of my previous
post, and its [@] footnote.)

You are apparently too invested in your mistakes to re-think this and
resolve your errors. Your problem, not mine.

Tom Roberts

On Sunday, December 24, 2023 at 9:31:14 AM UTC-8, Tom Roberts wrote:
> On 12/23/23 6:13 PM, Mike Fontenot wrote:
> > In [the Bell paradox scenario], [...] the accelerometers on the two
> > rockets will show different accelerations
> This is JUST PLAIN WRONG. Equal proper accelerations is stipulated in
> the setup. (IOW: the rockets are identical.)
>
> Please explain how, in the initial inertial frame, two identical rockets
> can have differently-shaped trajectories simply because they are started
> at different locations. You are claiming they do have differently-shaped
> trajectories, which is ABSURD. (See the "***" paragraph of my previous
> post, and its [@] footnote.)
>
> You are apparently too invested in your mistakes to re-think this and
> resolve your errors. Your problem, not mine.
>
> Tom Roberts

I wonder, let's say you put "the theory" on a timeline down the decades.

So, from 1900, there's electron physics, and, 1905, annus mirabilis, so every five years
or so, there's an, ..., improvement, to the theory.

So, not all the improvements, are compatible or sympatico, with the existing ones.
For example that "relativity is classical in the limit" or along these lines, it's "conservative",
while not compatible, is, "non-conservative", conservative in the sense of not really
changing the theory, vis-a-vis conservation in the usual sense meaning invariant theory
and symmetry laws and Noether's theorem and conserved quantities.

The Copenhagen interpretation or the stochastic model for the statistical ensemble is
an example, then about Bohm-de Broglie and real wave mechanics of wave collapse,
in events. Similarly resonance theory for the molecular and the differences between
atomic and molecular is an example of this kind of thing.

For relativity then the big deal seems about that SR is local. This wasn't in effect for
lots of interpretations, so now they would be seen as, ..., well, "wrong" is pretty strong,
but, no longer in effect, altogether.

Something like asymptotic freedom or that time symmetry is the only thing not shown
falsified, these are pretty major touchstones on the evolution of the theory, and the
fact that the popular accounts are usually quite a ways behind the novel accounts,
and also not necessarily at all reflecting, the practical accounts.

Then, re-visiting the definitions and derivations, also result, revisiting the data. The
data was gathered and tabulated according to the interpretation, about what it is.

So, re-visiting or re-thinking the theory, here has the benefit of this, and the challenge
of it, interpreting experiment as it's evolved in configuration and energy over time,
and, according to what were the pronounced and exoteric theories, and especially,
the practical or esoteric theories, is for dragging those out and helping people understand
how and why the opinions changed, so they don't feel disserved or basically so
that they don't distrust or dispute the competence, of, big and primary science.

Of course I'm kind of a personal aggrandizer myself and sort of really only trust
theory for its own sake to make the best mathematical interpretation how then
it's simplest to assign it clearest physical interpretations.

Otherwise, when there's "wall-papering", onto the theory, instead of "re-thinking",
it, from first theoretical principles establishing the surrounds of the definitions
and their derivations, I have feelings like "those people are incompetents and
don't know bubkus, and their latest wall-papering after coat-tailing, is not,
"quality construction".

Or, you know, "a theoretical physicist thinks this".

So, whose problem is that?

Tom Roberts wrote:
>
> This is JUST PLAIN WRONG. Equal proper accelerations is stipulated in
> the setup. (IOW: the rockets are identical.)
>

It WAS stipulated in the setup that the separation of the rockets,
according to the initial inertial observers, is constant. AND, it was
stipulated in the setup that that the accelerometers on the two rockets
show the same (constant) readings, and thus that the separation of the
rockets is constant, according to the people on the trailing rocket.
But those two stipulations are inconsistent ... they cannot both be
simultaneously true ... the length contraction equation (LCE) guarantees
that.

On Sunday, December 24, 2023 at 10:48:02 AM UTC-8, Ross Finlayson wrote:
> On Sunday, December 24, 2023 at 9:31:14 AM UTC-8, Tom Roberts wrote:
> > On 12/23/23 6:13 PM, Mike Fontenot wrote:
> > > In [the Bell paradox scenario], [...] the accelerometers on the two
> > > rockets will show different accelerations
> > This is JUST PLAIN WRONG. Equal proper accelerations is stipulated in
> > the setup. (IOW: the rockets are identical.)
> >
> > Please explain how, in the initial inertial frame, two identical rockets
> > can have differently-shaped trajectories simply because they are started
> > at different locations. You are claiming they do have differently-shaped
> > trajectories, which is ABSURD. (See the "***" paragraph of my previous
> > post, and its [@] footnote.)
> >
> > You are apparently too invested in your mistakes to re-think this and
> > resolve your errors. Your problem, not mine.
> >
> > Tom Roberts
> I wonder, let's say you put "the theory" on a timeline down the decades.
>
> So, from 1900, there's electron physics, and, 1905, annus mirabilis, so every five years
> or so, there's an, ..., improvement, to the theory.
>
> So, not all the improvements, are compatible or sympatico, with the existing ones.
> For example that "relativity is classical in the limit" or along these lines, it's "conservative",
> while not compatible, is, "non-conservative", conservative in the sense of not really
> changing the theory, vis-a-vis conservation in the usual sense meaning invariant theory
> and symmetry laws and Noether's theorem and conserved quantities.
>
> The Copenhagen interpretation or the stochastic model for the statistical ensemble is
> an example, then about Bohm-de Broglie and real wave mechanics of wave collapse,
> in events. Similarly resonance theory for the molecular and the differences between
> atomic and molecular is an example of this kind of thing.
>
> For relativity then the big deal seems about that SR is local. This wasn't in effect for
> lots of interpretations, so now they would be seen as, ..., well, "wrong" is pretty strong,
> but, no longer in effect, altogether.
>
> Something like asymptotic freedom or that time symmetry is the only thing not shown
> falsified, these are pretty major touchstones on the evolution of the theory, and the
> fact that the popular accounts are usually quite a ways behind the novel accounts,
> and also not necessarily at all reflecting, the practical accounts.
>
> Then, re-visiting the definitions and derivations, also result, revisiting the data. The
> data was gathered and tabulated according to the interpretation, about what it is.
>
> So, re-visiting or re-thinking the theory, here has the benefit of this, and the challenge
> of it, interpreting experiment as it's evolved in configuration and energy over time,
> and, according to what were the pronounced and exoteric theories, and especially,
> the practical or esoteric theories, is for dragging those out and helping people understand
> how and why the opinions changed, so they don't feel disserved or basically so
> that they don't distrust or dispute the competence, of, big and primary science.
>
> Of course I'm kind of a personal aggrandizer myself and sort of really only trust
> theory for its own sake to make the best mathematical interpretation how then
> it's simplest to assign it clearest physical interpretations.
>
> Otherwise, when there's "wall-papering", onto the theory, instead of "re-thinking",
> it, from first theoretical principles establishing the surrounds of the definitions
> and their derivations, I have feelings like "those people are incompetents and
> don't know bubkus, and their latest wall-papering after coat-tailing, is not,
> "quality construction".
>
> Or, you know, "a theoretical physicist thinks this".
>
> So, whose problem is that?

One can say the same for mathematics and about the "standard" and "non-standard"
in mathematics, and the conservative and non-conservative, about continuum mechanics,
and, especially, what mathematics _owes_ physics, if physics, is to have sufficient correct
mathematical models, which of course automatically equip physical models, of the
attachments of physical models to mathematical models.

https://www.youtube.com/watch?v=3SZXq-UqCdA&list=PLb7rLSBiE7F5_h5sSsWDQmbNGsmm97Fy5&index=31

Even defining a "continuous domain" today gets quite involved for measure theory,
then for these very interesting things in the interface between the discrete and continuous,
which would very well advise the conceit of the particle in quantum mechanics, and
why superstring theory is just a thing in continuum analysis, about doubling and halving,
the doubling-measures, doubling-spaces, angle-doubling, and so on, which are
quite, "real", mathematically, and mathematics is sort of short, owing physics.

So, better theory in physics involves any rehabilitations of mathematics, also.

It's a continuum mechanics, ....

Voice stress analysis is a sort of scientific approach to establish perceived veracity.

On 12/24/23 1:14 PM, Mike Fontenot wrote:
> Tom Roberts wrote:
>> [the Bell spaceship paradox] Equal proper accelerations is
>> stipulated in the setup. (IOW: the rockets are identical.)
>
> It WAS stipulated in the setup that the separation of the rockets,
> according to the initial inertial observers, is constant. AND, it
> was stipulated in the setup that that the accelerometers on the two
> rockets show the same (constant) readings, and thus that the
> separation of the rockets is constant, according to the people on
> the trailing rocket.

Nope. "according to the people on the trailing rocket" is YOUR mistake.
For instance that phrase does not appear in the Wikipedia article
referenced below. In adding it you have just confused yourself.

It should be replaced with "according to (people in) the initial
inertial frame".

> But those two stipulations are inconsistent ... they cannot both be
> simultaneously true ... the length contraction equation (LCE)
> guarantees that.

Yes. YOUR addition "according to the people on the trailing rocket" is
the source of the inconsistency. I have no idea why you think it applies.

Just THINK about it -- it makes no sense unless the rockets are
identical. That implies equal proper accelerations, and onboard
accelerometers read the same value.

Looking at https://en.wikipedia.org/wiki/Bell%27s_spaceship_paradox , I
do not see how you can misread it so badly. That page unequivocally says
the string will break, several times; equivalently your tape measure
will show the separation is increasing. Moreover, it repeatedly mentions
"equal accelerations" of the rockets, meaning either proper
accelerations or with respect to the initial inertial frame.

I repeat:
Please explain how, in the initial inertial frame, two identical rockets
can have differently-shaped trajectories simply because they are started
at different locations. You are claiming they do have differently-shaped
trajectories, which is ABSURD. (See the "***" paragraph of my previous
post, and its [@] footnote.)

You need to completely re-think this, because your claims are wrong. You
MUST learn what Born rigid motion [#] is. And isn't. And you MUST learn
to always specify which frame you are talking about. EVERY TIME.

[#] Born rigid motion is specified as an object
maintaining constant proper length. For an
acceleration along an axis, the object's leading
end must have a smaller proper acceleration than
its trailing end.

Tom Roberts

On Sunday, December 24, 2023 at 12:03:38 PM UTC-8, Ross Finlayson wrote:
> On Sunday, December 24, 2023 at 10:48:02 AM UTC-8, Ross Finlayson wrote:
> > On Sunday, December 24, 2023 at 9:31:14 AM UTC-8, Tom Roberts wrote:
> > > On 12/23/23 6:13 PM, Mike Fontenot wrote:
> > > > In [the Bell paradox scenario], [...] the accelerometers on the two
> > > > rockets will show different accelerations
> > > This is JUST PLAIN WRONG. Equal proper accelerations is stipulated in
> > > the setup. (IOW: the rockets are identical.)
> > >
> > > Please explain how, in the initial inertial frame, two identical rockets
> > > can have differently-shaped trajectories simply because they are started
> > > at different locations. You are claiming they do have differently-shaped
> > > trajectories, which is ABSURD. (See the "***" paragraph of my previous
> > > post, and its [@] footnote.)
> > >
> > > You are apparently too invested in your mistakes to re-think this and
> > > resolve your errors. Your problem, not mine.
> > >
> > > Tom Roberts
> > I wonder, let's say you put "the theory" on a timeline down the decades..
> >
> > So, from 1900, there's electron physics, and, 1905, annus mirabilis, so every five years
> > or so, there's an, ..., improvement, to the theory.
> >
> > So, not all the improvements, are compatible or sympatico, with the existing ones.
> > For example that "relativity is classical in the limit" or along these lines, it's "conservative",
> > while not compatible, is, "non-conservative", conservative in the sense of not really
> > changing the theory, vis-a-vis conservation in the usual sense meaning invariant theory
> > and symmetry laws and Noether's theorem and conserved quantities.
> >
> > The Copenhagen interpretation or the stochastic model for the statistical ensemble is
> > an example, then about Bohm-de Broglie and real wave mechanics of wave collapse,
> > in events. Similarly resonance theory for the molecular and the differences between
> > atomic and molecular is an example of this kind of thing.
> >
> > For relativity then the big deal seems about that SR is local. This wasn't in effect for
> > lots of interpretations, so now they would be seen as, ..., well, "wrong" is pretty strong,
> > but, no longer in effect, altogether.
> >
> > Something like asymptotic freedom or that time symmetry is the only thing not shown
> > falsified, these are pretty major touchstones on the evolution of the theory, and the
> > fact that the popular accounts are usually quite a ways behind the novel accounts,
> > and also not necessarily at all reflecting, the practical accounts.
> >
> > Then, re-visiting the definitions and derivations, also result, revisiting the data. The
> > data was gathered and tabulated according to the interpretation, about what it is.
> >
> > So, re-visiting or re-thinking the theory, here has the benefit of this, and the challenge
> > of it, interpreting experiment as it's evolved in configuration and energy over time,
> > and, according to what were the pronounced and exoteric theories, and especially,
> > the practical or esoteric theories, is for dragging those out and helping people understand
> > how and why the opinions changed, so they don't feel disserved or basically so
> > that they don't distrust or dispute the competence, of, big and primary science.
> >
> > Of course I'm kind of a personal aggrandizer myself and sort of really only trust
> > theory for its own sake to make the best mathematical interpretation how then
> > it's simplest to assign it clearest physical interpretations.
> >
> > Otherwise, when there's "wall-papering", onto the theory, instead of "re-thinking",
> > it, from first theoretical principles establishing the surrounds of the definitions
> > and their derivations, I have feelings like "those people are incompetents and
> > don't know bubkus, and their latest wall-papering after coat-tailing, is not,
> > "quality construction".
> >
> > Or, you know, "a theoretical physicist thinks this".
> >
> > So, whose problem is that?
> One can say the same for mathematics and about the "standard" and "non-standard"
> in mathematics, and the conservative and non-conservative, about continuum mechanics,
> and, especially, what mathematics _owes_ physics, if physics, is to have sufficient correct
> mathematical models, which of course automatically equip physical models, of the
> attachments of physical models to mathematical models.
>
> https://www.youtube.com/watch?v=3SZXq-UqCdA&list=PLb7rLSBiE7F5_h5sSsWDQmbNGsmm97Fy5&index=31
>
> Even defining a "continuous domain" today gets quite involved for measure theory,
> then for these very interesting things in the interface between the discrete and continuous,
> which would very well advise the conceit of the particle in quantum mechanics, and
> why superstring theory is just a thing in continuum analysis, about doubling and halving,
> the doubling-measures, doubling-spaces, angle-doubling, and so on, which are
> quite, "real", mathematically, and mathematics is sort of short, owing physics.
>
> So, better theory in physics involves any rehabilitations of mathematics, also.
>
> It's a continuum mechanics, ....
>
> Voice stress analysis is a sort of scientific approach to establish perceived veracity.

Quine, "Two Dogmas of Empiricism", "Things and their place in theories"

https://en.wikipedia.org/wiki/Quine%E2%80%93Putnam_indispensability_argument

"Putnam's Quibbles on Quine, pointless"

Paul Dirac gives a lecture, starting about why theoretical physicists are people.

"The wave function Psi is interpreted as referring to a physical state."

"Some physicists have always objected to that probability interpretation. ...."
"... One has to accept it. One cannot improve on it."

https://www.youtube.com/watch?v=Ci86Aps7CMo

"We can no longer just shut our eyes to the negative energy states."
(While it's still all positive probabilities, ..., as for what events.)

"... there is a further doubling ...".

(Dirac explains where positrons come from, also electron holes.)

De Broglie talks about electron waves.

https://www.youtube.com/watch?v=stRrf4DB_3Y

I especially enjoyed the interview with de Broglie at the Paris Academy with the bust of Fresnel.

They're actually both pretty right. People saying Dirac and de Broglie are at odds are underinformed.
Theorists not pulling them back together are just, well, they're stepping off.

https://www.youtube.com/watch?v=kgXYvaSfFdE

"Present day theoretical physics is not in a satisfactory state." -- Dirac

"Most physicists say that we can turn a blind eye toward the infinities, ....,
cutting out artificially the infinities, ... I feel very unhappy about it. ...
Mathematics does not allow you to discard infinities just when they
don't suit you. ... I think I'm pretty well alone among physicists this way,
...., but I'm hoping, ...." -- Dirac

"... resignation physics ...". -- https://en.wikipedia.org/wiki/Bruno_Touschek#/media/File:Bruno_Touschek.jpg

Merry Christmas

On Saturday 23 December 2023 at 21:42:46 UTC+1, Tom Roberts wrote:
> You need to completely re-think this, because your claims are wrong. You
> MUST learn what Born rigid motion [#] is. And isn't. And you MUST learn
> to always specify which frame you are talking about. EVERY TIME.

And you MUST learn that we're FORCED!!! To THE BEST WAY!!!

> On 12/21/23 1:48 PM, Mike Fontenot wrote:
> > The person on the trailing rocket would want NOTHING to do with the
> > momentarily co-moving inertial person (the MCMIP) or what the MCMIP
> > says about the separation of the rockets:
> That's very strange coming from you, as that is how you insist an
> accelerated observer determines the "current age of a distant person".
> > The accelerometers on the two rockets show the same (constant)
> > readings, and that results in the separation between the rockets
> > being constant,
> You keep saying stuff like this, WITHOUT SPECIFYING WHICH INERTIAL
> FRAMES ARE INVOLVED. The separation is constant IN THE INITIAL INERTIAL
> FRAME. But not in any instantaneously co-moving inertial frame of either
> rocket.

Fortunately, we have GPS now so we can be absolutely sure
that this insane mumble has nothing in common with real
clocks, real observers or real anything.

Here is what you're missing, Tom:

The length contraction equation (LCE) says that the initial inertial
observers (IIO's) will say that the separation of the two rockets
(whenever they are moving wrt the IIO's) is LESS than what the people on
the rockets say the separation is.

So, IF the initial inertial observers (the IIO's) say that the
separation of the rockets is CONSTANT, then the separation must be
increasing, according to the people on the rockets.

But in the Wiki article, it says that the initial inertial observers
(the IIO's) say the separation is constant, AND the Wiki article says
that the rockets are identical (i.e., that the two rockets are
undergoing equal acceleration according to their accelerometers, so
their separation is constant, according to the people on the rockets).
That VIOLATES the LCE, so the Wiki article is WRONG. If the IIO's say
the separation is constant, then the accelerometer on the leading rocket
must read HIGHER than the accelerometer on the trailing rocket, and the
separation must therefore be INCREASING, according to the people on the
rockets.

On 12/25/23 12:04 PM, Mike Fontenot wrote:
> in the Wiki article, it says that the initial inertial observers (the
> IIO's) say the separation is constant, AND the Wiki article says that
> the rockets are identical (i.e., that the two rockets are undergoing
> equal acceleration according to their accelerometers,

Yes.

> so their separation is constant, according to the people on the
> rockets).

NO! Justify this claim. Show your work.

[You'll find that you cannot justify this claim, for the
simple reason that it is WRONG.]

I have no idea where you got this notion.

I repeat:
Please explain how, in the initial inertial frame, two identical rockets
can have differently-shaped trajectories simply because they are started
at different locations. You are claiming they do have differently-shaped
trajectories, which is ABSURD. (See the "***" paragraph of my previous
post, and its [@] footnote.)

Tom Roberts

You agreed with this:

"the Wiki article says that the rockets are identical (i.e., that the
two rockets are undergoing
equal acceleration according to their accelerometers,"

And yet you disagreed with this:

"so their separation is constant, according to the people on the rockets)."

So you seem to be saying that when the two rockets are undergoing equal
accelerations, their separation isn't constant.

If that IS what you're saying, I certainly don't agree.