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Mar 14, 2022, 3:08:14 PMMar 14

to

The traveling twin starts and travels for 4 years at speed v = 0.866c

and then brakes, as seen in the animation

https://www.geogebra.org/m/jzc4amud

Calculate the Earth-spaceship distance, before and after braking (in

the spaceship reference).

Calculate how many turns the Earth has made around the sun, before and

after braking (in the spaceship reference).

and then brakes, as seen in the animation

https://www.geogebra.org/m/jzc4amud

Calculate the Earth-spaceship distance, before and after braking (in

the spaceship reference).

Calculate how many turns the Earth has made around the sun, before and

after braking (in the spaceship reference).

Mar 15, 2022, 4:36:07 AMMar 15

to

his trip. So they are each zero years old then. If the traveling twin

(he) travels for 4 years of his time, he will be 4 yours old when he

stops. (His age when he stops is an EVENT that all observers must agree

about, and so she also agrees that he is 4 years old when he stops. He

says he has traveled (0.866)(4) = 3.464 lightyears away from his twin

(her) then. She says he traveled 8 years of her time ... i.e., she says

she is 8 years old when he stops. She says he is (0.866)(8) = 6.928

lightyears away when he stops.

After he stops, she says that he remains 6.928 lightyears away from her

after that. And she says they age at the same rate after he stops. He

says that, during his essentially instantaneous stopping time, his age

essentially doesn't change during his stopping. She agrees with that.

But he says that during his essentially instantaneous stopping, SHE

essentially instantaneously gets older by 4 years ... i.e., he says that

she essentially instantaneously goes from being 4 years old to being 8

years old during the essentially instantaneous time in his life it takes

him to stop. And he also says that their distance apart essentially

instantaneously increases from 3.464 lightyears to 6.928 lightyears

while he is doing his essentially instantaneous stopping.

Mar 15, 2022, 8:28:44 AMMar 15

to

And how many turns around the Sun did the Earth make just before and

immediately after the stop, in the spaceship reference?

Mar 15, 2022, 9:55:10 AMMar 15

to

on how far apart they are. During the deceleration the moving twin

will observe the apparent expansion of the universe along the axis

of travel, and what while moving appeared to be 3.464 light years

will expand to 6.928 light years.

Something to keep in mind is that neither twin can see the other at

what each considers "now". They only see the other on their own

past light cone. So while the moving twin is stopping, he will NOT

see his twin back on earth suddenly aging. This is because what

he sees is not the instantaneous state of the earth, but an image

conveyed by light. Instead he will see her as she was about 6.928

years earlier. Thus what he sees is a much younger twin, only

about a year older than when he left earth. It is on the trip back

to earth that he sees her age rapidly as he passes the light

traveling outbound from earth.

Rich L.

Mar 15, 2022, 2:57:04 PMMar 15

to

I made a careless mistake in my previous post. Here is that post, down

to where my mistake occurred:

On 3/15/22 2:36 AM, Mike Fontenot wrote:

>

> Suppose the two twins have just been born when the traveling twin starts

> his trip. So they are each zero years old then. If the traveling twin

> (he) travels for 4 years of his time, he will be 4 yours old when he

> stops. (His age when he stops is an EVENT that all observers must agree

> about, and so she also agrees that he is 4 years old when he stops. He

> says he has traveled (0.866)(4) = 3.464 lightyears away from his twin

> (her) then. She says he traveled 8 years of her time ... i.e., she says

> she is 8 years old when he stops. She says he is (0.866)(8) = 6.928

> lightyears away when he stops.

>

> After he stops, she says that he remains 6.928 lightyears away from her

> after that. And she says they age at the same rate after he stops. He

> says that, during his essentially instantaneous stopping time, his age

> essentially doesn't change during his stopping. She agrees with that.

The above is all correct. But here is the sentence where I made the

careless error:

> But he says that during his essentially instantaneous stopping, SHE

> essentially instantaneously gets older by 4 years ... i.e., he says that

> she essentially instantaneously goes from being 4 years old to being 8

> years old during the essentially instantaneous time in his life it takes

> him to stop.

According to him, her age right before he stops is 2 years old, not 4

years old as I said above. Immediately after he stops, they both agree

about their respective ages. He says she is now 8 years old, so he says

her age increases by 6 years during his essentially instantaneous

stopping, not by 4 years as I stated in my previous post.

I should also have pointed out that each of the twins, during his

outbound trip, are entitled to use the famous time dilation equation for

inertial observers: That equation says that any inertial observer will

conclude that a person moving at speed "v" with respect to them is

ageing at a rate gamma times slower than they are, where

gamma = 1 / sqrt { 1 / (1 - v * v) },

where the asterisk indicates multiplication. For v = 0.866, gamma =

2.0. So on the outbound trip, each twin says the other twin is ageing

half as fast as their own rate of ageing. So right before he stops, she

says he is 4 and she is 8, but he says he is 4 and she is 2. And

immediately after he stops, they both agree that he is 4 and she is 8.

So he says she essentially instantaneously gets 6 years older during his

essentially instantaneous stopping.

There is an equation that I derived long ago that makes it easy to

calculate how her age changes (according to him) whenever he essentially

instantaneously changes his velocity. I call it the "delta_CADO" equation:

delta_CADO = -L * delta_v,

where L is their distance apart, according to her, and

delta_v = v2 - v1,

where v1 is his velocity before the change, and v2 is his velocity after

the change (with positive v being taken as the velocity when they are

moving apart).

So in this example,

L = 6.928 lightyears

v1 = 0.866 ly/y

v2 = 0.0 ly/y,

and so

delta_v = -0.866

and

delta_CADO = -6.928 * (-0.866) = 6.0 years.

We didn't need this equation to get the answer in the above particular

scenario, because his new velocity was zero, which makes things

especially easy. But when the two velocities are completely general,

it's necessary to either use the delta-CADO equation, or else do it

graphically with a Minkowski diagram, drawing lines of simultaneity.

to where my mistake occurred:

On 3/15/22 2:36 AM, Mike Fontenot wrote:

>

> Suppose the two twins have just been born when the traveling twin starts

> his trip. So they are each zero years old then. If the traveling twin

> (he) travels for 4 years of his time, he will be 4 yours old when he

> stops. (His age when he stops is an EVENT that all observers must agree

> about, and so she also agrees that he is 4 years old when he stops. He

> says he has traveled (0.866)(4) = 3.464 lightyears away from his twin

> (her) then. She says he traveled 8 years of her time ... i.e., she says

> she is 8 years old when he stops. She says he is (0.866)(8) = 6.928

> lightyears away when he stops.

>

> After he stops, she says that he remains 6.928 lightyears away from her

> after that. And she says they age at the same rate after he stops. He

> says that, during his essentially instantaneous stopping time, his age

> essentially doesn't change during his stopping. She agrees with that.

careless error:

> But he says that during his essentially instantaneous stopping, SHE

> essentially instantaneously gets older by 4 years ... i.e., he says that

> she essentially instantaneously goes from being 4 years old to being 8

> years old during the essentially instantaneous time in his life it takes

> him to stop.

years old as I said above. Immediately after he stops, they both agree

about their respective ages. He says she is now 8 years old, so he says

her age increases by 6 years during his essentially instantaneous

stopping, not by 4 years as I stated in my previous post.

I should also have pointed out that each of the twins, during his

outbound trip, are entitled to use the famous time dilation equation for

inertial observers: That equation says that any inertial observer will

conclude that a person moving at speed "v" with respect to them is

ageing at a rate gamma times slower than they are, where

gamma = 1 / sqrt { 1 / (1 - v * v) },

where the asterisk indicates multiplication. For v = 0.866, gamma =

2.0. So on the outbound trip, each twin says the other twin is ageing

half as fast as their own rate of ageing. So right before he stops, she

says he is 4 and she is 8, but he says he is 4 and she is 2. And

immediately after he stops, they both agree that he is 4 and she is 8.

So he says she essentially instantaneously gets 6 years older during his

essentially instantaneous stopping.

There is an equation that I derived long ago that makes it easy to

calculate how her age changes (according to him) whenever he essentially

instantaneously changes his velocity. I call it the "delta_CADO" equation:

delta_CADO = -L * delta_v,

where L is their distance apart, according to her, and

delta_v = v2 - v1,

where v1 is his velocity before the change, and v2 is his velocity after

the change (with positive v being taken as the velocity when they are

moving apart).

So in this example,

L = 6.928 lightyears

v1 = 0.866 ly/y

v2 = 0.0 ly/y,

and so

delta_v = -0.866

and

delta_CADO = -6.928 * (-0.866) = 6.0 years.

We didn't need this equation to get the answer in the above particular

scenario, because his new velocity was zero, which makes things

especially easy. But when the two velocities are completely general,

it's necessary to either use the delta-CADO equation, or else do it

graphically with a Minkowski diagram, drawing lines of simultaneity.

Mar 16, 2022, 3:22:55 AMMar 16

to

4 instead of 6 years, now I absolutely agree with everything you have

written.

But you didn't answer my question about the Earth's revolutions around

the Sun.

Since I want my question to be clear, I express myself with numbers and

dates.

The traveling twin leaves on January 1, 2022 and keeps his telescope

continuously pointed at the receding solar system at speed v = 0.866c,

so that he can count how many revolutions the Earth makes around the

Sun.

Obviously, the turns seen on the telescope will take place much slower

than one for each year, both for the finite speed of the light (which,

due to the recession, takes more and more time to get to the spaceship

from the solar system) and for the time dilation

And all this greatly complicates the calculations.

This is why I ask: is it possible to calculate how many turns the

traveler twin will have * seen * make from the Earth around the Sun on

the spacecraft's telescope, after its 4-year journey, before starting to

brake?

Mar 16, 2022, 1:46:20 PMMar 16

to

conjoined? How would the experiment go for the latter case?

Sylvia.

Mar 16, 2022, 1:47:08 PMMar 16

to

On 3/15/22 7:55 AM, Richard Livingston wrote:

>

> Keep in mind that when the moving twin stops, both twins will agree

> on how far apart they are. During the deceleration the moving twin

> will observe the apparent expansion of the universe along the axis

> of travel, and what while moving appeared to be 3.464 light years

> will expand to 6.928 light years.

>

That's true. But of the two effects (spatial and temporal), I think
>

> Keep in mind that when the moving twin stops, both twins will agree

> on how far apart they are. During the deceleration the moving twin

> will observe the apparent expansion of the universe along the axis

> of travel, and what while moving appeared to be 3.464 light years

> will expand to 6.928 light years.

>

what special relativity has to say about time is more interesting than

what it says about space (and distance).

The best example of that is the case of "negative ageing": if the

distant traveling twin (he) suddenly accelerates in the direction AWAY

from the home twin (her), he will conclude that she suddenly gets

YOUNGER during his velocity change. That result drives a lot of people

(including many physicists) crazy! Some physicists maintain that the

conclusions of the traveler during those occurrences must be ruled

inadmissible. But the negative ageing can't logically be ignored, or

disallowed, for the following reason: the traveler can do two

back-to-back instantaneous velocity reversals, which, taken together,

just cancel out. So we can't allow one of those velocity reversals, but

disallow the other.

For example, take the case where he is originally moving away from her

at speed

v = V1 = +V,

where V is some positive number. And let L be their distance apart

(according to her) at some instant. Then, at that instant, he suddenly

changes his velocity to

v = V2 = -V.

So

delta_v_1 = V2 - V1 = (-V) - V = - 2 * V.

And

delta_age_1 = -L * delta_v_1 = -L * (-2 * V) = 2 * L * V.

So he concludes that her age has instantaneously increased by (2 * L * V).

But suppose he IMMEDIATELY decides to reverse course again. He will

then conclude that her age has instantaneously DECREASED by (2 * L * V).

I.e.,

delta_v_2 = V - (-V) = V + V = 2 * V.

and

delta_age_2 = -L * delta_v_2 = -L * (2 * V) = -2 * L * V.

So he concludes that her age has instantaneously decreased by (2 * L * V).

So that gets her age (according to him) right back to where it was

before he did any accelerating ... everything is as if he had done NO

accelerating at all. But that means that we CANNOT say that

instantaneous age INCREASES are OK, but that instantaneous age DECREASES

are NOT OK. You can't allow one but disallow the other.

And Richard Livingston continues:

> Something to keep in mind is that neither twin can see the other at

> what each considers "now". They only see the other on their own

> past light cone. So while the moving twin is stopping, he will NOT

> see his twin back on earth suddenly aging. This is because what

> he sees is not the instantaneous state of the earth, but an image

> conveyed by light. Instead he will see her as she was about 6.928

> years earlier. Thus what he sees is a much younger twin, only

> about a year older than when he left earth. It is on the trip back

> to earth that he sees her age rapidly as he passes the light

> traveling outbound from earth.

>

from her ... those just tell him what she looked like in the past, and

how old she was in the past. Instead, I am interested in what he

DEDUCES about her CURRENT age at any given instant in his life, using

the laws of special relativity. I.e., I'm interested in his "NOW"

instant ... what does he say her age is "RIGHT NOW", at some instant in

his life. I'm purely interested in what he says about "simultaneity at

a distance".

Mar 17, 2022, 11:14:55 AMMar 17

to

On Wednesday, March 16, 2022 at 12:47:08 PM UTC-5, Mike Fontenot wrote:

> >

...

we actually experience the world on our past light cone and think of that

as "now". This a misconception. The "now" that Einstein defines with

his clock synchronization procedure is a useful concept for coordinates,

but as you are realizing, at any given event in space-time there is no

unique "now", it is highly observer dependent (i.e. depends on the

observers state of motion). I suggest that the only reality is on the

past light cone. That is something that all observers can agree on.

All observers will agree on WHAT is on the light cone and on the sequence

of events on the light cone (at least in a given direction), but may disagree

on when any event is on the light cone.

In particular, no matter what you do with direct observation, you will never

observe a clock going backwards or a person aging backwards. At most

you may CALCULATE that a clock on your "now" axis has gone backwards

due to your acceleration, but you will never be able to directly observe such

a thing. And I would argue that such a calculation is meaningless.

Proof of this is two events separated in space and occurring "simultaneously"

in some reference frame. The observer in that frame directly observing these

events from some time in the future says they occurred simultaneously at

{some time in the past}. A moving observer at that same place and time as

the first observer, will also see the two events occurring at the same time,

no matter how fast they are traveling. It is only when they calculate their

"now" times that the paradox of time appears.

This is why I think it is a mistake in quantum mechanics to talk about the

instantaneous collapse of the wave function CAUSED BY a measurement

event. There cannot be a consistent causal explanation directly linking

two events that are outside the light cone.

Rich L.

> >

...

> That's all true. But I am not interested in what TV images he receives

> from her ... those just tell him what she looked like in the past, and

> how old she was in the past. Instead, I am interested in what he

> DEDUCES about her CURRENT age at any given instant in his life, using

> the laws of special relativity. I.e., I'm interested in his "NOW"

> instant ... what does he say her age is "RIGHT NOW", at some instant in

> his life. I'm purely interested in what he says about "simultaneity at

> a distance".

Simultaneity at a distance is not observable. In our everyday experience
> from her ... those just tell him what she looked like in the past, and

> how old she was in the past. Instead, I am interested in what he

> DEDUCES about her CURRENT age at any given instant in his life, using

> the laws of special relativity. I.e., I'm interested in his "NOW"

> instant ... what does he say her age is "RIGHT NOW", at some instant in

> his life. I'm purely interested in what he says about "simultaneity at

> a distance".

we actually experience the world on our past light cone and think of that

as "now". This a misconception. The "now" that Einstein defines with

his clock synchronization procedure is a useful concept for coordinates,

but as you are realizing, at any given event in space-time there is no

unique "now", it is highly observer dependent (i.e. depends on the

observers state of motion). I suggest that the only reality is on the

past light cone. That is something that all observers can agree on.

All observers will agree on WHAT is on the light cone and on the sequence

of events on the light cone (at least in a given direction), but may disagree

on when any event is on the light cone.

In particular, no matter what you do with direct observation, you will never

observe a clock going backwards or a person aging backwards. At most

you may CALCULATE that a clock on your "now" axis has gone backwards

due to your acceleration, but you will never be able to directly observe such

a thing. And I would argue that such a calculation is meaningless.

Proof of this is two events separated in space and occurring "simultaneously"

in some reference frame. The observer in that frame directly observing these

events from some time in the future says they occurred simultaneously at

{some time in the past}. A moving observer at that same place and time as

the first observer, will also see the two events occurring at the same time,

no matter how fast they are traveling. It is only when they calculate their

"now" times that the paradox of time appears.

This is why I think it is a mistake in quantum mechanics to talk about the

instantaneous collapse of the wave function CAUSED BY a measurement

event. There cannot be a consistent causal explanation directly linking

two events that are outside the light cone.

Rich L.

Mar 17, 2022, 6:26:16 PMMar 17

to

On 3/16/22 1:22 AM, Luigi Fortunati wrote:

>

> This is why I ask: is it possible to calculate how many turns the

> traveler twin will have * seen * make from the Earth around the Sun on

> the spacecraft's telescope, after its 4-year journey, before starting to

> brake?

>

Yes. I've already shown how the traveling twin (he) can determine the
>

> This is why I ask: is it possible to calculate how many turns the

> traveler twin will have * seen * make from the Earth around the Sun on

> the spacecraft's telescope, after its 4-year journey, before starting to

> brake?

>

current age of the home twin (her) at any instant in his life. And, if

you know what her mom says the position of the earth in its orbit around

the sun was when her daughter (the home twin) was born, then that

establishes a one-to-one correspondence between the home twin's age and

the position of the earth in its orbit about the sun, and the number of

complete orbits it has made since she was born. So that allows the

traveling twin to determine the position of the earth in its orbit, and

the number of completed orbits since the home twin was born, at each

each instant in the life of the traveler (he), according to him. But

I'm not at all interested in that ... I just want to know what he

concludes about her current age at each instant of his life.

Mar 17, 2022, 6:27:03 PMMar 17

to

In article <d2b386bb-a22a-4cfa...@googlegroups.com>,

Galilean relativity expresses the idea that the concept of being in the

same place at different times is ill-defined (relative to what?), while

Special Relativity expresses the idea that the concept of happening at

the same time in different places is equally ill-defined.

Does anyone disagree?

Considering that one recovers non-relativistic physics in the limit that

the speed of light goes to infinity, is it fair to say that the finite

speed of light is the SOLE reason for differences between

non-relativistic and relativistic physics?

__

* _General Relativity: The Essentials_, by Carlo Rovelli (Cambridge

University Press), 2021. Pp. 180, 23 =D7 15.5 cm. Price =A314.99

(paperback, ISBN 978 1 00 9013697).

Richard Livingston <richali...@gmail.com> writes:

> > That's all true. But I am not interested in what TV images he receives

> > from her ... those just tell him what she looked like in the past, and

> > how old she was in the past. Instead, I am interested in what he

> > DEDUCES about her CURRENT age at any given instant in his life, using

> > the laws of special relativity. I.e., I'm interested in his "NOW"

> > instant ... what does he say her age is "RIGHT NOW", at some instant in

> > his life. I'm purely interested in what he says about "simultaneity at

> > a distance".

>

> Simultaneity at a distance is not observable.

In his most recent book*, Carlo Rovelli summarizes it like this:
> > That's all true. But I am not interested in what TV images he receives

> > from her ... those just tell him what she looked like in the past, and

> > how old she was in the past. Instead, I am interested in what he

> > DEDUCES about her CURRENT age at any given instant in his life, using

> > the laws of special relativity. I.e., I'm interested in his "NOW"

> > instant ... what does he say her age is "RIGHT NOW", at some instant in

> > his life. I'm purely interested in what he says about "simultaneity at

> > a distance".

>

> Simultaneity at a distance is not observable.

Galilean relativity expresses the idea that the concept of being in the

same place at different times is ill-defined (relative to what?), while

Special Relativity expresses the idea that the concept of happening at

the same time in different places is equally ill-defined.

Does anyone disagree?

Considering that one recovers non-relativistic physics in the limit that

the speed of light goes to infinity, is it fair to say that the finite

speed of light is the SOLE reason for differences between

non-relativistic and relativistic physics?

__

* _General Relativity: The Essentials_, by Carlo Rovelli (Cambridge

University Press), 2021. Pp. 180, 23 =D7 15.5 cm. Price =A314.99

(paperback, ISBN 978 1 00 9013697).

Mar 18, 2022, 5:27:19 PMMar 18

to

In an inertial system: Place a detector D midway between A

and B (using a yardstick). I assume that A, B and D are at

rest. Generate two signals at A and B. If they arrive at D

at the same time, they were sent at A and B at the same time.

This would be a kind of observation, albeit delayed.

> In our everyday experience

>we actually experience the world on our past light cone and think of that

>as "now". This a misconception.

For /everyday applications/ it does /not/ seem to be

a misconception, and when the difference between past

light cone surface and "now" starts to matter, it's

not an "everyday experience" anymore.

> I suggest that the only reality is on the

>past light cone. That is something that all observers can agree on.

The everyday reality consists of the things I can interact

with, like an automated teller machine (ATM). To get this

type of reality, the "now", in everyday life, needs to be

extended somewhat to an extended period of time like "today".

It cannot be only infinitesimally short, like a point of time.

This is the highest degree of reality: Something is very

real when one can interact with it, i.e., observe it /and/

affect it. Causality implies:

Systems of the past only have a semi-reality:

You can sometimes observe them, but not affect them.

For example, the Boston Tea Party. Also, systems of

the past are only inferred from records, so it is never

completely sure whether they even existed at all.

Systems of the future only have a semi-reality:

You can sometimes affect them, but not observe them.

For example, the Earth of the year 2023. Also, one

cannot be completely sure whether there will be such

an Earth.

>This is why I think it is a mistake in quantum mechanics to talk about the

>instantaneous collapse of the wave function CAUSED BY a measurement

>event. There cannot be a consistent causal explanation directly linking

>two events that are outside the light cone.

When we say "nothing can travel faster than light", this is

actually not quite correct. An imagined point can travel faster

than light. If I make a spot on the surface of the moon with

a laser beam, the spot can move there faster than light.

It is /energy-impulse transports/, which cannot move faster

than light (and therefore also information transports).

The collapse of an imagined function can be imagined in an

inertial frame quite as "everywhere at the same time",

as long as no energy-impulse is transported with superluminal

speed by this collapse.

and B (using a yardstick). I assume that A, B and D are at

rest. Generate two signals at A and B. If they arrive at D

at the same time, they were sent at A and B at the same time.

This would be a kind of observation, albeit delayed.

> In our everyday experience

>we actually experience the world on our past light cone and think of that

>as "now". This a misconception.

a misconception, and when the difference between past

light cone surface and "now" starts to matter, it's

not an "everyday experience" anymore.

> I suggest that the only reality is on the

>past light cone. That is something that all observers can agree on.

with, like an automated teller machine (ATM). To get this

type of reality, the "now", in everyday life, needs to be

extended somewhat to an extended period of time like "today".

It cannot be only infinitesimally short, like a point of time.

This is the highest degree of reality: Something is very

real when one can interact with it, i.e., observe it /and/

affect it. Causality implies:

Systems of the past only have a semi-reality:

You can sometimes observe them, but not affect them.

For example, the Boston Tea Party. Also, systems of

the past are only inferred from records, so it is never

completely sure whether they even existed at all.

Systems of the future only have a semi-reality:

You can sometimes affect them, but not observe them.

For example, the Earth of the year 2023. Also, one

cannot be completely sure whether there will be such

an Earth.

>This is why I think it is a mistake in quantum mechanics to talk about the

>instantaneous collapse of the wave function CAUSED BY a measurement

>event. There cannot be a consistent causal explanation directly linking

>two events that are outside the light cone.

actually not quite correct. An imagined point can travel faster

than light. If I make a spot on the surface of the moon with

a laser beam, the spot can move there faster than light.

It is /energy-impulse transports/, which cannot move faster

than light (and therefore also information transports).

The collapse of an imagined function can be imagined in an

inertial frame quite as "everywhere at the same time",

as long as no energy-impulse is transported with superluminal

speed by this collapse.

Mar 19, 2022, 2:27:38 PMMar 19

to

On 3/18/22 4:27 PM, Stefan Ram wrote:

> Richard Livingston <richali...@gmail.com> writes:

>> Simultaneity at a distance is not observable.

>

> In an inertial system: Place a detector D midway between A and B

> (using a yardstick). I assume that A, B and D are at rest. Generate

> two signals at A and B. If they arrive at D at the same time, they

> were sent at A and B at the same time. This would be a kind of

> observation, albeit delayed.

That is not observing simultaneity at A and B, it is observing
> Richard Livingston <richali...@gmail.com> writes:

>> Simultaneity at a distance is not observable.

>

> In an inertial system: Place a detector D midway between A and B

> (using a yardstick). I assume that A, B and D are at rest. Generate

> two signals at A and B. If they arrive at D at the same time, they

> were sent at A and B at the same time. This would be a kind of

> observation, albeit delayed.

simultaneity at D. From that observation and the setup and the inertial

frame, we can INFER that the signals from A and B were sent at the same

time IN THAT INERTIAL FRAME. Inference is not observation.

Observation implies a physical quantity is being observed. Simultaneity

at different spatial points is not any kind of physical quantity, it is

a CONVENTION based on the time coordinate of a particular inertial

frame; such coordinate-dependent quantities cannot possibly be physical

quantities.

> [...]

Attempting to apply modern physical theories to our everyday experience

is hopeless, because there are too many approximations involved.

Similarly, attempting to discuss "collapse of the wave function" in

terms of simultaneity and SR is also hopeless, because such "collapse"

is not observable (one can observe the system transitioning between

states, but not any "collapse").

A major lesson of modern physics is to discuss only measurable

(observable) quantities [#]. Both "everyday lives" and "wavefunction

collapse" violate that dictum (in very different ways).

[#] Interestingly, this applies to both QM and GR (for

very different reasons).

Tom Roberts

Mar 20, 2022, 6:44:33 AMMar 20

to

On 3/19/22 12:27 PM, Tom Roberts wrote:

>

> Observation implies a physical quantity is being observed. Simultaneity

> at different spatial points is not any kind of physical quantity, it is

> a CONVENTION based on the time coordinate of a particular inertial

> frame

>

Tom, what is your "take" on the use of an array of clocks, stationary in
>

> Observation implies a physical quantity is being observed. Simultaneity

> at different spatial points is not any kind of physical quantity, it is

> a CONVENTION based on the time coordinate of a particular inertial

> frame

>

some inertial frame, that have been synchronized using only the

assumption that the speed of light is equal to the universal constant

"c" in that frame. Each of those clocks is attended by a human "helper

friend" (HF), who can observe his immediate local surroundings. Another

particular observer (whom I'll refer to as "he"), also stationary in

that inertial frame, wants to know (when his watch shows time tau) the

current reading on a particular distant clock which is NOT stationary

with respect to that array of clocks. It seems reasonable that he is

entitled to say that the current reading on that distant clock is what

the HF, who happens to be colocated with that distant clock at the

instant when the HF's clock reads tau, directly observes it to be.

Doesn't that convey a sense of "meaningfulness", to the observers who

are stationary in that frame? I think Einstein thought it does.

Mar 20, 2022, 1:49:16 PMMar 20

to

On Friday, March 18, 2022 at 4:27:19 PM UTC-5, Stefan Ram wrote:

> Richard Livingston <richali...@gmail.com> writes:

> >Simultaneity at a distance is not observable.

> In an inertial system: Place a detector D midway between A

> and B (using a yardstick). I assume that A, B and D are at

> rest. Generate two signals at A and B. If they arrive at D

> at the same time, they were sent at A and B at the same time.

> This would be a kind of observation, albeit delayed.

Delayed is the key word. You cannot observe "now" now, you
> Richard Livingston <richali...@gmail.com> writes:

> >Simultaneity at a distance is not observable.

> In an inertial system: Place a detector D midway between A

> and B (using a yardstick). I assume that A, B and D are at

> rest. Generate two signals at A and B. If they arrive at D

> at the same time, they were sent at A and B at the same time.

> This would be a kind of observation, albeit delayed.

can only observe it when it becomes on your past light cone.

...

>

> This is the highest degree of reality: Something is very

> real when one can interact with it, i.e., observe it /and/

> affect it. Causality implies:

Only events on the past light cone can affect you. Only
> This is the highest degree of reality: Something is very

> real when one can interact with it, i.e., observe it /and/

> affect it. Causality implies:

events on your future light cone can be affected by you

at this moment. Events inside your future light cone can

be affected in your future.

>

> Systems of the past only have a semi-reality:

> You can sometimes observe them, but not affect them.

> For example, the Boston Tea Party. Also, systems of

> the past are only inferred from records, so it is never

> completely sure whether they even existed at all.

(accurately) remembered are something that everyone

can agree on. That is as close to reality as we will

ever get.

>

...

> The collapse of an imagined function can be imagined in an

> inertial frame quite as "everywhere at the same time",

> as long as no energy-impulse is transported with superluminal

> speed by this collapse.

I agree wrt a mathematical function as it applies to any single
> inertial frame quite as "everywhere at the same time",

> as long as no energy-impulse is transported with superluminal

> speed by this collapse.

observer. Yet the wave function does represent something

that is real, imperfectly. I'm not saying the wave function is

real or that it is exactly something real, but that it somehow

does capture some aspect of reality. The question is exactly

what of the wave function is real and what is a mathematical

fiction, or represents various alternate possibilities. I am

coming to the conclusion it would be better to call it a

possibility function rather than a probability function.

Rich L.

Mar 20, 2022, 1:50:52 PMMar 20

to

Tom Roberts <tjrobe...@sbcglobal.net> writes:

>A major lesson of modern physics is to discuss only measurable

>(observable) quantities

In quantum theory, the comprehensive framework theory of
>A major lesson of modern physics is to discuss only measurable

>(observable) quantities

physics, the state of a system plays the central role.

This state is not an observable, but discussed extensively!

In almost all areas of physics, also outside of quantum

physics, for example in GR, quantities are modeled by real

numbers, which are also not observable.

Mar 20, 2022, 2:30:37 PMMar 20

to

On Saturday, March 19, 2022 at 1:27:38 PM UTC-5, Tom Roberts wrote:

...

[[Mod. note -- I too would be interested in what Tom says.

My take would be that in GR, there is no preferred coordinate system

and all physical quantities (= those that are measurable, at least in

a gedanken sense) should be independent of the coordinate system in use.

Notably:

* the coordinate "time" of an event, or the difference between the

coordinate times of two events) is merely a coordinate; it has no

inherent physical meaning and can be changed arbitrarily by changing

our coordinate system

* *proper* time along some (timelike) worldline is measurable (it's

what an (ideal) clock moving along that worldline would measure),

can be said to have an inherent physical meaning (as the observable

result of that measurement), and *doesn't* change when we change

coordinates

* similarly, the coordinate position of an object, or the (coordinate)

distance between two objects, is also a coordinate, has no inherent

physical meaning, and can be changed arbitrarily by changing our

coordinate system

* the *proper* distance along a given path is measurable (at least in

a gedanken sense: one can imagine laying down a sequence of standard

rulers end-to-end along the path), and doesn't change when we change

coordinates;

* coordinate singularities (and the set of events where they occur)

have no inherent physical meaning, and a change in coordinates can

change the set of events where there is a coordinate singularity;

only singularities in observable quantities like curvature invariants,

proper times/distances, etc, are physically meaningful

-- jt]]

...

> A major lesson of modern physics is to discuss only measurable

> (observable) quantities [#]. Both "everyday lives" and "wavefunction

> collapse" violate that dictum (in very different ways).

>

> [#] Interestingly, this applies to both QM and GR (for

> very different reasons).

>

> Tom Roberts

Tom, I would be very interested in your expanding a bit on how this all applies to GR. -Rich L.
> (observable) quantities [#]. Both "everyday lives" and "wavefunction

> collapse" violate that dictum (in very different ways).

>

> [#] Interestingly, this applies to both QM and GR (for

> very different reasons).

>

> Tom Roberts

[[Mod. note -- I too would be interested in what Tom says.

My take would be that in GR, there is no preferred coordinate system

and all physical quantities (= those that are measurable, at least in

a gedanken sense) should be independent of the coordinate system in use.

Notably:

* the coordinate "time" of an event, or the difference between the

coordinate times of two events) is merely a coordinate; it has no

inherent physical meaning and can be changed arbitrarily by changing

our coordinate system

* *proper* time along some (timelike) worldline is measurable (it's

what an (ideal) clock moving along that worldline would measure),

can be said to have an inherent physical meaning (as the observable

result of that measurement), and *doesn't* change when we change

coordinates

* similarly, the coordinate position of an object, or the (coordinate)

distance between two objects, is also a coordinate, has no inherent

physical meaning, and can be changed arbitrarily by changing our

coordinate system

* the *proper* distance along a given path is measurable (at least in

a gedanken sense: one can imagine laying down a sequence of standard

rulers end-to-end along the path), and doesn't change when we change

coordinates;

* coordinate singularities (and the set of events where they occur)

have no inherent physical meaning, and a change in coordinates can

change the set of events where there is a coordinate singularity;

only singularities in observable quantities like curvature invariants,

proper times/distances, etc, are physically meaningful

-- jt]]

Mar 25, 2022, 6:57:18 AMMar 25

to

I'd like to add a bit to my above argument.

I think a sizeable number of physicists DO believe that simultaneity at

a distance is a meaningless concept, and I've even noticed a trend of

trying to de-emphasize talking about simultaneity-at-a-distance in

introductory special relativity courses. But I think that is a big

mistake. It certainly wasn't Einstein's view, at least for inertial

observers. (I've seen a quote from Einstein somewhere where he said he

hardly recognizes his theory when he reads some modern descriptions of

it.)

My above question of Tom Roberts was prompted mostly by his use of the

word "Convention" in describing simultaneity at a distance for an

inertial observer. To me, the term "Convention" implies that there is

more than one possible answer to the question "How old is that distant

person (she), right now", when asked and answered by a particular

inertial observer. "Convention" implies that one can pick from among

multiple alternatives, all equally good.

But I don't believe that is true, given my above description of how an

array of synchronized clocks (all permanently stationary with respect to

the given inertial observer) can be set up, creating a common "NOW"

instant for him and for all of the HF's ("helper friends") co-located

and co-stationary with the clocks. At any given instant "tau" in the

life of the given inertial observer, it's clear that there is just a

single answer to the question "How old is that particular distant person

(she) right now (at the given time "tau" in the life of the inertial

observer): it is what the particular HF (he) who happens to be

momentarily co-located with the distant person (she), says it is, at the

instant when he is age "tau". The only way there could be any other

allowable answer is if the synchronization of the clocks isn't valid,

and that is impossible if the velocity of light in that inertial

reference frame is equal to the universal constant "c".

Mar 26, 2022, 4:31:42 PMMar 26

to

Mar 28, 2022, 5:36:58 AMMar 28

to

On Friday, March 25, 2022 at 5:57:18 AM UTC-5, Mike Fontenot wrote:

...

...

"now" at a distant location is that people take it as something

real and meaningful, and I think an argument can be made that it

is not very meaningful.

What is useful for physics is establishing a coordinate framework

that allows us to describe physics in a consistent way. For this

purpose "now" at a distant location makes sense. But our

mathematics is in a sense all knowing in that we keep track of

events at all locations and times, before they are able to interact

with other objects in the future.

For an individual, however, what is "now" at a distant location is

not something that has a consistent answer. Two different

observers at the same event can have very different ideas about

what is happening "now" someplace else. What is indisputably

real, however, is what these observers can see on their past

light cone. All observers at an event will see the same things

on their past light cones.

Rich L.

Mar 28, 2022, 5:37:28 AMMar 28

to

On 3/26/22 2:31 PM, jtmpreno wrote:

>

> What if the twins (or clocks) were quantum-entangled?

If we were talking about molecular-size objects or smaller, we'd need to
>

> What if the twins (or clocks) were quantum-entangled?

use quantum mechanics in the analysis. But we're not.

Mar 29, 2022, 6:19:18 AMMar 29

to

On 3/28/22 3:36 AM, Richard Livingston wrote:

> On Friday, March 25, 2022 at 5:57:18 AM UTC-5, Mike Fontenot wrote:

>> [...] At any given instant "tau" in the
> On Friday, March 25, 2022 at 5:57:18 AM UTC-5, Mike Fontenot wrote:

>> life of the given inertial observer, it's clear that there is just a

>> single answer to the question "How old is that particular distant person

>> (she) right now (at the given time "tau" in the life of the inertial

>> observer): it is what the particular HF (he) who happens to be

>> momentarily co-located with the distant person (she), says it is, at the

>> instant when he is age "tau". The only way there could be any other

>> allowable answer is if the synchronization of the clocks isn't valid,

>> and that is impossible if the velocity of light in that inertial

>> reference frame is equal to the universal constant "c".

>

> I think I mostly agree with you, but still think that the problem with

> "now" at a distant location is that people take it as something

> real and meaningful, and I think an argument can be made that it

> is not very meaningful.

>

My argument above is that, IF those clocks are synchronized (according
>> single answer to the question "How old is that particular distant person

>> (she) right now (at the given time "tau" in the life of the inertial

>> observer): it is what the particular HF (he) who happens to be

>> momentarily co-located with the distant person (she), says it is, at the

>> instant when he is age "tau". The only way there could be any other

>> allowable answer is if the synchronization of the clocks isn't valid,

>> and that is impossible if the velocity of light in that inertial

>> reference frame is equal to the universal constant "c".

>

> I think I mostly agree with you, but still think that the problem with

> "now" at a distant location is that people take it as something

> real and meaningful, and I think an argument can be made that it

> is not very meaningful.

>

to the given observer), then he can't help but conclude that the current

age of that distant person IS completely meaningful TO HIM. And the

only way that those clocks AREN'T synchronized according to him, is if

the velocity of light in his inertial reference frame ISN'T equal to the

universal constant "c". But the fundamental assumption of special

relativity IS that light will be measured in all inertial reference

frames to have the value "c". Therefore, FOR any given inertial

observer (he), the current age of a distant person is completely

meaningful to him.

But what about a non-inertial observer? In particular, what about a

given observer who is undergoing a constant acceleration? What does HE

say the current age of a distant person is? It turns out to be possible

for such an accelerating observer to rely on an array of clocks and

associated "helper friends" (HF's) to give him the answer. Unlike in

the inertial case, those clocks DON'T run at the same rate. But the

ratio of the rates of those clocks can be CALCULATED by the given

observer. And if he (and the HF's) are initially stationary and

unaccelerated, they can start out with synchronized clocks (and ages).

Then, if they all fire their identical rockets at the same instant, they

can each CALCULATE the current reading of each of the other clocks, at

each instant in their lives. The calculations of each of the HF's all

agree. So, at any instant in their lives during that acceleration, they

each share the same "NOW" instant with all of the other HF's. That

means that the given observer (he), at any instant "tau" in his life,

can obtain the current age "T" of some distant person (her), by asking

the HF, who happens to be momentarily co-located with her at that NOW

instant, what her age is then.

Apr 2, 2022, 2:22:56 AMApr 2

to

On 3/20/22 5:44 AM, Mike Fontenot wrote:

> On 3/19/22 12:27 PM, Tom Roberts wrote:

>> Observation implies a physical quantity is being observed.

>> Simultaneity at different spatial points is not any kind of

>> physical quantity, it is a CONVENTION based on the time coordinate

>> of a particular inertial frame

>

> Tom, what is your "take" on the use of an array of clocks,

> stationary in some inertial frame, that have been synchronized using

> only the assumption that the speed of light is equal to the universal

> constant "c" in that frame. Each of those clocks is attended by a

> human "helper friend" (HF), who can observe his immediate local

> surroundings. Another particular observer (whom I'll refer to as

> "he"), also stationary in that inertial frame, wants to know (when

> his watch shows time tau) the current reading on a particular

> distant clock which is NOT stationary with respect to that array of

> clocks. It seems reasonable that he is entitled to say that the

> current reading on that distant clock is what the HF, who happens to

> be colocated with that distant clock at the instant when the HF's

> clock reads tau, directly observes it to be.

Sure, one could do that. Though there seems to be little motivation to
> On 3/19/22 12:27 PM, Tom Roberts wrote:

>> Observation implies a physical quantity is being observed.

>> Simultaneity at different spatial points is not any kind of

>> physical quantity, it is a CONVENTION based on the time coordinate

>> of a particular inertial frame

>

> Tom, what is your "take" on the use of an array of clocks,

> stationary in some inertial frame, that have been synchronized using

> only the assumption that the speed of light is equal to the universal

> constant "c" in that frame. Each of those clocks is attended by a

> human "helper friend" (HF), who can observe his immediate local

> surroundings. Another particular observer (whom I'll refer to as

> "he"), also stationary in that inertial frame, wants to know (when

> his watch shows time tau) the current reading on a particular

> distant clock which is NOT stationary with respect to that array of

> clocks. It seems reasonable that he is entitled to say that the

> current reading on that distant clock is what the HF, who happens to

> be colocated with that distant clock at the instant when the HF's

> clock reads tau, directly observes it to be.

do so.

The particular observer NEVER knows "the current reading" of that

distant clock (for any meaning of "current"), he can only learn what it

was at some time in the past (e.g. at time tau), after the HF transmits

their result to him. Note that in your scenario the particular observer

must transmit the value of tau to all HFs well in advance;

alternatively, each HF could record values whenever the distant clock

passes by, and they all send those records to the particular observer,

who can then pick and choose among them, after the fact.

> Doesn't that convey a sense of "meaningfulness", to the observers who

> are stationary in that frame? I think Einstein thought it does.

you synchronized the clocks differently you would get a different

result. It says nothing at all about other frames.

Tom Roberts

Apr 2, 2022, 2:22:56 AMApr 2

to

On 3/20/22 1:30 PM, Richard Livingston wrote:

> On Saturday, March 19, 2022 at 1:27:38 PM UTC-5, Tom Roberts wrote:

>> A major lesson of modern physics is to discuss only measurable

>> (observable) quantities [#]. Both "everyday lives" and

>> "wavefunction collapse" violate that dictum (in very different

>> ways).

>> [#] Interestingly, this applies to both QM and GR (for very

>> different reasons).

>

> Tom, I would be very interested in your expanding a bit on how this

> all applies to GR. -Rich L.

Note that coordinates are arbitrary human constructs, which we use to
> all applies to GR. -Rich L.

simplify, codify, and quantify our observations and descriptions. Nature

clearly uses no coordinates, so the choice of coordinates used to

describe some natural phenomenon cannot possibly affect that phenomenon.

That is the importance of coordinate independence in GR (and in all of

theoretical physics) -- for a quantity to correspond to some physical

phenomenon, it must be independent of coordinates (aka invariant).

For instance, each and every measurement is a definite value for

whatever physical phenomenon is being measured, and is inherently

invariant. So observer A can construct a locally inertial frame and use

it to measure the kinetic energy of a baseball, and all other observers

will agree that is the value A measures in that frame, even though they

themselves use other frames to measure a different value.

[This has been called a "coordinate-dependent invariant

quantity -- the value depends on which coordinates are

used, but the result is invariant because it is

inextricably bound to the coordinates used.]

Take careful note of the wording: kinetic energy is NOT invariant,

but the kinetic energy of a designated object relative to a specified

inertial frame is indeed invariant. So observers using other frames can

make measurements of the designated object, transform them to the

specified frame, and agree on the value obtained in the specified frame.

> Mod. note -- I too would be interested in what Tom says.

> My take would be that in GR, there is no preferred coordinate system

> and all physical quantities (= those that are measurable, at least in

> a gedanken sense) should be independent of the coordinate system in

> use.

Also beware of "preferred coordinate system", because those words are

ambiguous -- physicists use that phrase in the sense of a coordinate

system that appears explicitly in the equations of the dynamics; but in

many/most cases there is a particular choice of coordinates relative to

which the calculations are simplified, and we invariably prefer to use

them. The invariance of physical quantities ensures we can do so.

> Notably:

> * the coordinate "time" of an event, or the difference between the

> coordinate times of two events) is merely a coordinate; it has no

> inherent physical meaning and can be changed arbitrarily by changing

> our coordinate system

> * *proper* time along some (timelike) worldline is measurable (it's

> what an (ideal) clock moving along that worldline would measure),

> can be said to have an inherent physical meaning (as the observable

> result of that measurement), and *doesn't* change when we change

> coordinates

> * similarly, the coordinate position of an object, or the (coordinate)

> distance between two objects, is also a coordinate, has no inherent

> physical meaning, and can be changed arbitrarily by changing our

> coordinate system

> * the *proper* distance along a given path is measurable (at least in

> a gedanken sense: one can imagine laying down a sequence of standard

> rulers end-to-end along the path), and doesn't change when we change

> coordinates;

> * coordinate singularities (and the set of events where they occur)

> have no inherent physical meaning, and a change in coordinates can

> change the set of events where there is a coordinate singularity;

> only singularities in observable quantities like curvature invariants,

> proper times/distances, etc, are physically meaningful

Tom Roberts

Apr 2, 2022, 2:22:56 AMApr 2

to

On 3/25/22 5:57 AM, Mike Fontenot wrote:

> My above question of Tom Roberts was prompted mostly by his use of

> the word "Convention" in describing simultaneity at a distance for

> an inertial observer. To me, the term "Convention" implies that

> there is more than one possible answer to the question "How old is

> that distant person (she), right now", when asked and answered by a

> particular inertial observer. "Convention" implies that one can pick

> from among multiple alternatives, all equally good.

Right, that's what it means: there are an infinite number of coordinate
> My above question of Tom Roberts was prompted mostly by his use of

> the word "Convention" in describing simultaneity at a distance for

> an inertial observer. To me, the term "Convention" implies that

> there is more than one possible answer to the question "How old is

> that distant person (she), right now", when asked and answered by a

> particular inertial observer. "Convention" implies that one can pick

> from among multiple alternatives, all equally good.

systems from which to choose, and in GR (and modern physics in general),

all are equally good for describing what happens. (Note that none of

them actually affects what happens, they only describe it differently.)

> But I don't believe that is true, given my above description of how

> an array of synchronized clocks (all permanently stationary with

As I said before, you simply applied the convention of using Einstein

synchronization in an inertial frame. There is no compulsion to do so,

it just so happens that it is (usually) the easiest and simplest system

of coordinates to use in the case where the observer is at rest in the

inertial frame.

IOW the frame does not determine the coordinates, the human observer

does so. We humans generally select the coordinates in which

calculations are simplest, but that is all it is. Don't confuse an

ordinary human desire for simplicity (laziness) with anything more profound.

Richard Livingston then wrote:

> I think I mostly agree with you, but still think that the problem

> with "now" at a distant location is that people take it as something

> real and meaningful, and I think an argument can be made that it is

> not very meaningful.

modern physics: "now at a distant location" does not contribute to any

current model of the world. In GR such spacelike intervals are outside

the past lightcone and so cannot affect what happens at the event in

question (i.e. now at the speaker's location); in QFT, fields evaluated

at such a spacelike interval always commute (and thus do not contribute

to any amplitudes).

> What is useful for physics is establishing a coordinate framework

> that allows us to describe physics in a consistent way.

> For this purpose "now" at a distant location makes sense.

For describing what happened, AFTER THE FACT, based on reports received

from distant 'helper friends', sure. But for modeling the world, it is

not useful at all (see my previous paragraph).

Mike Fontenot then wrote:

> IF those clocks are synchronized (according to the given observer),

> then he can't help but conclude that the current age of that distant

> person IS completely meaningful TO HIM.

a convention. For an inertial observer, using the coordinates of their

rest frame is the simplest way to interpret "now" at distant locations,

but they are well advised to remember it is merely a convention to do it

that way, one based on simplicity TO HUMANS, not any physical basis.

Don't confuse an ordinary human desire for simplicity (laziness) with

anything more profound.

> But what about a non-inertial observer?

accelerating observer, "now" has no definite meaning, and attempting to

give it one is just foolish, and no sensible person would ever believe

it. They can calculate whatever they like, but no sensible person would

think that just by turning their spaceship around their distant friend

gets younger -- they would KNOW that this is purely an artifact of the

math used in the calculation and their current acceleration, and that

has nothing whatsoever to do with their friend. Any astronaut in a

spacecraft capable of traveling at an appreciable fraction of c would

already know that their time is completely divorced from that of their

friends back home.

Tom Roberts

Apr 2, 2022, 1:36:44 PMApr 2

to

On 3/29/22 4:19 AM, (I) Mike Fontenot wrote:

>

> But what about a non-inertial observer? In particular, what about a

> given observer who is undergoing a constant acceleration? What does HE

> say the current age of a distant person is? It turns out to be possible

> for such an accelerating observer to rely on an array of clocks and

> associated "helper friends" (HF's) to give him the answer. Unlike in

> the inertial case, those clocks DON'T run at the same rate. But the

> ratio of the rates of those clocks can be CALCULATED by the given

> observer. And if he (and the HF's) are initially stationary and

> unaccelerated, they can start out with synchronized clocks (and ages).

> Then, if they all fire their identical rockets at the same instant, they

> can each CALCULATE the current reading of each of the other clocks, at

> each instant in their lives. The calculations of each of the HF's all

> agree. So, at any instant in their lives during that acceleration, they

> each share the same "NOW" instant with all of the other HF's. That

> means that the given observer (he), at any instant "tau" in his life,

> can obtain the current age "T" of some distant person (her), by asking

> the HF, who happens to be momentarily co-located with her at that NOW

> instant, what her age is then.

>

In the above, I said that the given accelerating observer (he)
>

> But what about a non-inertial observer? In particular, what about a

> given observer who is undergoing a constant acceleration? What does HE

> say the current age of a distant person is? It turns out to be possible

> for such an accelerating observer to rely on an array of clocks and

> associated "helper friends" (HF's) to give him the answer. Unlike in

> the inertial case, those clocks DON'T run at the same rate. But the

> ratio of the rates of those clocks can be CALCULATED by the given

> observer. And if he (and the HF's) are initially stationary and

> unaccelerated, they can start out with synchronized clocks (and ages).

> Then, if they all fire their identical rockets at the same instant, they

> can each CALCULATE the current reading of each of the other clocks, at

> each instant in their lives. The calculations of each of the HF's all

> agree. So, at any instant in their lives during that acceleration, they

> each share the same "NOW" instant with all of the other HF's. That

> means that the given observer (he), at any instant "tau" in his life,

> can obtain the current age "T" of some distant person (her), by asking

> the HF, who happens to be momentarily co-located with her at that NOW

> instant, what her age is then.

>

(abbreviated, the "AO"), at each instant of his life, can CALCULATE the

current reading on each of the HF's clocks. What IS that calculation?

Let t = 0 be the reading on his clock at the instant that the constant

acceleration "A" begins, and let all the HFs' clocks also read zero at

that instant. Thereafter, he and all of the HFs are accelerating at "A"

ls/s/s, and the ratio R of any given HF's clock rate to his (the

observer's (he) whose conclusions we are seeking) clock rate is

R(t) = [ 1 +- L A sech^2 (A t) ],

where L is the constant distance between him and the given HF, and

sech() is the hyperbolic secant (which is the reciprocal of cosh(), the

hyperbolic cosine). The "^2" after the sech indicates the square of the

sech. The "+-" in the above equation means that the second term is

ADDED to 1 for the HF's who are LEADING the accelerating observer, and

the second term is SUBTRACTED from 1 for the HF's who are TRAILING the

accelerating observer. For brevity, I'll just take the case where the

HF of interest is a leading HF.

The limit of R(t), as "t" goes to zero, is 1 + L A. The limit of R(t),

as "t" goes to infinity, is 1.0 So R(t) starts out at some positive

number greater than 1, and then approaches 1.0 as t goes to infinity.

So eventually, all the clocks essentially tic at the same rate, but

early in the acceleration, the ratio of the tic rates varies

significantly with time.

The current reading of the HF's clock (the "Age Change" or "AC"), when

the AO's clock reads "tau", is

AC(tau) = integral, from zero to tau, of { R(t) dt }

= tau + L tanh( A tau ).

The above result depends on the fact that

sech^2(u) = d{tanh(u)} / d{u}.

As tau goes to zero, AC goes to zero. As tau goes to infinity, AC goes

to tau + L, which goes to infinity, approaching a slope of 1.0 from above.

So there you have it. That's the calculation that defines "NOW" for the

AO and all of the HF's, and makes simultaneity at a distance a

meaningful concept for them. Simultaneity at a distance is not a choice.

Apr 2, 2022, 1:51:27 PMApr 2

to

fundamental assumption that special relativity is based on: that the

speed of light in any inertial frame is always equal to the universal

constant "c".

Apr 3, 2022, 1:13:51 PMApr 3

to

On 4/2/22 11:36 AM, (I) Mike Fontenot wrote:

>

> So there you have it. That's the calculation that defines "NOW" for the

> AO and all of the HF's, and makes simultaneity at a distance a

> meaningful concept for them. Simultaneity at a distance is not a choice.

>

But what does the above say about the current age of the home twin
>

> So there you have it. That's the calculation that defines "NOW" for the

> AO and all of the HF's, and makes simultaneity at a distance a

> meaningful concept for them. Simultaneity at a distance is not a choice.

>

(she), according to the traveling twin (he), for each instant in his

life on his trip? The answer is that the above equations give the same

results as the Co-Moving-Inertial-Frames (CMIF) simultaneity method.

That is very fortuitous, because the CMIF method is relatively easy to

use. The value of the array of clocks discussed above (which establish

a "NOW" moment for the accelerating observer that extends throughout all

space) is that they GUARANTEE that the CMIF results are fully meaningful

to the traveler, and that the CMIF method is the ONLY correct

simultaneity method for him. He has no other choice.

Apr 3, 2022, 6:15:21 PMApr 3

to

one synchronized those clocks differently, they would not yield the time

coordinate of an inertial frame, so the assumptions of SR simply would

not apply, and can be ignored.

[Don't ask me why anyone would do that, I'm merely pointing

out that it is possible. The usual Einstein synchronization

is used because it simplifies the math. As I said before:

Don't confuse an ordinary human desire for simplicity

(laziness) with anything more profound.]
Tom Roberts

Apr 3, 2022, 6:15:23 PMApr 3

to

On 3/20/22 1:30 PM, Richard Livingston wrote:

> On Saturday, March 19, 2022 at 1:27:38 PM UTC-5, Tom Roberts wrote:

>> A major lesson of modern physics is to discuss only measurable

>> (observable) quantities [#]. Both "everyday lives" and

>> "wavefunction collapse" violate that dictum (in very different

>> ways).

>> [#] Interestingly, this applies to both QM and GR (for very

>> different reasons).

>

>> A major lesson of modern physics is to discuss only measurable

>> (observable) quantities [#]. Both "everyday lives" and

>> "wavefunction collapse" violate that dictum (in very different

>> ways).

>> [#] Interestingly, this applies to both QM and GR (for very

>> different reasons).

>

> Tom, I would be very interested in your expanding a bit on how this

> all applies to GR. -Rich L.

> all applies to GR. -Rich L.

Note that coordinates are arbitrary human constructs, which we use to

simplify, codify, and quantify our observations and descriptions. Nature

clearly uses no coordinates, so the choice of coordinates used to

describe some natural phenomenon cannot possibly affect that phenomenon.

That is the importance of coordinate independence in GR (and in all of

theoretical physics) -- for a quantity to correspond to some physical

phenomenon, it must be independent of coordinates (aka invariant).

For instance, each and every measurement is a definite value for

whatever physical phenomenon is being measured, and is inherently

invariant. So observer A can construct a locally inertial frame and use

it to measure the kinetic energy of a baseball, and all other observers

will agree that is the value A measures in that frame, even though they

themselves use other frames to measure a different value.

[This has been called a "coordinate-dependent invariant

quantity -- the value depends on which coordinates are

used, but the result is invariant because it is

inextricably bound to the coordinates used.]

Take careful note of the wording: kinetic energy is NOT invariant,

but the kinetic energy of a designated object relative to a specified

inertial frame is indeed invariant. So observers using other frames can

make measurements of the designated object, transform them to the

specified frame, and agree on the value obtained in the specified frame.

simplify, codify, and quantify our observations and descriptions. Nature

clearly uses no coordinates, so the choice of coordinates used to

describe some natural phenomenon cannot possibly affect that phenomenon.

That is the importance of coordinate independence in GR (and in all of

theoretical physics) -- for a quantity to correspond to some physical

phenomenon, it must be independent of coordinates (aka invariant).

For instance, each and every measurement is a definite value for

whatever physical phenomenon is being measured, and is inherently

invariant. So observer A can construct a locally inertial frame and use

it to measure the kinetic energy of a baseball, and all other observers

will agree that is the value A measures in that frame, even though they

themselves use other frames to measure a different value.

[This has been called a "coordinate-dependent invariant

quantity -- the value depends on which coordinates are

used, but the result is invariant because it is

inextricably bound to the coordinates used.]

Take careful note of the wording: kinetic energy is NOT invariant,

but the kinetic energy of a designated object relative to a specified

inertial frame is indeed invariant. So observers using other frames can

make measurements of the designated object, transform them to the

specified frame, and agree on the value obtained in the specified frame.

> Mod. note -- I too would be interested in what Tom says.

> My take would be that in GR, there is no preferred coordinate system

> and all physical quantities (= those that are measurable, at least in

> a gedanken sense) should be independent of the coordinate system in

> use.

> My take would be that in GR, there is no preferred coordinate system

> and all physical quantities (= those that are measurable, at least in

> a gedanken sense) should be independent of the coordinate system in

> use.

Yes, "should be" => "are".

Also beware of "preferred coordinate system", because those words are

ambiguous -- physicists use that phrase in the sense of a coordinate

system that appears explicitly in the equations of the dynamics; but in

many/most cases there is a particular choice of coordinates relative to

which the calculations are simplified, and we invariably prefer to use

them. The invariance of physical quantities ensures we can do so.

Also beware of "preferred coordinate system", because those words are

ambiguous -- physicists use that phrase in the sense of a coordinate

system that appears explicitly in the equations of the dynamics; but in

many/most cases there is a particular choice of coordinates relative to

which the calculations are simplified, and we invariably prefer to use

them. The invariance of physical quantities ensures we can do so.

> Notably:

> * the coordinate "time" of an event, or the difference between the

> coordinate times of two events) is merely a coordinate; it has no

> inherent physical meaning and can be changed arbitrarily by changing

> our coordinate system

> * *proper* time along some (timelike) worldline is measurable (it's

> what an (ideal) clock moving along that worldline would measure),

> can be said to have an inherent physical meaning (as the observable

> result of that measurement), and *doesn't* change when we change

> coordinates

> * similarly, the coordinate position of an object, or the (coordinate)

> distance between two objects, is also a coordinate, has no inherent

> physical meaning, and can be changed arbitrarily by changing our

> coordinate system

> * the *proper* distance along a given path is measurable (at least in

> a gedanken sense: one can imagine laying down a sequence of standard

> rulers end-to-end along the path), and doesn't change when we change

> coordinates;

> * coordinate singularities (and the set of events where they occur)

> have no inherent physical meaning, and a change in coordinates can

> change the set of events where there is a coordinate singularity;

> only singularities in observable quantities like curvature invariants,

> proper times/distances, etc, are physically meaningful

> * the coordinate "time" of an event, or the difference between the

> coordinate times of two events) is merely a coordinate; it has no

> inherent physical meaning and can be changed arbitrarily by changing

> our coordinate system

> * *proper* time along some (timelike) worldline is measurable (it's

> what an (ideal) clock moving along that worldline would measure),

> can be said to have an inherent physical meaning (as the observable

> result of that measurement), and *doesn't* change when we change

> coordinates

> * similarly, the coordinate position of an object, or the (coordinate)

> distance between two objects, is also a coordinate, has no inherent

> physical meaning, and can be changed arbitrarily by changing our

> coordinate system

> * the *proper* distance along a given path is measurable (at least in

> a gedanken sense: one can imagine laying down a sequence of standard

> rulers end-to-end along the path), and doesn't change when we change

> coordinates;

> * coordinate singularities (and the set of events where they occur)

> have no inherent physical meaning, and a change in coordinates can

> change the set of events where there is a coordinate singularity;

> only singularities in observable quantities like curvature invariants,

> proper times/distances, etc, are physically meaningful

Apr 3, 2022, 6:15:23 PMApr 3

to

On 3/20/22 5:44 AM, Mike Fontenot wrote:

> On 3/19/22 12:27 PM, Tom Roberts wrote:

>> Observation implies a physical quantity is being observed.

>> Simultaneity at different spatial points is not any kind of

>> physical quantity, it is a CONVENTION based on the time coordinate

>> of a particular inertial frame

>

> Tom, what is your "take" on the use of an array of clocks,

> stationary in some inertial frame, that have been synchronized using

> only the assumption that the speed of light is equal to the universal

> constant "c" in that frame. Each of those clocks is attended by a

> human "helper friend" (HF), who can observe his immediate local

> surroundings. Another particular observer (whom I'll refer to as

> "he"), also stationary in that inertial frame, wants to know (when

> his watch shows time tau) the current reading on a particular

> distant clock which is NOT stationary with respect to that array of

> clocks. It seems reasonable that he is entitled to say that the

> current reading on that distant clock is what the HF, who happens to

> be colocated with that distant clock at the instant when the HF's

> clock reads tau, directly observes it to be.

>> Observation implies a physical quantity is being observed.

>> Simultaneity at different spatial points is not any kind of

>> physical quantity, it is a CONVENTION based on the time coordinate

>> of a particular inertial frame

>

> Tom, what is your "take" on the use of an array of clocks,

> stationary in some inertial frame, that have been synchronized using

> only the assumption that the speed of light is equal to the universal

> constant "c" in that frame. Each of those clocks is attended by a

> human "helper friend" (HF), who can observe his immediate local

> surroundings. Another particular observer (whom I'll refer to as

> "he"), also stationary in that inertial frame, wants to know (when

> his watch shows time tau) the current reading on a particular

> distant clock which is NOT stationary with respect to that array of

> clocks. It seems reasonable that he is entitled to say that the

> current reading on that distant clock is what the HF, who happens to

> be colocated with that distant clock at the instant when the HF's

> clock reads tau, directly observes it to be.

Sure, one could do that. Though there seems to be little motivation to

do so.

The particular observer NEVER knows "the current reading" of that

distant clock (for any meaning of "current"), he can only learn what it

was at some time in the past (e.g. at time tau), after the HF transmits

their result to him. Note that in your scenario the particular observer

must transmit the value of tau to all HFs well in advance;

alternatively, each HF could record values whenever the distant clock

passes by, and they all send those records to the particular observer,

who can then pick and choose among them, after the fact.

do so.

The particular observer NEVER knows "the current reading" of that

distant clock (for any meaning of "current"), he can only learn what it

was at some time in the past (e.g. at time tau), after the HF transmits

their result to him. Note that in your scenario the particular observer

must transmit the value of tau to all HFs well in advance;

alternatively, each HF could record values whenever the distant clock

passes by, and they all send those records to the particular observer,

who can then pick and choose among them, after the fact.

> Doesn't that convey a sense of "meaningfulness", to the observers who

> are stationary in that frame? I think Einstein thought it does.

> are stationary in that frame? I think Einstein thought it does.

You simply implemented the CONVENTION of Einstein synchronization. If

you synchronized the clocks differently you would get a different

you synchronized the clocks differently you would get a different

Apr 5, 2022, 3:53:36 PMApr 5

to

On 4/3/22 12:13 PM, Mike Fontenot wrote:

> On 4/2/22 11:36 AM, (I) Mike Fontenot wrote:

>> So there you have it. That's the calculation that defines "NOW"

>> for the AO and all of the HF's, and makes simultaneity at a

>> distance a meaningful concept for them. Simultaneity at a

>> distance is not a choice.

Yes, simultaneity at a distance is a choice. Your approach is
> On 4/2/22 11:36 AM, (I) Mike Fontenot wrote:

>> So there you have it. That's the calculation that defines "NOW"

>> for the AO and all of the HF's, and makes simultaneity at a

>> distance a meaningful concept for them. Simultaneity at a

>> distance is not a choice.

outrageously unphysical -- maneuvering the ship causes unphysical

changes in the "age" ascribed to a distant friend.

> But what does the above say about the current age of the home twin

> (she), according to the traveling twin (he), for each instant in his

> life on his trip? The answer is that the above equations give the

> same results as the Co-Moving-Inertial-Frames (CMIF) simultaneity

> method. That is very fortuitous, because the CMIF method is

> relatively easy to use. The value of the array of clocks discussed

> above (which establish a "NOW" moment for the accelerating observer

> that extends throughout all space) is that they GUARANTEE that the

> CMIF results are fully meaningful to the traveler, and that the CMIF

> method is the ONLY correct simultaneity method for him.

unphysical. If the traveling twin maneuvers his spaceship, the "age" he

ascribes to a distant friend can change very rapidly. No sensible person

would believe that local actions he takes can "change" his friend's age.

> He has no other choice.

completely divorced from that of his friend far away. If the age of his

friend is important to him, he would keep track of his motion relative

to the ICRF, knowing that regardless of his motion or location, the

current time of the ICRF can be used to calculate the current age of his

friend (for all practical purposes his friend on earth is at rest in

the ICRF). Any sensible astronaut would do that.

Tom Roberts

Apr 5, 2022, 3:54:06 PMApr 5

to

(This is an improved version of a posting that I submitted yesterday

[4-3-22], but which hasn't shown up yet)

In 1907, Einstein published a VERY long paper (in several volumes) on

his "relativity principle". In volume 2, section 18, page 302, titled

"Space and time in a uniformly accelerated reference frame", he

investigated how the tic rates compare for two clocks separated by the

constant distance L, with both clocks undergoing a constant acceleration

"A". He restricted the analysis to very small accelerations (and very

small resulting velocities). His result (on page 305) was that the

leading clock tics at a rate

R = 1 + L A

faster than the rear clock. Note that that result agrees with my

equation, for very small "L" and "A". But he then said:

"From the fact that the choice of the coordinate origin must not

affect the relation, one must conclude that, strictly speaking, equation

(30) should be replaced by the equation R = exp(L A). Nevertheless, we

shall maintain formula (30)."

I've never understood that one sentence argument he gave, for replacing

his linear equation with the exponential equation. But I DID assume he

was right (because he was rarely wrong), until I tried applying his

exponential equation to the case of essentially instantaneous velocity

changes that are useful in twin "paradox" scenarios in special

relativity. Specifically, I worked a series of examples where the

separation of the two clocks is always

L = 7.52 ls (lightseconds)

and where the final speed (with the initial speed being zero) is always

v = 0.866 ls/s.

That speed implies a final "rapidity" of

theta = atanh(0.866) = 1.317 ls/s.

("Rapidity" is a non-linear version of velocity. They have a one-to-one

correspondence. In special relativity, velocity can never exceed 1.0

ls/s in magnitude, but rapidity can have an infinite magnitude. An

acceleration of "A" ls/s/s lasting for "t" seconds changes the rapidity

theta by the product of "A" and "t".)

So in this case, when we are starting from zero velocity and thus zero

rapidity, at the end of the acceleration,

theta = A tau,

where tau is the duration of the acceleration (according to the rear

clock). So, if we know theta and tau, we then know the acceleration:

A = theta / tau.

I do a sequence of calculations, each starting at t = 0, with the two

clocks reading zero, and with zero acceleration for t < 0.

First, I set the duration tau of the acceleration to 1 second. The

acceleration then needs to be

A = theta / tau = 1.317 / 1.0 = 1.317 ls/s/s (that's roughly

40 g's).

So for this first case, the tic rate of the leading clock during the one

second acceleration is

R = exp( L A ) = exp(9.9034), or about 20000.

(I picked that weird value of "L" so that this value of "R" for the fist

case would be a round number, just to make the calculations easier.)

Since R is constant during the acceleration, the CURRENT reading on the

leading clock (which I'll denote as AC, for "Age Change") is

AC = tau R = 2x10sup4 = 20000

(where 10sup4 means "10 raised to the 4th power").

I then start over and work a second case, with ten times the

acceleration (13.17 ls/s/s), but with tau ten times smaller (0.1

second). That keeps the final rapidity the same as in the first case,

and the final speed is also 0.866, as before. For the second case,

AC = 1.02x10sup42.

So when we made the acceleration an order of magnitude larger, and the

duration an order of magnitude smaller, the current reading "AC" on the

leading clock got about 38 orders of magnitude larger.

Next, I start over again and work a third case, again increasing the

acceleration by a factor of 10, and the decreasing the duration by a

factor of 10, so "A" = 131.7 ls/s/s and tau = 0.01 second. Then, AC =

1.27x10sup428. So this time, when we increased "A" by a factor of 10,

and decreased tau by a factor of ten, AC got about 380 orders of

magnitude larger.

AC is not approaching a finite limit as tau goes to zero and "A" goes to

infinity. In each iteration, the change in AC compared to the previous

change gets MUCH larger. Clearly, the clock reading is NOT converging

to a finite limit. It is going to infinity as tau goes to zero.

We can see this, even without doing the above detailed calculations. Since

AC = tau exp(L A),

the tau factor goes to zero LINEARLY as tau goes to zero, but exp(L A)

goes to infinity EXPONENTIALLY as tau goes to zero, so their product is

obviously not going to be finite as tau goes to zero.

So, for the idealization of an essentially instantaneous velocity

change, the change of the reading on the leading clock is INFINITE

during the infinitesimal change of the rear clock. That means that,

when the traveling twin instantaneously changes his speed from zero to

0.866 (toward the home twin), the exponential version of the R equation

says that the home twin's age becomes infinite. But we know that's not

true, because the home twin is entitled to use the time dilation

equation for a perpetually-inertial observer, and that equation tells

her that for a speed of 0.866 ls/s, the traveler's age is always

increasing half as fast as her age is increasing. So when they are

reunited, she is twice as old he is, NOT infinitely older than he is, as

the exponential form of the gravitational time dilation equation claims.

The time dilation equation for a perpetually-inertial observer is the

gold standard in special relativity. Therefore the exponential form of

the gravitational time dilation equation is incorrect.

The correct gravitational time dilation equation turns out to

approximately agree with what Einstein used in his "small acceleration"

analysis, for very small accelerations, but differs substantially for

larger accelerations. And the correct gravitational time dilation

equation agrees with the ages of the twins when they are reunited. It

also exactly agrees with the CMIF simultaneity method for the traveler's

conclusions about the sudden increase in the home twin's age when the

traveler suddenly changes his velocity. The CMIF method provides a

practical way to compute the change in the home twin's age when the

traveler instantaneously changes his velocity. But it is the new

gravitational time dilation equation, and its array of clocks with a

common "NOW" moment, that guarantees that the CMIF result is fully

meaningful to the traveling twin, and that the CMIF method is the ONLY

correct simultaneity method for the traveling twin.

[4-3-22], but which hasn't shown up yet)

In 1907, Einstein published a VERY long paper (in several volumes) on

his "relativity principle". In volume 2, section 18, page 302, titled

"Space and time in a uniformly accelerated reference frame", he

investigated how the tic rates compare for two clocks separated by the

constant distance L, with both clocks undergoing a constant acceleration

"A". He restricted the analysis to very small accelerations (and very

small resulting velocities). His result (on page 305) was that the

leading clock tics at a rate

R = 1 + L A

faster than the rear clock. Note that that result agrees with my

equation, for very small "L" and "A". But he then said:

"From the fact that the choice of the coordinate origin must not

affect the relation, one must conclude that, strictly speaking, equation

(30) should be replaced by the equation R = exp(L A). Nevertheless, we

shall maintain formula (30)."

I've never understood that one sentence argument he gave, for replacing

his linear equation with the exponential equation. But I DID assume he

was right (because he was rarely wrong), until I tried applying his

exponential equation to the case of essentially instantaneous velocity

changes that are useful in twin "paradox" scenarios in special

relativity. Specifically, I worked a series of examples where the

separation of the two clocks is always

L = 7.52 ls (lightseconds)

and where the final speed (with the initial speed being zero) is always

v = 0.866 ls/s.

That speed implies a final "rapidity" of

theta = atanh(0.866) = 1.317 ls/s.

("Rapidity" is a non-linear version of velocity. They have a one-to-one

correspondence. In special relativity, velocity can never exceed 1.0

ls/s in magnitude, but rapidity can have an infinite magnitude. An

acceleration of "A" ls/s/s lasting for "t" seconds changes the rapidity

theta by the product of "A" and "t".)

So in this case, when we are starting from zero velocity and thus zero

rapidity, at the end of the acceleration,

theta = A tau,

where tau is the duration of the acceleration (according to the rear

clock). So, if we know theta and tau, we then know the acceleration:

A = theta / tau.

I do a sequence of calculations, each starting at t = 0, with the two

clocks reading zero, and with zero acceleration for t < 0.

First, I set the duration tau of the acceleration to 1 second. The

acceleration then needs to be

A = theta / tau = 1.317 / 1.0 = 1.317 ls/s/s (that's roughly

40 g's).

So for this first case, the tic rate of the leading clock during the one

second acceleration is

R = exp( L A ) = exp(9.9034), or about 20000.

(I picked that weird value of "L" so that this value of "R" for the fist

case would be a round number, just to make the calculations easier.)

Since R is constant during the acceleration, the CURRENT reading on the

leading clock (which I'll denote as AC, for "Age Change") is

AC = tau R = 2x10sup4 = 20000

(where 10sup4 means "10 raised to the 4th power").

I then start over and work a second case, with ten times the

acceleration (13.17 ls/s/s), but with tau ten times smaller (0.1

second). That keeps the final rapidity the same as in the first case,

and the final speed is also 0.866, as before. For the second case,

AC = 1.02x10sup42.

So when we made the acceleration an order of magnitude larger, and the

duration an order of magnitude smaller, the current reading "AC" on the

leading clock got about 38 orders of magnitude larger.

Next, I start over again and work a third case, again increasing the

acceleration by a factor of 10, and the decreasing the duration by a

factor of 10, so "A" = 131.7 ls/s/s and tau = 0.01 second. Then, AC =

1.27x10sup428. So this time, when we increased "A" by a factor of 10,

and decreased tau by a factor of ten, AC got about 380 orders of

magnitude larger.

AC is not approaching a finite limit as tau goes to zero and "A" goes to

infinity. In each iteration, the change in AC compared to the previous

change gets MUCH larger. Clearly, the clock reading is NOT converging

to a finite limit. It is going to infinity as tau goes to zero.

We can see this, even without doing the above detailed calculations. Since

AC = tau exp(L A),

the tau factor goes to zero LINEARLY as tau goes to zero, but exp(L A)

goes to infinity EXPONENTIALLY as tau goes to zero, so their product is

obviously not going to be finite as tau goes to zero.

So, for the idealization of an essentially instantaneous velocity

change, the change of the reading on the leading clock is INFINITE

during the infinitesimal change of the rear clock. That means that,

when the traveling twin instantaneously changes his speed from zero to

0.866 (toward the home twin), the exponential version of the R equation

says that the home twin's age becomes infinite. But we know that's not

true, because the home twin is entitled to use the time dilation

equation for a perpetually-inertial observer, and that equation tells

her that for a speed of 0.866 ls/s, the traveler's age is always

increasing half as fast as her age is increasing. So when they are

reunited, she is twice as old he is, NOT infinitely older than he is, as

the exponential form of the gravitational time dilation equation claims.

The time dilation equation for a perpetually-inertial observer is the

gold standard in special relativity. Therefore the exponential form of

the gravitational time dilation equation is incorrect.

The correct gravitational time dilation equation turns out to

approximately agree with what Einstein used in his "small acceleration"

analysis, for very small accelerations, but differs substantially for

larger accelerations. And the correct gravitational time dilation

equation agrees with the ages of the twins when they are reunited. It

also exactly agrees with the CMIF simultaneity method for the traveler's

conclusions about the sudden increase in the home twin's age when the

traveler suddenly changes his velocity. The CMIF method provides a

practical way to compute the change in the home twin's age when the

traveler instantaneously changes his velocity. But it is the new

gravitational time dilation equation, and its array of clocks with a

common "NOW" moment, that guarantees that the CMIF result is fully

meaningful to the traveling twin, and that the CMIF method is the ONLY

correct simultaneity method for the traveling twin.

Apr 6, 2022, 2:22:44 PMApr 6

to

On Tuesday, April 5, 2022 at 2:54:06 PM UTC-5, Mike Fontenot wrote:

>

... {long derivation related to Ehrenfest Paradox and Rendler Coordinates}

Coordinates. What myself and others have been trying to get you

to understand is that the acceleration of the observer does not actually

change anything about the distant twin. By your own calculations

the age of the distant twin can be anything +/- c*d depending on the

relative state of motion and accelerations. Furthermore, with sufficiently

high acceleration the observer cannot "see" the distant twin at all.

Please note that an inertial observer at the same location as your

traveling twin, watching everything as the traveling twin accelerates,

does not see any change in the rest of the universe. All these

coordinate transformations are entirely observer dependent and

do not represent anything real for the physics. They only affect the

APPEARANCE of the world to that observer. Any attempt to place

greater significance to these appearances is misguided.

> The correct gravitational time dilation equation turns out to

> approximately agree with what Einstein used in his "small acceleration"

> analysis, for very small accelerations, but differs substantially for

> larger accelerations. And the correct gravitational time dilation

> equation agrees with the ages of the twins when they are reunited. It

> also exactly agrees with the CMIF simultaneity method for the traveler's

> conclusions about the sudden increase in the home twin's age when the

> traveler suddenly changes his velocity. The CMIF method provides a

> practical way to compute the change in the home twin's age when the

> traveler instantaneously changes his velocity. But it is the new

> gravitational time dilation equation, and its array of clocks with a

> common "NOW" moment, that guarantees that the CMIF result is fully

> meaningful to the traveling twin, and that the CMIF method is the ONLY

> correct simultaneity method for the traveling twin.

Again, you should study the Ehrenfest Paradox and Rindler Coordinates.

You still don't seem to appreciate the true significance (or lack thereof)

of the calculated "now".

Rich L.

>

... {long derivation related to Ehrenfest Paradox and Rendler Coordinates}

>

> So, for the idealization of an essentially instantaneous velocity

> change, the change of the reading on the leading clock is INFINITE

> during the infinitesimal change of the rear clock. That means that,

> when the traveling twin instantaneously changes his speed from zero to

> 0.866 (toward the home twin), the exponential version of the R equation

> says that the home twin's age becomes infinite. But we know that's not

> true, because the home twin is entitled to use the time dilation

> equation for a perpetually-inertial observer, and that equation tells

> her that for a speed of 0.866 ls/s, the traveler's age is always

> increasing half as fast as her age is increasing. So when they are

> reunited, she is twice as old he is, NOT infinitely older than he is, as

> the exponential form of the gravitational time dilation equation claims.

> The time dilation equation for a perpetually-inertial observer is the

> gold standard in special relativity. Therefore the exponential form of

> the gravitational time dilation equation is incorrect.

>

Your calculations are all related to the Ehrenfest Paradox and Rindler
> So, for the idealization of an essentially instantaneous velocity

> change, the change of the reading on the leading clock is INFINITE

> during the infinitesimal change of the rear clock. That means that,

> when the traveling twin instantaneously changes his speed from zero to

> 0.866 (toward the home twin), the exponential version of the R equation

> says that the home twin's age becomes infinite. But we know that's not

> true, because the home twin is entitled to use the time dilation

> equation for a perpetually-inertial observer, and that equation tells

> her that for a speed of 0.866 ls/s, the traveler's age is always

> increasing half as fast as her age is increasing. So when they are

> reunited, she is twice as old he is, NOT infinitely older than he is, as

> the exponential form of the gravitational time dilation equation claims.

> The time dilation equation for a perpetually-inertial observer is the

> gold standard in special relativity. Therefore the exponential form of

> the gravitational time dilation equation is incorrect.

>

Coordinates. What myself and others have been trying to get you

to understand is that the acceleration of the observer does not actually

change anything about the distant twin. By your own calculations

the age of the distant twin can be anything +/- c*d depending on the

relative state of motion and accelerations. Furthermore, with sufficiently

high acceleration the observer cannot "see" the distant twin at all.

Please note that an inertial observer at the same location as your

traveling twin, watching everything as the traveling twin accelerates,

does not see any change in the rest of the universe. All these

coordinate transformations are entirely observer dependent and

do not represent anything real for the physics. They only affect the

APPEARANCE of the world to that observer. Any attempt to place

greater significance to these appearances is misguided.

> The correct gravitational time dilation equation turns out to

> approximately agree with what Einstein used in his "small acceleration"

> analysis, for very small accelerations, but differs substantially for

> larger accelerations. And the correct gravitational time dilation

> equation agrees with the ages of the twins when they are reunited. It

> also exactly agrees with the CMIF simultaneity method for the traveler's

> conclusions about the sudden increase in the home twin's age when the

> traveler suddenly changes his velocity. The CMIF method provides a

> practical way to compute the change in the home twin's age when the

> traveler instantaneously changes his velocity. But it is the new

> gravitational time dilation equation, and its array of clocks with a

> common "NOW" moment, that guarantees that the CMIF result is fully

> meaningful to the traveling twin, and that the CMIF method is the ONLY

> correct simultaneity method for the traveling twin.

You still don't seem to appreciate the true significance (or lack thereof)

of the calculated "now".

Rich L.

Apr 7, 2022, 12:04:08 AMApr 7

to

On 4/6/22 12:22 PM, Richard Livingston wrote:

>

> Your calculations are all related to the Ehrenfest Paradox and Rindler

> Coordinates.

I looked up Ehrenfest Paradox on Wiki, and it says it's about a rotating
>

> Your calculations are all related to the Ehrenfest Paradox and Rindler

> Coordinates.

disk. The work I've been doing has nothing to do with a rotating disk.

Apr 7, 2022, 2:02:18 PMApr 7

to

Sorry about that. I should have referenced the Bell Spaceship paradox.

That is a closely related effect for a linearly accelerating reference

frame that is closer to what you are analyzing.

Rich L.

Apr 8, 2022, 3:05:57 AMApr 8

to

On 4/6/22 12:22 PM, Richard Livingston wrote:

>

> What myself and others have been trying to get you (Mike Fontenot)
>

> to understand is that the acceleration of the observer does not actually

> change anything about the distant twin.

It's not clear what that statement even MEANS. Obviously, the distant
> change anything about the distant twin.

twin (she) doesn't suddenly feel like she's getting younger. At each

instant in her life, her brain is in a state that is different from all

of her other brain states. Nothing can change those states. But the

accelerating observer DOES conclude that she instantaneously gets

younger when he instantaneously changes his velocity in the direction

away from her. And so, FOR HIM, she ACTUALLY gets younger. All

perpetually-inertial observers disagree with him about her getting

younger when he instantaneously changes his velocity, but they also all

disagree among themselves about what her current age is when the

accelerating observer changes his velocity. And FOR EACH OF THEM, she

ACTUALLY has the current age they compute. That's just the way special

relativity IS ... different observers disagree, they all think they are

right, and none of them is wrong!

What is really new, though, in my latest results, is the fact that the

accelerating observer can assemble an array of clocks (and attending

"helper friends" (HF's)), which give him a "NOW" that extends throughout

all space (analogous to what Einstein did for inertial observers). And

THAT guarantees that the accelerating observer's conclusions about the

home twin's age are fully MEANINGFUL to him. His conclusions agree with

the CMIF simultaneity method, which means that the CMIF simultaneity

method is the only correct simultaneity method.

[[Mod. note -- I think you're mistaken in a couple of places:

1. An accelerating obserer ("he") does not (or to be pedantic, should

not, if he is doing physics correctly) conclude that the distant twin

("she") instantaneously gets younger when he instantaneously changes

his velocity in the direction away from her. Rather he concludes

that her age coordinate in inertial reference frame #2 (after his

velocity change) < her age coordinate in inertial reference frame #1

(before his velocity change). But these are two DIFFERENT inertial

reference frames, with DIFFERENT time coordinates. Attributing

physical meaning to a comparison between DIFFERENT inertial frame's

time coordinates is no more valid than (say) attributing physical

meaning to the difference between 2022 (the current year on Earth

in the Gregorian calendar) and 4720 (the current year on Earth in

the Chinese calendar). If I install new calendar software on my

computer, I don't suddenly get 4720-2022 years younger or older for

any sensible meaning of "younger" or "older". :)

2. What does it mean to say a time coordinate is "physically meaningful"?

I would argue that it means that you can write the laws of physics

in a sensible form in terms of that time coordinate. So, what would

(say) Newton's 2nd law look like using the CMIF time coordinate of

an accelerating observer? Ick, not nice at all. Or how about Maxwell's

equations? Or even something very simple like the radioactive decay

law

N_atoms(t) = N_atoms(0) * exp(-lambda*t)

for a fixed lambda. Again, not nice at all if "t" on the left-hand

side and "t" on the right-hand-side are the time coordinate of different

inertial frames.

The fact that these and other laws of physics don't have a sensible

form when written in a mixture of different time coordinates (such

as CMIF times for accelerating observers) is, I would argue, prima

facie evidence that such a mixture of time coordinates is *not*

physically meaningful.

3. You write that "the CMIF simultaneity method is the only correct

simultaneity method". But this begs the question of how to define

"correct". There are other ways of doing distant clock synchronization

which differ from Einstein synchronization (e.g., slow (adiabatic)

clock transport, which gives a different synchronization result

for each choice of the inertial reference frame in which the clock

transport is "slow").

[That is, suppose we are at (fixed) position A in some inertial

reference frame F0, and set a (gedanken) ideal clock M to match

our A clock. Then we transport M at velocity v << c to some

other (fixed) position B a distance d away in this same inertial

reference frame F0. This takes a time d/v. Since M's Lorentz

time Lorentz time dialation factor is quadratic in v (for v << c),

the accumulated time dialation effect on effect on M's clock

by the time M arrives at B is linear in v, and hence can be

made arbitrarily small by choosing v small enough (and waiting

long enough for M to arrive at B). Then when M (eventually)

arrives at B, we set B's clock to M's reading.

This defines the "slow clock transport" clock synchronization

scheme.

The interesting -- and slightly counterintuitive -- thing is

that if we observe this entire process from some other inertial

reference frame F1 which is moving (along the A-B direction)

with respect to our original inertial reference frame F0, and

use F1's definition of "slow motion", then it turns out that

we'll get a *different* clock synchronization.]

Can you point to a law of physics which specifically picks out

Einstein synchronization as "correct" and other synchronizations

as "incorrect"? If not, what basis do we have for saying that

one of these is "correct".

-- jt]]

Apr 8, 2022, 10:03:57 PMApr 8

to

On 4/8/22 1:05 AM, Mike Fontenot wrote:

>

> What is really new, though, in my latest results, is the fact that the

> accelerating observer can assemble an array of clocks (and attending

> "helper friends" (HF's)), which give him a "NOW" that extends throughout

> all space (analogous to what Einstein did for inertial observers). And

> THAT guarantees that the accelerating observer's conclusions about the

> home twin's age are fully MEANINGFUL to him. His conclusions agree with

> the CMIF simultaneity method, which means that the CMIF simultaneity

> method is the only correct simultaneity method.

>

> [[Mod. note -- I think you're mistaken in a couple of places [...]:
>

> What is really new, though, in my latest results, is the fact that the

> accelerating observer can assemble an array of clocks (and attending

> "helper friends" (HF's)), which give him a "NOW" that extends throughout

> all space (analogous to what Einstein did for inertial observers). And

> THAT guarantees that the accelerating observer's conclusions about the

> home twin's age are fully MEANINGFUL to him. His conclusions agree with

> the CMIF simultaneity method, which means that the CMIF simultaneity

> method is the only correct simultaneity method.

>

I WOULD like to hear your "take" on my arguments here:

First, consider a perpetually-inertial observer (PIO). Einstein showed

us how that PIO (he) can construct an array of synchronized clocks that

are stationary wrt him, extending throughout all of space. The clocks

have been synchronized by using light signals. The fundamental (and

really only) assumption that defines special relativity is that, in ANY

inertial reference frame, the velocity of light is always equal to the

universal constant "c". We can also imagine that, co-located with each

clock is a "helper friend" (HF), whose age is always the same as the

PIO's age.

So, if the PIO wants to know "How old is that distant person (she)

"right now" (say, when the PIO is age T1), he just needs to know which

HF is momentarily co-located with her when the HF's age is T1. He can

eventually determine that, from messages sent him by all the HF's. He

has previously told all HF's to report to him all encounters with all

people, telling him what the encountered person's age was, who it was,

and what the observing HF's age was then. The PIO reviews all those

responses, and eventually will find one that tells him that, when that

HF was T1 years old, he was momentarily co-located with the particular

distant person the PIO is interested in, and her age was T2.

Now, here is the important question: Given the above, should the PIO

regard that age of the distant person (that he has eventually

determined) to be MEANINGFUL? Many people tell me the answer is NO.

But I claim that, if the PIO says that, he will effectively be saying

that he doesn't believe that the speed of light is equal to "c" in his

inertial frame. And if he doesn't believe that, he doesn't believe in

special relativity.

All of the above applies equally well to the array of clocks and

helper-friends I've described for someone (the "AO") who is initially

unaccelerated, but who then undergoes a constant non-zero acceleration

for some length of time. That AO can also be mutually stationary with

respect to an array of clocks that establish a "NOW" moment for him,

extending throughout all space. The previous arguments all apply to the

AO as well. The only difference is that, if the AO doesn't regard the

answer he has gotten for the distant person's current age to be

MEANINGFUL, that doesn't imply that he doesn't believe that the speed of

light is "c" (he already knows that the speed of light in his frame is

NOT "c"). If the AO doesn't regard the answer he has gotten for the

distant person's current age to be MEANINGFUL, that implies that he

doesn't believe that the equations he has used to calculate the current

reading on each of the HFs' clocks are correct. If he DOES believe

those equations are correct, then he MUST conclude that the distant

person's current age he has determined IS meaningful. I believe those

equations are correct. Others may believe they are not correct. I

think they ARE potentially testable.

[[Mod. note --

What do you mean by the word "meaningful"?

If the AO accelerates, he will assign a different CMIF-time to a given

(fixed) event (e.g., the explosion of the first hydrogen bomb on Earth),

and correspondingly assign the label "now @ Earth worldline" to a

different event along the Earth's worldline.

But does anything in the universe (other than AO's motion and the

observations AO makes) change when the AO accelerates? If not, then

what is the basis for declaring changes in AO-CMIF-time "meaningful"?

It might be useful to conceptualize the AO and his CMIF definition of

"now @ Earth worldline" as a "time viewer" than can observe the Earth

at any point (event) on the Earth's past worldline. Accelerating the AO

(changing the AO's velocity with respect to some inertial reference frame)

then corresponds to turning the control knob on this "time viewer" back

and forth (and hence moving the AO's "now @ Earth worldline" observation

point forwards and backwards in time along the Earth's past worldline).

Do you consider this change in observation point to be "meaningful"

(beyond its obvious change in what AO himself observes)?

This change in observation point is certainly not unique -- another

accelerating observer AO' will in general ascribe a different observation

point. And, this observation point can move superluminally both forwards

and backwards in time. And, no observation on Earth (apart from asking

AO to report what he is observing) changes when AO moves his observation

point.

To me, this all (very strongly) suggests that the motion of this

observation point (i.e., AO's CMIF-time definition of "now" at the Earth's

position) doesn't deserve to be called "physically meaningful".

-- jt]]

Apr 10, 2022, 2:47:52 PMApr 10

to

On Saturday, 9 April 2022 at 04:03:57 UTC+2, Mike Fontenot wrote:

> On 4/8/22 1:05 AM, Mike Fontenot wrote:

> >

> > What is really new, though, in my latest results, is the fact that the

> > accelerating observer can assemble an array of clocks (and attending

> > "helper friends" (HF's)), which give him a "NOW" that extends throughout

> > all space (analogous to what Einstein did for inertial observers). And

> > THAT guarantees that the accelerating observer's conclusions about the

> > home twin's age are fully MEANINGFUL to him. His conclusions agree with

> > the CMIF simultaneity method, which means that the CMIF simultaneity

> > method is the only correct simultaneity method.

> >

> > [[Mod. note -- I think you're mistaken in a couple of places [...]:

>

> I WOULD like to hear your "take" on my arguments here:

(IMO) You are perfectly right: relativity as it is usually presented
> On 4/8/22 1:05 AM, Mike Fontenot wrote:

> >

> > What is really new, though, in my latest results, is the fact that the

> > accelerating observer can assemble an array of clocks (and attending

> > "helper friends" (HF's)), which give him a "NOW" that extends throughout

> > all space (analogous to what Einstein did for inertial observers). And

> > THAT guarantees that the accelerating observer's conclusions about the

> > home twin's age are fully MEANINGFUL to him. His conclusions agree with

> > the CMIF simultaneity method, which means that the CMIF simultaneity

> > method is the only correct simultaneity method.

> >

> > [[Mod. note -- I think you're mistaken in a couple of places [...]:

>

> I WOULD like to hear your "take" on my arguments here:

and interpreted is simply inconsistent and arbitrary nonsense unless

one does fix the notion of *proper time* and what that even means.

Indeed yes, if I and you synchronize our clocks, and as long as the

clocks keep working, forever and ever I and you will be reading the

same exact time at at the same exact moment, aka we age the same

just like clocks tick the same (amd I think this is already some

postulate, and if not it should be). The fact that we on the other

hand move in space-time entails we are not anymore on the same plane

of simultaneity, it does not and cannot change the synchronization

of our clocks any more than it does in Galilean physics, just we

here drift in space-time instead of just space. Proper time is

just not coordinate time which has rather to do with coordinate

systems. And if we drop that postulate I am saying, physics indeed

becomes "disconnected" and plain arbitrary...

Please look at this diagram to begin with: isn't there already, in it's elementarity indeed, the unescapable answer to all above questions?

<https://jp-diegidio.github.io/STUDY.Physics.SpecialRelativity/InertialFrames/App/index.html>

Julio

[[Mod. note -- When you write

> I and you synchronize our clocks, and as long as the

> clocks keep working, forever and ever I and you will be reading the

> same exact time at at the same exact moment

that's only true if we follow the same worldline, i.e., if our positions

are the same at all times. If our positions differ then in general we'll

see different clock readings when we get back together again -- this was

experimentally tested by (among others) the Hafele-Keating experiment

(1972)

https://paulba.no/paper/Hafele_Keating.pdf

-- jt]]

Apr 10, 2022, 2:52:27 PMApr 10

to

On 4/8/22 8:03 PM, the Moderator (JT) wrote:

>

> What do you mean by the word "meaningful"?

>

If I were ever able to take an actual long-term, high-speed space
>

> What do you mean by the word "meaningful"?

>

voyage, I'm sure I would often wonder what my wife back home was doing

"right now". I definitely wouldn't believe that she had ceased to exist

just because we were separated.

If she exists "right now", then she must be doing something specific

right now. And that "doing something right now" is associated with a

certain unique state of her brain right now. And each unique state of

her brain corresponds to a unique specific time in her life. So I would

regard her current age during each instant in my life on my trip as

being completely meaningful to me.

And if my maneuvering on my trip resulted in my calculating that she was

exactly the same age at two widely separated instants in my life, I

would just say "WOW, isn't that interesting!". I would believe it. It

would be completely meaningful to me.

[[Mod. note -- So basically you're saying that what you observe is

meaningful to you, regardless of whether anything else in the universe

is affected.

-- jt]]

Apr 11, 2022, 4:00:15 AMApr 11

to

On 4/10/22 12:52 PM, the Moderator (JT) wrote:

> So basically you're saying that what you observe is

> meaningful to you, regardless of whether anything else in the universe

> is affected.

>

If I am an accelerating observer, and if I OBSERVE a TV image of the
> So basically you're saying that what you observe is

> meaningful to you, regardless of whether anything else in the universe

> is affected.

>

distant person, that tells me what that distant person looked like a

long time ago. That's not meaningful to me, because I don't know how to

determine how much she aged while the message was in transit.

But if I'm mutually stationary wrt the array of clocks that I have

previously described, which provides a "NOW" for me extending throughout

space, that DOES give me a meaningful answer to the question of how old

she currently is. And by "meaningful", I mean that I REALLY believe

that she is currently that age. The only way I can be wrong about her

current age is if my equation for the rate ratio of the two clocks is

wrong. I'm confident that it is correct. I think it IS experimentally

testable.

I don't understand what you meant in the above, when you said

"regardless of whether anything else in the universe

is affected". Although I realize that the way I accelerate affects what
I conclude about how her age changes, I don't contend that that has ANY

effect on what other observers (including she herself) conclude about

her age changes. Different people disagree about simultaneity at a

distance. That's just the way special relativity is.

Michael Leon Fontenot

Apr 11, 2022, 3:18:54 PMApr 11

to

On 4/11/22 2:00 AM, (I) Mike Fontenot wrote:

>

> If I am an accelerating observer, and if I OBSERVE a TV image of the

> distant person, that tells me what that distant person looked like a

> long time ago. That's not meaningful to me, because I don't know how to

> determine how much she aged while the message was in transit.

>

I need to correct that last sentence. Observing the TV image of the
>

> If I am an accelerating observer, and if I OBSERVE a TV image of the

> distant person, that tells me what that distant person looked like a

> long time ago. That's not meaningful to me, because I don't know how to

> determine how much she aged while the message was in transit.

>

distant person WOULD be meaningful to me. ALL observations are

meaningful, almost by definition. But what I was thinking when I made

that statement was that, that observation wouldn't help me determine her

current age "right now", because I don't know how to determine how much

she aged while the message was in transit.

> But if I'm mutually stationary wrt the array of clocks that I have

> previously described, which provides a "NOW" for me extending throughout

> space, that DOES give me a meaningful answer to the question of how old

> she currently is. And by "meaningful", I mean that I REALLY believe

> that she is currently that age. The only way I can be wrong about her

> current age is if my equation for the rate ratio of the two clocks is

> wrong. I'm confident that it is correct. I think it IS experimentally

> testable.

>

The ability to construct an array of clocks (mutually stationary with
> But if I'm mutually stationary wrt the array of clocks that I have

> previously described, which provides a "NOW" for me extending throughout

> space, that DOES give me a meaningful answer to the question of how old

> she currently is. And by "meaningful", I mean that I REALLY believe

> that she is currently that age. The only way I can be wrong about her

> current age is if my equation for the rate ratio of the two clocks is

> wrong. I'm confident that it is correct. I think it IS experimentally

> testable.

>

the accelerating observer) establishes a "NOW" moment for him, and

answers his question about her current age in a way that is fully

meaningful. But that hinges on my equations for the rate ratio R(t) and

the ace change AC(t) being correct.

The rate ratio equation is

R(t) = [ 1 +- L A sech^2 (A t) ],

where L is the constant distance between him and the given HF, and

sech() is the hyperbolic secant (which is the reciprocal of cosh(), the

hyperbolic cosine). The "^2" after the sech indicates the square of the

sech. The "+-" in the above equation means that the second term is

ADDED to 1 for the HF's who are LEADING the accelerating observer, and

the second term is SUBTRACTED from 1 for the HF's who are TRAILING the

accelerating observer.

Apr 11, 2022, 3:19:51 PMApr 11

to

On 4/11/22 3:00 AM, Mike Fontenot wrote:

> if I'm mutually stationary wrt the array of clocks that I have

> previously described, which provides a "NOW" for me extending

> throughout space, [...]
> if I'm mutually stationary wrt the array of clocks that I have

> previously described, which provides a "NOW" for me extending

If you are an astronaut in a spaceship that can travel at an appreciable

fraction of c, and which you maneuver, then such an array of clocks is

impossible -- each such clock must vary its acceleration in concert with

yours, so the spaceships carrying those clocks must be clairvoyant,

because they are separated from you by spacelike intervals. Moreover,

such clocks located sufficiently far away from you will require an

unphysical acceleration and/or velocity to remain on station; you

cannot cover the universe with them, only a region "close" to you (how

close depends on the details of your maneuvering).

[I suppose you could plan out your trip in exquisite

detail, and the spaceships carrying the other clocks

could pre-compute their accelerations to match. But

anyone who has ever driven a car knows how poorly

such plans are followed.]

If you carefully keep track of your acceleration, velocity, and position

relative to some coordinates, then you can calculate what "now" means to

you at a distant location, as you maneuver. As I have pointed out many

times before, that in general gives nonsensical and unphysical results.

If you "believe" that your wife back home can grow younger due to your

maneuvering, then you will believe anything, which is useless, and is

certainly not physics.

Tom Roberts

Apr 12, 2022, 3:21:23 AMApr 12

to

On 4/11/22 2:00 AM, (I) Mike Fontenot wrote:

>

>

> If I am an accelerating observer, and if I OBSERVE a TV > image of

the distant person, that tells me what that distant > person looked like

along time ago. That's not meaningful > to me, because I don't know how
the distant person, that tells me what that distant > person looked like

to determine how much > she aged while the message was in transit.

>

>

I need to correct that last sentence. Observing the TV image of the

distant person WOULD be meaningful to me. ALL observations are

meaningful, almost by definition. But what I was thinking when I made

that statement was that, that observation wouldn't help me determine her

current age "right now", because I don't know how to determine how much
distant person WOULD be meaningful to me. ALL observations are

meaningful, almost by definition. But what I was thinking when I made

that statement was that, that observation wouldn't help me determine her

she aged while the message was in transit.

> But if I'm mutually stationary wrt the array of clocks that I > have

previously described, which provides a "NOW" for >me extending

throughout space, that DOES give me a >meaningful answer to the question

of how old

>she currently is. And by "meaningful", I mean that I >REALLY believe

that she is currently that age. The only >way I can be wrong about her

current age is if my equation >for the rate ratio of the two clocks is

wrong. I'm confident >that it is correct. I think it IS experimentally

testable.

> But if I'm mutually stationary wrt the array of clocks that I > have

previously described, which provides a "NOW" for >me extending

throughout space, that DOES give me a >meaningful answer to the question

of how old

>she currently is. And by "meaningful", I mean that I >REALLY believe

that she is currently that age. The only >way I can be wrong about her

current age is if my equation >for the rate ratio of the two clocks is

wrong. I'm confident >that it is correct. I think it IS experimentally

testable.

The ability to construct an array of clocks (mutually stationary with

the accelerating observer) establishes a "NOW" moment for him, and

answers his question about her current age in a way that is fully

meaningful. But that hinges on my equations for the rate ratio R(t) and

the age change AC(t) being correct.
the accelerating observer) establishes a "NOW" moment for him, and

answers his question about her current age in a way that is fully

meaningful. But that hinges on my equations for the rate ratio R(t) and

The rate ratio equation is

R(t) = [ 1 +- L A sech^2 (A t) ],

where L is the constant distance between him and the given HF, and

sech() is the hyperbolic secant (which is the reciprocal of cosh(), the

hyperbolic cosine). The "^2" after the sech indicates the square of the

sech. The "+-" in the above equation means that the second term is

ADDED to 1 for the HF's who are LEADING the accelerating observer, and

the second term is SUBTRACTED from 1 for the HF's who are TRAILING the

accelerating observer.

The current reading of the HF's clock (the "Age Change" or "AC"), when

the AO's clock reads "tau", is

AC(tau) = integral, from zero to tau, of { R(t) dt }

= tau + L tanh( A tau ).

If anyone can spot an error in my derivation of those two equations,
the AO's clock reads "tau", is

AC(tau) = integral, from zero to tau, of { R(t) dt }

= tau + L tanh( A tau ).

please let me know about it. The derivations are fairly lengthy, but

are shown completely in the paper that I put on the viXra on-line

repository:

https://vixra.org/abs/2201.0015

Michael Leon Fontenot

mlf...@comcast.net

Apr 12, 2022, 3:21:23 AMApr 12

to

On 4/11/22 1:19 PM, Tom Roberts wrote:

>

> If you are an astronaut in a spaceship that can travel at an appreciable

> fraction of c, and which you maneuver, then such an array of clocks is

> impossible -- each such clock must vary its acceleration in concert with

> yours [...]
>

> If you are an astronaut in a spaceship that can travel at an appreciable

> fraction of c, and which you maneuver, then such an array of clocks is

> impossible -- each such clock must vary its acceleration in concert with

No, that's not correct. According to the accelerating observer (the

AO), whose conclusions we seek, he and each of his "helper friends"

(HF's) undergo EXACTLY the same (constant) acceleration, as recorded on

their accelerometers. This is clear by looking at the equivalent

scenario in the case of a constant gravitational field with no

accelerations (via the equivalence principle) ... all of those people

are motionless, unaccelerated, and mutually stationary. And according

to them, the distance between each of them is also constant. In the

acceleration scenario (in the infinite flat spacetime of special

relativity), perpetually-inertial observers, who are initially

stationary with respect to the AO and the HF's, WILL conclude that the

accelerations of the AO and the various HF's, and their distances apart,

DO vary with time. But it is not their conclusions that I am interested in.

Apr 12, 2022, 2:28:58 PMApr 12

to

On 4/12/22 2:21 AM, Mike Fontenot wrote:

> On 4/11/22 1:19 PM, Tom Roberts wrote:

>> If you are an astronaut in a spaceship that can travel at an

>> appreciable fraction of c, and which you maneuver, then such an

>> array of clocks is impossible -- each such clock must vary its

>> acceleration in concert with yours [...]

>

> No, that's not correct.

Yes, it is correct. Finally you say what you are thinking behind the
> On 4/11/22 1:19 PM, Tom Roberts wrote:

>> If you are an astronaut in a spaceship that can travel at an

>> appreciable fraction of c, and which you maneuver, then such an

>> array of clocks is impossible -- each such clock must vary its

>> acceleration in concert with yours [...]

>

> No, that's not correct.

scenes, and I can now explain that you are thinking of an inappropriate

analogy.

> According to the accelerating observer (the AO), whose conclusions

> we seek, he and each of his "helper friends" (HF's) undergo EXACTLY

> the same (constant) acceleration, as recorded on their

> accelerometers.

proper distance from the accelerating observer -- i.e. in each

successive instantaneously co-moving inertial frame (ICIF) those

distances are constant. That is Born rigid motion, and it is well

known that HFs lower than the AO must have larger proper accelerations

than the AO, and HFs above the AO must have smaller proper

accelerations; there is often a limit below which no HF can possibly

keep up, so in general the HFs cannot cover the manifold.

[Note that accelerometers display their proper acceleration.]

Moreover, whenever the observer maneuvers (changes his proper

acceleration), all of the HFs must SIMULTANEOUSLY (in the current ICIF)

make corresponding changes to their proper accelerations -- that

requires either clairvoyance or detailed pre-planning, because they are

separated by spacelike intervals from the AO. As such detailed

pre-planning cannot hold for a spacefaring astronaut (who will maneuver

his spacecraft based on current observations), I said that this array

of HFs is impossible.

> This is clear by looking at the equivalent scenario in the case of a

> constant gravitational field with no accelerations (via the

> equivalence principle) ... all of those people are motionless,

> unaccelerated, and mutually stationary. And according to them, the

> distance between each of them is also constant.

those people are located at various altitudes with each

4-velocity parallel to the timelike Killing vector, and

the field is uniform in that their proper accelerations

are all equal. I also presume that "all of those people"

are the AO and all the HFs. Note this is not "equivalent"

to the above scenario, as I discuss next.)

This is wrong at several levels.

1) The HFs are not "motionless" or "mutually stationary" in any of the

AO's ICIFs; this is not Born rigid motion.

2) the HFs are not "unaccelerated" -- each has a nonzero proper

acceleration (even though they have zero coordinate acceleration [#]).

3) the equivalence principle applies only in a region small enough that

the curvature of spacetime is negligibly small (compared to measurement

accuracy); it CLEARLY does not apply here.

4) the distances between the HFs and the AO are not "constant" in any

ICIF -- you are confusing constant coordinate difference [#] with

constant distance in an ICIF -- the AO and HFs have constant coordinate

values (and differences) [#], but not constant distances in any of the

ICIFs (as required by your scenario above).

[#] Implicitly using coordinates aligned with the static

gravitational field. These are not the coordinates of any

of the ICIFs.

It seems you have implicitly been thinking of this inappropriate analogy

all along. Relativity is more complicated than that (even in flat

spacetime).

> In the acceleration scenario (in the infinite flat spacetime of

> special relativity), perpetually-inertial observers, who are

> initially stationary with respect to the AO and the HF's, WILL

> conclude that the accelerations of the AO and the various HF's, and

> their distances apart, DO vary with time.

adhere to a detailed, prearranged plan of accelerations, so each HF can

pre-compute their own detailed plan of accelerations. The AO cannot

maneuver to, say, land on a discovered planet or orbit a discovered star.

> But it is not their conclusions that I am interested in.

nonsensical and unphysical. And the AO + HFs scenario you have in mind

is either impossible, or requires unacceptably rigid adherence to a

pre-computed plan (and even then can be limited in scope).

Tom Roberts

Apr 12, 2022, 6:55:39 PMApr 12

to

On Sunday, 10 April 2022 at 20:47:52 UTC+2, Julio Di Egidio wrote:

> On Saturday, 9 April 2022 at 04:03:57 UTC+2, Mike Fontenot wrote:

> On Saturday, 9 April 2022 at 04:03:57 UTC+2, Mike Fontenot wrote:

> > On 4/8/22 1:05 AM, Mike Fontenot wrote:

> > >

> > > What is really new, though, in my latest results, is the fact that the

> > > accelerating observer can assemble an array of clocks (and attending

> > > "helper friends" (HF's)), which give him a "NOW" that extends throughout

> > > all space (analogous to what Einstein did for inertial observers). And

> > > THAT guarantees that the accelerating observer's conclusions about the

> > > home twin's age are fully MEANINGFUL to him. His conclusions agree with

> > > the CMIF simultaneity method, which means that the CMIF simultaneity

> > > method is the only correct simultaneity method.

> > >

> > > [[Mod. note -- I think you're mistaken in a couple of places [...]:

> >

> > I WOULD like to hear your "take" on my arguments here:

> > >

> > > What is really new, though, in my latest results, is the fact that the

> > > accelerating observer can assemble an array of clocks (and attending

> > > "helper friends" (HF's)), which give him a "NOW" that extends throughout

> > > all space (analogous to what Einstein did for inertial observers). And

> > > THAT guarantees that the accelerating observer's conclusions about the

> > > home twin's age are fully MEANINGFUL to him. His conclusions agree with

> > > the CMIF simultaneity method, which means that the CMIF simultaneity

> > > method is the only correct simultaneity method.

> > >

> > > [[Mod. note -- I think you're mistaken in a couple of places [...]:

> >

> > I WOULD like to hear your "take" on my arguments here:

> (IMO) You are perfectly right: relativity as it is usually presented

> and interpreted is simply inconsistent and arbitrary nonsense unless

> one does fix the notion of *proper time* and what that even means.

> Indeed yes, if I and you synchronize our clocks, and as long as the

> clocks keep working, forever and ever I and you will be reading the

> same exact time at at the same exact moment, aka we age the same

> just like clocks tick the same (amd I think this is already some

> postulate, and if not it should be). The fact that we on the other

> hand move in space-time entails we are not anymore on the same plane

> of simultaneity, it does not and cannot change the synchronization

> of our clocks any more than it does in Galilean physics, just we

> here drift in space-time instead of just space. Proper time is

> just not coordinate time which has rather to do with coordinate

> systems. And if we drop that postulate I am saying, physics indeed

> becomes "disconnected" and plain arbitrary...

>

> Please look at this diagram to begin with: isn't there already, in it's elementarity indeed, the unescapable answer to all above questions?

>

> <https://jp-diegidio.github.io/STUDY.Physics.SpecialRelativity/InertialFrames/App/index.html>

No comments on that? That is the most concrete and immediate alleged
> and interpreted is simply inconsistent and arbitrary nonsense unless

> one does fix the notion of *proper time* and what that even means.

> Indeed yes, if I and you synchronize our clocks, and as long as the

> clocks keep working, forever and ever I and you will be reading the

> same exact time at at the same exact moment, aka we age the same

> just like clocks tick the same (amd I think this is already some

> postulate, and if not it should be). The fact that we on the other

> hand move in space-time entails we are not anymore on the same plane

> of simultaneity, it does not and cannot change the synchronization

> of our clocks any more than it does in Galilean physics, just we

> here drift in space-time instead of just space. Proper time is

> just not coordinate time which has rather to do with coordinate

> systems. And if we drop that postulate I am saying, physics indeed

> becomes "disconnected" and plain arbitrary...

>

> Please look at this diagram to begin with: isn't there already, in it's elementarity indeed, the unescapable answer to all above questions?

>

> <https://jp-diegidio.github.io/STUDY.Physics.SpecialRelativity/InertialFrames/App/index.html>

proof of my point: easy to read, impossible to equivocate upon,

easy to debunk if that's the case: and should you just call that

"arbitrary" (how proper time becomes the very relation between

different frames/observers), then you should tell me what's your

picture of it and how it even works. And please notice that I clam

that that is SR, not something else: i.e. I am not proposing an

alternative theory here, just reading the existing one.

> [[Mod. note -- When you write

> > I and you synchronize our clocks, and as long as the

> > clocks keep working, forever and ever I and you will be reading the

> > same exact time at at the same exact moment

> that's only true if we follow the same worldline, i.e., if our positions

> are the same at all times.

*locally* I and you experience the one and only universal time, aka

*proper* time (as do our clocks and everything else).

> If our positions differ then in general we'll

> see different clock readings when we get back together again

take a trip away from you and later come back, the reading of our

(spacial) mileage would be different, yet that doesn't mean space

for me is not the same as space for you... exactly the same in SR,

just here it's the space-time mileage: to reiterate, an altogether

different notion than proper time/distance.

I risk to botch the terminology, but the problem there is essentially

mixing simultaneity (which is a bunch of operational definitions

to compute from *within* a frame) with synchronicity (isochronous

lines and so on), which is simply something else, namely *elapsed

proper time/distance*.

-- this was

> experimentally tested by (among others) the Hafele-Keating experiment

> (1972)

> https://paulba.no/paper/Hafele_Keating.pdf

result.

BTW, thanks for the reply, appreciated.

Julio

Apr 14, 2022, 9:32:54 AMApr 14

to

Tom, you've misunderstood what I'm doing.

Start with the gravitational scenario, with no acceleration and no

motion at all. Imagine that there is a high-rise building, with many

floors. A clock and the "AO" (whose "viewpoint" we are seeking) is

located on the first floor. A clock and an attending HF is on each of

the higher floors. The distance between the AO and each of the HF's is

constant. They are all motionless and unaccelerated.

There is initially no gravitational field. And initially all of the

clocks are synchronized and ticking at the same rate. So initially, the

rate ratio R, for each HF's clock, is just equal to 1.0.

But at some instant (say, t = 0), there suddenly appears a constant and

uniform gravitational field, of strength "g", directed downwards, and

acting over the entire length of the building. Each person suddenly

feels exactly the same force per unit mass, trying to pull them

downwards against the floor. (But they don't move, because they were

already tethered in that position). They could be constantly standing

on a bathroom scale, displaying their weight.

The gravitational time dilation equation says that, according to the AO,

each HF's clock suddenly starts ticking faster than the AO's clock, by

the rate ratio

R(t) = [ 1 + L g sech^2 (g t) ],

where "L" is the distance between the AO and that particular HF. And,

according to the AO, the change in age (AC) of each HF (relative to his

age when the field suddenly appeared), is

AC(tau) = integral, from zero to tau, of { R(t) dt }

So that's the outcome of the gravitational scenario.

We now use the equivalence principle (EP) to convert the above

gravitational scenario to the EQUIVALENT scenario with the constant and

uniform GRAVITATIONAL FIELD acting on the AO and each HF replaced by a

constant and uniform ACCELERATION acting on the AO and each HF.

Everything else stays exactly the same, except the gravitational field

is replaced by an acceleration.

Just as in the gravitational scenario, each person suddenly feels

exactly the same force per unit mass, trying to pull them against the

floor. (But they don't move, because they were already tethered in that

position). They could be constantly standing on a bathroom scale,

displaying their weight. That serves as an accelerometer.

The equivalence principle says that EVERYTHING stays the same as in the

gravitational scenario, except that the parameter "g" just gets replaced

by the parameter "A" in the equations, with each having the same

numerical value. So we still have the same equation for R and for AC as

we had above, with "g" replaced by "A", with equal numerical values. The

fact that "L" and "g" don't vary with time in the gravitational scenario

means that "L" and "A" don't vary with time in the acceleration scenario

either.

Mike Fontenot

Apr 15, 2022, 12:25:34 AMApr 15

to

Tom, you've badly misunderstood what I'm doing.

Apr 15, 2022, 12:25:48 AMApr 15

to

Tom, you've misunderstood what I'm doing.

Michael Leon Fontenot

Apr 15, 2022, 2:11:58 PMApr 15

to

On Thursday, April 14, 2022 at 11:25:34 PM UTC-5, Mike Fontenot wrote:

> ...

longer remains constant. If you force the distances to remain constant

then the helper observers cannot have the same acceleration. Please

study the "Spaceship Paradox" and Rindler coordinates. You are

making an assumption that is not correct.

Rich L.

[[Mod. note -- Bell's "spaceship paradox" is indeed highly relevant

here. The Wikipedia article

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

is a nice introduction.

In this context, when trying to understand the meaning and implications

of the phrase "there suddenly appears", it's important to ask "suddenly

in which inertial reference frame?", and to think about whether things

would still happen "suddenly" in other inertial reference frames.

-- jt]]

> ...

> But at some instant (say, t = 0), there suddenly appears a constant and

> uniform gravitational field, of strength "g", directed downwards, and

> acting over the entire length of the building. Each person suddenly

> feels exactly the same force per unit mass, trying to pull them

> downwards against the floor. (But they don't move, because they were

> already tethered in that position). They could be constantly standing

> on a bathroom scale, displaying their weight.

If you do this you will find that the distance to each helper observer no
> uniform gravitational field, of strength "g", directed downwards, and

> acting over the entire length of the building. Each person suddenly

> feels exactly the same force per unit mass, trying to pull them

> downwards against the floor. (But they don't move, because they were

> already tethered in that position). They could be constantly standing

> on a bathroom scale, displaying their weight.

longer remains constant. If you force the distances to remain constant

then the helper observers cannot have the same acceleration. Please

study the "Spaceship Paradox" and Rindler coordinates. You are

making an assumption that is not correct.

Rich L.

[[Mod. note -- Bell's "spaceship paradox" is indeed highly relevant

here. The Wikipedia article

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

is a nice introduction.

In this context, when trying to understand the meaning and implications

of the phrase "there suddenly appears", it's important to ask "suddenly

in which inertial reference frame?", and to think about whether things

would still happen "suddenly" in other inertial reference frames.

-- jt]]

Apr 15, 2022, 7:06:26 PMApr 15

to

You (Richard Livingston and moderator JT) are both confusing the

conclusions of the people who are undergoing acceleration with the

conclusions of people who are perpetually-inertial and who are observing

the people who are accelerating. The perpetually-inertial people DO

conclude that the distance between the accelerating people decreases

when they accelerate, but the people who are accelerating don't agree.

Mike Fontenot

conclusions of the people who are undergoing acceleration with the

conclusions of people who are perpetually-inertial and who are observing

the people who are accelerating. The perpetually-inertial people DO

conclude that the distance between the accelerating people decreases

when they accelerate, but the people who are accelerating don't agree.

Mike Fontenot

Apr 16, 2022, 2:57:15 AMApr 16

to

1. You presume that the principle of equivalence (POE) applies,

and base your conclusion on it: you are discussing Case 2

(below), and incorrectly believe the POE permits you to apply

the constancy of Case 1 (also below); it doesn't.

2. You are claiming a coordinate dependence for measurements that

are invariant [@] -- all observers ("people") will agree on

the results of a measurement (or series of measurements),

regardless of whether the observers are inertial or accelerated.

Bottom line: the POE applies ONLY in regions of spacetime that are small

enough that any curvature is negligible (compared to measurement

accuracies). For the case you have in mind, with helper friends

("people") near a distant friend while the accelerated observer ("AO")

roams the universe, those people span an enormous spatial region, over a

very long time. (Parentheticals relate your earlier and later notations.)

Case 1: all people are at rest in a uniform and static gravitational

field [#]. They will indeed measure their pairwise distances to all be

constant over time [@]. As the field is uniform, they all have identical

proper accelerations.

[#] I.e. their 4-velocities are parallel to the timelike

Killing vector.

[@] Measuring pairwise distances in the AO's instantaneously

co-moving inertial frame (ICIF) at a given time.

Case 2: all people are in in flat spacetime, initially at rest in some

inertial frame, each with an identical proper acceleration. They will

NOT measure their pairwise distances to be constant [@], because this is

not Born rigid motion (for which lower people must have larger proper

accelerations than higher people).

[In Case 2, if one measured those distances in the initial

inertial frame, they would be constant. But the changing

inertial frames of successive measurements, and the

structure of Lorentz transforms between frames, makes them

be not constant in successive ICIFs of the AO. See Bell's

spaceship paradox.]

This has nothing to do with different measurement methods, or the use of

inertial or non-inertial coordinates, or any supposed coordinate

dependence of invariant measurements; it is due the different ways the

two collections of people evolve in the two cases.

Tom Roberts

Apr 16, 2022, 2:57:23 AMApr 16

to

On 4/14/22 11:25 PM, Mike Fontenot wrote:

> Tom, you've misunderstood what I'm doing.

No, I don't think I have. But you have misunderstood basic relativity,
> Tom, you've misunderstood what I'm doing.

and have misunderstood when the equivalence principle applies, and when

it doesn't. See my recent post about this.

> [... completely new scenario involving clocks at different floors of

> a high-rise building]

1. In the gravitational scenario, if you have good enough

measurement accuracy to distinguish the elapsed proper times

of the clocks, then you cannot apply the equivalence principle

(EP), because the curvature of spacetime is not negligible.

2. Because of #1, your two scenarios do not correspond as you

claim -- they are NOT "equivalent" because the EP does not

apply.

3. GR does NOT say "each HF's clock suddenly starts ticking faster

than the AO's clock", because clocks always tick at their usual

(intrinsic) rate [#]. IOW: a clock's proper tick rate is

independent of its instantaneously co-moving inertial frame. --

this is a direct consequence of Einstein's first postulate

of SR, as it applies in GR.

4. But you are not actually comparing clock tick rates, you are

comparing their elapsed proper times. In GR a clock's elapsed

proper time is computed by integrating the metric over its path

through spacetime. The equation you use is the difference between

two such integrals, applied to your specific physical situation.

That difference is not due to different clock tick rates, but

rather is due to the difference in the metric at their locations

-- examine the derivation and you'll see it assumes equal proper

(intrinsic) tick rates but different values of the metric.

[#] But signals from a distant clock can tick at a

different rate from that of a local, identical clock.

This is due to the way such signals are measured, which

is the basis of all types of redshift measurements.

Bottom line: as before in your earlier scenarios, you have misunderstood

basic relativity, and have misapplied the equivalence principle.

Tom Roberts

Apr 17, 2022, 4:03:04 AMApr 17

to

On 4/16/22 12:57 AM, Tom Roberts wrote:

>

> Bottom line: the POE applies ONLY in regions of spacetime that are small

> enough that any curvature is negligible (compared to measurement

> accuracies). For the case you have in mind, with helper friends

> ("people") near a distant friend while the accelerated observer ("AO")

> roams the universe, those people span an enormous spatial region, over a

> very long time.

>

The theory of special relativity places no limits AT ALL on the extent
>

> Bottom line: the POE applies ONLY in regions of spacetime that are small

> enough that any curvature is negligible (compared to measurement

> accuracies). For the case you have in mind, with helper friends

> ("people") near a distant friend while the accelerated observer ("AO")

> roams the universe, those people span an enormous spatial region, over a

> very long time.

>

of spacetime. THAT is the domain of my scenario with acceleration.

Apr 18, 2022, 11:46:27 AMApr 18