On 8/15/21 8:24 AM, Mike Fontenot wrote:
>
> It's now looking like to me that Einstein's 1907 method of defining an
> array of clocks for an accelerating observer agrees completely with the
> CMIF method. If so, that means that CMIF is the law of the land, no
> further assumptions required. I can also now see what the error in my
> proof (that negative ageing doesn't occur) was. Details to follow.
>

That was apparently wishful thinking on my part. I still can't find an
error in my proof that negative ageing doesn't occur ... the error that
I THOUGHT I saw didn't "pan out".

Then, I did an analysis which approximates instantaneous (and large)
velocity changes (in both directions). When the acceleration was
directed TOWARD the distant person (she), the analysis said she got much
older during the acceleration ... consistent with the CMIF simultaneity
method. But when the acceleration was directed AWAY from the distant
person (she), the analysis said her age changed very little, and she
didn't get younger ... which is NOT consistent with the CMIF
simultaneity method. In fact, the those two results, taken together, are
clearly inconsistent with the standard twin "paradox" scenario: suppose
he keeps instantaneously changing his velocity, first accelerating
toward her, then immediately away from her, over and over. According to
my results using the array of clocks (and "helper friends", HF's), each
of those accelerations TOWARD her produces a large increase in her age
(according to him), but each of those accelerations AWAY from her
produces NO decrease in her age, and very little change in her age at
all. So he can make her be as old as he wants to, by continuing to do
those paired accelerations, over and over. So when he quits doing all
those paired accelerations, and then accelerates toward her one last
time, and then coasts back to their reunion (with the usual slow ageing
by her, according to him), his computation of her age at his arrival
won't be what is required by the twin "paradox" result. (They HAVE to
agree with each other about their respective ages at the reunion). So
this analysis produces an absurd and inconsistent result, and it can't
be correct. But Einstein's gravitational time dilation equation had been
well-tested, so how could it produce an erroneous result when its
acceleration equivalent (using the equivalence principle) is used? Is it
possibly because the gravitational time dilation equation is not
intended to be used with gravity being switched on and off, and
therefore we can't use it to describe what happens when the observer
switches his acceleration on and off?

Or maybe I've just made a mistake in my analysis somewhere. I'll give a
few facts about my analysis that will allow anyone who wishes, to check
my work. I use an acceleration of +-1 ls/s/s (equivalent to about 30.5
million g's), and the acceleration lasts only 1.317 seconds. That
results in a velocity of +-0.866, which gives the convenient gamma =
2.0. When computing distances traveled by various observers, I integrate
the velocity v with respect to t, the accelerating person's time. The
relation between velocity v and "rapidity", theta, is v = tanh(theta).
Theta is simply related to acceleration A and time t: theta = A t.
(Rapidity is a non-linear equivalent of velocity: rapidity can vary from
-infinity to +infinity, whereas velocity can't exceed the speed of light
in magnitude.) The integral of tanh is equal to ln(cosh). But you can
get a rough idea of the magnitude of the results by just integrating
theta rather than v to get approximate distances.

I've had a new thought that is seeming "air tight" to me:

If some person (the "HF") is momentarily co-located with the home twin
(she), the HF cannot possibly witness her age to instantaneously change
at that instant, either positively of negatively. That would be an
absurdity.

The distant accelerating observer (the "AO") is able to say that the HF
always shares his (the AO's) notion of "NOW". Therefore the AO must also
conclude that the home twin's age didn't instantaneously change (either
positively or negatively) at that instant.

If the above argument is correct, then the CMIF simultaneity method
can't be correct.

On 8/23/21 12:10 PM, Mike Fontenot wrote:
>
>
> I've had a new thought that is seeming "air tight" to me:
>
> If some person (the "HF") is momentarily co-located with the home twin
> (she), the HF cannot possibly witness her age to instantaneously change
> at that instant, either positively of negatively. That would be an
> absurdity.
>
> The distant accelerating observer (the "AO") is able to say that the HF
> always shares his (the AO's) notion of "NOW". Therefore the AO must also
> conclude that the home twin's age didn't instantaneously change (either
> positively or negatively) at that instant.
>
> If the above argument is correct, then the CMIF simultaneity method
> can't be correct.
>

The way the accelerating observer (the "AO") defines his "NOW" instant
at distant locations comes directly from the gravitational time dilation
equation, via the equivalence principle. It says that a "helper friend"
(HF) who always is accelerating exactly as the AO is accelerating, with
acceleration A, will age at a rate that is a fixed known ratio of the
AO's rate. The given HF and the AO are always a constant distance "d"
apart. If the chosen HF is BEHIND the AO (compared to the direction of
the acceleration), that HF will age SLOWER than the AO by the factor
exp(A d). To keep things as simple as possible, we can always let all of
the HF's and the AO's ages be the same, immediately before they all
start accelerating. Then the ratio of the age of the "behind" HF's age
to the AO's age is just 1/exp(A d). And if, instead, another HF is AHEAD
of the AO (compared to the direction of the acceleration), then the
ratio of that "ahead" HF's age to the AO's age is just exp(A d). (Of
course, different "behind" HF's will have different distances "d" to the
AO, and likewise for the "ahead" HF's.) So, at some instant T in the
AO's life, he computes that the original "behind" HF's current age is
T/exp(A d). Or, alternatively, he computes that the "ahead" HF's current
age is T exp(A d) The way he SELECTS the HF from among all possible HF's
(both ahead and behind him) is such that the chosen HF is momentarily
co-located with the home twin (her) at the instant the AO wants to know
her current age.

So, if all of the above is correct, that allows the AO to construct an
array of (effectively) synchronized clocks and helper observers attached
to him, similar to what a perpetually-inertial observer can do, that can
put an observer momentarily co-located with the distant twin (her) at
the instant in the AO's life when he wants to know her current age. And
in both the perpetually-inertial and the accelerated cases, it would be
ABSURD for that momentarily co-located observer to observe a large and
abrupt change in her age at that instant.

Gravity and motion cannot stop time....
therefor it cannot go backward.
It is forward order as all order is.
It can be a slow forward like
in space...

Mitchell Raemsch

On 8/25/21 1:48 PM, Mike Fontenot wrote:
> The way the accelerating observer (the "AO") defines his "NOW" [...]

As I keep saying, that is irrelevant. No space-faring astronaut would
ever use their instantaneously co-moving inertial frame. Just like no
truck or ship does that here on earth. (Vehicle-referenced coordinates
are sometimes used for nearby operations, but NEVER for distant objects.)

As I keep saying, your entire program is useless. For determining "the
current age of a distant observer", astronauts would surely use the rest
frame of nearby stars, which is approximately the same as earth's rest
frame. For distances over a few thousand lightyears, where those frames
are not close to the same, things get much more complicated; that is
unlikely to be an issue....

Tom Roberts

Tom Roberts wrote:

> As I keep saying, your entire program is useless. For determining "the
> current age of a distant observer", astronauts would surely use the rest
> frame of nearby stars, which is approximately the same as earth's rest
> frame. For distances over a few thousand lightyears, where those frames
> are not close to the same, things get much more complicated; that is
> unlikely to be an issue....

It is. If Earth lies inside the *habitable_zone* so does the Moon. The
question is how life disappeared on moon, for us to know how to travel to
other star system habitable zone. That would be not by speed, but by
curvature of spacetime (low speed).

To accomplish that we need element 115 stable along islands of stability.

On 8/23/21 12:10 PM, Mike Fontenot wrote:
>
>
> I've had a new thought that is seeming "air tight" to me:
>
> If some person (the "HF") is momentarily co-located with the home twin
> (she), the HF cannot possibly witness her age to instantaneously change
> at that instant, either positively of negatively. That would be an
> absurdity.
>
> The distant accelerating observer (the "AO") is able to say that the HF
> always shares his (the AO's) notion of "NOW". Therefore the AO must also
> conclude that the home twin's age didn't instantaneously change (either
> positively or negatively) at that instant.
>
> If the above argument is correct, then the CMIF simultaneity method
> can't be correct.
>

I now see that the above argument is NOT correct. The fact that it is
not correct DOESN'T prove that she never abruptly gets older, however.
It may be true that she doesn't abruptly get older, but the above
argument doesn't prove that.

I think the only way to prove that she doesn't abruptly get older, or to
prove the opposite, is to make use of two DIFFERENT HF's. Immediately
before the speed change, she is co-located with HF1. Immediately after
the abrupt speed change, she is co-located with HF2. If she DOES get a
lot older because of the speed change, HF2 will be far from HF1. If HF2
is close to Hf1, then she DIDN'T get much older. Which one of those
outcomes actually happens isn't trivial to determine ... I think it can
be done, but I think it will be complicated. It will require, among
other things, looking at it from her perspective, and that is
complicated by the fact that, according to her, the distances between
the various HF's isn't constant. (Those distances ARE constant,
according to the HF's and the AO.)

So, I've got a lot of work to do. But I HAVEN'T been able to find a flaw
in my original proof that she can't abruptly get younger, according to
the AO. So as of now, I think that proof is valid. If so, the CMIF
simultaneity method is incorrect. And I also believe that if she can't
abruptly get younger, then she can't abruptly get older either ... they
either must both be true, or else they must both be false.

Instantaneous Velocity Changes in the Equivalence Principle Version of
the Gravitational Time Dilation Equation

When using the CMIF simultaneity method, the analysis is GREATLY
simplified by using instantaneous velocity changes, rather than finite
accelerations that last for a finite amount of time. So I decided to
try using instantaneous velocity changes in the Equivalence-Principle
Version of the Gravitational Time Dilation equation (the "EPVGTD"
equation). The result (assuming I haven't made a mistake somewhere) is
unexpected and disturbing. My analysis found that the age change of the
HF, produced by an instantaneous velocity change by the AO and the HF,
from zero to 0.866 lightseconds/second (ls/s), directed toward the home
twin (her), is INFINITE!

I'll describe my analysis, and perhaps someone can find an error somewhere.

Before the instantaneous velocity change, the AO (he), HF, and the home
twin (she) are all mutually stationary. She and the HF are initially
co-located, and the AO (he) is "d" lightseconds away from her and the HF.

I start by considering a constant acceleration "A" ls/s/s that lasts for
a very short but finite time of "tau" seconds. That acceleration over
tau seconds causes the rapidity, theta, (which starts at zero) to
increase to

theta = A tau ls/s,

and so we get the following relationship:

A = theta / tau.

We will need the above relationship shortly.

(Rapidity has a one-to-one relationship to velocity. Velocity of any
object that has mass can never be equal to or greater than the velocity
of light in magnitude, but rapidity can vary from -infinity to +infinity.)

We want the velocity, beta, to be 0.866 ls/s after the acceleration.
Rapidity, theta, is related to velocity, beta, by the equation

theta = arctanh (beta) = (1/2) ln [ (1 + beta) / (1 - beta) ].

("arctanh" just means the inverse of the hyperbolic tangent function.)

So velocity = 0.866 corresponds to a rapidity of about 1.317 ls/s.

The "EPVGTD" equation says that the acceleration A will cause the HF to
age faster than the AO by the factor exp(A d), where d is the constant
separation between the AO and the HF.

Note that the argument in the exponential exp(A d) can be separated like
this:

exp(A d) = [exp(d)] sup A,

where "sup A" means "raise the quantity exp(d) to the power "A" ". The
rationale for doing that is because the quantity exp(d) won't change as
we make the acceleration greater and greater, and the duration of the
acceleration shorter and shorter. That will make the production of the
table below easier.

The change in the age of the HF, caused by an acceleration "A" that
lasts "tau" seconds is just

tau [exp(d)] sup A,

because [exp(d)] sup A is the constant rate at which the HF is ageing,
during the acceleration, and tau is how long that rate lasts.

But we earlier found that A = theta / tau, so we get

tau [exp(d)] sup {theta / tau}

for the change in the age of the HF due to the short acceleration. So
we have an expression for the change in the age of the HF that is a
function of only the single variable tau ... all other quantities in the
equation (d and theta) are fixed. We can now use that equation to
create a table that shows the change in the age of the HF, as a function
of the duration of the acceleration (while keeping the area under the
acceleration curve constant).

In order to make the table as easy to produce as possible, I chose the
arbitrary value of the distance "d" to be such that

exp(d theta) = 20000.

Therefore we need

ln[ exp (d theta) ] = d theta = ln (20000) = 9.903,

and since theta = 1.317, d = 7.52 lightseconds.

If we were creating this table for the CMIF simultaneity method, we
would find that as the duration of the acceleration decreases (with a
corresponding increase in the magnitude of the acceleration, so that the
product remains the same), the amount of ageing by the HF approaches a
finite limit. I.e., in CMIF, eventually it makes essentially no
difference in the age of the HF when we halve the duration of the
acceleration, and make the acceleration twice as great.

But here is what I got for the EPVGTD simultaneity method:

(in the table, "10sup4" means "10 raised to the 4th power".)

tau | (tau) (2000)sup(1/tau)

____________________________

1.0 | 2x10sup4 = 20000

0.5 | 2x10sup8

0.4 | 2.26x10sup10

0.3 | 6.3x10sup13

0.2 | 0.64x10sup21

0.1 | 1.02x10sup42

0.01 | 1.27x10sup428

0.001 | ? (My calculator overflowed at 10sup500)

Clearly, for the EPVGTD simultaneity method, the HF's age goes to
infinity as the acceleration interval goes to zero. That seems like an
absurd answer to me. And it is radically different from what happens
with CMIF simultaneity, where the HF's age quickly approaches a finite
limit as tau goes to zero.

Mike Fontenot wrote:

> When using the CMIF simultaneity method, the analysis is GREATLY
> simplified by using instantaneous velocity changes, rather than finite
> accelerations that last for a finite amount of time. So I decided to
> try using instantaneous velocity changes in the Equivalence-Principle
> Version of the Gravitational Time Dilation equation (the "EPVGTD"
> equation). The

Fauci Basically Says: Vaxxed Or Unvaxxed Either Way...Youre Fucked
https://153news.net/watch_video.php?v=HSN7RMGKDM71

On 9/1/21 11:29 AM, Mike Fontenot wrote:
>
> [...]
>

Instantaneous Velocity Changes in the Equivalence Principle Version of
the Gravitational Time Dilation Equation - Revised Model (the LGTD Model)

_______________________________________________________

I repeated my previous analysis of the instantaneous increase in the
home person's (her) age (according to the accelerating person, AO, him),
according to the Equivalence Principle Version of the Gravitational Time
Dilation Equation, (the "EPVGTD" equation), and replaced it with the new
equation, which I'll call the "Linearized Gravitational Time Dilation
Equation", (the "LGTD" equation). I simply replace the exponential
exp(A d) with the quantity (1 + A d). (This is the same approximation
that Einstein used in his 1907 paper). In what follows below, I'll
repeat each affected calculation that I made in my last post, and show
the revised calculation.

[...]

[Previous]:

The "EPVGTD" equation says that the acceleration A will cause the HF to
age faster than the AO by the factor exp(A d), where d is the constant
separation between the AO and the HF.

[Revised]:

The "LGTD" equation says that the acceleration A will cause the HF to
age faster than the AO by the factor (1 + A d), where d is the constant
separation between the AO and the HF.

(Both of the above are for the case where the AO accelerates TOWARD the
unaccelerated person (her).)

[...]

[Previous]:

The change in the age of the HF, caused by an acceleration "A" that
lasts "tau" seconds is just

tau [exp(d)] sup A,

because [exp(d)] sup A is the constant rate at which the HF is ageing,
during the acceleration, and tau is how long that rate lasts.

[Revised]:

The change in the age of the HF, caused by an acceleration "A" that
lasts "tau" seconds is just

tau (1 + A d),

because (1 + A d) is the constant rate at which the HF is ageing, during
the acceleration, and tau is how long that rate lasts.

[Previous]:

But we earlier found that A = theta / tau, so we get

tau [exp(d)] sup {theta / tau}

[Revised]:

But we earlier found that A = theta / tau, so we get

tau (1 + [ ( theta d ) / tau ] = tau + (theta d)

[...]

It is still true that d = 7.52 lightseconds and theta = 1.317.

Therefore the revised result is that the change in HF's age during the
acceleration is equal to

tau + ( theta d ) = tau + (1.317)(7.52) = tau + 9.904.

So, in the revised model, as tau approaches zero (to give an
instantaneous velocity change), the change in the HF's age during the
speed change approaches 9.904 seconds from above. So the HF's age
increased by a finite amount, unlike the infinite increase that the
EPVGTD equation gave.

Before the instantaneous velocity change, the AO, the HF, and the home
twin (she) were all the same age. She and the HF were co-located. So
after the instantaneous speed change, the AO hasn't aged at all, but the
HF is 9.904 seconds older than he was before the speed change, according
to the AO. And since she and the HF have been colocated during the
instantaneous speed change, they couldn't have ever differed in age
during the speed change ... it would be absurd for either of them to see
the other have an age different from their own age at any instant. So
after the instantaneous speed change, the AO must conclude that she and
the HF both instantaneously got 9.904 seconds older than they were
immediately before the speed change.

By comparison, the CMIF simultaneity method says that the AO will
conclude that her age instantaneously increases by 6.51 seconds, so the
LGTD and CMIF don't agree.

I just repeated my previous analysis of instantaneous velocity changes
in the "linearized" (LGTD) version of the equivalence principle version
of the gravitational time dilation equation, but for the case where the
instantaneous velocity change is AWAY FROM the home twin (her). The
result is exactly like the previous result, except that she
instantaneously gets YOUNGER, not older. (This contradicts my previous
possible proof that negative ageing doesn't occur.)

Below, I'll repeat the previous calculations, and show the changes.

[Previous]:

I simply replace the exponential exp(A d) with the quantity (1 + A d).

[New]:

I simply replace the exponential exp(-A d) with the quantity (1 - A d).

[Previous]:

The "LGTD" equation says that the acceleration A will cause the HF to
age FASTER than the AO by the factor (1 + A d), where d is the constant
separation between the AO and the HF.

(The above is for the case where the AO accelerates TOWARD the
unaccelerated person (her).)

[New]:

The "LGTD" equation says that the acceleration A will cause the HF to
age SLOWER than the AO by the factor (1 - A d), where d is the constant
separation between the AO and the HF.

(The above is for the case where the AO accelerates AWAY FROM the
unaccelerated person (her).)

[...]

[Previous]:

The change in the age of the HF, caused by an acceleration "A" that
lasts "tau" seconds is just

tau (1 + A d),

because (1 + A d) is the constant rate at which the HF is ageing, during
the acceleration, and tau is how long that rate lasts.

[New]:

The change in the age of the HF, caused by an acceleration "A" that
lasts "tau" seconds is just

tau (1 - A d),

because (1 - A d) is the constant rate at which the HF is ageing, during
the acceleration, and tau is how long that rate lasts.

[Previous]:

But we earlier found that A = theta / tau, so we get

tau (1 + [ ( theta d ) / tau ] ) = tau + (theta d)

[New]:

But we earlier found that A = theta / tau, so we get

tau (1 - [ ( theta d ) / tau ] ) = tau - (theta d)

[both Previous and New]:

It is still true that d = 7.52 lightseconds and theta = 1.317.

[Previous]:

Therefore the revised result is that the change in HF's age during the
acceleration is equal to

tau + ( theta d ) = tau + (1.317)(7.52) = tau + 9.904.

[New]:

Therefore the revised result is that the change in HF's age during the
acceleration is equal to

tau - ( theta d ) = tau - (1.317)(7.52) = tau - 9.904.

[Previous]

So, in the revised model, as tau approaches zero (to give an
instantaneous velocity change), the change in the HF's age during the
speed change approaches 9.904 seconds from above. So with an
instantaneous velocity change, the HF's age INCREASED instantaneously by
a finite amount.

[New]

So, in the revised model, as tau approaches zero (to give an
instantaneous velocity change), the change in the HF's age during the
speed change approaches -9.904 seconds from above. So with an
instantaneous velocity change, the HF's age DECREASED instantaneously by
a finite amount.

[Previous]:

Before the instantaneous velocity change, the AO, the HF, and the home
twin (she) were all the same age. She and the HF were co-located. So
after the instantaneous speed change, the AO hasn't aged at all, but the
HF is 9.904 seconds OLDER than he was before the speed change, according
to the AO. And since she and the HF have been colocated during the
instantaneous speed change, they couldn't have ever differed in age
during the speed change ... it would be absurd for either of them to see
the other have an age different from their own age at any instant. So
after the instantaneous speed change, the AO must conclude that she and
the HF both instantaneously got 9.904 seconds OLDER than they were
immediately before the speed change.

By comparison, the CMIF simultaneity method says that the AO will
conclude that her age instantaneously increases by 6.51 seconds, so the
LGTD and CMIF don't agree.

[New]:

Before the instantaneous velocity change, the AO, the HF, and the home
twin (she) were all the same age. She and the HF were co-located. So
after the instantaneous speed change, the AO hasn't aged at all, but the
HF is 9.904 seconds YOUNGER than he was before the speed change,
according to the AO. And since she and the HF have been colocated during
the instantaneous speed change, they couldn't have ever differed in age
during the speed change ... it would be absurd for either of them to see
the other have an age different from their own age at any instant. So
after the instantaneous speed change, the AO must conclude that she and
the HF both instantaneously got 9.904 seconds YOUNGER than they were
immediately before the speed change.

By comparison, the CMIF simultaneity method says that the AO will
conclude that her age instantaneously decreases by 6.51 seconds, so the
LGTD and CMIF don't agree.

So, what to make of all these different and contradictory results?

The "EPVGTD Equation" (the one with the exponential), says that, if the
AO (he) instantaneously changes his velocity in the direction TOWARD the
home time (her), she instantaneously gets INFINITELY older, according to
him. That's nonsense, because it gives incorrect ages for the twins
when they are reunited.

On the other hand, when he instantaneously changes his velocity in the
direction AWAY from her, the EPVGTD equation says that her age doesn't
change instantaneously. While it's not certain that that result itself
is incorrect, it seems to result in an inconsistency at the reunion. The
EPVGTD equation says that, with zero acceleration, he and all the HF's
age at the same rate. That seems to require that on the outbound and
inbound legs, his conclusion about the correspondence between his and
her ages must be the same. And clearly, on the OUTBOUND leg, he MUST
say she is ageing SLOWER than he is, by the factor gamma. So he must
say that, on the INBOUND leg, she is ageing slower by the factor gamma.
But in that case, their conclusions about the correspondence between
their ages at the reunion won't be consistent: she says she is the
OLDER, but he says she is the YOUNGER. So his conclusions won't match
her conclusions at the reunion, which is impossible since they are
colocated then and they MUST agree about the correspondence between
their ages then.

So much for the EPVGTD equation. What about the LGTD equation? The
linearized equation (the LGTD equation) gives results that are
qualitatively similar to the CMIF simultaneity method: her age
instantaneously changes, according to him, during his instantaneous
velocity change (instantaneously increasing when his momentarily
infinite acceleration is TOWARD her, and instantaneously decreasing when
his momentarily infinite acceleration is AWAY FROM her). But the AMOUNT
of the instantaneous change is greater than CMIF says it should be. It
is interesting that the amount of the instantaneous age changes would be
exactly the same for CMIF and LGTD if the linearized equation multiplied
the distance "d" by the velocity "v", rather than by the rapidity
"theta". But, in determining the velocity effect obtained by
integrating the acceleration "A", it IS necessary to use the rapidity
"theta", not the velocity "v", as the variable of integration. (Taylor
and Wheeler go over this in detail).

WHY does the EPVGTD equation fail so miserably in this example? Isn't
the GTD equation a well-established result in general relativity? And
the equivalence principle is certainly well-established. Is the GTD
equation WRONG?

And WHY goes the LGTD work better than the EPVGTD, at least
qualitatively? The LGTD should be a justified approximation of the
EPVGTD only when the argument (A d) is small, and an infinite "A" (even
though it lasts only an infinitesimal time) certainly isn't small! The
LGTD equation shouldn't give results that are even qualitatively
correct, but it does. Why?

Mike Fontenot wrote:

> The "EPVGTD Equation" (the one with the exponential), says that, if the
> AO (he) instantaneously changes his velocity in the direction TOWARD the
> home time (her), she instantaneously gets INFINITELY older, according to
> him. That's nonsense, because it gives incorrect ages for the twins when
> they are reunited.

not true. Before the covid_19 fraud they were busy solving by investing
in the hospital beds, equipment etc. Not anymore. There are no problems
with hospital capacities anywhere. Just read the newspapers before the
corona. I'm not making bullshit.