We know that in accelerated frames of reference the average speed is
proportional to the instantaneous speed.
Let Vrm=(1/2)Vri
We are talking about real relativistic speeds (Richard Verret's hobby).
But we know that relativistic physicists do not use this notion, and it is
important to remind them of the relationship between real speed and
observable speed.
Vr=Vo/sqrt(1-Vo²/c²)
This immediately leads us to
Vom/sqrt(1-Vom²/c²)=(1/2)Voi/sqrt(1-Voi²/c²)
and therefore to:
Vom²(1-Voi²/c²)=(1/4)Voi²(1-Vom²/c²)
Let Vom²=(1/4)Voi²+(3/4)Voi².Vom²/c²
Hence Vom=(1/2)Voi/sqrt(1-(3/4)Vom²/c²) and, conversely,
Voi=2.Vom/sqrt(1+3Vom²/c²)

Thank you for your kind attention.
R.H.

Den 12.03.2024 10:00, skrev Richard Hachel:
> We know that in accelerated frames of reference the average speed is
> proportional to the instantaneous speed.
>
> Let Vrm=(1/2)Vri

This is meaningless without definition of the entities.

But I can guess:
You are not talking about "speed in an accelerated frame".

You are talking about the speed of a stationary object
in an accelerated frame, measured in an inertial frame.

If the object is instantly at rest at t = 0, and
the coordinate acceleration in the inertial frame is constant a,
Then the speed Vri(t) = at
and the average speed from t=0 to t=t is Vrm(t) = at/2.

So Vrm=(1/2)Vri

>
> We are talking about real relativistic speeds (Richard Verret's hobby).

According to SR:

For the above to be true, the coordinate acceleration must
be constant. This means that the proper acceleration must
increase with time.

Let 1g = 1 c per year = 9.4998 m/s².

To keep the coordinate acceleration a equal to 1 g
the proper acceleration A must be:
at t = 0 year A = 1.00 g
at t = 0.8 year A = 1.65 g
at t = 0.9 year A = 3.33 g
at t = 0.99 year A = 33.4 g
at t = 0.999 year A = 333.5 g
at t = 1.000 year A = infinite

when t ≥ 1.0 year the coordinate acceleration can't
be kept equal to 1 g.

Generally:
The coordinate acceleration a can't be kept equal to n g
when t ≥ 1/n year.

It is obviously normal to keep the proper acceleration constant,
and then Vrm ≠ (1/2)Vri

>
> But we know that relativistic physicists do not use this notion, and it
> is important to remind them of the relationship between real speed and
> observable speed.
>
> Vr=Vo/sqrt(1-Vo²/c²)

This is nonsense.
According to "relativistic physicists" there is no difference
between the "real speed" and the "observable (measurable) speed"
in the inertial frame.

>
> This immediately leads us to Vom/sqrt(1-Vom²/c²)=(1/2)Voi/sqrt(1-Voi²/c²)
>
> and therefore to:
>
> Vom²(1-Voi²/c²)=(1/4)Voi²(1-Vom²/c²)
>
> Let Vom²=(1/4)Voi²+(3/4)Voi².Vom²/c²
>
> Hence Vom=(1/2)Voi/sqrt(1-(3/4)Vom²/c²) and, conversely,
> Voi=2.Vom/sqrt(1+3Vom²/c²)
>
>
> Thank you for your kind attention.
>
> R.H.

--
Paul

https://paulba.no/

Le 12/03/2024 à 20:19, "Paul B. Andersen" a écrit :
> Den 12.03.2024 10:00, skrev Richard Hachel:
>> We know that in accelerated frames of reference the average speed is
>> proportional to the instantaneous speed.
>>
>> Let Vrm=(1/2)Vri
>
> This is meaningless without definition of the entities.
>
> But I can guess:
> You are not talking about "speed in an accelerated frame".
>
> You are talking about the speed of a stationary object
> in an accelerated frame, measured in an inertial frame.
>
> If the object is instantly at rest at t = 0, and
> the coordinate acceleration in the inertial frame is constant a,
> Then the speed Vri(t) = at
> and the average speed from t=0 to t=t is Vrm(t) = at/2.
>
> So Vrm=(1/2)Vri

That is what I am saying.

Vr=a.Tr

Vrm=(1/2)Vri

>
>>
>> We are talking about real relativistic speeds (Richard Verret's hobby).
>
> According to SR:
>
> For the above to be true, the coordinate acceleration must
> be constant. This means that the proper acceleration must
> increase with time.
>
> Let 1g = 1 c per year = 9.4998 m/s².
>
> To keep the coordinate acceleration a equal to 1 g
> the proper acceleration A must be:
> at t = 0 year A = 1.00 g
> at t = 0.8 year A = 1.65 g
> at t = 0.9 year A = 3.33 g
> at t = 0.99 year A = 33.4 g
> at t = 0.999 year A = 333.5 g
> at t = 1.000 year A = infinite
>
> when t ≥ 1.0 year the coordinate acceleration can't
> be kept equal to 1 g.
>
> Generally:
> The coordinate acceleration a can't be kept equal to n g
> when t ≥ 1/n year.
>
>
> It is obviously normal to keep the proper acceleration constant,
> and then Vrm ≠ (1/2)Vri

I don't understand what you are saying.

I think that between you and me, there is a different understanding of
things.

>
>
>>
>> But we know that relativistic physicists do not use this notion, and it
>> is important to remind them of the relationship between real speed and
>> observable speed.
>>
>> Vr=Vo/sqrt(1-Vo²/c²)
>
> This is nonsense.
> According to "relativistic physicists" there is no difference
> between the "real speed" and the "observable (measurable) speed"
> in the inertial frame.

That is what I am saying.
Physicists do not differentiate between Vo and Vr.

>
>>
>> This immediately leads us to Vom/sqrt(1-Vom²/c²)=(1/2)Voi/sqrt(1-Voi²/c²)
>>
>> and therefore to:
>>
>> Vom²(1-Voi²/c²)=(1/4)Voi²(1-Vom²/c²)
>>
>> Let Vom²=(1/4)Voi²+(3/4)Voi².Vom²/c²
>>
>> Hence Vom=(1/2)Voi/sqrt(1-(3/4)Vom²/c²) and, conversely,
>> Voi=2.Vom/sqrt(1+3Vom²/c²)
>>
>>
>> Thank you for your kind attention.

It is really a shame that a large majority of physicists are not very
intelligent, they understand nothing of what they are saying,
which is dramatic since their number serves as truth.
A bit like in Nazi Germany everyone believed they were right because
everyone held out their arm in front of Hitler.
Physicists are educated, but very few are intelligent.

On usenet, there are perhaps five or six people with whom we can seriously
discuss relativity, without immediately falling into hysterical reactions.
(Julien Arlandis, Michel Talon, Paul B Anderson...). The others not only
learned anything, but answer nonsense when asked a simple problem.

A good example of this madness here is Python, as stupid as he is
aggressive.

R.H.

Le 12/03/2024 à 20:19, "Paul B. Andersen" a écrit :
> Den 12.03.2024 10:00, skrev Richard Hachel:

> Let 1g = 1 c per year = 9.4998 m/s².
>
> To keep the coordinate acceleration a equal to 1 g
> the proper acceleration A must be:
> at t = 0 year A = 1.00 g
> at t = 0.8 year A = 1.65 g
> at t = 0.9 year A = 3.33 g
> at t = 0.99 year A = 33.4 g
> at t = 0.999 year A = 333.5 g
> at t = 1.000 year A = infinite

No.

It's not the current problem.

at t = 0 year A = 1.00 g
at t = 0.8 year A = 1.00 g
at t = 0.9 year A = 1.00 g
at t = 0.99 year A = 1.00 g
at t = 0.999 year A = 1.00 g
at t = 1.000 year A = 1.00 g

I beg you to understand something:
in the rocket's frame of reference, the acceleration is constant.
The motors are manufactured to give a constant acceleration of 10m/s²
(a=1.052ly/y²) and there is no need to look for rabbit crones.
Certainly, in the terrestrial reference frame, this acceleration will
appear to gradually decrease over time and this will give the following
equation for the acceleration observed in the terrestrial reference frame:

<http://news2.nemoweb.net/jntp?xw8jiaP3Bbvt3aHF_FHQ1Rt5-Jc@jntp/Data.Media:1>

But in the framework of the rocket, built for that, there is no need to
make any unnecessary modifications.

<http://news2.nemoweb.net/?DataID=xw8jiaP3Bbvt3aHF_FHQ1Rt5-Jc@jntp>

R.H.

Le 12/03/2024 à 20:19, "Paul B. Andersen" a écrit :
> Den 12.03.2024 10:00, skrev Richard Hachel:
>> We know that in accelerated frames of reference the average speed is
>> proportional to the instantaneous speed.
>>
>> Let Vrm=(1/2)Vri
>
> This is meaningless without definition of the entities.
>
> But I can guess:
> You are not talking about "speed in an accelerated frame".
>
> You are talking about the speed of a stationary object
> in an accelerated frame, measured in an inertial frame.
>
> If the object is instantly at rest at t = 0, and
> the coordinate acceleration in the inertial frame is constant a,
> Then the speed Vri(t) = at
> and the average speed from t=0 to t=t is Vrm(t) = at/2.
>
> So Vrm=(1/2)Vri

That is what I am saying.

Vr=a.Tr

Vrm=(1/2)Vri

>
>>
>> We are talking about real relativistic speeds (Richard Verret's hobby).
>
> According to SR:
>
> For the above to be true, the coordinate acceleration must
> be constant. This means that the proper acceleration must
> increase with time.
>
> Let 1g = 1 c per year = 9.4998 m/s².
>
> To keep the coordinate acceleration a equal to 1 g
> the proper acceleration A must be:
> at t = 0 year A = 1.00 g
> at t = 0.8 year A = 1.65 g
> at t = 0.9 year A = 3.33 g
> at t = 0.99 year A = 33.4 g
> at t = 0.999 year A = 333.5 g
> at t = 1.000 year A = infinite
>
> when t ≥ 1.0 year the coordinate acceleration can't
> be kept equal to 1 g.
>
> Generally:
> The coordinate acceleration a can't be kept equal to n g
> when t ≥ 1/n year.
>
>
> It is obviously normal to keep the proper acceleration constant,
> and then Vrm ≠ (1/2)Vri

I don't understand what you are saying.

I think that between you and me, there is a different understanding of
things.

>
>
>>
>> But we know that relativistic physicists do not use this notion, and it
>> is important to remind them of the relationship between real speed and
>> observable speed.
>>
>> Vr=Vo/sqrt(1-Vo²/c²)
>
> This is nonsense.
> According to "relativistic physicists" there is no difference
> between the "real speed" and the "observable (measurable) speed"
> in the inertial frame.

That is what I am saying.
Physicists do not differentiate between Vo and Vr.

>
>>
>> This immediately leads us to Vom/sqrt(1-Vom²/c²)=(1/2)Voi/sqrt(1-Voi²/c²)
>>
>> and therefore to:
>>
>> Vom²(1-Voi²/c²)=(1/4)Voi²(1-Vom²/c²)
>>
>> Let Vom²=(1/4)Voi²+(3/4)Voi².Vom²/c²
>>
>> Hence Vom=(1/2)Voi/sqrt(1-(3/4)Vom²/c²) and, conversely,
>> Voi=2.Vom/sqrt(1+3Vom²/c²)
>>
>>
>> Thank you for your kind attention.

It is really a shame that a large majority of physicists are not very
intelligent, they understand nothing of what they are saying,
which is dramatic since their number serves as truth.
A bit like in Nazi Germany everyone believed they were right because
everyone held out their arm in front of Hitler.
Physicists are educated, but very few are intelligent.

On usenet, there are perhaps five or six people with whom we can seriously
discuss relativity, without immediately falling into hysterical reactions.
(Julien Arlandis, Michel Talon, Paul B Andersen...). The others not only
learned anything, but answer nonsense when asked a simple problem.

A good example of this madness here is Python, as stupid as he is
aggressive.

R.H.

On 03/12/2024 12:20 PM, Paul B. Andersen wrote:
> Den 12.03.2024 10:00, skrev Richard Hachel:
>> We know that in accelerated frames of reference the average speed is
>> proportional to the instantaneous speed.
>>
>> Let Vrm=(1/2)Vri
>
> This is meaningless without definition of the entities.
>
> But I can guess:
> You are not talking about "speed in an accelerated frame".
>
> You are talking about the speed of a stationary object
> in an accelerated frame, measured in an inertial frame.
>
> If the object is instantly at rest at t = 0, and
> the coordinate acceleration in the inertial frame is constant a,
> Then the speed Vri(t) = at
> and the average speed from t=0 to t=t is Vrm(t) = at/2.
>
> So Vrm=(1/2)Vri
>
>>
>> We are talking about real relativistic speeds (Richard Verret's hobby).
>
> According to SR:
>
> For the above to be true, the coordinate acceleration must
> be constant. This means that the proper acceleration must
> increase with time.
>
> Let 1g = 1 c per year = 9.4998 m/s².
>
> To keep the coordinate acceleration a equal to 1 g
> the proper acceleration A must be:
> at t = 0 year A = 1.00 g
> at t = 0.8 year A = 1.65 g
> at t = 0.9 year A = 3.33 g
> at t = 0.99 year A = 33.4 g
> at t = 0.999 year A = 333.5 g
> at t = 1.000 year A = infinite
>
> when t ≥ 1.0 year the coordinate acceleration can't
> be kept equal to 1 g.
>
> Generally:
> The coordinate acceleration a can't be kept equal to n g
> when t ≥ 1/n year.
>
>
> It is obviously normal to keep the proper acceleration constant,
> and then Vrm ≠ (1/2)Vri
>
>
>>
>> But we know that relativistic physicists do not use this notion, and
>> it is important to remind them of the relationship between real speed
>> and observable speed.
>>
>> Vr=Vo/sqrt(1-Vo²/c²)
>
> This is nonsense.
> According to "relativistic physicists" there is no difference
> between the "real speed" and the "observable (measurable) speed"
> in the inertial frame.
>
>>
>> This immediately leads us to Vom/sqrt(1-Vom²/c²)=(1/2)Voi/sqrt(1-Voi²/c²)
>>
>> and therefore to:
>>
>> Vom²(1-Voi²/c²)=(1/4)Voi²(1-Vom²/c²)
>>
>> Let Vom²=(1/4)Voi²+(3/4)Voi².Vom²/c²
>>
>> Hence Vom=(1/2)Voi/sqrt(1-(3/4)Vom²/c²) and, conversely,
>> Voi=2.Vom/sqrt(1+3Vom²/c²)
>>
>>
>> Thank you for your kind attention.
>>
>> R.H.
>

I'm wondering about the infinitely-many higher orders
of acceleration, with respect to v = dp/dt, a = dv/dt = v',
and alll the infinitely-many higher orders of the derivatives,
"v-prime-infty", an infinite series of terms that go through
changes each term from zero to non-zero and back again in
any establishment of any difference of acceleration,
with regards to all those terms in the series vanishing,
in the establishment of uniform motion or rest.

Eg, "accelerated frame", or, "accelerating frame".

Frames and spaces, spaces and frames, we all know
relativity of infinitely-many infinitely-nested
frames in a space of all spaces with all their coordinate
settings, frames in space, what if frame-spaces and
space-frames basically alternate, just adding a
frame-space and space-frame between any two frames
in any two coordinate settings of space, the geodesy.

The geodesy, ..., which is orbits.

W dniu 12.03.2024 o 20:42, Richard Hachel pisze:

> On usenet, there are perhaps five or six people with whom we can
> seriously discuss relativity, without immediately falling into
> hysterical reactions. (Julien Arlandis, Michel Talon, Paul B
> Anderson...). The others not only learned anything, but answer nonsense
> when asked a simple problem.

Nope, no relativistic idiot can be discussed. The
Shit is not training its doggiesd for discussing,
it's training them for barking.

Den 12.03.2024 20:42, skrev Richard Hachel:
> Le 12/03/2024 à 20:19, "Paul B. Andersen" a écrit :
>> Den 12.03.2024 10:00, skrev Richard Hachel:
>>> We know that in accelerated frames of reference the average speed is
>>> proportional to the instantaneous speed.
>>>
>>> Let Vrm=(1/2)Vri
>>
>> This is meaningless without definition of the entities.
>>
>> But I can guess:
>> You are not talking about "speed in an accelerated frame".
>>
>> You are talking about the speed of a stationary object
>> in an accelerated frame, measured in an inertial frame.
>>
>> If the object is instantly at rest at t = 0, and
>> the coordinate acceleration in the inertial frame is constant a,
>> Then the speed Vri(t) = at
>> and the average speed from t=0 to t=t is Vrm(t) = at/2.
>>
>> So  Vrm=(1/2)Vri
>
> That is what I am saying.

Yes. And I agree.

NOTE THIS:
If the object is instantly at rest at t = 0, and
the coordinate acceleration in the inertial frame is constant a,
Then the speed Vri(t) = at

>
> Vr=a.Tr

Where Vr (Vri(t)) is the speed in the inertial frame,
and Tr (t) is the time coordinate in the inertial frame, and
----------------------------------------------------------------
a is the constant coordinate acceleration in the inertial frame!
================================================================

The consequence of this is that when t > c/a v > c
which is impossible in SR.

That means that the coordinate acceleration a can't be constant!
==============================================================

>>
>> According to SR:
>>
>> For the above to be true, the coordinate acceleration must
>> be constant. This means that the proper acceleration must
>> increase with time.
>>
>> Let 1g = 1 c per year = 9.4998 m/s².
>>
>>
>> when t ≥ 1.0 year the coordinate acceleration can't
>> be kept equal to 1 g.
>>
>> Generally:
>> The coordinate acceleration a can't be kept equal to n g
>> when t ≥ 1/n year.
>>
>>
>> It is obviously normal to keep the proper acceleration constant,
>> and then Vrm  ≠ (1/2)Vri

As you said yourself:
"I beg you to understand something:
in the rocket's frame of reference, the acceleration is constant."

That is the proper acceleration A is constant, and then
the coordinate acceleration a is NOT constant, it is
decreasing with time, Vri < at and Vrm > (1/2)Vri.

Se exact calculation below.

>
> I don't understand what you are saying.
>
> I think that between you and me, there is a different understanding of
> things.

Indeed!

Understand this:
What SR predicts is not a matter of opinion,
it is a matter of fact.

https://paulba.no/pdf/TwinsByMetric.pdf
see equation (38)

It is a FACT that according to SR, the speed of
an object with constant proper acceleration A is:

Vri(t) = A⋅t/√(1+(A⋅t/c)²)

Note that:
Vri → A⋅t when t → 0
Vri → c when t → ∞

The average speed Vrm at the time t is:
Vrm = (integral from t=0 to t=t of Vri(t)dt)/t
Vrm = c²⋅(√(1+(A⋅t/c)²)-1)/A⋅t

Note that:
Vrm → A⋅t/2 when t → 0
Vrm → c when t → ∞

So:
Vrm/Vri → 1/2 when t → 0
Vrm/Vri → 1 when t → ∞

So for any t > 0 Vrm > (1/2)Vri

It is not possible to make SR predict anything else!
====================================================

The coordinate acceleration a is:
a = dVri/dt = A/(√(1+(A⋅t/c)²))³
where A is the proper acceleration

Note that:
a → A when t → 0
a → 0 when t → ∞

>>>
>>> But we know that relativistic physicists do not use this notion, and
>>> it is important to remind them of the relationship between real speed
>>> and observable speed.
>>>
>>> Vr=Vo/sqrt(1-Vo²/c²)

>>
>> This is nonsense.
>> According to "relativistic physicists" there is no difference
>> between the "real speed" and the "observable (measurable) speed"
>> in the inertial frame.

>
> That is what I am saying.
> Physicists do not differentiate between Vo and Vr.

Because there is no such difference.

You are claiming that when you measure the speed of a passing object,
then you will always measure the real speed divided by γ.

Can you please explain how you arrived at this conclusion?
Show the maths, please.

> It is really a shame that a large majority of physicists are not very
> intelligent, they understand nothing of what they are saying,
> which is dramatic since their number serves as truth.

:-D

The "large majority of physicists" are obviously much more
intelligent than average. They have to be to pass the exams.
(I am not a physicist.)

> A bit like in Nazi Germany everyone believed they were right because
> everyone held out their arm in front of Hitler.
> Physicists are educated, but very few are intelligent.

A hysterical reaction!

>
> On usenet, there are perhaps five or six people with whom we can
> seriously discuss relativity, without immediately falling into
> hysterical reactions. (Julien Arlandis, Michel Talon, Paul B
> Anderson...). The others not only learned anything, but answer nonsense
> when asked a simple problem.
>

Above you have demonstrated that you belong to the group that
falls into hysterical reactions.

--
Paul

https://paulba.no/

On 03/13/2024 02:00 PM, Paul B. Andersen wrote:
> Den 12.03.2024 20:42, skrev Richard Hachel:
>> Le 12/03/2024 à 20:19, "Paul B. Andersen" a écrit :
>>> Den 12.03.2024 10:00, skrev Richard Hachel:
>>>> We know that in accelerated frames of reference the average speed is
>>>> proportional to the instantaneous speed.
>>>>
>>>> Let Vrm=(1/2)Vri
>>>
>>> This is meaningless without definition of the entities.
>>>
>>> But I can guess:
>>> You are not talking about "speed in an accelerated frame".
>>>
>>> You are talking about the speed of a stationary object
>>> in an accelerated frame, measured in an inertial frame.
>>>
>>> If the object is instantly at rest at t = 0, and
>>> the coordinate acceleration in the inertial frame is constant a,
>>> Then the speed Vri(t) = at
>>> and the average speed from t=0 to t=t is Vrm(t) = at/2.
>>>
>>> So Vrm=(1/2)Vri
>>
>> That is what I am saying.
>
> Yes. And I agree.
>
> NOTE THIS:
> If the object is instantly at rest at t = 0, and
> the coordinate acceleration in the inertial frame is constant a,
> Then the speed Vri(t) = at
>
>>
>> Vr=a.Tr
>
> Where Vr (Vri(t)) is the speed in the inertial frame,
> and Tr (t) is the time coordinate in the inertial frame, and
> ----------------------------------------------------------------
> a is the constant coordinate acceleration in the inertial frame!
> ================================================================
>
> The consequence of this is that when t > c/a v > c
> which is impossible in SR.
>
> That means that the coordinate acceleration a can't be constant!
> ==============================================================
>
>
>>>
>>> According to SR:
>>>
>>> For the above to be true, the coordinate acceleration must
>>> be constant. This means that the proper acceleration must
>>> increase with time.
>>>
>>> Let 1g = 1 c per year = 9.4998 m/s².
>>>
>>>
>>> when t ≥ 1.0 year the coordinate acceleration can't
>>> be kept equal to 1 g.
>>>
>>> Generally:
>>> The coordinate acceleration a can't be kept equal to n g
>>> when t ≥ 1/n year.
>>>
>>>
>>> It is obviously normal to keep the proper acceleration constant,
>>> and then Vrm ≠ (1/2)Vri
>
> As you said yourself:
> "I beg you to understand something:
> in the rocket's frame of reference, the acceleration is constant."
>
> That is the proper acceleration A is constant, and then
> the coordinate acceleration a is NOT constant, it is
> decreasing with time, Vri < at and Vrm > (1/2)Vri.
>
> Se exact calculation below.
>
>>
>> I don't understand what you are saying.
>>
>> I think that between you and me, there is a different understanding of
>> things.
>
> Indeed!
>
> Understand this:
> What SR predicts is not a matter of opinion,
> it is a matter of fact.
>
> https://paulba.no/pdf/TwinsByMetric.pdf
> see equation (38)
>
> It is a FACT that according to SR, the speed of
> an object with constant proper acceleration A is:
>
> Vri(t) = A⋅t/√(1+(A⋅t/c)²)
>
> Note that:
> Vri → A⋅t when t → 0
> Vri → c when t → ∞
>
> The average speed Vrm at the time t is:
> Vrm = (integral from t=0 to t=t of Vri(t)dt)/t
> Vrm = c²⋅(√(1+(A⋅t/c)²)-1)/A⋅t
>
> Note that:
> Vrm → A⋅t/2 when t → 0
> Vrm → c when t → ∞
>
> So:
> Vrm/Vri → 1/2 when t → 0
> Vrm/Vri → 1 when t → ∞
>
> So for any t > 0 Vrm > (1/2)Vri
>
> It is not possible to make SR predict anything else!
> ====================================================
>
> The coordinate acceleration a is:
> a = dVri/dt = A/(√(1+(A⋅t/c)²))³
> where A is the proper acceleration
>
> Note that:
> a → A when t → 0
> a → 0 when t → ∞
>
>
>>>>
>>>> But we know that relativistic physicists do not use this notion, and
>>>> it is important to remind them of the relationship between real
>>>> speed and observable speed.
>>>>
>>>> Vr=Vo/sqrt(1-Vo²/c²)
>
>>>
>>> This is nonsense.
>>> According to "relativistic physicists" there is no difference
>>> between the "real speed" and the "observable (measurable) speed"
>>> in the inertial frame.
>
>>
>> That is what I am saying.
>> Physicists do not differentiate between Vo and Vr.
>
> Because there is no such difference.
>
> You are claiming that when you measure the speed of a passing object,
> then you will always measure the real speed divided by γ.
>
> Can you please explain how you arrived at this conclusion?
> Show the maths, please.
>
>> It is really a shame that a large majority of physicists are not very
>> intelligent, they understand nothing of what they are saying,
>> which is dramatic since their number serves as truth.
>
> :-D
>
> The "large majority of physicists" are obviously much more
> intelligent than average. They have to be to pass the exams.
> (I am not a physicist.)
>
>> A bit like in Nazi Germany everyone believed they were right because
>> everyone held out their arm in front of Hitler.
>> Physicists are educated, but very few are intelligent.
>
> A hysterical reaction!
>
>>
>> On usenet, there are perhaps five or six people with whom we can
>> seriously discuss relativity, without immediately falling into
>> hysterical reactions. (Julien Arlandis, Michel Talon, Paul B
>> Anderson...). The others not only learned anything, but answer
>> nonsense when asked a simple problem.
>>
>
> Above you have demonstrated that you belong to the group that
> falls into hysterical reactions.
>

It's sort of so that accelerating has a "first start"
and that decelerating has a "last stop", yet
it is "non-standard", because our model is "real-valued",
and the real numbers have a standard definition,
and in it, there is no smallest positive real number (iota).

It's much after atomism, whether there "are",
"fundamental particles", in fact it's very much
the same sort of conceit, the concession the idea,
the "infinitely-divisible" or "non-atomic", divisible, and
the "infinitely-divided" or "atomic", non-divisible.

So, the idea of "smooth acceleration" vis-a-vis
"constant acceleration", really sort of requires
a combined "standard", and "non-standard",
together "super-standard", view, or model,
in the mathematical model, for the physical model,
"real numbers or the real-valued or the mechanics
of continuous domains: continuum mechanics,
dynamical modeling", "physics: parameterized by t".

Newton kind of keeps things simple,
"it's all encapsulated to an instant with
an instantaneous exchange of kinetic
energy as the juxtaposition of two
non-deformable bodies geometrically
in perfect in-elastic collision", ..., "their
equal and opposite reactions".

So is the theory, ....

This is after Galileo keeps things simple,
"rest at rest motion at motion".

Then Einstein keeps things simple,
"the above is the classical limit, though
motion involves contraction and relaxation
of the space of the bodies that they are in,
and the space of the bodies that they are".

So, mathematics _owes_ physics, a proper
model of "super-standard change".

Dynamics, ....

It's a continuum mechanics, ....

Le 13/03/2024 à 21:59, "Paul B. Andersen" a écrit :
> Den 12.03.2024 20:42, skrev Richard Hachel:

>>> So  Vrm=(1/2)Vri
>>
>> That is what I am saying.
>
> Yes. And I agree.
>
> NOTE THIS:
> If the object is instantly at rest at t = 0, and
> the coordinate acceleration in the inertial frame is constant a,
> Then the speed Vri(t) = at
>
>>
>> Vr=a.Tr
>
> Where Vr (Vri(t)) is the speed in the inertial frame,
> and Tr (t) is the time coordinate in the inertial frame, and
> ----------------------------------------------------------------
> a is the constant coordinate acceleration in the inertial frame!
> ================================================================
>
> The consequence of this is that when t > c/a v > c
> which is impossible in SR.
>
> That means that the coordinate acceleration a can't be constant!

In the rocket frame, a is constant.
Always.
a=10m/s² (a=1.052ly/y²)
The rocket is at rest in its frame of reference, and the speed Vr of the
surrounding space becomes Vr=a.Tr
There is no problem, the speed of the rocket, that is to say the real
speed of movement of the terrestrial frame of reference, is indeed Vr.
But you know the conversion equation that I gave forty years ago:
Vo=Vr/sqrt(1+Vr²/c²)

Everything is remarkably clear and of great theoretical beauty if you
understand what I am saying.

R.H.

Le 13/03/2024 à 21:59, "Paul B. Andersen" a écrit :
> Den 12.03.2024 20:42, skrev Richard Hachel:

>>> It is obviously normal to keep the proper acceleration constant,
>>> and then Vrm  ≠ (1/2)Vri

We know that in accelerated frames of reference the average speed is
proportional to the instantaneous speed.
Let Vrm=(1/2)Vri
We are talking about real relativistic speeds (Richard Verret's hobby).
But we know that relativistic physicists do not use this notion, and it is
important to remind them of the relationship between real speed and
observable speed.
Vr=Vo/sqrt(1-Vo²/c²)
This immediately leads us to
Vom/sqrt(1-Vom²/c²)=(1/2)Voi/sqrt(1-Voi²/c²)
and therefore to:
Vom²(1-Voi²/c²)=(1/4)Voi²(1-Vom²/c²)
Let Vom²=(1/4)Voi²+(3/4)Voi².Vom²/c²
Hence
Vom=(1/2)Voi/sqrt(1-(3/4)Vom²/c²)
and, conversely,
Voi=2.Vom/sqrt(1+3Vom²/c²)

R.H.

Le 13/03/2024 à 21:59, "Paul B. Andersen" a écrit :
> Den 12.03.2024 20:42, skrev Richard Hachel:

> Understand this:
> What SR predicts is not a matter of opinion,
> it is a matter of fact.

Above all, we must prioritize experimentation.
And if two theories face each other, we must take the one which has the
approval of the experimenters.

If we take Einstein's RR, which is taken from the Poincaré equation and
the Minkowski metric, and which is called "local", we realize that two
enormous problems appear.
- The Langevin paradox (which we camouflaged, but which resurfaces using
apparent speeds, that is to say what we would observe if we had very good
telescopes and sufficient rocket technology).
- The principle of non-locality of Aspect and its contradiction with
instantaneous transfers of information.

These contradictions do not exist with me, and I have never seen a single
fact contradicting everything I have said for 40 years.

R.H.

Le 13/03/2024 à 21:59, "Paul B. Andersen" a écrit :
> Den 12.03.2024 20:42, skrev Richard Hachel:

> It is a FACT that according to SR, the speed of
> an object with constant proper acceleration A is:
>
> Vri(t) = A⋅t/√(1+(A⋅t/c)²)

? ? ?

Vri(t)=a.Tr

Voi(Tr!!!)=Vri/sqrt(1+Vri²/c²)

Voi=[1+c²/2ax]^(-1/2)

To=Tr.sqrt[1+(1/4)Vri²/c²]

>
> Note that:
> Vri → A⋅t when t → 0
> Vri → c when t → ∞
>
> The average speed Vrm at the time t is:
> Vrm = (integral from t=0 to t=t of Vri(t)dt)/t
> Vrm = c²⋅(√(1+(A⋅t/c)²)-1)/A⋅t
>
> Note that:
> Vrm → A⋅t/2 when t → 0
> Vrm → c when t → ∞

No.

Vrm → ∞

Vr is not Vo.

>
> So:
> Vrm/Vri → 1/2 when t → 0
> Vrm/Vri → 1 when t → ∞

No.

>> Physicists do not differentiate between Vo and Vr.
>
> Because there is no such difference.

? ? ?

> The "large majority of physicists" are obviously much more
> intelligent than average. They have to be to pass the exams.
> (I am not a physicist.)

Yes, they have to take exams.

Like everyone.

Personally, I'm happy to be theoretically logical and experimental in
racing.

This is NOT the current condition of physicists.

Their theory is imperfect and contradictory (Vapp in Langevin), it is
refuted by experimentation (their Sr is local, but not mine).

>> A bit like in Nazi Germany everyone believed they were right because
>> everyone held out their arm in front of Hitler.
>> Physicists are educated, but very few are intelligent.
>
> A hysterical reaction!

No. In SR, is fact.

Ils ne comprennent pas ce qu'ils disent, ce n'est PAS normal.

>> On usenet, there are perhaps five or six people with whom we can
>> seriously discuss relativity, without immediately falling into
>> hysterical reactions. (Julien Arlandis, Michel Talon, Paul B
>> Andersen...). The others not only learned anything, but answer nonsense
>> when asked a simple problem.
>>
>
> Above you have demonstrated that you belong to the group that
> falls into hysterical reactions.

Don't worry about my reactions.
Simply ask yourself: “Is this man lying, or is he telling the truth?”

R.H.

On 03/13/2024 02:43 PM, Ross Finlayson wrote:
> On 03/13/2024 02:00 PM, Paul B. Andersen wrote:
>> Den 12.03.2024 20:42, skrev Richard Hachel:
>>> Le 12/03/2024 à 20:19, "Paul B. Andersen" a écrit :
>>>> Den 12.03.2024 10:00, skrev Richard Hachel:
>>>>> We know that in accelerated frames of reference the average speed is
>>>>> proportional to the instantaneous speed.
>>>>>
>>>>> Let Vrm=(1/2)Vri
>>>>
>>>> This is meaningless without definition of the entities.
>>>>
>>>> But I can guess:
>>>> You are not talking about "speed in an accelerated frame".
>>>>
>>>> You are talking about the speed of a stationary object
>>>> in an accelerated frame, measured in an inertial frame.
>>>>
>>>> If the object is instantly at rest at t = 0, and
>>>> the coordinate acceleration in the inertial frame is constant a,
>>>> Then the speed Vri(t) = at
>>>> and the average speed from t=0 to t=t is Vrm(t) = at/2.
>>>>
>>>> So Vrm=(1/2)Vri
>>>
>>> That is what I am saying.
>>
>> Yes. And I agree.
>>
>> NOTE THIS:
>> If the object is instantly at rest at t = 0, and
>> the coordinate acceleration in the inertial frame is constant a,
>> Then the speed Vri(t) = at
>>
>>>
>>> Vr=a.Tr
>>
>> Where Vr (Vri(t)) is the speed in the inertial frame,
>> and Tr (t) is the time coordinate in the inertial frame, and
>> ----------------------------------------------------------------
>> a is the constant coordinate acceleration in the inertial frame!
>> ================================================================
>>
>> The consequence of this is that when t > c/a v > c
>> which is impossible in SR.
>>
>> That means that the coordinate acceleration a can't be constant!
>> ==============================================================
>>
>>
>>>>
>>>> According to SR:
>>>>
>>>> For the above to be true, the coordinate acceleration must
>>>> be constant. This means that the proper acceleration must
>>>> increase with time.
>>>>
>>>> Let 1g = 1 c per year = 9.4998 m/s².
>>>>
>>>>
>>>> when t ≥ 1.0 year the coordinate acceleration can't
>>>> be kept equal to 1 g.
>>>>
>>>> Generally:
>>>> The coordinate acceleration a can't be kept equal to n g
>>>> when t ≥ 1/n year.
>>>>
>>>>
>>>> It is obviously normal to keep the proper acceleration constant,
>>>> and then Vrm ≠ (1/2)Vri
>>
>> As you said yourself:
>> "I beg you to understand something:
>> in the rocket's frame of reference, the acceleration is constant."
>>
>> That is the proper acceleration A is constant, and then
>> the coordinate acceleration a is NOT constant, it is
>> decreasing with time, Vri < at and Vrm > (1/2)Vri.
>>
>> Se exact calculation below.
>>
>>>
>>> I don't understand what you are saying.
>>>
>>> I think that between you and me, there is a different understanding of
>>> things.
>>
>> Indeed!
>>
>> Understand this:
>> What SR predicts is not a matter of opinion,
>> it is a matter of fact.
>>
>> https://paulba.no/pdf/TwinsByMetric.pdf
>> see equation (38)
>>
>> It is a FACT that according to SR, the speed of
>> an object with constant proper acceleration A is:
>>
>> Vri(t) = A⋅t/√(1+(A⋅t/c)²)
>>
>> Note that:
>> Vri → A⋅t when t → 0
>> Vri → c when t → ∞
>>
>> The average speed Vrm at the time t is:
>> Vrm = (integral from t=0 to t=t of Vri(t)dt)/t
>> Vrm = c²⋅(√(1+(A⋅t/c)²)-1)/A⋅t
>>
>> Note that:
>> Vrm → A⋅t/2 when t → 0
>> Vrm → c when t → ∞
>>
>> So:
>> Vrm/Vri → 1/2 when t → 0
>> Vrm/Vri → 1 when t → ∞
>>
>> So for any t > 0 Vrm > (1/2)Vri
>>
>> It is not possible to make SR predict anything else!
>> ====================================================
>>
>> The coordinate acceleration a is:
>> a = dVri/dt = A/(√(1+(A⋅t/c)²))³
>> where A is the proper acceleration
>>
>> Note that:
>> a → A when t → 0
>> a → 0 when t → ∞
>>
>>
>>>>>
>>>>> But we know that relativistic physicists do not use this notion, and
>>>>> it is important to remind them of the relationship between real
>>>>> speed and observable speed.
>>>>>
>>>>> Vr=Vo/sqrt(1-Vo²/c²)
>>
>>>>
>>>> This is nonsense.
>>>> According to "relativistic physicists" there is no difference
>>>> between the "real speed" and the "observable (measurable) speed"
>>>> in the inertial frame.
>>
>>>
>>> That is what I am saying.
>>> Physicists do not differentiate between Vo and Vr.
>>
>> Because there is no such difference.
>>
>> You are claiming that when you measure the speed of a passing object,
>> then you will always measure the real speed divided by γ.
>>
>> Can you please explain how you arrived at this conclusion?
>> Show the maths, please.
>>
>>> It is really a shame that a large majority of physicists are not very
>>> intelligent, they understand nothing of what they are saying,
>>> which is dramatic since their number serves as truth.
>>
>> :-D
>>
>> The "large majority of physicists" are obviously much more
>> intelligent than average. They have to be to pass the exams.
>> (I am not a physicist.)
>>
>>> A bit like in Nazi Germany everyone believed they were right because
>>> everyone held out their arm in front of Hitler.
>>> Physicists are educated, but very few are intelligent.
>>
>> A hysterical reaction!
>>
>>>
>>> On usenet, there are perhaps five or six people with whom we can
>>> seriously discuss relativity, without immediately falling into
>>> hysterical reactions. (Julien Arlandis, Michel Talon, Paul B
>>> Anderson...). The others not only learned anything, but answer
>>> nonsense when asked a simple problem.
>>>
>>
>> Above you have demonstrated that you belong to the group that
>> falls into hysterical reactions.
>>
>
> It's sort of so that accelerating has a "first start"
> and that decelerating has a "last stop", yet
> it is "non-standard", because our model is "real-valued",
> and the real numbers have a standard definition,
> and in it, there is no smallest positive real number (iota).
>
> It's much after atomism, whether there "are",
> "fundamental particles", in fact it's very much
> the same sort of conceit, the concession the idea,
> the "infinitely-divisible" or "non-atomic", divisible, and
> the "infinitely-divided" or "atomic", non-divisible.
>
>
> So, the idea of "smooth acceleration" vis-a-vis
> "constant acceleration", really sort of requires
> a combined "standard", and "non-standard",
> together "super-standard", view, or model,
> in the mathematical model, for the physical model,
> "real numbers or the real-valued or the mechanics
> of continuous domains: continuum mechanics,
> dynamical modeling", "physics: parameterized by t".
>
>
> Newton kind of keeps things simple,
> "it's all encapsulated to an instant with
> an instantaneous exchange of kinetic
> energy as the juxtaposition of two
> non-deformable bodies geometrically
> in perfect in-elastic collision", ..., "their
> equal and opposite reactions".
>
> So is the theory, ....
>
> This is after Galileo keeps things simple,
> "rest at rest motion at motion".
>
> Then Einstein keeps things simple,
> "the above is the classical limit, though
> motion involves contraction and relaxation
> of the space of the bodies that they are in,
> and the space of the bodies that they are".
>
>
> So, mathematics _owes_ physics, a proper
> model of "super-standard change".
>
> Dynamics, ....
>
> It's a continuum mechanics, ....
>
>

Den 14.03.2024 03:09, skrev Richard Hachel:
> Le 13/03/2024 à 21:59, "Paul B. Andersen" a écrit :
>
>> Understand this:
>> What SR predicts is not a matter of opinion,
>> it is a matter of fact.

The subject line is:
"SR: Usefulness of real velocities in accelerated relativistic frames of
reference."

I take this to mean that you are stating what you claim SR predicts.

>
> Above all, we must prioritize experimentation.
> And if two theories face each other, we must take the one which has the
> approval of the experimenters.

Indeed.
And you know of course that SR is confirmed by innumerable
experiments and falsified by none.
Some of them:
https://paulba.no/paper/index.html

But the issue is:
Does SR predict what you claim it predicts?

>
> If we take Einstein's RR, which is taken from the Poincaré equation and
> the Minkowski metric, and which is called "local", we realize that two
> enormous problems appear.
> - The Langevin paradox (which we camouflaged, but which resurfaces using
> apparent speeds, that is to say what we would observe if we had very
> good telescopes and sufficient rocket technology).
> - The principle of non-locality of Aspect and its contradiction with
> instantaneous transfers of information.

Your opinion of SR is irrelevant.

SR is a consistent theory, and the issue is:
"Does SR predict that accelerated objects will behave as
you claim they do?"

>
> These contradictions do not exist with me, and I have never seen a
> single fact contradicting everything I have said for 40 years.

This is probably true, because it is obvious that you never
read the contradicting facts.

So let us review your claims and the contradicting facts.

PLEASE READ THEM FOR THE FIRST TIME IN 40 YEARS!

The scenario as defined by you:
"In the rocket frame, a is constant. The rocket is at rest
in its frame of reference, and the speed Vr of the surrounding
space becomes Vr=a.Tr."

A bit more precisely put:
A rocket is accelerating at the constant proper acceleration a.
An inertial frame of reference K(x,t) is at the time t = 0
instantly co-moving with the rocket.

You claim:
According to SR the speed of the rocket in K is Vr(t) = a⋅t
===========================================================

Note that this means that Vr > c when t > c/a
which according to SR is impossible.

Contradicting fact:
-------------------
So this is wrong.
You can see the correct derivation here:
https://paulba.no/pdf/TwinsByMetric.pdf
See chapter 2.3, equation (15)

Vr(t) = a⋅t/√(1+(a⋅t/c)²)

Note that:
Vr → a⋅t when t → 0
Vr → c when t → ∞

Your problem is that you do not understand the difference
between proper acceleration of the rocket, and the rocket's
coordinate acceleration in the inertial frame.

If A is the coordinate acceleration in K, we have:

A = dVr/dt = a/(√(1+(a⋅t/c)²))³

Note that:
A → a when t → 0
A → 0 when t → ∞

So Vr(t) = ∫(from 0 to t)A⋅dt = a⋅t/√(1+(a⋅t/c)²)

You claim:
According to SR is the average speed of the rocket Vm(t) = Vr(t)/2
=====================================================================

Contradicting fact:
-------------------
This is wrong.

Vr(t) = a⋅t/√(1+(a⋅t/c)²)

The average speed Vm at the time t is:
Vm = (integral from t=0 to t=t of Vr(t)dt)/t
Vm = c²⋅(√(1+(a⋅t/c)²)-1)/a⋅t

Note that:
Vm → a⋅t/2 when t → 0
Vm → c when t → ∞

So:
Vm/Vr → 1/2 when t → 0
rm/Vr → 1 when t → ∞

So for any t > 0 Vm > Vr/2

It is not possible to make SR predict anything else!
====================================================

--
Paul

https://paulba.no/

W dniu 14.03.2024 o 15:04, Paul B. Andersen pisze:

> And you know of course that SR is confirmed by innumerable
> experiments and falsified by none.

Most unfortunately, however, in the meantime
in the real world - forbidden by your bunch
of idiots "improper" clocks keep measuring
t'=t, just like all serious clocks always did.

Le 14/03/2024 à 15:02, "Paul B. Andersen" a écrit :
> The subject line is:
> "SR: Usefulness of real velocities in accelerated relativistic frames of
> reference."
>
> I take this to mean that you are stating what you claim SR predicts.
>
>>
>> Above all, we must prioritize experimentation.
>> And if two theories face each other, we must take the one which has the
>> approval of the experimenters.
>
> Indeed.
> And you know of course that SR is confirmed by innumerable
> experiments and falsified by none.
> Some of them:
> https://paulba.no/paper/index.html
>
> But the issue is:
> Does SR predict what you claim it predicts?

Here is the problem:
We now know that Newtonian physics is out of the running, and that we must
use a relativistic theory.
This is certain, and the evidence is so abundant that no one disputes it
anymore, except a few crazy people.
But here we have, face to face, two ways of seeing the SR.
That of Einstein and Minkowski, and that of Hachel and Aspect.
Both theories predict the same things.
Except that Einstein and Minkowski's theory is ridiculous and
contradictory on paper (internal imperfection), and that it is
contradicted by the non-locality experiment (external refutation).
I am the only one to propose a coherent theory, theoretically unassailable
and flawless, and with all the experiments on my side (including the
instantaneous longitudinal transmission of information and the
impossibility of transverse transmissions greater than c).

R.H.

Le 14/03/2024 à 15:02, "Paul B. Andersen" a écrit :
> Your opinion of SR is irrelevant.
>
> SR is a consistent theory, and the issue is:
> "Does SR predict that accelerated objects will behave as
> you claim they do?"

No, YOU are saying that my concepts are irrelevant.

As for accelerated frames of reference, I said that things are poorly
explained by physicists and that certain equations are false.

Some are correct, like
To=(x/c).sqrt(1+2c²/ax)
Or
x=(c²/a)[sqrt(1+a²To²/c²)-1]

But many others are incorrect.

Same thing for rotating frames of reference where we sink into conceptual
madness by proposing a crazy geometry where a rotating disk becomes an
unknown figure on the earth (LOL).

R.H.

Le 14/03/2024 à 15:02, "Paul B. Andersen" a écrit :
> Den 14.03.2024 03:09, skrev Richard Hachel:

> Contradicting fact:
> -------------------
> So this is wrong.
> You can see the correct derivation here:
> https://paulba.no/pdf/TwinsByMetric.pdf
> See chapter 2.3, equation (15)
>
> Vr(t) = a⋅t/√(1+(a⋅t/c)²)
>
> Note that:
> Vr → a⋅t when t → 0
> Vr → c when t → ∞
>
>
> Your problem is that you do not understand the difference
> between proper acceleration of the rocket, and the rocket's
> coordinate acceleration in the inertial frame.
>
> If A is the coordinate acceleration in K, we have:
>
> A = dVr/dt = a/(√(1+(a⋅t/c)²))³
>
> Note that:
> A → a when t → 0
> A → 0 when t → ∞
>
> So Vr(t) = ∫(from 0 to t)A⋅dt = a⋅t/√(1+(a⋅t/c)²)
>
> You claim:
> According to SR is the average speed of the rocket Vm(t) = Vr(t)/2
> =====================================================================
>
> Contradicting fact:
> -------------------
> This is wrong.
>
> Vr(t) = a⋅t/√(1+(a⋅t/c)²)
>
> The average speed Vm at the time t is:
> Vm = (integral from t=0 to t=t of Vr(t)dt)/t
> Vm = c²⋅(√(1+(a⋅t/c)²)-1)/a⋅t
>
> Note that:
> Vm → a⋅t/2 when t → 0
> Vm → c when t → ∞
>
> So:
> Vm/Vr → 1/2 when t → 0
> rm/Vr → 1 when t → ∞
>
> So for any t > 0 Vm > Vr/2
>
> It is not possible to make SR predict anything else!
> ====================================================

You don't understand anything I'm telling you...

In these conditions, it is very difficult to discuss.

R.H.

Richard Hachel wrote:

> Le 14/03/2024 à 15:02, "Paul B. Andersen" a écrit :
>> Your opinion of SR is irrelevant.
>> SR is a consistent theory, and the issue is: "Does SR predict that
>> accelerated objects will behave as you claim they do?"
>
> No, YOU are saying that my concepts are irrelevant.
> As for accelerated frames of reference, I said that things are poorly
> explained by physicists and that certain equations are false.
> Some are correct, like To=(x/c).sqrt(1+2c²/ax) Or
> x=(c²/a)[sqrt(1+a²To²/c²)-1] But many others are incorrect.

I beg you to reconsider

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Richard Hachel wrote:

> Le 14/03/2024 à 15:02, "Paul B. Andersen" a écrit :
>> https://paulba.no/paper/index.html But the issue is:
>> Does SR predict what you claim it predicts?
>
> Here is the problem: We now know that Newtonian physics is out of the
> running, and that we must use a relativistic theory.

are we sure??

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Richard Hachel wrote:

> Le 13/03/2024 à 21:59, "Paul B. Andersen" a écrit :
>> Above you have demonstrated that you belong to the group that
>> falls into hysterical reactions.
>
> Don't worry about my reactions.
> Simply ask yourself: “Is this man lying, or is he telling the truth?”

no, Einstine was lying. He was not even a scientists. Mostly, but mostly,
an entertainer. He pushed lectures to the public, he didn't undrestand. He
was a shareholder.

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Richard Hachel wrote:

> Le 14/03/2024 à 15:02, "Paul B. Andersen" a écrit :
>> So for any t > 0 Vm > Vr/2
>> It is not possible to make SR predict anything else!
>> ====================================================
>
> You don't understand anything I'm telling you...
> In these conditions, it is very difficult to discuss.

no, that's you. There are mainly 2 ways of observation in fluid dynamics (eulerian). You either move with the particle, or you observe it fixed from outside. Russia is a threat to them, not to us.

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W dniu 14.03.2024 o 17:03, Richard Hachel pisze:
> Le 14/03/2024 à 15:02, "Paul B. Andersen" a écrit :
>> The subject line is:
>> "SR: Usefulness of real velocities in accelerated relativistic frames
>> of reference."
>>
>> I take this to mean that you are stating what you claim SR predicts.
>>
>>>
>>> Above all, we must prioritize experimentation.
>>> And if two theories face each other, we must take the one which has
>>> the approval of the experimenters.
>>
>> Indeed.
>> And you know of course that SR is confirmed by innumerable
>> experiments and falsified by none.
>> Some of them:
>> https://paulba.no/paper/index.html
>>
>> But the issue is:
>> Does SR predict what you claim it predicts?
>
> Here is the problem:
> We now know that Newtonian physics is out of the running, and that we
> must use a relativistic theory.
> This is certain, and the evidence is so abundant that no one disputes it
> anymore, except a few crazy people.

And we also know communism must win,
as it's the best.
We know it, of course, except a few
crazy people.

Den 14.03.2024 17:13, skrev Richard Hachel:
> Le 14/03/2024 à 15:02, "Paul B. Andersen" a écrit :
>> Your opinion of SR is irrelevant.
>>
>> SR is a consistent theory, and the issue is:
>> "Does SR predict that accelerated objects will behave as
>>   you claim they do?"
>
> No, YOU are saying that my concepts are irrelevant.

I am saying that SR does not predict that accelerated objects
will behave as you claim they do.

> As for accelerated frames of reference, I said that things are poorly
> explained by physicists and that certain equations are false.

I suppose you are referring to my "false" equations:
Speed: Vr(t) = a⋅t/√(1+(a⋅t/c)²)
Average speed Vm(t) = c²⋅(√(1+(a⋅t/c)²)-1)/a⋅t

where your "correct" equations are:
Speed: Vr(t) = a⋅t
Average speed Vm(t) = a⋅t/2

:-D

----------------------------------------------

It seems that you still haven't the contradicting facts.

So let us yet again review your claims and the contradicting facts.
PLEASE READ THEM FOR THE FIRST TIME IN 40 YEARS!

A rocket is accelerating at the constant proper acceleration a.
An inertial frame of reference K(x,t) is at the time t = 0
instantly co-moving with the rocket.

You claim:
According to SR the speed of the rocket in K is Vr(t) = a⋅t
===========================================================

Note that this means that Vr > c when t > c/a
which according to SR is impossible.

Contradicting fact:
-------------------
So this is wrong.
You can see the correct derivation here:
https://paulba.no/pdf/TwinsByMetric.pdf
See chapter 2.3, equation (15)

Vr(t) = a⋅t/√(1+(a⋅t/c)²)

Note that:
Vr → a⋅t when t → 0
Vr → c when t → ∞

Your problem is that you do not understand the difference
between proper acceleration of the rocket, and the rocket's
coordinate acceleration in the inertial frame.

If A is the coordinate acceleration in K, we have:

A = dVr/dt = a/(√(1+(a⋅t/c)²))³

Note that:
A → a when t → 0
A → 0 when t → ∞

So Vr(t) = ∫(from 0 to t)A⋅dt = a⋅t/√(1+(a⋅t/c)²)

You claim:
According to SR is the average speed of the rocket Vm(t) = Vr(t)/2
=====================================================================

Contradicting fact:
-------------------
This is wrong.

Vr(t) = a⋅t/√(1+(a⋅t/c)²)

The average speed Vm at the time t is:
Vm = (integral from t=0 to t=t of Vr(t)dt)/t
Vm = c²⋅(√(1+(a⋅t/c)²)-1)/a⋅t

Note that:
Vm → a⋅t/2 when t → 0
Vm → c when t → ∞

So:
Vm/Vr → 1/2 when t → 0
rm/Vr → 1 when t → ∞

So for any t > 0 Vm > Vr/2

It is not possible to make SR predict anything else!
====================================================

--
Paul

https://paulba.no/