If the proper time is small, an accelerated reference frame can be
considered equivalent to a Galilean reference frame in uniform motion.

This is something relativists do, and I wanted to make sure that's not
where the mistake they make is in calculating proper times in accelerated
frames.

The demonstration is easy.

I'll give it to you (how lucky you are to have me).

We will therefore have to look elsewhere for the cause of the error, and
we will eventually find it.

R.H.

Le 21/08/2022 à 22:12, Richard Hachel a écrit :
> If the proper time is small, an accelerated reference frame can be considered
> equivalent to a Galilean reference frame in uniform motion.
>
> This is something relativists do, and I wanted to make sure that's not where the
> mistake they make is in calculating proper times in accelerated frames.
>
> The demonstration is easy.
>
> I'll give it to you (how lucky you are to have me).
>
> We will therefore have to look elsewhere for the cause of the error, and we will
> eventually find it.
>
> R.H.

(1) ΔTo²=ΔTr²+ΔEt²

(2) ΔTo²=ΔTr²+(Δx²/c²)

(3) Δx=x2-x1

(4) Δx= (1/2)a.Tr2² - (1/2)a.Tr1²

(5) ΔTo²=ΔTr²+ [(1/2)(a)(Tr2²-Tr1²)]²/c²

(6) ΔTo²=ΔTr²+ [(1/4)(a²)((Tr2-Tr1)(Tr2+Tr1))²]/c²

(7) Tr2-Tr1=ΔTr

(8) Tr2+Tr1=2Tr

(9) ΔTo²=ΔTr²+ [(1/4)(a²)((ΔTr)(2Tr))²]/c²

(10) ΔTo²=ΔTr² [ 1+ [(1/4)(a²)(4Tr²)]/c²]

(11) Vri=a.Tr

(12) ΔTo²=ΔTr² [ 1+ Vri²/c²]

(13) ΔTo=ΔTr.sqrt(1+Vr²/c²)

(14) ΔTo=ΔTr/sqrt(1-Vo²/c²)

CQFD.

R.H.

On Sunday, August 21, 2022 at 1:30:58 PM UTC-7, Richard Hachel wrote:
>snipe cretinisms<
Cretin. Stubborn. Stubborn cretin

Le 21/08/2022 à 23:13, "Dono." a écrit :
> On Sunday, August 21, 2022 at 1:30:58 PM UTC-7, Richard Hachel wrote:

> Cretin. Stubborn. Stubborn cretin

No, you shouldn't insult.

If you don't understand, ask.

You have a problem with which line(s)

R.H.

On Sunday, August 21, 2022 at 1:12:04 PM UTC-7, Richard Hachel wrote:
> If the proper time is small, an accelerated reference frame can be
> considered equivalent to a Galilean reference frame in uniform motion.

This is false, in both Newtonian and Einsteinian mechanics. For example,
a rotating frame will have fictitious forces assigned to it whose magnitudes
do not even depend on the length of the time interval.

You seem confused by the fact that an accelerated material particle CAN
be treated as moving uniformly over short time intervals (i.e., given an
error margin, one can find a time interval short enough that the discrepancy
falls within that margin; this cannot be done with frames as e.g. their
fictitious forces do not decrease with time intervals).

> This is something relativists do,

No, see above. This is high school physics BTW.

> and I wanted to make sure that's not
> where the mistake they make is in calculating proper times in accelerated
> frames.

Nobody is making any "mistakes" there. Proper time is defined as the arc
length of the particle trajectory.

> The demonstration is easy.
>
> I'll give it to you (how lucky you are to have me).
>
> We will therefore have to look elsewhere for the cause of the error, and
> we will eventually find it.

There is no error. You simply don't understand the subject.

--
Jan

On Sunday, August 21, 2022 at 1:30:58 PM UTC-7, Richard Hachel wrote:
> If the proper time is small, an accelerated reference frame can be considered
> equivalent to a Galilean reference frame in uniform motion.

You aren't dealing with an accelerating frame, you are describing everything in terms of a single inertial coordinate system x,t. You are positing an accelerating object, not an accelerating frame.

> (1) Δt² = ΔTAU² + Δx²

No, the general relation is dt² = dtau² + dx². You are confusing dTAU for dtau. In this context, dtau is the incremental proper time along the essentially inertial path between two events separated by an incremental interval with components dt and dx.

All the rest of your equations are wrong because of this fundamental error. (They also contain numerous other errors, but this one error is sufficient to invalidate all of them.) Understand?

Le 21/08/2022 à 23:54, JanPB a écrit :
> On Sunday, August 21, 2022 at 1:12:04 PM UTC-7, Richard Hachel wrote:

> There is no error. You simply don't understand the subject.

Yes, I know, I had already been told that when I demonstrated that the
relativistic explanations of Langevin's traveler did not hold if we went
into apparent speeds.

It seems that it was me who did not understand anything.

> Jan

R.H.

Le 21/08/2022 à 23:13, "Dono." a écrit :

Viva Donald Trump!

Trump président!

Trump is the best!

R.H.

Richard, you keep confusing yourself with your oddball notation of To
and Tr. Specifically, there are three different time variables, which
others call t, tau and TAU. You keep mixing up tau and TAU with your
oddball name Tr.

On Sunday, August 21, 2022 at 3:22:58 PM UTC-7, Richard Hachel wrote:
> Le 21/08/2022 à 23:13, "Dono." a écrit :
> Viva Donald Trump!
>
> Trump président!
>
> Trump is the best!
>
> R.H.

Do you understand that Trump mostly won in areas where the population was less educated and that Clinton/Biden won in areas with the highest education rate? What does this indicate to you?

Le 22/08/2022 à 05:42, Paul Alsing a écrit :
> On Sunday, August 21, 2022 at 3:22:58 PM UTC-7, Richard Hachel wrote:
>> Le 21/08/2022 à 23:13, "Dono." a écrit :
>> Viva Donald Trump!
>>
>> Trump président!
>>
>> Trump is the best!
>>
>> R.H.
>
> Do you understand that Trump mostly won in areas where the population was less
> educated and that Clinton/Biden won in areas with the highest education rate? What
> does this indicate to you?

Well, Trump is more concerned with the fate of the poor and Biden with the
fate of the rich.

It makes mathematical sense.

R.H.

On Sunday, August 21, 2022 at 3:12:56 PM UTC-7, Richard Hachel wrote:
> Le 21/08/2022 à 23:54, JanPB a écrit :
> > On Sunday, August 21, 2022 at 1:12:04 PM UTC-7, Richard Hachel wrote:
>
> > There is no error. You simply don't understand the subject.
> Yes, I know, I had already been told that when I demonstrated that the
> relativistic explanations of Langevin's traveler did not hold if we went
> into apparent speeds.
>
> It seems that it was me who did not understand anything.

No, you really don't understand Einstein's theory.

Essentially everything of substance you've posted on this NG over last
several years is incorrect and a waste of your time.

--
Jan

On Sunday, August 21, 2022 at 8:42:47 PM UTC-7, Paul Alsing wrote:
> On Sunday, August 21, 2022 at 3:22:58 PM UTC-7, Richard Hachel wrote:
> > Le 21/08/2022 à 23:13, "Dono." a écrit :
> > Viva Donald Trump!
> >
> > Trump président!
> >
> > Trump is the best!
> >
> > R.H.
> Do you understand that Trump mostly won in areas where the population was less educated and that Clinton/Biden won in areas with the highest education rate? What does this indicate to you?

That intellectuals are more prone to certain types of propaganda. The classic
example of this was the western(*) intellectuals' great sympathy for the Soviet
Union which only ended in the late 1970s after the publication of Solzhenitsyn's
"Gulag Archipelago".

This curious paradox follows from the fact that in most developed countries
intellectuals tend to be a part of the middle class which makes them to a large
extent immune to many of the negative consequences of their political preferences.
IOW, they can afford indulging in certain fantasies which make them feel good.

But people who have to think hard about paying rent and which food to buy and
compromise on to survive to next month(**) will obviously be forced to have very
different views.

(*) Esp. French.

(**) The median household income of a wage-earner family with 2 children
in the US is close to the official poverty line (about $30K/year +/- epsilon)
according to the U.S. Bureau of Labor Statistics.

Bottom line is correlation does not imply causation.

--
Jan

On Monday, August 22, 2022 at 3:25:21 AM UTC-7, Richard Hachel wrote:
> Le 22/08/2022 à 05:42, Paul Alsing a écrit :
> > On Sunday, August 21, 2022 at 3:22:58 PM UTC-7, Richard Hachel wrote:
> >> Le 21/08/2022 à 23:13, "Dono." a écrit :
> >> Viva Donald Trump!
> >>
> >> Trump président!
> >>
> >> Trump is the best!
> >>
> >> R.H.
> >
> > Do you understand that Trump mostly won in areas where the population was less
> > educated and that Clinton/Biden won in areas with the highest education rate? What
> > does this indicate to you?
> Well, Trump is more concerned with the fate of the poor and Biden with the
> fate of the rich.
>
> It makes mathematical sense.

I agree with you here. Perhaps you should stay away from physics then :-)

I don't know if Trump's actions come from his genuine concern for the poor or
are just a result of some political calculation but the fact is that during Trump's
term the black unemployment rate fell to the lowest rate in 50 years. He also
initiated a prison review process which resulted in an early release of several
thousand of black inmates (what a word) doing very long terms for minor
offences like stealing a chocolate bar several times or smoking a joint. This
was something that e.g. Obama did not do. Same with Trump's issuing
an order to sell insulin at world's prices (i.e., low). Incidentally, this very
order has been reverted recently by Biden! Naturally the media have not
covered this. The reason given by Biden was that Trump's order resulted
in an excessive paperwork burden(!)

And now let's just think what diabetics' vote will look like.

--
Jan