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tech / sci.physics.relativity / Re: [SR] Where does this strange (1/4) come from?

SubjectAuthor
* [SR] Where does this strange (1/4) come from?Richard Hachel
+* Re: [SR] Where does this strange (1/4) come from?Python
|`* Re: [SR] Where does this strange (1/4) come from?Richard Hachel
| `* Re: [SR] Where does this strange (1/4) come from?Python
|  `* Re: [SR] Where does this strange (1/4) come from?Richard Hachel
|   `* Re: [SR] Where does this strange (1/4) come from?Python
|    `* Re: [SR] Where does this strange (1/4) come from?Richard Hachel
|     `* Re: [SR] Where does this strange (1/4) come from?Python
|      +- Re: [SR] Where does this strange (1/4) come from?Richard Hachel
|      `- Re: [SR] Where does this strange (1/4) come from?Maciej Wozniak
+- Re: [SR] Where does this strange (1/4) come from?Ross A. Finlayson
`- Re: [SR] Where does this strange (1/4) come from?Richard Hachel

1
[SR] Where does this strange (1/4) come from?

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From: r.hac...@tiscali.fr (Richard Hachel)
 by: Richard Hachel - Thu, 19 May 2022 21:25 UTC

A user asks me where this strange 1/4 comes from that appears in my
equation To=Tr.sqrt(1+(1/4)Vr²/c²)

Let To²=Tr²+Et²

Let To²=Tr²+(x/c)²

Let us pose, since we are working here in real velocities and since it is
a uniformly accelerated frame of reference:
x=(1/2.a.Tr²)

Let To²=Tr²+(1/2.a.Tr²)²/c²

Let still be if Vr=a.Tr

To²=Tr²+(1/4.Vr².Tr²)/c²

Or To=Tr.sqrt(1+(1/4)Vr²/c²)

It's math.

R.H.

Re: [SR] Where does this strange (1/4) come from?

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 by: Python - Thu, 19 May 2022 21:32 UTC

Richard "Hachel" Lengrand (M.D.) wrote:
> A user asks me where this strange 1/4 comes from that appears in my
> equation To=Tr.sqrt(1+(1/4)Vr²/c²)
>
> Let To²=Tr²+Et²
>
> Let To²=Tr²+(x/c)²
>
> Let us pose, since we are working here in real velocities and since it
> is a uniformly accelerated frame of reference:
> x=(1/2.a.Tr²)
>
> Let To²=Tr²+(1/2.a.Tr²)²/c²
>
> Let still be if Vr=a.Tr
>
> To²=Tr²+(1/4.Vr².Tr²)/c²
>
> Or To=Tr.sqrt(1+(1/4)Vr²/c²)
>
> It's math.

As usual, as no term is defined ("real"/"not real" velocity??), it's not
worth reading it. It is not math, it's garbage.

Anyway, the formula cannot be right. As it is independent from
the actual acceleration is should be true also for an arbitrarily
small acceleration.

but... sqrt(1+(1/4)Vr²/c²) does not depend on acceleration, so
its limit when a->0 cannot be the value for no acceleration at
all i.e. equal to Tr.sqrt(1+Vr²/c²).

You can compare to what SR actually predict and make a tends to
0. It works.

What about considering learning SR, Richard? It's about time...

Re: [SR] Where does this strange (1/4) come from?

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From: r.hac...@tiscali.fr (Richard Hachel)
 by: Richard Hachel - Thu, 19 May 2022 21:58 UTC

Le 19/05/2022 à 23:32, Python a écrit :
>
> but... sqrt(1+(1/4)Vr²/c²) does not depend on acceleration, so
> its limit when a->0 cannot be the value for no acceleration at
> all i.e. equal to Tr.sqrt(1+Vr²/c²).

S'il n'y a pas d'accélération, on retombe sur la formule usuelle:
To=Tr/sqrt(1-Vo²/c²).

Car comme To=Tr.sqrt(1+Vr²/c²) si Vo=Vr/sqrt(1+Vr²/c²)
alors To=Tr/sqrt(1-Vo²/c²).

To²=Tr²+(x/c)²

To²=Tr²+(Vr.Tr/c)²

To=Tr.sqrt(1+Vr²/c²)

R.H.

Re: [SR] Where does this strange (1/4) come from?

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 by: Python - Thu, 19 May 2022 22:59 UTC

Richard "Hachel" Lengrand (M.D.) wrote:
> Le 19/05/2022 à 23:32, Python a écrit :
>>
>> but... sqrt(1+(1/4)Vr²/c²) does not depend on acceleration, so
>> its limit when a->0 cannot be the value for no acceleration at
>> all i.e. equal to Tr.sqrt(1+Vr²/c²).
>
> S'il n'y a pas d'accélération, on retombe sur la formule usuelle:
> To=Tr/sqrt(1-Vo²/c²).
>
> Car comme To=Tr.sqrt(1+Vr²/c²) si Vo=Vr/sqrt(1+Vr²/c²)
> alors To=Tr/sqrt(1-Vo²/c²).
>
> To²=Tr²+(x/c)²
>
> To²=Tr²+(Vr.Tr/c)²
> To=Tr.sqrt(1+Vr²/c²)

You never read, Richard, do you? You are pathologically unable
to even consider an argument that oppose your prejudice. You
should ask for medical help.

The limit for low accelerations MUST be the value for 0 acceleration.

It is not the case with your formulas.

Re: [SR] Where does this strange (1/4) come from?

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From: r.hac...@tiscali.fr (Richard Hachel)
 by: Richard Hachel - Thu, 19 May 2022 23:26 UTC

Le 20/05/2022 à 00:59, Python a écrit :
> Richard "Hachel" Lengrand (M.D.) wrote:
>> Le 19/05/2022 à 23:32, Python a écrit :
>>>
>>> but... sqrt(1+(1/4)Vr²/c²) does not depend on acceleration, so
>>> its limit when a->0 cannot be the value for no acceleration at
>>> all i.e. equal to Tr.sqrt(1+Vr²/c²).
>>
>> S'il n'y a pas d'accélération, on retombe sur la formule usuelle:
>> To=Tr/sqrt(1-Vo²/c²).
>>
>> Car comme To=Tr.sqrt(1+Vr²/c²) si Vo=Vr/sqrt(1+Vr²/c²)
>> alors To=Tr/sqrt(1-Vo²/c²).
>>
>> To²=Tr²+(x/c)²
>>
>> To²=Tr²+(Vr.Tr/c)²
>> To=Tr.sqrt(1+Vr²/c²)

> The limit for low accelerations MUST be the value for 0 acceleration.

Of course.

x = 1/2aTr² + Vi.Tr

If no acceleration, a=0 and x=Vi.Tr

You are right.

And?

R.H.

Re: [SR] Where does this strange (1/4) come from?

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 by: Python - Thu, 19 May 2022 23:40 UTC

Richard "Hachel" Lengrand (M.D.) wrote:
> Le 20/05/2022 à 00:59, Python a écrit :
>> Richard "Hachel" Lengrand (M.D.) wrote:
>>> Le 19/05/2022 à 23:32, Python a écrit :
>>>>
>>>> but... sqrt(1+(1/4)Vr²/c²) does not depend on acceleration, so
>>>> its limit when a->0 cannot be the value for no acceleration at
>>>> all i.e. equal to Tr.sqrt(1+Vr²/c²).
>>>
>>> S'il n'y a pas d'accélération, on retombe sur la formule usuelle:
>>> To=Tr/sqrt(1-Vo²/c²).
>>>
>>> Car comme To=Tr.sqrt(1+Vr²/c²) si Vo=Vr/sqrt(1+Vr²/c²)
>>> alors To=Tr/sqrt(1-Vo²/c²).
>>>
>>> To²=Tr²+(x/c)²
>>>
>>> To²=Tr²+(Vr.Tr/c)²
>>> To=Tr.sqrt(1+Vr²/c²)
>
>> The limit for low accelerations MUST be the value for 0 acceleration.
>
> Of course.
> x = 1/2aTr² + Vi.Tr
>
> If no acceleration, a=0 and x=Vi.Tr
>
> You are right.
> And?

sqrt(1+(1/4)Vr²/c²) does not depend on acceleration, so
its limit when a->0 cannot be the value for no acceleration at
all i.e. equal to Tr.sqrt(1+Vr²/c²).

you are even more ridiculous than ever, Richard.

Re: [SR] Where does this strange (1/4) come from?

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From: r.hac...@tiscali.fr (Richard Hachel)
 by: Richard Hachel - Fri, 20 May 2022 00:09 UTC

Le 20/05/2022 à 01:40, Python a écrit :

> sqrt(1+(1/4)Vr²/c²) does not depend on acceleration

The correct équation is To=Tr.sqrt(1+(1/4)Vr²/c²) in the case of
accelerated frame,
and To=Tr.sqrt(1+Vr²/c²) in the case of constant speed.

In To=Tr.sqrt(1+(1/4)Vr²/c²) : Vr depends on acceleration.

Vr is Vr=a.Tr

----

To²=Tr²+Et² (if vi=0 in accelerated frame).

To²=Tr²+[(1/2)a.Tr²/c]²

To=Tr.sqrt(1+(1/4)a².Tr²/c²)

a is in this équation.

But if Vr=a.Tr then a².Tr²/c²=Vr²/c²

No?

R.H.

Re: [SR] Where does this strange (1/4) come from?

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 by: Python - Fri, 20 May 2022 00:19 UTC

Richard "Hachel" Lengrand (M.D.) wrote:
> Le 20/05/2022 à 01:40, Python a écrit :
>
>> sqrt(1+(1/4)Vr²/c²) does not depend on acceleration
>
> The correct équation is To=Tr.sqrt(1+(1/4)Vr²/c²) in the case of
> accelerated frame,
> and To=Tr.sqrt(1+Vr²/c²) in the case of constant speed.
>
> In  To=Tr.sqrt(1+(1/4)Vr²/c²) : Vr depends on acceleration.
> Vr is Vr=a.Tr
>
> ----
>
> To²=Tr²+Et² (if vi=0 in accelerated frame).
>
> To²=Tr²+[(1/2)a.Tr²/c]²
>
> To=Tr.sqrt(1+(1/4)a².Tr²/c²)
>
> a is in this équation.
>
> But if Vr=a.Tr then a².Tr²/c²=Vr²/c²
>
> No?

I don't care to spot where you did a mistake, none of
your intermediate equations makes sense to me.

The result is just plain ABSURD. *sigh* It's basic
stuff...

Re: [SR] Where does this strange (1/4) come from?

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From: r.hac...@tiscali.fr (Richard Hachel)
 by: Richard Hachel - Fri, 20 May 2022 00:40 UTC

Le 20/05/2022 à 02:19, Python a écrit :
> I don't care to spot where you did a mistake, none of
> your intermediate equations makes sense to me.
>
> The result is just plain ABSURD. *sigh* It's basic
> stuff...

Jean-Pierre, you are tired. Go to sleep, and tomorrow, you might see
things a little more clearly.

R.H.

Re: [SR] Where does this strange (1/4) come from?

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Subject: Re: [SR] Where does this strange (1/4) come from?
From: ross.fin...@gmail.com (Ross A. Finlayson)
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 by: Ross A. Finlayson - Fri, 20 May 2022 05:43 UTC

On Thursday, May 19, 2022 at 2:25:33 PM UTC-7, Richard Hachel wrote:
> A user asks me where this strange 1/4 comes from that appears in my
> equation To=Tr.sqrt(1+(1/4)Vr²/c²)
>
> Let To²=Tr²+Et²
>
> Let To²=Tr²+(x/c)²
>
> Let us pose, since we are working here in real velocities and since it is
> a uniformly accelerated frame of reference:
> x=(1/2.a.Tr²)
>
> Let To²=Tr²+(1/2.a.Tr²)²/c²
>
> Let still be if Vr=a.Tr
>
> To²=Tr²+(1/4.Vr².Tr²)/c²
>
> Or To=Tr.sqrt(1+(1/4)Vr²/c²)
>
> It's math.
>
> R.H.

No, no: _inverse_ square.

Re: [SR] Where does this strange (1/4) come from?

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Subject: Re: [SR] Where does this strange (1/4) come from?
From: maluwozn...@gmail.com (Maciej Wozniak)
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 by: Maciej Wozniak - Fri, 20 May 2022 08:38 UTC

On Friday, 20 May 2022 at 02:19:27 UTC+2, Python wrote:
> Richard "Hachel" Lengrand (M.D.) wrote:
> > Le 20/05/2022 à 01:40, Python a écrit :
> >
> >> sqrt(1+(1/4)Vr²/c²) does not depend on acceleration
> >
> > The correct équation is To=Tr.sqrt(1+(1/4)Vr²/c²) in the case of
> > accelerated frame,
> > and To=Tr.sqrt(1+Vr²/c²) in the case of constant speed.
> >
> > In To=Tr.sqrt(1+(1/4)Vr²/c²) : Vr depends on acceleration.
> > Vr is Vr=a.Tr
> >
> > ----
> >
> > To²=Tr²+Et² (if vi=0 in accelerated frame).
> >
> > To²=Tr²+[(1/2)a.Tr²/c]²
> >
> > To=Tr.sqrt(1+(1/4)a².Tr²/c²)
> >
> > a is in this équation.
> >
> > But if Vr=a.Tr then a².Tr²/c²=Vr²/c²
> >
> > No?
> I don't care to spot where you did a mistake, none of

Oh, stinker Python is opening its muzzle again,
and trying to pretend he knows something.
Tell me, poor stinker, what is your definition of
a "theory" in the terms of Peano arithmetic?
See: if a theorem is going to be a part of a theory,
it has to be formulable in the language of the
theory. Do you get it? Or are you too stupid even for
that, poor stinker?

Re: [SR] Where does this strange (1/4) come from?

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From: r.hac...@tiscali.fr (Richard Hachel)
 by: Richard Hachel - Fri, 20 May 2022 21:41 UTC

Le 19/05/2022 à 23:25, Richard Hachel a écrit :
> A user asks me where this strange 1/4 comes from that appears in my equation
> To=Tr.sqrt(1+(1/4)Vr²/c²)
>
> Let To²=Tr²+Et²
>
> Let To²=Tr²+(x/c)²
>
> Let us pose, since we are working here in real velocities and since it is a
> uniformly accelerated frame of reference:
> x=(1/2.a.Tr²)
>
> Let To²=Tr²+(1/2.a.Tr²)²/c²
>
> Let still be if Vr=a.Tr
>
> To²=Tr²+(1/4.Vr².Tr²)/c²
>
> Or To=Tr.sqrt(1+(1/4)Vr²/c²)
>
> It's math.
>
> R.H.

More specifically, we know that:

Let To²=Tr²+Et²

Let To²=Tr²+(x/c)²

If x = (1/2)aTr²+Vri.Tr

So To²=Tr²+[(1/2)aTr²+Vri.Tr]²/c²

And To=Tr.sqrt([1/4Vr²+Vri²+Vr.Vri]/c²)

Nota bene : if Vri=0 (initial speed=0) ---> To=Tr.sqrt(1+(1/4)Vr²/c²)
accelerated mode

if a=0 (no acceleration), Vr=0 ---> To=Tr.sqrt(1+Vri²/c²)
constant speed mode

In this two cases, To²=Tr²+Et²

But Warning!

When we trigger the clocks at the start, the two protagonists must be
conjoined.

If they are not spouses, you have to use the equation I gave.

ΔTo2=ΔTr2.[(2.sqrt(1+Vrm²/c²)-sqrt(1+(1/4)Vrm²/c²)]

R.H.

1
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