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tech / sci.physics.relativity / Re: Annotated version of SRT

SubjectAuthor
* Annotated version of SRTThomas Heger
+* Re: Annotated version of SRTJanPB
|+- Re: Annotated version of SRTEvodio Bayon
|`* Re: Annotated version of SRTThomas Heger
| +* Re: Annotated version of SRTJanPB
| |`* Re: Annotated version of SRTThomas Heger
| | +* Re: Annotated version of SRTJanPB
| | |`* Re: Annotated version of SRTThomas Heger
| | | +- Re: Annotated version of SRTThomas Heger
| | | `* Re: Annotated version of SRTJanPB
| | |  `* Re: Annotated version of SRTThomas Heger
| | |   +* Re: Annotated version of SRTPython
| | |   |+- Re: Annotated version of SRTMaciej Wozniak
| | |   |`* Re: Annotated version of SRTThomas Heger
| | |   | `- Re: Annotated version of SRTVance Rera
| | |   `* Re: Annotated version of SRTJanPB
| | |    `* Re: Annotated version of SRTThomas Heger
| | |     `* Re: Annotated version of SRTJanPB
| | |      +* Re: Annotated version of SRTMaciej Wozniak
| | |      |`* Re: Annotated version of SRTThomas Heger
| | |      | `* Re: Annotated version of SRTJanPB
| | |      |  `- Re: Annotated version of SRTThomas Heger
| | |      `* Re: Annotated version of SRTThomas Heger
| | |       `* Re: Annotated version of SRTJanPB
| | |        +- Re: Annotated version of SRTThomas Heger
| | |        +* Re: Annotated version of SRTRichie Cruze
| | |        |`* Re: Annotated version of SRTMichael Moroney
| | |        | `* Re: Annotated version of SRTRichie Cruze
| | |        |  +* Re: Annotated version of SRTMichael Moroney
| | |        |  |`- Re: Annotated version of SRTRichie Cruze
| | |        |  `* Re: Annotated version of SRTJanPB
| | |        |   `* Re: Annotated version of SRTRichie Cruze
| | |        |    `* Re: Annotated version of SRTJanPB
| | |        |     `* Re: Annotated version of SRTElmer Joss
| | |        |      `* Re: Annotated version of SRTJanPB
| | |        |       `* Re: Annotated version of SRTVance Rera
| | |        |        `* Re: Annotated version of SRTJanPB
| | |        |         `* Re: Annotated version of SRTVance Rera
| | |        |          `* Re: Annotated version of SRTJanPB
| | |        |           +* Re: Annotated nazi excrement JanPB failed the eugenicist IQ-testHagan Koon
| | |        |           |+* Re: Annotated nazi excrement JanPB failed the eugenicist IQ-testJanPB
| | |        |           ||+- Re: Annotated nazi excrement JanPB failed the eugenicist IQ-testLamar Main
| | |        |           ||`* Re: Annotated nazi excrement JanPB failed the eugenicist IQ-testPaul Alsing
| | |        |           || +* Re: Annotated nazi excrement JanPB failed the eugenicist IQ-testMichael Moroney
| | |        |           || |+- Re: Annotated nazi excrement JanPB failed the eugenicist IQ-testwhodat
| | |        |           || |`* Re: Annotated nazi excrement JanPB failed the eugenicist IQ-testJanPB
| | |        |           || | +- Re: Annotated nazi excrement JanPB failed the eugenicist IQ-testMichael Moroney
| | |        |           || | +- Re: Annotated nazi excrement JanPB failed the eugenicist IQ-testLamar Main
| | |        |           || | `- Re: Annotated nazi excrement JanPB failed the eugenicist IQ-testJanPB
| | |        |           || `- Re: Annotated nazi excrement JanPB failed the eugenicist IQ-testLamar Main
| | |        |           |`* Re: Annotated nazi excrement JanPB failed the eugenicist IQ-testJanPB
| | |        |           | `- Re: Annotated nazi excrement JanPB failed the eugenicist IQ-testLamar Main
| | |        |           `- Re: Annotated version of SRTThomas Heger
| | |        `* Re: Annotated version of SRTThomas Heger
| | |         +- Re: Annotated version of SRTJanPB
| | |         +* Re: Annotated version of SRTOdd Bodkin
| | |         |`* Re: Annotated version of SRTThomas Heger
| | |         | +* Re: Annotated version of SRTJanPB
| | |         | |`- Re: Annotated version of SRTThomas Heger
| | |         | `* Re: Annotated version of SRTOdd Bodkin
| | |         |  `* Re: Annotated version of SRTThomas Heger
| | |         |   +* Re: Annotated version of SRTMichael Moroney
| | |         |   |`- Re: Annotated version of SRTThomas Heger
| | |         |   `* Re: Annotated version of SRTOdd Bodkin
| | |         |    `* Re: Annotated version of SRTThomas Heger
| | |         |     `* Re: Annotated version of SRTOdd Bodkin
| | |         |      +* Re: Annotated version of SRTMaciej Wozniak
| | |         |      |`* Re: Annotated version of SRTOdd Bodkin
| | |         |      | `- Re: Annotated version of SRTMaciej Wozniak
| | |         |      `* Re: Annotated version of SRTThomas Heger
| | |         |       `* Re: Annotated version of SRTOdd Bodkin
| | |         |        `- Re: Annotated version of SRTThomas Heger
| | |         +* Re: Annotated version of SRTMichael Moroney
| | |         |`* Re: Annotated version of SRTThomas Heger
| | |         | +- Re: Annotated version of SRTJ. J. Lodder
| | |         | +* Re: Annotated version of SRTOdd Bodkin
| | |         | |+* Re: Annotated version of SRTThomas Heger
| | |         | ||+* Re: Annotated version of SRTJ. J. Lodder
| | |         | |||`* Re: Annotated version of SRTMaciej Wozniak
| | |         | ||| `- Re: Annotated version of SRTThomas Heger
| | |         | ||+* Re: Annotated version of SRTOdd Bodkin
| | |         | |||`* Re: Annotated version of SRTMichael Moroney
| | |         | ||| `* Re: Annotated version of SRTOdd Bodkin
| | |         | |||  `* Re: Annotated version of SRTThomas Heger
| | |         | |||   +* Re: Annotated version of SRTOdd Bodkin
| | |         | |||   |`- Re: Annotated version of SRTThomas Heger
| | |         | |||   `* Re: Annotated version of SRTMitch Yamaguchi
| | |         | |||    +- Re: Annotated version of SRTthor stoneman
| | |         | |||    `- Re: Annotated version of SRTThomas Heger
| | |         | ||`* Re: Annotated version of SRTMichael Moroney
| | |         | || +* Re: Annotated version of SRTThomas Heger
| | |         | || |+* Re: Annotated version of SRTThomas Heger
| | |         | || ||`* Re: Annotated version of SRTJanPB
| | |         | || || `* Re: Annotated version of SRTThomas Heger
| | |         | || ||  `- Re: Annotated version of SRTJanPB
| | |         | || |`* Re: Annotated version of SRTJanPB
| | |         | || | `* Re: Annotated version of SRTThomas Heger
| | |         | || |  +* Re: Annotated version of SRTJanPB
| | |         | || |  |`* Re: Annotated version of SRTThomas Heger
| | |         | || |  | +* Re: Annotated version of SRTMichael Moroney
| | |         | || |  | |`* Re: Annotated version of SRTThomas Heger
| | |         | || |  | `- Re: Annotated version of SRTThomas Heger
| | |         | || |  `* Re: Annotated version of SRTPython
| | |         | || `* Re: Annotated version of SRTCoke Hishikawa
| | |         | |`* Re: Annotated version of SRTThomas Heger
| | |         | `- Re: Annotated version of SRTMichael Moroney
| | |         +- Re: Annotated version of SRTPaul B. Andersen
| | |         `- Re: Annotated version of SRTJ. J. Lodder
| | `- Re: Annotated version of SRTMikko
| `* Re: Annotated version of SRTMikko
+- Re: Annotated version of SRTPaparios
+- Re: Annotated version of SRTDono.
`* Re: Annotated version of SRTMichael Moroney

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Re: Annotated version of SRT

<jebm5hF7rgiU1@mid.individual.net>

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https://www.novabbs.com/tech/article-flat.php?id=90262&group=sci.physics.relativity#90262

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From: ttt_...@web.de (Thomas Heger)
Newsgroups: sci.physics.relativity
Subject: Re: Annotated version of SRT
Date: Sun, 15 May 2022 08:50:28 +0200
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In-Reply-To: <0787f688-0032-4f81-ac37-398fb4bcd077n@googlegroups.com>
 by: Thomas Heger - Sun, 15 May 2022 06:50 UTC

Am 15.05.2022 um 04:29 schrieb JanPB:
>> These two items move with constant distance along the x/xsi-axis into
>> >the direction of higher xsi-values.
>> >
>> >This 'tandem' is observed from the zero spot of K, which moves with
>> >velocity v relative to the system into the negative direction with -v*t.
>> >
>> >But none of Einstein's equations would fit to that setting.
> Again, you are expressing the physical situation in mathematical
> terms that do not represent the physical situation.

WHAT?

The situation is EXTREMELY simple:

You have a coordinate system K and a copy of K set into motion along the
x-axis of K with velocity v.

Now both systems use the same unit vectors, which point into the same
directions, but the zero spot of k is set into motion.

It would be an addition of a displacement v*t to the positions of K,
which would gain equivalent points in k and K (like the zero spot of k).

Now the same points have coordinates in both system, too, but we need
subtraction for a coordinate transform.

So a point (a, b, c) in K has the coordinates (a- v*t, b, c) in k.

This is totally simple and obvious for slow velocities v (what is the
realm we could possibly measure).

Now it gets tricky, if the velocity v is getting into the realm of the
speed of light, but in the slow case the problem is trivial.

>> >Instead of a coordinate transformation he developed an obscure partial
>> >differential equation, which I think is faulty and which I'm unable to
>> >associate with the setting from above.
> It's a very simple equation. The coordinate transformation is
> presumed linear, so the tau component of it is presumed
> to look like this:
>
> tau(x', y, z, t) = Ax' + By + Cz + Dt

But the actually meant Lorentz transform is not a linear function.

Also: displacement of a coordinate system would make the transformation
function non-linear, too.

>
> This means that dtau/dx' = A, dtau/dy = B, dtau/dz = C, dtau/dt = D.
>
>> >I have complained about this point several times, too.
> Without merit.
>
>> >But apparently you know how to derive Einstein's equation. So, please
>> >let me know, how that works.
> It's written out in the paper. Given the equation (1/2)*(tau_0 + tau_2) = tau_1,
> one differentiates it wrt x' and that yields the equation constraining the
> A and D constants.

In system k x' is a constant (the difference between emitter and
mirror), what would forbid the operation you have mentioned, because you
can differentiate wrt variables only.

TH

Re: Annotated version of SRT

<t5qdgj$apl$1@dont-email.me>

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https://www.novabbs.com/tech/article-flat.php?id=90265&group=sci.physics.relativity#90265

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From: mikko.le...@iki.fi (Mikko)
Newsgroups: sci.physics.relativity
Subject: Re: Annotated version of SRT
Date: Sun, 15 May 2022 11:26:59 +0300
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 by: Mikko - Sun, 15 May 2022 08:26 UTC

On 2022-05-12 19:05:22 +0000, Thomas Heger said:

> Am 12.05.2022 um 09:31 schrieb Mikko:
>> On 2022-05-12 05:39:45 +0000, Thomas Heger said:
>>
>>> You need to distinguish numbers, vectors and points.
>>
>> In Einstein's text that is simple: all symbols represent scalars
>> unless otherwise specified.
>
> Well, no, I do not agree.
>
> Einstein made no distinction between different types of mathematical
> objects, but did not only use scalars.
>
> So, any Latin letter can represent several types of objects and
> Einstein gave no hints, which would allow to identify the intended
> meaning.

At the time it was commonly thought that all formulas, or at least the
useful ones, were always about numbers and only numbers, as most formulas
indeed were. Therefore it wast not necessary to point out that a symbol
in a formula represents a scalar but very important to clearly say if
it represents something else.

> To assume, that only scalars were meant was plain wrong, because also
> functions and vectors had similar symbols, which the reader was
> requested to identify.

Functions can be identified as fucntions because function symbols are
only used before a left parenthesis (except for a small number of well
known symbols). Unless otherwise specified, function values are scalar.

> I have complained several times about this, but JanPB meant, that the
> intended audience could decipher Einstein's intentions with ease.
>
> I do not quite agree, but would accept, that professionals certainly
> know, what Einstein wanted.

And that is sufficient.

> But still you cannot claim, that all symbols mean scalars. Which
> interpretations was intended, that is a riddle, which the reader was
> requested to solve.

Not all, only those that are not specified to mean something else.

> And that riddle is not as easy as you apparently think.

Easy enough.

>> You should be clear with your symbols. When discussing Einstein's text,
>> you should use the same conventions. Einstein's x and xi are scalars,
>> so for points you should use different symbols.
>
> Points had large Latin letters, like 'A' or 'B' (I guess there was also
> a 'C', but as far as I can recall, there was no 'D').

Yes, that is the common style in geometry. However, upper case letters
were also used for other purposes. Where A and B are introduced in the
article they are clearly identified as points.

>> Coordinates are scalars. The xi-coordinate of "zero spot of k" is
>> zero because "zero spot of k" means the poit where xi = 0, eta = 0,
>> and zeta = 0.
>
> Not really. A component of a vector is a scalar, but 'coordinate' could
> be interpreted as a vector, too. That would be a scaled version of the
> unit vector in that direction.

Yes really. Nobody wanted to think about any other possibility without
a very good reason.

> But also 'numerical value of the entry of the position vector of a
> point' would fit to the description, what is a scalar.
>
> Usually the author should tell, how he liked his variables to be
> interpreted. But Einstein left that more or less to the reader.

Not just should but did. But not what the readers would consider
self-evident. Unless otherwise told, every symbol is scalar by
default.

>>> The xsi-component of the position vector of the zero spot is called
>>> xsi_0, which has the numerical value zero.
>>
>> You don't need any position vectors because you already have coordinates.
>
> A point has a location, which is represented by a position vector.

Not in Einstein's article, where coordinates are used instead.

> That vector has components, which we can call 'coordinates'.
> If you add them together, you get the postion vector of thee point.
>
> It's not really necessary to do so, because you could actually provide
> only coordinates.
>
> But still the position vector exists, whether you need it or not.

In certain sense yes but here it is an irrelevant distraction.

Mikko

Re: Annotated version of SRT

<315799b5-db63-4608-a85f-9456228cebe9n@googlegroups.com>

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Subject: Re: Annotated version of SRT
From: film...@gmail.com (JanPB)
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 by: JanPB - Sun, 15 May 2022 19:53 UTC

On Saturday, May 14, 2022 at 11:34:38 PM UTC-7, Thomas Heger wrote:
> Am 15.05.2022 um 04:49 schrieb JanPB:
> ..
> >>>
> >>>
> >>> After a number of messages exchanged with JanPB, we came to the result,
> >>> that a mirror stationary in k at same distance to xsi_0 on the xsi-axis
> >>> would be a valid assumption for the intended setting.
> >>>
> >>> These two items move with constant distance along the x/xsi-axis into
> >>> the direction of higher xsi-values.
> >>>
> >>> This 'tandem' is observed from the zero spot of K, which moves with
> >>> velocity v relative to the system into the negative direction with -v*t.
> >>>
> >>> But none of Einstein's equations would fit to that setting.
> >>>
> >>> Instead of a coordinate transformation he developed an obscure partial
> >>> differential equation, which I think is faulty and which I'm unable to
> >>> associate with the setting from above.
> >> This is the equation:
> >>
> >> 1/2*(1/(c −v) + 1/(c +v))* ∂τ/∂t = ∂τ/∂x' + 1/(c +v)* ∂τ/∂t
> >>
> >>
> >> As justification for this equation Einstein wrote:
> >>
> >> "Hence, if x' be chosen infinitesimally small,..."
> >>
> >> I have complained, that x' cannot be chosen "infinitesimally small",
> >
> > This is just the 1905 way of saying "let's differentiate this equation
> > with respect to x' ".
> That function (NOT equation) was tau and can only differentiated to its
> variables. But x' is not a variable.

It is. And you can differentiate wrt it. Einstein is using an overkill to solve
this problem, BTW. The tau function is presumed linear so its
coefficients can be found by a bit of algebra, no calculus is needed.
But it would be more work that way, and calculus solves this in basically
one line.

> In the meant context x' can be treated as a constant.

It is a constant for the duration of one experiment. This thought experiment
can be performed for different values of the constant x'. The results then
have to obey the differential equation.

> x' is actually moving in system K, but not in system k.

x' is not "moving", it's number.

> For the possible case v=0 we have K=k, hence this identity is a possible
> setting, where x' is actually a constant.

N/A.

> Now you cannot differentiate function in respect to constants.

It's not a constant, it's a variable. It's fixed only for the duration of one
experiment, just like the distance between a parked car and a street
corner is fixed, but in general this distance is a variable depending on
the details of how the car is parked on different days, whether the car
is being driven or not, etc.

> That
> would be nonsense, because 'small variations of a constant' are an oxymoron.

x' is not a constant in this sense. It varies from one experiment to the next.

> >> because x' was defined as position of the mirror at a fixed position in
> >> k, but in K-coordinates.
> >
> > The differentiation means we consider several instances of the experiment,
> > each at different x' value, and compute the limit of the relevant difference quotient.
> 'The experiment' cannot be carried out, anyhow, because inertial
> movement of a pair of an emitter and a mirror, seen from a remote
> location in (fast) relative motion, is nothing you could possibly do in
> real.

You are not making any sense.

> So, we have here a 'thought experiment', which you do not need to carry
> out with different values for the distance between mirror and emitter.

You do, in order to calculate the coefficients of the (multi-)linear transformation tau.

> > In this case the transformation is presumed linear, so it's only necessary to
> > consider TWO instances of the experiment, each at different values of x',
> > so Einstein's use of calculus here is an overkill meant to shorten the process.
> Well, I think this equation is plain wrong.
>
> And as this particular equation is essential for the entire paper, there
> will be no remainder, if the error is removed.

There is no error.

> > It's not wrong.
> >
> >> This position is moving in K, to which the variable x' belongs.
> >>
> >> The movement of x' in K is rather simple, because it moves with velocity
> >> v along the x-axis of K.
> >> Now my question was, what these partial derivatives were meant to
> >> represent, if we have only a one-dimensional problem.
> >
> > I don't think this is something I can teach you on a forum like this.
> A link to the derivation would be sufficiant.
>
> I think, this partial differential equation is nonsense.
>
> reason:
>
> he attempted to derive a function, which was meant as coordinate
> transformation between system K and k.
>
> As system k is actually the same as system K, but set into motion to
> velocity v, I would simply add the displacement between K and k and the
> case is closed.

The transformation is presumed (multi-)linear, and Einstein starts with
calculating its tau component. In general such linear transformation
looks like this:

tau(x', y, z, t) = Ax' + By + Cz + Dt

....for some v-dependent constants A, B, C, D. Instead of using a more
tedious purely algebraic approach, Einstein uses the basic calculus fact here:

dtau/dx' = A
dtau/dy = B
dtau/dz = C
dtau/dt = D

....and calculates the relevant dtau/d... by differentiating the constraining
tau equation. Recall that the constraining equation for tau is valid for
*any* value of the x': whether the mirror is positioned at x' = 2 or x' =17,
the equation will hold. This implies that certain constrainst will likewise hold
on the *rates of change* of tau wrt certain quantities.

This yields the relationship involving only dtau/dx' and dtau/dt:

dtau/dx' + (v/(c^2 - v^2)) * dtau/dt = 0

To obtain the remaining two coefficients (dtau/dy and dtau/dz) Einstein
considers a similar experiment except the mirror is positioned at some
distance from the source along the Y-axis, and then one more with the mirror
along the Z-axis.

He omits the exact derivation as repetitive and obvious but we can do it here.

First we need to write the constraining equation for the first situation (mirror along
the Y-axis). Start with the (x', y, z, t) coordinates of the events:

the light pulse emission: (0, 0, 0, t)
reflection: (0, y, 0, t + delta) [we need to calculate delta in a moment]
the pulse back at the source: (0, 0, 0, t + 2*delta)

....where delta is the light pulse flight time source->mirror (or mirror->source,
since they are the same by symmetry).

So the emission takes place at time t (according to K) and the mirror sits
y units away from the source in the Y direction, again according to K.

To calculate the light ray flight time delta (source->mirror) we can for example
calculate the distance between the position of the light pulse emission and
its arrival at the mirror in TWO ways and then equate them:

the first way: distance = c*delta [the speed of light times the flight time]

the second way: distance = sqrt(y^2 + v^2 delta^2) [Pythagoras]

(the second equation follows from the fact that during the flight time delta
the mirror moves v*delta units (of K) in the X-axis direction).

So we have:

c*delta = sqrt(y^2 + v^2 delta^2)

Solving for delta:

delta = y/sqrt(c^2 - v^2)

(That's where Einstein's remark that "...light is ... propagated ...
when viewed from the stationary system with the velocity
sqrt(c^2 - v^2)" comes from. He means viewed from the
(x', y, z, t) standpoint; from the (x,y,z,t) standpoint that speed is,
of course, c.).

Now we can write the constraining equation for tau:

(1/2)*( tau(0, 0, 0, t) + tau(0, 0, 0, t + 2*y/sqrt(c^2 - v^2)) )
= tau(0, y, 0, t + y/sqrt(c^2 - v^2))

Differentiating wrt y yields:

(1/2) * dtau/dt * (2/sqrt(c^2 - v^2)) = dtau/dy + dtau/dt * (1/sqrt(c^2 - v^2))

The 2's and the dtau/dt terms cancel out and what's left is:

dtau/dy = 0.

An almost exact replica of the above wrt the Z direction gives dtau/dz = 0.

> For what reason did he develop that partial differential equation, in
> the first place?

Because we assume that:

tau(x', y, z, t) = Ax' + By + Cz + Dt

and therefore A = dtau/dx', B = dtau/dy, C = dtau/dz, and D = dtau/dt.

And Einstein obtains the following 3 equations involving those:


Click here to read the complete article
Re: Annotated version of SRT

<jejf3bFmmebU1@mid.individual.net>

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https://www.novabbs.com/tech/article-flat.php?id=90465&group=sci.physics.relativity#90465

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From: ttt_...@web.de (Thomas Heger)
Newsgroups: sci.physics.relativity
Subject: Re: Annotated version of SRT
Date: Wed, 18 May 2022 07:38:59 +0200
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In-Reply-To: <t5qdgj$apl$1@dont-email.me>
 by: Thomas Heger - Wed, 18 May 2022 05:38 UTC

Am 15.05.2022 um 10:26 schrieb Mikko:
> On 2022-05-12 19:05:22 +0000, Thomas Heger said:
>
>> Am 12.05.2022 um 09:31 schrieb Mikko:
>>> On 2022-05-12 05:39:45 +0000, Thomas Heger said:
>>>
>>>> You need to distinguish numbers, vectors and points.
>>>
>>> In Einstein's text that is simple: all symbols represent scalars
>>> unless otherwise specified.
>>
>> Well, no, I do not agree.
>>
>> Einstein made no distinction between different types of mathematical
>> objects, but did not only use scalars.
>>
>> So, any Latin letter can represent several types of objects and
>> Einstein gave no hints, which would allow to identify the intended
>> meaning.
>
> At the time it was commonly thought that all formulas, or at least the
> useful ones, were always about numbers and only numbers, as most formulas
> indeed were. Therefore it wast not necessary to point out that a symbol
> in a formula represents a scalar but very important to clearly say if
> it represents something else.

Vectors and vector equations were already known in the 19th century.
Especially in connection to electromagnetism vector equations were state
of the art since Maxwell's times.

>> To assume, that only scalars were meant was plain wrong, because also
>> functions and vectors had similar symbols, which the reader was
>> requested to identify.
>
> Functions can be identified as fucntions because function symbols are
> only used before a left parenthesis (except for a small number of well
> known symbols). Unless otherwise specified, function values are scalar.

Parenthesises can have different meanings. To distinguish a function a
of argument x in a(x)=0 from a multiplication of a scalar a with the
vector (x) in a(x)=0, we need certain signs, which distinguish different
uses of the used symbols.

>> I have complained several times about this, but JanPB meant, that the
>> intended audience could decipher Einstein's intentions with ease.
>>
>> I do not quite agree, but would accept, that professionals certainly
>> know, what Einstein wanted.
>
> And that is sufficient.

Sure, but not all professional physicists can read Einstein's mind.

To enable common mortals to understand something, it is useful, if an
arbitrary reader is able to identify, what an author tries to express.

It can eventualy be difficult. But finally the reader should be able to
find out, what was actually meant.

>> But still you cannot claim, that all symbols mean scalars. Which
>> interpretations was intended, that is a riddle, which the reader was
>> requested to solve.
>
> Not all, only those that are not specified to mean something else.
???

An author of a scientific paper is obliged to be specific. There should
be no space for interpretations and questions about the intended meaning
of a certain symbol.

If an author fails to distinguish between possible interpretations, the
reader may chose, what would fit to the possible interpretations to his
own liking, what in most cases is not, what the author wanted.

Therefore a reader can disprove a paper, simply by finding a possible
interpretation of the text, which leads to nonsense.

In this case the text flies into the waste bin.

Even if this sounds a little tough, you should bear in mind, that
scientific papers are not toys.

>> And that riddle is not as easy as you apparently think.
>
> Easy enough.
>
>>> You should be clear with your symbols. When discussing Einstein's text,
>>> you should use the same conventions. Einstein's x and xi are scalars,
>>> so for points you should use different symbols.
>>
>> Points had large Latin letters, like 'A' or 'B' (I guess there was
>> also a 'C', but as far as I can recall, there was no 'D').
>
> Yes, that is the common style in geometry. However, upper case letters
> were also used for other purposes. Where A and B are introduced in the
> article they are clearly identified as points.

There were eight different uses of the capital 'A' in Einstein's text.

This alone would be sufficiant to dismiss the entire paper.

>>> Coordinates are scalars. The xi-coordinate of "zero spot of k" is
>>> zero because "zero spot of k" means the poit where xi = 0, eta = 0,
>>> and zeta = 0.
>>
>> Not really. A component of a vector is a scalar, but 'coordinate'
>> could be interpreted as a vector, too. That would be a scaled version
>> of the unit vector in that direction.
>
> Yes really. Nobody wanted to think about any other possibility without
> a very good reason.

You should meantion, which of the possibilities above is that obvious.

Is a coordinate a scalar or a vector?

>> But also 'numerical value of the entry of the position vector of a
>> point' would fit to the description, what is a scalar.
>>
>> Usually the author should tell, how he liked his variables to be
>> interpreted. But Einstein left that more or less to the reader.
>
> Not just should but did. But not what the readers would consider
> self-evident. Unless otherwise told, every symbol is scalar by
> default.
>
>>>> The xsi-component of the position vector of the zero spot is called
>>>> xsi_0, which has the numerical value zero.
>>>
>>> You don't need any position vectors because you already have
>>> coordinates.
>>
>> A point has a location, which is represented by a position vector.
>
> Not in Einstein's article, where coordinates are used instead.

A postition vector in three dimensional space has three components,
called 'coordinates'.

Now is essential to define the meaning of 'coordinate'.

I would use a orthogonal set of three unit vectors as coordinate system
and unitless vectors, where the entries are sclalars, that multiply with
the cooresponding unit vectors. These scaled unit vectors are added to
the position vector of the point.

What Einstein wanted to use, that would be his decision. It would have
been nice, if he had told the reader, which decisions he made.

....

TH

Re: Annotated version of SRT

<jejge0Fmts7U1@mid.individual.net>

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https://www.novabbs.com/tech/article-flat.php?id=90466&group=sci.physics.relativity#90466

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From: ttt_...@web.de (Thomas Heger)
Newsgroups: sci.physics.relativity
Subject: Re: Annotated version of SRT
Date: Wed, 18 May 2022 08:01:45 +0200
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In-Reply-To: <315799b5-db63-4608-a85f-9456228cebe9n@googlegroups.com>
 by: Thomas Heger - Wed, 18 May 2022 06:01 UTC

Am 15.05.2022 um 21:53 schrieb JanPB:
> On Saturday, May 14, 2022 at 11:34:38 PM UTC-7, Thomas Heger wrote:
>> Am 15.05.2022 um 04:49 schrieb JanPB:
>> ..
>>>>>
>>>>>
>>>>> After a number of messages exchanged with JanPB, we came to the result,
>>>>> that a mirror stationary in k at same distance to xsi_0 on the xsi-axis
>>>>> would be a valid assumption for the intended setting.
>>>>>
>>>>> These two items move with constant distance along the x/xsi-axis into
>>>>> the direction of higher xsi-values.
>>>>>
>>>>> This 'tandem' is observed from the zero spot of K, which moves with
>>>>> velocity v relative to the system into the negative direction with -v*t.
>>>>>
>>>>> But none of Einstein's equations would fit to that setting.
>>>>>
>>>>> Instead of a coordinate transformation he developed an obscure partial
>>>>> differential equation, which I think is faulty and which I'm unable to
>>>>> associate with the setting from above.
>>>> This is the equation:
>>>>
>>>> 1/2*(1/(c −v) + 1/(c +v))* ∂τ/∂t = ∂τ/∂x' + 1/(c +v)* ∂τ/∂t
>>>>
>>>>
>>>> As justification for this equation Einstein wrote:
>>>>
>>>> "Hence, if x' be chosen infinitesimally small,..."
>>>>
>>>> I have complained, that x' cannot be chosen "infinitesimally small",
>>>
>>> This is just the 1905 way of saying "let's differentiate this equation
>>> with respect to x' ".
>> That function (NOT equation) was tau and can only differentiated to its
>> variables. But x' is not a variable.
>
> It is. And you can differentiate wrt it. Einstein is using an overkill to solve
> this problem, BTW. The tau function is presumed linear so its
> coefficients can be found by a bit of algebra, no calculus is needed.
> But it would be more work that way, and calculus solves this in basically
> one line.
>
>> In the meant context x' can be treated as a constant.
>
> It is a constant for the duration of one experiment. This thought experiment
> can be performed for different values of the constant x'. The results then
> have to obey the differential equation.

No, sorry.

An arbitrary value is not a variable, even if you can use a variety of
settings.

Example:

running as a sport.

You have distances from 100 m to 42 km for a single run in sport events.

Now you want to describe the position of the runnners as a function of time.

But you choose the distance first and then derive that function. But you
would never ever treat the distance to run as a variable in a certain event.

It could be useful to derive a function, however, which determains, when
the mean runner reaches a distance of say 1000m from the starting point,
where the distance to run is a variable.

But that would be an entirely different problem, then a function of the
runners in a certain race.

>> x' is actually moving in system K, but not in system k.
>
> x' is not "moving", it's number.

NO.

The point, where the mirror is located in k has coordinates in K, too.
That point of the mirror at rest in k is moving in K, hence also the
coordinates would 'run'.

>
>> For the possible case v=0 we have K=k, hence this identity is a possible
>> setting, where x' is actually a constant.
>
> N/A.
>
>> Now you cannot differentiate function in respect to constants.
>
> It's not a constant, it's a variable. It's fixed only for the duration of one
> experiment, just like the distance between a parked car and a street
> corner is fixed, but in general this distance is a variable depending on
> the details of how the car is parked on different days, whether the car
> is being driven or not, etc.

The meant function tau was meant to describe a certain experiment, not
the outcome of all possible experiments as function of this particular
setting.

In a single experiment the distance between emitter and mirror is constant.

This distance determines the function of position x' as a function of
time in system K.

But instead of that, Einstein used the inverse ∂τ/∂x' in his equation,
as if time tau would be a function of the postion of the mirror, what
made no sense whatever.

That term ∂τ/∂x' is also infinite for the setting v=0.

Therefor the entire partial differential equation is nonsense.

>> That
>> would be nonsense, because 'small variations of a constant' are an oxymoron.
>
> x' is not a constant in this sense. It varies from one experiment to the next.

Sure. All adjustable parameters can be adjusted for a certain experiment.

But that would not make these settings a variable for a single
experiment, but constants.

Only if a different question is considered, where the variation of that
setting is adressed, the different settings become a variable.

....

TH

Re: Annotated version of SRT

<t62qb1$l6a$1@dont-email.me>

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https://www.novabbs.com/tech/article-flat.php?id=90470&group=sci.physics.relativity#90470

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From: mikko.le...@iki.fi (Mikko)
Newsgroups: sci.physics.relativity
Subject: Re: Annotated version of SRT
Date: Wed, 18 May 2022 15:54:57 +0300
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References: <jaaflrFde2kU1@mid.individual.net> <jcn29aF5f6dU1@mid.individual.net> <03cc52d5-9636-485a-a9f3-7c8350619c31n@googlegroups.com> <jcpcmoFj8lpU1@mid.individual.net> <b5b02531-42cc-4714-9799-1043df76199fn@googlegroups.com> <jcr2n2Ftcv2U1@mid.individual.net> <eacd0116-ac91-4cea-bcd2-35aa422bf510n@googlegroups.com> <jcum4nFjnusU1@mid.individual.net> <t4eg8l$cal$5@gioia.aioe.org> <jd1egjF5iktU1@mid.individual.net> <t4gn2d$103s$2@gioia.aioe.org> <jd6sulF6r8bU1@mid.individual.net> <t4ltn8$18d6$1@gioia.aioe.org> <jd9ah1Fl21cU1@mid.individual.net> <6d94bbeb-a2c5-419a-b266-9da8392b3870n@googlegroups.com> <jdef6bFkkvpU1@mid.individual.net> <0837699b-4179-4249-9a72-98371b5c05b8n@googlegroups.com> <jdhb42F6rmbU1@mid.individual.net> <aee5dec3-f2e0-4307-9827-14feb5a3ea8dn@googlegroups.com> <jdjv29Fm4q8U1@mid.individual.net> <t53a60$sct$1@dont-email.me> <jdmejrF64u5U1@mid.individual.net> <t55j44$n5g$1@dont-email.me> <jdp6h3FlvhoU1@mid.individual.net>
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 by: Mikko - Wed, 18 May 2022 12:54 UTC

On 2022-05-08 06:33:09 +0000, Thomas Heger said:

> Sure, but the text should have specified the used variables.

It does.

> A missing part cannot be used as justification of something. Instead
> missing parts are always treated, as if the author meant the wrong
> thing.

As I already said, there is no need to tell what the target audience
already knows.

> But we are generous in this case and marter our current brains to find
> a valid solution.
>
> So: unitless numerical values area a possible interpretation for
> 'coordinates', which inherit their meaning from the related coordinate
> system.

> Another prossible interpretation for a coordinate x would be a vector,
> which contains values only in the x-position, while the others contain
> zeros.

No, that is not a possible interpretation.

> But we can be generous only once, hence must apply one interpretation
> to all other occurances of the term 'coordinate'.

Except that they may be coordinates of another coordinate system.

> In any case, the term 'coordinate' can only have one meaning, hence
> coordinates in k and K are treated on the same basis.

Each coordinate has a different meaning.

> From this would follow, that we in fact can do, what you have rejected
> and derive coordinates in K from coordinates in k.

The relation of the two coordinate systems is specified so it is possible
to derive the relationship between them, and that's what Einstein is
going to do. The relation is found to be the Lorentz transformation.

Mikko

Re: Annotated version of SRT

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Subject: Re: Annotated version of SRT
From: maluwozn...@gmail.com (Maciej Wozniak)
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 by: Maciej Wozniak - Wed, 18 May 2022 13:17 UTC

On Wednesday, 18 May 2022 at 14:55:00 UTC+2, Mikko wrote:

> The relation of the two coordinate systems is specified so it is possible
> to derive the relationship between them, and that's what Einstein is
> going to do. The relation is found to be the Lorentz transformation.

In the meantime in the real world, however, forbidden
by your insane religion TAI and GPS keep measuring t'=t,
just like all serious clocks always did.

Re: Annotated version of SRT

<t62t53$b5i$1@dont-email.me>

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https://www.novabbs.com/tech/article-flat.php?id=90472&group=sci.physics.relativity#90472

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Subject: Re: Annotated version of SRT
Date: Wed, 18 May 2022 16:42:59 +0300
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 by: Mikko - Wed, 18 May 2022 13:42 UTC

On 2022-05-18 05:38:59 +0000, Thomas Heger said:

> Vectors and vector equations were already known in the 19th century.
> Especially in connection to electromagnetism vector equations were
> state of the art since Maxwell's times.

When mathematical formulas were first introduced all symbols represented
scalars. It was not necessary to say that they are scalars as nobody
thought that they could be anything else. It was not even possible to
say that tey represent scalars as the concept was not introduced until
somebody discovered that a symbol can represent something else. Even
then most formulas were about scalars and those that weren't were
considered unususual. Therefore the traditional convention that all
symbols are scalars remained.

>>> To assume, that only scalars were meant was plain wrong, because also
>>> functions and vectors had similar symbols, which the reader was
>>> requested to identify.
>>
>> Functions can be identified as fucntions because function symbols are
>> only used before a left parenthesis (except for a small number of well
>> known symbols). Unless otherwise specified, function values are scalar.
>
> Parenthesises can have different meanings. To distinguish a function a
> of argument x in a(x)=0 from a multiplication of a scalar a with the
> vector (x) in a(x)=0, we need certain signs, which distinguish
> different uses of the used symbols.

Readers are expected to know and understand conventional mathematical
notations.

>>> I have complained several times about this, but JanPB meant, that the
>>> intended audience could decipher Einstein's intentions with ease.
>>>
>>> I do not quite agree, but would accept, that professionals certainly
>>> know, what Einstein wanted.
>>
>> And that is sufficient.
>
> Sure, but not all professional physicists can read Einstein's mind.

None can do that, but all of that time could read and understand his
words and formulas.

> To enable common mortals to understand something, it is useful, if an
> arbitrary reader is able to identify, what an author tries to express.

When the article was published it was not yet determined whether there
is any new wisdom in the article that a common mortal should know.

> It can eventualy be difficult. But finally the reader should be able to
> find out, what was actually meant.

In this case it is not difficult. Physicists of the time found out
pretty quickly.

>>> But still you cannot claim, that all symbols mean scalars. Which
>>> interpretations was intended, that is a riddle, which the reader was
>>> requested to solve.
>>
>> Not all, only those that are not specified to mean something else.
> ???
>
> An author of a scientific paper is obliged to be specific.

That the article was accepted by the publisher proves that it was
specific enough.

> There should be no space for interpretations and questions about the
> intended meaning of a certain symbol.

There are many words in the article that are not defined in the article
but are simply assumed to be well known.

> If an author fails to distinguish between possible interpretations, the
> reader may chose, what would fit to the possible interpretations to his
> own liking, what in most cases is not, what the author wanted.

If the reader wants to apply insane interpretations that is nobody's
problem but the reader's.

> Therefore a reader can disprove a paper, simply by finding a possible
> interpretation of the text, which leads to nonsense.

Or at least his own credibility.

> In this case the text flies into the waste bin.

An a little bit more intelligent reader would never by a text that is
too difficult for his limited reading skills.

> Even if this sounds a little tough, you should bear in mind, that
> scientific papers are not toys.

You are free to use them as toys. However, it is not always a good idea
to show in a public place how you play with your toys.

>>> And that riddle is not as easy as you apparently think.
>>
>> Easy enough.
>>
>>>> You should be clear with your symbols. When discussing Einstein's text,
>>>> you should use the same conventions. Einstein's x and xi are scalars,
>>>> so for points you should use different symbols.
>>>
>>> Points had large Latin letters, like 'A' or 'B' (I guess there was
>>> also a 'C', but as far as I can recall, there was no 'D').
>>
>> Yes, that is the common style in geometry. However, upper case letters
>> were also used for other purposes. Where A and B are introduced in the
>> article they are clearly identified as points.
>
> There were eight different uses of the capital 'A' in Einstein's text.

I didn't find that many. For all I found the meaning was clearly
specified when the symbol was introduced.

> This alone would be sufficiant to dismiss the entire paper.
>
>>>> Coordinates are scalars. The xi-coordinate of "zero spot of k" is
>>>> zero because "zero spot of k" means the poit where xi = 0, eta = 0,
>>>> and zeta = 0.
>>>
>>> Not really. A component of a vector is a scalar, but 'coordinate'
>>> could be interpreted as a vector, too. That would be a scaled version
>>> of the unit vector in that direction.
>>
>> Yes really. Nobody wanted to think about any other possibility without
>> a very good reason.
>
> You should meantion, which of the possibilities above is that obvious.

Already done. See above.

> Is a coordinate a scalar or a vector?

Scalar.

>>> But also 'numerical value of the entry of the position vector of a
>>> point' would fit to the description, what is a scalar.
>>>
>>> Usually the author should tell, how he liked his variables to be
>>> interpreted. But Einstein left that more or less to the reader.
>>
>> Not just should but did. But not what the readers would consider
>> self-evident. Unless otherwise told, every symbol is scalar by
>> default.
>>
>>>>> The xsi-component of the position vector of the zero spot is called
>>>>> xsi_0, which has the numerical value zero.
>>>>
>>>> You don't need any position vectors because you already have
>>>> coordinates.
>>>
>>> A point has a location, which is represented by a position vector.
>>
>> Not in Einstein's article, where coordinates are used instead.
>
> A postition vector in three dimensional space has three components,
> called 'coordinates'.

Irrelevant, as the article under discussion does not use position vectors.

> Now is essential to define the meaning of 'coordinate'.

A general definition is not important. For this discussion is sufficent
to understand the particular coordinates that were used in the article.

> I would use a orthogonal set of three unit vectors as coordinate system
> and unitless vectors, where the entries are sclalars, that multiply
> with the cooresponding unit vectors. These scaled unit vectors are
> added to the position vector of the point.

It does not matter what you would use. The article did not use vectors
for the purpose but three orthogonal axes and orthogonal projections
to those axes; and the fourth coordinate was time.

> What Einstein wanted to use, that would be his decision. It would have
> been nice, if he had told the reader, which decisions he made.

He did whenever he chose something else than the most ordinary.

Mikko

Re: Annotated version of SRT

<6284fa3d$0$3558$426a74cc@news.free.fr>

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 by: Python - Wed, 18 May 2022 13:53 UTC

Maciej Wozniak schwrote:
> On Wednesday, 18 May 2022 at 14:55:00 UTC+2, Mikko wrote:
>
>> The relation of the two coordinate systems is specified so it is possible
>> to derive the relationship between them, and that's what Einstein is
>> going to do. The relation is found to be the Lorentz transformation.
>
> In the meantime in the real world, however, forbidden
> by your insane religion TAI and GPS keep measuring t'=t,
> just like all serious clocks always did.

And Newton's laws of motion don't hold good anymore, but it
does not matter, right dear "one of the great logician humanity
ever had" (LOL)?

Re: Annotated version of SRT

<39c25dc2-f639-4670-8061-6a3aac7bc19cn@googlegroups.com>

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Subject: Re: Annotated version of SRT
From: maluwozn...@gmail.com (Maciej Wozniak)
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 by: Maciej Wozniak - Wed, 18 May 2022 14:05 UTC

On Wednesday, 18 May 2022 at 15:53:03 UTC+2, Python wrote:
> Maciej Wozniak schwrote:
> > On Wednesday, 18 May 2022 at 14:55:00 UTC+2, Mikko wrote:
> >
> >> The relation of the two coordinate systems is specified so it is possible
> >> to derive the relationship between them, and that's what Einstein is
> >> going to do. The relation is found to be the Lorentz transformation.
> >
> > In the meantime in the real world, however, forbidden
> > by your insane religion TAI and GPS keep measuring t'=t,
> > just like all serious clocks always did.
> And Newton's laws of motion don't hold good anymore, but it
> does not matter, right dear "one of the great logician humanity
> ever had" (LOL)?

Even if it wasn't an impudent lie - how would it change
the direct measurement result of t'=t in GPS?

Re: Annotated version of SRT

<62850989$0$3574$426a74cc@news.free.fr>

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 by: Python - Wed, 18 May 2022 14:58 UTC

Maciej Wozniak schwrote:
> On Wednesday, 18 May 2022 at 15:53:03 UTC+2, Python wrote:
>> Maciej Wozniak schwrote:
>>> On Wednesday, 18 May 2022 at 14:55:00 UTC+2, Mikko wrote:
>>>
>>>> The relation of the two coordinate systems is specified so it is possible
>>>> to derive the relationship between them, and that's what Einstein is
>>>> going to do. The relation is found to be the Lorentz transformation.
>>>
>>> In the meantime in the real world, however, forbidden
>>> by your insane religion TAI and GPS keep measuring t'=t,
>>> just like all serious clocks always did.
>> And Newton's laws of motion don't hold good anymore, but it
>> does not matter, right dear "one of the great logician humanity
>> ever had" (LOL)?
>
> Even if it wasn't an impudent lie - how would it change
> the direct measurement result of t'=t in GPS?

Think, Maciej, think.

Re: Annotated version of SRT

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Subject: Re: Annotated version of SRT
From: film...@gmail.com (JanPB)
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 by: JanPB - Wed, 18 May 2022 17:02 UTC

On Sunday, May 15, 2022 at 12:53:05 PM UTC-7, I wrote:
>
> > He used partial derivatives, for what there was no
> > reason, because the other variables (y/eta and z/zeta) were not involved.
>
> They were but their values were identically zero, so Einstein
> didn't include them in the equation.

Sorry, I got carried away by the other part of the derivation. Here the answer
is that the derivatives wrt y and z are not present because in the first tau
equation the variable x' is not present in the y and z slots of tau.

That's why in order to calculate dtau/dy and dtau/dz it's necessary to set up
tau equations with the y and z variables present (that's what setting up the
mirror in the Y and Z directions does).

--
Jan

Re: Annotated version of SRT

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From: ttt_...@web.de (Thomas Heger)
Newsgroups: sci.physics.relativity
Subject: Re: Annotated version of SRT
Date: Thu, 19 May 2022 08:39:25 +0200
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 by: Thomas Heger - Thu, 19 May 2022 06:39 UTC

Am 15.05.2022 um 04:29 schrieb JanPB:
>> But apparently you know how to derive Einstein's equation. So, please
>> >let me know, how that works.
> It's written out in the paper. Given the equation (1/2)*(tau_0 + tau_2) = tau_1,
> one differentiates it wrt x' and that yields the equation constraining the
> A and D constants.

Einstein did something VERY nasty:

he reused the symbol tau for two different things.

a) One is a time measure called tau

b) another one is a function called tau.

Now he used the time measure tau from a) in the equation (1/2)*(tau_0 +
tau_2) = tau_1

But he used the function tau in the partial differential equation.

That tau is a coordinate transformation in form of a function of
four-vectors, which produces transformed four vectors.

Now we cannot equate both uses of the same symbol, because both denote
different types of mathematical objects.

But to use a measure in a differential equation would not make sense,
because tau a) means 'local time measure in system k'.

We can only differentiate functions, hence must use b) here.

The differential equation is derived from a vector equation, which is
also wrong.

There were a number of errors in the vector equation.

One simple thing is, that tau_0 is not equivalent to 't', because 't'
has no index, while tau_0 has.

Also an error is, that vectors have brackets and functions have
brackets, too. This would require a form like "...tau((x,y,z,t))..."
with double-brackets.

Another error is, that a linear function tau would allow to multiply the
factor 1/2 into the brackets and from there into the vectors.

This would require x'=0, what is wrong, because for v>0 x'is moving in
K, hence can be zero only for a certain point in time.

At a different point in time we have t=tau=0.

Now we could plug in t=0 into the vector equation and see, what we get
for that value:

1/2(tau(0,0,0,0) + tau(0,0,0, x'/(c-v) + x'/(c+v)) = tau(x',0,0,x'/(c-v))

tau is a linear coordinate transformation, hence must transform the zero
spot of k to the zero spot of K for the condition t=tau=0.

But the vector equation does not, because the point x' is not zero at
time t=tau=0. Now a linear function tau cannot produce (0,0,0,0) from
(x',0,0,x'(c-v)) for non-zero x', if also (0,0,0,0) shall transform to
(0,0,0,0), because that would require a curved function, which is not
linear.

TH

Re: Annotated version of SRT

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Subject: Re: Annotated version of SRT
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 by: Thomas Heger - Thu, 19 May 2022 06:57 UTC

Am 18.05.2022 um 14:54 schrieb Mikko:

>> So: unitless numerical values area a possible interpretation for
>> 'coordinates', which inherit their meaning from the related coordinate
>> system.
>
>> Another prossible interpretation for a coordinate x would be a vector,
>> which contains values only in the x-position, while the others contain
>> zeros.
>
> No, that is not a possible interpretation.

As I mentioned two possibilities and you certainly exclude only one, you
therefore need to say, which one you want to reject.

>> But we can be generous only once, hence must apply one interpretation
>> to all other occurances of the term 'coordinate'.
>
> Except that they may be coordinates of another coordinate system.
>
>> In any case, the term 'coordinate' can only have one meaning, hence
>> coordinates in k and K are treated on the same basis.
>
> Each coordinate has a different meaning.

The word 'coordinate' shall have only one meaning in a text.

It is absulutely inacceptable to alter the meaning of a phrase like
'coordinate' within a certain paper.

What you meant was something different, which is not called 'meaning'.

You wanted to say, that coordinates belong to a certain coordinate
system and get their 'meaning' from there.

In more scientific terms I would say, that coordinates inherit their
units from the coordinate system to which they belong.

>> From this would follow, that we in fact can do, what you have
>> rejected and derive coordinates in K from coordinates in k.
>
> The relation of the two coordinate systems is specified so it is possible
> to derive the relationship between them, and that's what Einstein is
> going to do. The relation is found to be the Lorentz transformation.

'Lorentz transformation' was only mentined once, but in a footnote on
page 8'.

The usual phrase was simply 'transformation' in this text.

Since realively slow velocities were required, to conduct the
'experiment', a simple Galileo transformation would also be a possibility.

TH

Re: Annotated version of SRT

<t64vss$kp7$1@dont-email.me>

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Subject: Re: Annotated version of SRT
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 by: Mikko - Thu, 19 May 2022 08:42 UTC

On 2022-05-19 06:57:24 +0000, Thomas Heger said:

> Am 18.05.2022 um 14:54 schrieb Mikko:
>
>>> Another prossible interpretation for a coordinate x would be a vector,
>>> which contains values only in the x-position, while the others contain
>>> zeros.
>>
>> No, that is not a possible interpretation.
>
> As I mentioned two possibilities and you certainly exclude only one,
> you therefore need to say, which one you want to reject.

Obviously the one quoted above.

>>> But we can be generous only once, hence must apply one interpretation
>>> to all other occurances of the term 'coordinate'.

More specifically, the usual one.

> What you meant was something different, which is not called 'meaning'.
>
> You wanted to say, that coordinates belong to a certain coordinate
> system and get their 'meaning' from there.

Yes. Without a coordinate system a number is not a coordinate.

> In more scientific terms I would say, that coordinates inherit their
> units from the coordinate system to which they belong.

Units are not relevant in "Zur elektrodynamik bewegter körper".

Mikko

Re: Annotated version of SRT

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 by: Python - Thu, 19 May 2022 09:03 UTC

Thomas Heger wrote:
....
> Einstein did something VERY nasty:
>
> he reused the symbol tau for two different things.
>
> a) One is a time measure called tau
>
> b) another one is a function called tau.

They are the same, the value of tau for a given event can be
expressed as a function of coordinates in the other frame.

> Now he used the time measure tau from a) in the equation (1/2)*(tau_0 +
> tau_2) = tau_1
>
> But he used the function tau in the partial differential equation.
>
> That tau is a coordinate transformation in form of a function of
> four-vectors, which produces transformed four vectors.

Nowhere in the article there is a way to interpret tau as a
a function "producing" a four coordinates vector. tau is
ONE coordinate, this is clear all along the text. You are
making up stuff.

Re: Annotated version of SRT

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Subject: Re: Annotated version of SRT
From: film...@gmail.com (JanPB)
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 by: JanPB - Thu, 19 May 2022 09:05 UTC

On Wednesday, May 18, 2022 at 11:39:30 PM UTC-7, Thomas Heger wrote:
> Am 15.05.2022 um 04:29 schrieb JanPB:
> >> But apparently you know how to derive Einstein's equation. So, please
> >> >let me know, how that works.
> > It's written out in the paper. Given the equation (1/2)*(tau_0 + tau_2) = tau_1,
> > one differentiates it wrt x' and that yields the equation constraining the
> > A and D constants.
> Einstein did something VERY nasty:
>
> he reused the symbol tau for two different things.
>
> a) One is a time measure called tau
>
> b) another one is a function called tau.

This is standard. Pick any math or physics textbook printed over last 100
years and you'll see this sort of thing all over the place.

> Now he used the time measure tau from a) in the equation (1/2)*(tau_0 +
> tau_2) = tau_1
>
> But he used the function tau in the partial differential equation.
>
> That tau is a coordinate transformation in form of a function of
> four-vectors, which produces transformed four vectors.
>
> Now we cannot equate both uses of the same symbol, because both denote
> different types of mathematical objects.

No, this is correct.

> But to use a measure in a differential equation would not make sense,
> because tau a) means 'local time measure in system k'.
>
> We can only differentiate functions, hence must use b) here.
>
> The differential equation is derived from a vector equation, which is
> also wrong.
>
> There were a number of errors in the vector equation.
>
> One simple thing is, that tau_0 is not equivalent to 't', because 't'
> has no index, while tau_0 has.

I propose that we stop this discussion.

The problem is that you are the classic case of the "fractally wrong"
phenomenon. You simply have an infinite potential for making
mistakes 100% of the time (literally).

> Also an error is, that vectors have brackets and functions have
> brackets, too. This would require a form like "...tau((x,y,z,t))..."
> with double-brackets.

The conclusion is the same as in the beginning: your annotations
are a waste of time. They have nothing to do with mathematics
or physics, they are silly fantasies.

--
Jan

Re: Annotated version of SRT

<550fc87a-5728-445e-873d-5d91a5517dd8n@googlegroups.com>

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Subject: Re: Annotated version of SRT
From: maluwozn...@gmail.com (Maciej Wozniak)
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 by: Maciej Wozniak - Thu, 19 May 2022 13:56 UTC

On Thursday, 19 May 2022 at 11:03:17 UTC+2, Python wrote:
> Thomas Heger wrote:
> ...
> > Einstein did something VERY nasty:
> >
> > he reused the symbol tau for two different things.
> >
> > a) One is a time measure called tau
> >
> > b) another one is a function called tau.
> They are the same, the value of tau for a given event can be

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: Annotated version of SRT

<46267d46-8ce4-45fd-9de7-54f2b131bc1en@googlegroups.com>

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Subject: Re: Annotated version of SRT
From: maluwozn...@gmail.com (Maciej Wozniak)
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 by: Maciej Wozniak - Thu, 19 May 2022 13:57 UTC

On Thursday, 19 May 2022 at 10:42:08 UTC+2, Mikko wrote:

> Units are not relevant in "Zur elektrodynamik bewegter körper".

When a fanatic idiot is asserting - it simply must be true.

Re: Annotated version of SRT

<1ps7mb1.1ip6lm7145by7eN%nospam@de-ster.demon.nl>

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From: nos...@de-ster.demon.nl (J. J. Lodder)
Newsgroups: sci.physics.relativity
Subject: Re: Annotated version of SRT
Date: Thu, 19 May 2022 16:17:24 +0200
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 by: J. J. Lodder - Thu, 19 May 2022 14:17 UTC

Mikko <mikko.levanto@iki.fi> wrote:

> On 2022-05-19 06:57:24 +0000, Thomas Heger said:
>
> > Am 18.05.2022 um 14:54 schrieb Mikko:
> >
> >>> Another prossible interpretation for a coordinate x would be a vector,
> >>> which contains values only in the x-position, while the others contain
> >>> zeros.
> >>
> >> No, that is not a possible interpretation.
> >
> > As I mentioned two possibilities and you certainly exclude only one,
> > you therefore need to say, which one you want to reject.
>
> Obviously the one quoted above.
>
> >>> But we can be generous only once, hence must apply one interpretation
> >>> to all other occurances of the term 'coordinate'.
>
> More specifically, the usual one.
>
> > What you meant was something different, which is not called 'meaning'.
> >
> > You wanted to say, that coordinates belong to a certain coordinate
> > system and get their 'meaning' from there.
>
> Yes. Without a coordinate system a number is not a coordinate.
>
> > In more scientific terms I would say, that coordinates inherit their
> > units from the coordinate system to which they belong.
>
> Units are not relevant in "Zur elektrodynamik bewegter körper".

A forteriori, units are never relevant for any law of physics.
If a result depends on the choice of one particular set of units
it is not a physical result.
Conversely, any physical result can be obtained
with any (consistent) system of units,

Jan

Re: Annotated version of SRT

<f2ab3ffb-572f-4e41-b214-c28d1bb5f571n@googlegroups.com>

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Subject: Re: Annotated version of SRT
From: maluwozn...@gmail.com (Maciej Wozniak)
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 by: Maciej Wozniak - Thu, 19 May 2022 14:41 UTC

On Thursday, 19 May 2022 at 16:17:27 UTC+2, J. J. Lodder wrote:
> Mikko <mikko....@iki.fi> wrote:
>
> > On 2022-05-19 06:57:24 +0000, Thomas Heger said:
> >
> > > Am 18.05.2022 um 14:54 schrieb Mikko:
> > >
> > >>> Another prossible interpretation for a coordinate x would be a vector,
> > >>> which contains values only in the x-position, while the others contain
> > >>> zeros.
> > >>
> > >> No, that is not a possible interpretation.
> > >
> > > As I mentioned two possibilities and you certainly exclude only one,
> > > you therefore need to say, which one you want to reject.
> >
> > Obviously the one quoted above.
> >
> > >>> But we can be generous only once, hence must apply one interpretation
> > >>> to all other occurances of the term 'coordinate'.
> >
> > More specifically, the usual one.
> >
> > > What you meant was something different, which is not called 'meaning'..
> > >
> > > You wanted to say, that coordinates belong to a certain coordinate
> > > system and get their 'meaning' from there.
> >
> > Yes. Without a coordinate system a number is not a coordinate.
> >
> > > In more scientific terms I would say, that coordinates inherit their
> > > units from the coordinate system to which they belong.
> >
> > Units are not relevant in "Zur elektrodynamik bewegter körper".
> A forteriori, units are never relevant for any law of physics.

Whan a fanatic idiot is asserting - it simply must be true.

> If a result depends on the choice of one particular set of units
> it is not a physical result.

Your bunch of idiotts doesn't have any physical results,
then.

Re: Annotated version of SRT

<62867478$0$22080$426a74cc@news.free.fr>

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From: pyt...@invalid (Python)
Date: Thu, 19 May 2022 18:46:35 +0200
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 by: Python - Thu, 19 May 2022 16:46 UTC

Maciej Wozniak schwrote:
> On Thursday, 19 May 2022 at 16:17:27 UTC+2, J. J. Lodder wrote:
....
>> If a result depends on the choice of one particular set of units
>> it is not a physical result.
>
> Your bunch of idiotts doesn't have any physical results,
> then.

"One of the greatest logician Humanity ever had" is not able
to understand how a formula like x = g*t^2/2 could match an
actual trajectory when expressed in meters, meters by second
by second and seconds (for x, g and t) and also when using
furlongs, furlongs by days and days. How come? Are logicians
really THAT bad?

Re: Annotated version of SRT

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Subject: Re: Annotated version of SRT
From: maluwozn...@gmail.com (Maciej Wozniak)
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 by: Maciej Wozniak - Thu, 19 May 2022 17:22 UTC

On Thursday, 19 May 2022 at 18:46:51 UTC+2, Python wrote:
> Maciej Wozniak schwrote:
> > On Thursday, 19 May 2022 at 16:17:27 UTC+2, J. J. Lodder wrote:
> ...
> >> If a result depends on the choice of one particular set of units
> >> it is not a physical result.
> >
> > Your bunch of idiotts doesn't have any physical results,
> > then.
> "One of the greatest logician Humanity ever had" is not able
> to understand how a formula like x = g*t^2/2 could match an
> actual trajectory when expressed in meters, meters by second
> by second and seconds (for x, g and t) and also when using
> furlongs, furlongs by days and days. '

Rather, relativistic idiot Python is not able to unserstand it couldn't.
No surprise from a relativistic idiot. How come? Are relativistic
idiots really THAT bad? Sure.

Re: Annotated version of SRT

<gBvhK.933555$I_K3.558383@fx14.ams4>

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From: paul.b.a...@paulba.no (Paul B. Andersen)
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 by: Paul B. Andersen - Thu, 19 May 2022 18:00 UTC

Den 19.05.2022 08:39, skrev Thomas Heger:
>
> Einstein did something VERY nasty:
>
> he reused the symbol tau for two different things.
>
> a) One is a time measure called tau
>
> b) another one is a function called tau.
>

Good grief! :-D

--
Paul

https://paulba.no/

Re: Annotated version of SRT

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From: ttt_...@web.de (Thomas Heger)
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Subject: Re: Annotated version of SRT
Date: Fri, 20 May 2022 09:17:40 +0200
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 by: Thomas Heger - Fri, 20 May 2022 07:17 UTC

Am 19.05.2022 um 11:05 schrieb JanPB:
> On Wednesday, May 18, 2022 at 11:39:30 PM UTC-7, Thomas Heger wrote:
>> Am 15.05.2022 um 04:29 schrieb JanPB:
>>>> But apparently you know how to derive Einstein's equation. So, please
>>>>> let me know, how that works.
>>> It's written out in the paper. Given the equation (1/2)*(tau_0 + tau_2) = tau_1,
>>> one differentiates it wrt x' and that yields the equation constraining the
>>> A and D constants.
>> Einstein did something VERY nasty:
>>
>> he reused the symbol tau for two different things.
>>
>> a) One is a time measure called tau
>>
>> b) another one is a function called tau.
>
> This is standard. Pick any math or physics textbook printed over last 100
> years and you'll see this sort of thing all over the place.

Well, no.
Bad habbits are still bad, even if they are common practice.

Here we have two different mathematical objects, which cannot be equated.

At least a discussion would be necessary, why the author thought, that a
time measure and a coordinate transformation should be equal.

>> Now he used the time measure tau from a) in the equation (1/2)*(tau_0 +
>> tau_2) = tau_1
>>
>> But he used the function tau in the partial differential equation.
>>
>> That tau is a coordinate transformation in form of a function of
>> four-vectors, which produces transformed four vectors.
>>
>> Now we cannot equate both uses of the same symbol, because both denote
>> different types of mathematical objects.
>
> No, this is correct.

No. 'Equal' means 'one thing may replace the other entirely'.

But a function is not the same thing as a measure in physics.

>> But to use a measure in a differential equation would not make sense,
>> because tau a) means 'local time measure in system k'.
>>
>> We can only differentiate functions, hence must use b) here.
>>
>> The differential equation is derived from a vector equation, which is
>> also wrong.
>>
>> There were a number of errors in the vector equation.
>>
>> One simple thing is, that tau_0 is not equivalent to 't', because 't'
>> has no index, while tau_0 has.
>
> I propose that we stop this discussion.
>
> The problem is that you are the classic case of the "fractally wrong"
> phenomenon. You simply have an infinite potential for making
> mistakes 100% of the time (literally).

Well, everybody can make mistakes.

I actually like mistakes, but like to correct these mistakes.

That's why I write my texts in several versions. The first versions
usually contain a lot of errors, which I iron out over time.

That allows to produce shiny marbles, which contain no errors (at least
not many).

And my current version of 'Annotated version of SRT' is not the final
step, as I have found out.

The method to find those errors are actually such discussions like this
one with you (to maintain I'm very thankful to you).

>> Also an error is, that vectors have brackets and functions have
>> brackets, too. This would require a form like "...tau((x,y,z,t))..."
>> with double-brackets.
>
> The conclusion is the same as in the beginning: your annotations
> are a waste of time. They have nothing to do with mathematics
> or physics, they are silly fantasies.

No.

My annotations are getting gradually better, while Einstein's text
remains crap forever.

TH

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