A question that can be asked is that of the difference between the real
time Tr and the proper time Tp.

Is it the same thing?

If we study the reference frames in uniform relativistic motions, it
immediately appears that it is the same thing.

The real time taken by a twin to reach a solar system at 0.8c located at
12 ly, is 9 years.

Tr=9 years.

But it is also its own time.

Tp=9 years.

The observable time is To=15 years.

And the apparent time is Tapp=27 years.

All this is very simple and is no longer to be discussed.

But what about in accelerated repositories?

Can we say, in this frames, that Tp=Tr?

R.H.

Richard "Hachel" Lengrand (M.D.) wrote:
....
> But what about in accelerated repositories?

Why do you persist in using incorrect translations, improper
terms like "repository", when you've been advised they are
wrong and the correct one has been provided to you?

Richard Hachel wrote:

> A question that can be asked is that of the difference between the real
> time Tr and the proper time Tp.
>
> Is it the same thing?

“Real time” is another concept and term that you invented out of ignorance,
so only you can know.

PointedEars
--
Q: What did the female magnet say to the male magnet?
A: From the back, I found you repulsive, but from the front
I find myself very attracted to you.
(from: WolframAlpha)

Le 14/02/2022 à 14:05, Richard Hachel a écrit :

> Can we say, in this frames, that Tp=Tr?
> R.H.

If we consider that an instantaneous speed corresponds to an infinitesimal
strip of space traversed by the rocket at a given instant, it comes that
we can consider that, on this strip, the acceleration being negligible, we
can admit that the 'we are in the case of a relation
To=Tr.sqrt(1+Vr²/c²)
And therefore dTo=dTr.sqrt(1+Vr²/c²) inside this band.
In short, this means that I have the right to consider that Tr=Tp during
this brief instant.
And that we can consider that the long evolution of the rocket in an
accelerated medium is only a coherent sequence of small quantities of
uniform speeds where, always, Tp=Tr.

I therefore do not dissociate Tr from Tp in accelerated repositories.

Contrary to what relativist scientists seem to do.

On the other hand, they seem to confuse something else, that is to say Vr
and Vr+dVr
and simplify Vr+dVr by Vr in the equations.

But are we right to do this?

Is it the same thing?

Aren't we confusing what you can do with a turnip with what you can do
with a carrot?

I explain:
Yes, I can consider that Tr=Tp, that is to say replace the real time by
the proper time in the equations, since we can consider that the rocket
evolves not in an accelerated way friends according to an infinity of
constant speeds always infinitesimally greater than the previous speed.
BUT I say nothing more about these speeds between them. And I affirm that
these are not the same speeds.
I will therefore not go further than setting Tp=Tr=To/sqrt(1+Vr²/c²).

I absolutely do not set Vr+dVr=Vr and I do not simplify
To=Tr.sqrt(1+(Vr+dVr)²/c)² to
To=Tr.sqrt(1+Vr²/c²)

Do you understand the difference?

Please have two or three cups of coffee before replying to this post.

In short, I do (as usual), just the opposite of what they do.

Am I wrong?

Am I a bad terrorist?

A thug, a bandit?

Simply because I want to clearly understand what I'm doing when I make a
relativistic description.

R.H.

Le 14/02/2022 à 14:29, Thomas 'PointedEars' Lahn a écrit :
> Richard Hachel wrote:
>
>> A question that can be asked is that of the difference between the real
>> time Tr and the proper time Tp.
>>
>> Is it the same thing?
>
> “Real time” is another concept and term that you invented out of ignorance,
> so only you can know.
>
>
> PointedEars

Please try to understand my question before answering.
If you don't understand my question, don't answer it.
The question I am asking here is not simple, and is not, I admit, easily
understandable for an average mind, or even a consistent IQ.
It is impossible to answer what I have just said without at least giving
it some thought.

R.H.

Richard "Hachel" Lengrand (M.D.) wrote:
....
> Simply because I want to clearly understand what I'm doing when I make a
> relativistic description.

A good start would be to take time to follow a course on Relativity.

This course is quite a good one:

Relativité restreinte, 2022 : séance 1
https://www.youtube.com/watch?v=UUdRIbidJRM

Relativité restreinte, 2022 : séance 2
https://www.youtube.com/watch?v=d7KTzM2i7oU

Relativité restreinte, 2022 : séance 3
https://www.youtube.com/watch?v=f4B-pu24-6g

The same teacher is providing more details about the time coordinate
in reference frames in a less technical course at 10:30 there:

Physique pour non spécialistes : séance 3
https://www.youtube.com/watch?v=vSN7mJ6Wo5M

Richard Hachel <r.hachel@tiscali.fr> wrote:
> A question that can be asked is that of the difference between the real
> time Tr and the proper time Tp.

“Real time” doesn’t mean anything. Do you know what “proper time” means?
Need a book recommendation?

>
> Is it the same thing?
>
> If we study the reference frames in uniform relativistic motions, it
> immediately appears that it is the same thing.
>
> The real time taken by a twin to reach a solar system at 0.8c located at
> 12 ly, is 9 years.
>
> Tr=9 years.
>
> But it is also its own time.
>
> Tp=9 years.
>
> The observable time is To=15 years.
>
> And the apparent time is Tapp=27 years.
>
> All this is very simple and is no longer to be discussed.
>
> But what about in accelerated repositories?
>
> Can we say, in this frames, that Tp=Tr?
>
> R.H.
>

--
Odd Bodkin -- maker of fine toys, tools, tables

Richard Hachel <r.hachel@tiscali.fr> wrote:
> Le 14/02/2022 à 14:29, Thomas 'PointedEars' Lahn a écrit :
>> Richard Hachel wrote:
>>
>>> A question that can be asked is that of the difference between the real
>>> time Tr and the proper time Tp.
>>>
>>> Is it the same thing?
>>
>> “Real time” is another concept and term that you invented out of ignorance,
>> so only you can know.
>>
>>
>> PointedEars
>
> Please try to understand my question before answering.
> If you don't understand my question, don't answer it.

No sir. If you spout nonsense, you’re going to get called on it.

You have not earned the right to speak whatever you wish and to have people
pay attention to it, other than to note that you are spouting nonsense.

> The question I am asking here is not simple, and is not, I admit, easily
> understandable for an average mind, or even a consistent IQ.
> It is impossible to answer what I have just said without at least giving
> it some thought.
>
> R.H.
>

--
Odd Bodkin -- maker of fine toys, tools, tables

Richard Hachel wrote:

> If we consider that an instantaneous speed corresponds to an infinitesimal
> strip of space traversed by the rocket at a given instant, it comes that
> we can consider that, on this strip, the acceleration being negligible, we
> can admit that the 'we are in the case of a relation
> To=Tr.sqrt(1+Vr²/c²)

But we are not. And this can be easily shown.
If two events e₁ = (t₁, x₁, y₁, z₁) and e₂ = (t₂, x₂, y₂, z₂) are connected
by a light signal, then there are two ways by which the spatial distance
between them can be calculated.

One is the Euclidean distance given by the square root of the sum of the
squared differences between their spatial Cartesian coordinates (actually
just the multiple application of the Pythagorean theorem):

Δs = √((x₂ − x₁)² + (y₂ − y₁)² + (z₂ − z₁)²) =: √((Δx)² + (Δy)² + (Δz)²).

The other is by the time that light requires to travel the distance:

c = Δs/(t₂ − t₁) =: Δs/Δt.

⇔ Δs = c Δt.

As these distances are equal, we have

c Δt = √((Δx)² + (Δy)² + (Δz)²)

or (to get rid of the square root)

c² (Δt)² = (Δx)² + (Δy)² + (Δz)².

[From here on I will omit the parentheses around the squared quantity,
as is customary.]

⇔ 0 = Δx² + Δy² + Δz² − c² Δt²
⇔ 0 = −Δx² − Δy² − Δz² + c² Δt²
⇔ 0 = c² Δt² − Δx² − Δy² − Δz².

If the two events are not identical, then Δt ≠ 0 and we may divide by Δt²,
so we can extract it without an accident:

0 = Δt² [c² − Δx²/Δt² − Δy²/Δt² − Δt²/Δz²]
⇔ 0 = Δt² [c² − (Δx²/Δt² + Δy²/Δt² + Δz²/Δt²)].

The sum there is nothing else but the square of the velocity, which (as
velocity is a vector) is equal to the square of the norm (or magnitude) of
velocity v⃗ = (v_x, v_y, v_z), the speed v:

⇔ 0 = Δt² [c² − ([Δx/Δt]² + [Δy/Δt]² + [Δz/Δt]²)]
= Δt² [c² − (v_x² + v_y² + v_z²)]
= Δt² (c² − v²).

We may further extract c² (≠ 0), divide by it, and take the square root:

0 = Δt² c² (1 − v²/c²)
⇔ 0 = Δt (1 − v²/c²)
⇔ 0 = Δt √(1 − v²/c²).

Now if Δx, Δy and Δz are not all equal to 0 (length units), then Δt is the
time that elapsed in a reference frame in which we said that whatever
connected the events was in motion. If we say that it was not in motion,
i.e. Δx = Δy = Δz = 0 (length units), i.e. in the rest frame of the "moving"
object, the elapsed time *then* is not necessarily the same (in fact, we
will find that is not ever the same).

We call it the *elapsed _proper_ time* because it is measured by a clock at
rest in that frame, and introduce for it the symbol Δτ:

0 = c² Δτ².

If we divide by c² and take the square root again, then we have two
quantities which are both equal to 0; so they are equal to each other, and
we can write

Δτ = Δt √(1 − v²/c²). (1)

[And NOT “To=Tr.sqrt(1+Vr²/c²)”. The sign in your formula is WRONG.]

[In passing, we note that if a clock traveling with a light signal would
measure that no time at all would have elapsed. Sometimes this is
worded in popular-scientific sources as “photons/light do(es) not
experience time”.]

It is useful to define the *Lorentz factor* (named so because it appears in
the *Lorentz transformation* which is named after Hendrik Antoon Lorentz who
first proposed it)

γ ≔ 1/√(1 − v²/c²), (2)

and we can write eq. (1) as

Δτ = Δt/γ.

From eq. (2) we can see that if v ≠ 0, then γ > 1.

From this we can then see that the elapsed proper time Δτ and the elapsed
*coordinate time* Δt are usually not equal: If v ≠ 0, then the elapsed
proper time – the time measured to have elapsed by a clock in relative
motion – is shorter than the elapsed coordinate time – the time an observer
who considers that clock to be in motion measures according to clocks at
rest relative to them:

Δτ < Δt.

But the (Galilean) principle of relativity says that every observer can
consider themselves to be at rest, and clocks that are not moving relative
to them to be at rest. So this *time dilation* effect has to be and
actually is symmetric: An observer that is considered to be moving by the
first observer will say the same about the clocks (and the time) of the
first observer when they compare it with their own clock (and own time).

The German term for “proper time”, which I think was coined first, is
actually „Eigenzeit“ which literally translates to “own time” (cf. terms
like “eigenvector”, “eigenvalue”, and “eigenfunction” which made it from
German mathematics to English-speaking mathematics literally instead).

In a (Minkowski/spacetime) diagram the connection of two events by a light
signal can be illustrated as follows:

c t
^
: Δx = c Δt
t₂ + .----------. e₂
: : .'
: : .'
: Δt : .' Δτ = Δs = 0 (here)
: : .'
: :.'
t₁ + e₁ '
:
'-----+----------+-------> x
x₁ x₂

Note that there *seems* to be a contradiction here: Δτ seems to be longer,
not shorter, than Δt, and that it should be given by √(Δx² + Δt²), and it
certainly does not look like 0 for light. But we have seen that this is NOT
so.

The reason is that spatial dimensions and temporal dimensions must be
treated *differently*: it is a *pseudo*-Euclidean metric that must be used
to determine Δτ, namely Δs² = c² Δτ² = c² Δt² − Δx² (assuming that Δy = Δz
= 0).

If the two events are not connected by a light signal, but e.g. by a
material object (v < c), then the (timelike) *worldline* that does is
steeper (as less distance is traveled in the same coordinate time):

c t
^ c Δt
: ,-----'----. v = c
: Δx .'
t₂ + .-----. e₂ .'
: : : .'
: : Δτ: .'
: Δt : : .'
: : :.'
: ::
t₁ + e₁ '
:
'-----+-----+-----------> x
x₁ x₂

We can see that with this sign convention for this *timelike* worldline we
have Δs² > 0. Whereas for events that are not causally connected (if the
speed of light in vacuum is the maximum speed), the *spacetime interval* is
*spacelike*, Δs² < 0.

See also: <https://en.wikipedia.org/wiki/Proper_time>

> Am I wrong?

Yes.

PointedEars
--
Q: What did the nuclear physicist post on the laboratory door
when he went camping?
A: 'Gone fission'.
(from: WolframAlpha)

Richard Hachel wrote:

> Le 14/02/2022 à 14:29, Thomas 'PointedEars' Lahn a écrit :
>> Richard Hachel wrote:
>>> A question that can be asked is that of the difference between the real
>>> time Tr and the proper time Tp.
>>>
>>> Is it the same thing?
>>
>> “Real time” is another concept and term that you invented out of
>> ignorance, so only you can know.
>
> Please try to understand my question before answering.

I can understand that you are suffering from the delusion that what you
are saying would make sense and could be understood, but that is not so.

PointedEars
--
Q: What did the female magnet say to the male magnet?
A: From the back, I found you repulsive, but from the front
I find myself very attracted to you.
(from: WolframAlpha)

Den 14.02.2022 14:34, skrev Richard Hachel:
>
> If we consider that an instantaneous speed corresponds to an
> infinitesimal strip of space traversed by the rocket at a given instant,
> it comes that we can consider that, on this strip, the acceleration
> being negligible, we can admit that the 'we are in the case of a
> relation To=Tr.sqrt(1+Vr²/c²)
> And therefore dTo=dTr.sqrt(1+Vr²/c²) inside this band.

!!!!

> In short, this means that I have the right to consider that Tr=Tp during
> this brief instant.
> And that we can consider that the long evolution of the rocket in an
> accelerated medium is only a coherent sequence of small quantities of
> uniform speeds where, always, Tp=Tr.
>
> I therefore do not dissociate Tr from Tp in accelerated repositories.
>
> Contrary to what relativist scientists seem to do.
>
> On the other hand, they seem to confuse something else, that is to say
> Vr and Vr+dVr
> and simplify Vr+dVr by Vr in the equations.

!!!!

>
> But are we right to do this?
>
> Is it the same thing?
>
> Aren't we confusing what you can do with a turnip with what you can do
> with a carrot?
>
> I explain:
> Yes, I can consider that Tr=Tp, that is to say replace the real time by
> the proper time in the equations, since we can consider that the rocket
> evolves not in an accelerated way friends according to an infinity of
> constant speeds always infinitesimally greater than the previous speed.
> BUT I say nothing more about these speeds between them. And I affirm
> that these are not the same speeds.
> I will therefore not go further than setting Tp=Tr=To/sqrt(1+Vr²/c²).

Your problem is simple.
You are ignorant of calculus.

See 2.3. in the following article.
It shows how you can handle accelerated motion.
https://paulba.no/pdf/TwinsByMetric.pdf

But you will never learn, of course.

--
Paul

https://paulba.no/

Le 14/02/2022 à 20:18, "Paul B. Andersen" a écrit :

> Your problem is simple.
> You are ignorant of calculus.

No, no, I don't think that's the problem.

The problem is simply that I've always liked figuring things out for
myself, and not just repeating them.

I was born like this. With what Descartes called "methodical doubt".

Take the case of the newspaper. Have you ever read a newspaper? It is
April 15, 1912 in the morning, and you read in the newspaper: "The liner
Titanic sank last night after hitting an iceberg".
What are you doing, Paul?
You swallow it.
I have this superiority over the average man that I don't swallow it.
That's all.

And I'm the one who's right, not seven thousand other humans who
mindlessly swallow all the bullshit they're told.

The theory of relativity, yes.

Of course I admit it and defend it.

But not just any and not said anyhow.

R.H.

On 2/15/2022 3:12 PM, Richard Hachel wrote:

> I have this superiority over the average man that I don't swallow it.
> That's all.
>
> And I'm the one who's right, not seven thousand other humans who
> mindlessly swallow all the bullshit they're told.
>
>
Now where was that recent post discussing NPD/megalomania and how it's
possibly due to bipolar or schizophrenia?

Den 15.02.2022 21:12, skrev Richard Hachel:
> Le 14/02/2022 à 20:18, "Paul B. Andersen" a écrit :
>
>> Your problem is simple.
>> You are ignorant of calculus.
>
> No, no, I don't think that's the problem.
>
> The problem is simply that I've always liked figuring things out for
> myself, and not just repeating them.

Your way of figuring calculus out for yourself
isn't very successful.

>
> I was born like this. With what Descartes called "methodical doubt".
>
> Take the case of the newspaper. Have you ever read a newspaper?

Not to learn calculus.

> And I'm the one who's right, not seven thousand other humans who
> mindlessly swallow all the bullshit they're told.

I see. Mathematicians and physicists are idiots
since they 'swallow' calculus.

BTW, the number of humans who master calculus is very
much higher than seven thousand.

I understand that you will never be among them,
because you know you are right when calling it bullshit.

--
Paul

https://paulba.no/

On Wednesday, 16 February 2022 at 09:44:04 UTC+1, Paul B. Andersen wrote:
> Den 15.02.2022 21:12, skrev Richard Hachel:
> > Le 14/02/2022 à 20:18, "Paul B. Andersen" a écrit :
> >
> >> Your problem is simple.
> >> You are ignorant of calculus.
> >
> > No, no, I don't think that's the problem.
> >
> > The problem is simply that I've always liked figuring things out for
> > myself, and not just repeating them.
> Your way of figuring calculus out for yourself
> isn't very successful.
> >
> > I was born like this. With what Descartes called "methodical doubt".
> >
> > Take the case of the newspaper. Have you ever read a newspaper?
> Not to learn calculus.
> > And I'm the one who's right, not seven thousand other humans who
> > mindlessly swallow all the bullshit they're told.
> I see. Mathematicians and physicists are idiots
> since they 'swallow' calculus.

Stop fucking, stinker. When your idiot guru told you
that 2000 years old math is false - you simply swallowed
it. Your invoking the basic math authority is only funny
now.

Le 16/02/2022 à 09:44, "Paul B. Andersen" a écrit :

> I see. Mathematicians and physicists are idiots

No, I'm not saying that.
I think human intelligence is relatively decent in general.
I don't think the problem of mathematicians or physicists is really a
problem of intelligence.
I think it's more of a man's problem.
When Poincaré states the theory of relativity, we manage to give the
Nobel to Einstein (the guy who copied the patents in Bern). When Diesel
goes to England to discuss his engine patent, we find his body floating in
the English Channel. Etc...
I don't think it's an intelligence issue at all.
Physicists and mathematicians are men. That's mostly their problem.

R.H.

On 2/16/2022 6:01 AM, Richard Hachel wrote:
> Le 16/02/2022 à 09:44, "Paul B. Andersen" a écrit :
>
>>>> You are ignorant of calculus.

>>> And I'm the one who's right, not seven thousand other humans who mindlessly swallow all the bullshit they're told.

>> I see. Mathematicians and physicists are idiots
>
> No, I'm not saying that.

Yet you stated that those who "swallow" the "bullshit" of calculus are
idiots. Please clarify.

> When Poincaré states the theory of relativity, we manage to give the
> Nobel to Einstein (the guy who copied the patents in Bern).

Einstein never received any Nobel for relativity.

Le 17/02/2022 à 02:12, Michael Moroney a écrit :

> Einstein never received any Nobel for relativity.

C'est ce que je dis.

Quand on a voulu donner le prix Nobel pour la théorie de la relativité
restreinte à Einstein, et pas à Poincaré, le véritable père de toute
la théorie, théorie qu'Einstein de son bureau des brevets de Berne avait
recopié point par point, les français, écoeurés se sont levés et ont
quitté la salle.

Ils sont alors revenus sur leur décision, mais ont tout de même donné
le prix Nobel à Einstein pour un papier ridicule traitant de l'effet
photo-électrique.

Déjà à cette époque, les prix Nobel ça puait la rage.

Obama et Arafat n'avait pas encore celui de la paix, mais...

C'est un métier, la politique.

R.H.

On 2/16/2022 8:48 PM, Richard Hachel wrote:
> Le 17/02/2022 à 02:12, Michael Moroney a écrit :
>
>> Einstein never received any Nobel for relativity.
>
> C'est ce que je dis.
>
> Quand on a voulu donner le prix Nobel pour la théorie de la relativité
> restreinte à Einstein, et pas à Poincaré, le véritable père de toute la
> théorie, théorie qu'Einstein de son bureau des brevets de Berne avait
> recopié point par point, les français, écoeurés se sont levés et ont
> quitté la salle.
>
> Ils sont alors revenus sur leur décision, mais ont tout de même donné le
> prix Nobel à Einstein pour un papier ridicule traitant de l'effet
> photo-électrique.
>
> Déjà à cette époque, les prix Nobel ça puait la rage.
>
> Obama et Arafat n'avait pas encore celui de la paix, mais...
>
> C'est un métier, la politique.
>

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod
tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim
veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea
commodo consequat. Duis aute irure dolor in reprehenderit in voluptate
velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint
occaecat cupidatat non proident, sunt in culpa qui officia deserunt
mollit anim id est laborum.

Richard "Hachel" Lengrand (M.D.) wrote:
> Le 17/02/2022 à 02:12, Michael Moroney a écrit :
>
>> Einstein never received any Nobel for relativity.
>
> C'est ce que je dis.
>
> Quand on a voulu donner le prix Nobel pour la théorie de la relativité
> restreinte à Einstein, et pas à Poincaré, le véritable père de toute la
> théorie, théorie qu'Einstein de son bureau des brevets de Berne avait
> recopié point par point, les français, écoeurés se sont levés et ont
> quitté la salle.
>
> Ils sont alors revenus sur leur décision, mais ont tout de même donné le
> prix Nobel à Einstein pour un papier ridicule traitant de l'effet
> photo-électrique.
>
> Déjà à cette époque, les prix Nobel ça puait la rage.
>
> Obama et Arafat n'avait pas encore celui de la paix, mais...
>
> C'est un métier, la politique.

For those not fluent in French, what Hachel/Lengrand is claiming here
is that while the Nobel Committee was about to attribute to Albert
Einstein a prize in physics for Special Relativity the whole team
of French representation (whatever it means) left the room in anger
because Einstein did plagiarize Poincaré's work.

This is outrageously FALSE. There is absolutely nothing Hachel/Lengrand
can present as an evidence for this.

The main reason everyone ignores Lengrand's posts on fr.sci.physique
these days is because he has the habit to make up idiotic stuff of
this kind. After 20+ years of this despicable behaviour, people gave
up on considering this disgusting person, except as laughing stock.

Then this kook claims that Einstein papers on photo-electric effect
is "ridiculous". Quite a pathetic claim from a charlatan who fails
not only on understanding SR (or any kind of physics btw), but also
complex numbers or calculus.

Python <python@example.invalid> wrote:
> Richard "Hachel" Lengrand (M.D.) wrote:
>> Le 17/02/2022 à 02:12, Michael Moroney a écrit :
>>
>>> Einstein never received any Nobel for relativity.
>>
>> C'est ce que je dis.
>>
>> Quand on a voulu donner le prix Nobel pour la théorie de la relativité
>> restreinte à Einstein, et pas à Poincaré, le véritable père de toute la
>> théorie, théorie qu'Einstein de son bureau des brevets de Berne avait
>> recopié point par point, les français, écoeurés se sont levés et ont
>> quitté la salle.
>>
>> Ils sont alors revenus sur leur décision, mais ont tout de même donné le
>> prix Nobel à Einstein pour un papier ridicule traitant de l'effet
>> photo-électrique.
>>
>> Déjà à cette époque, les prix Nobel ça puait la rage.
>>
>> Obama et Arafat n'avait pas encore celui de la paix, mais...
>>
>> C'est un métier, la politique.
>
> For those not fluent in French, what Hachel/Lengrand is claiming here
> is that while the Nobel Committee was about to attribute to Albert
> Einstein a prize in physics for Special Relativity the whole team
> of French representation (whatever it means) left the room in anger
> because Einstein did plagiarize Poincaré's work.

Yeah, I read that and laughed.

People like Richard have difficulties separating reality from fantasies.

He declines to get help for his mental state, and insists that he’s not the
one with the problem. There’s only so much others can do.

>
> This is outrageously FALSE. There is absolutely nothing Hachel/Lengrand
> can present as an evidence for this.
>
> The main reason everyone ignores Lengrand's posts on fr.sci.physique
> these days is because he has the habit to make up idiotic stuff of
> this kind. After 20+ years of this despicable behaviour, people gave
> up on considering this disgusting person, except as laughing stock.
>
> Then this kook claims that Einstein papers on photo-electric effect
> is "ridiculous". Quite a pathetic claim from a charlatan who fails
> not only on understanding SR (or any kind of physics btw), but also
> complex numbers or calculus.
>
>

--
Odd Bodkin -- maker of fine toys, tools, tables

Thomas 'PointedEars' Lahn wrote:

> If two events e₁ = (t₁, x₁, y₁, z₁) and e₂ = (t₂, x₂, y₂, z₂) are
> connected by a light signal, then there are two ways by which the spatial
> distance between them can be calculated.
>
> One is the Euclidean distance given by the square root of the sum of the
> squared differences between their spatial Cartesian coordinates (actually
> just the multiple application of the Pythagorean theorem):
>
> Δs = √((x₂ − x₁)² + (y₂ − y₁)² + (z₂ − z₁)²) =: √((Δx)² + (Δy)² +
> (Δz)²).

For those for whom this is not obvious (IIRC, it wasn’t to me just a few
years ago, before I studied Physics/Mathematics): Consider that the distance
between two points in 3D space Euclidean space, Δs, is given by the
Pythagorean theorem (or: the Theorem of Pythagoras)

(Δs)² = (Δs')² + (Δz)²,

where Δs' is the length of the orthogonal projection of Δs (or rather the
vector of which Δs is the norm/length) onto the (parallel to the) x–y plane,
itself given by the Pythagorean theorem:

(Δs')² = (Δx)² + (Δy)²,

so

(Δs)² = (Δs')² + (Δz)² = (Δx)² + (Δy)² + (Δz)². ∎

z
^
: .
: .':
: .' :
: .' :
: .' :
: .' :
: .' :
: Δs .' : Δz
: .' :
: .' :
: .' :
: .' .--:
: .' Δs' :__:
: .' ___...---''_.-'
: .'___...---''' _.-' Δy
---_+'''------------------'-----------> x
.-' : Δx __
y : |PE

This means that the Pythagorean theorem can be generalized to higher
dimensions, i.e. n-dimensional Euclidean spaces (where coordinates are
measured parallel to straight coordinate axes that are all perpendicular to
each other), and one can define the *Euclidean norm* (or 2-norm) of a vector
v⃗ = (v₁, v₂, …, vₙ):

‖v⃗‖₂ ≔ √[∑_i (v_i)²].

See also:
<https://www.britannica.com/topic/Albert-Einstein-on-Space-Time-1987141>

8-)

PointedEars
--
Q: What did the nuclear physicist order for lunch?
A: Fission chips.

(from: WolframAlpha)