From Newsgroup: sci.physics.relativity

An internet user called me a moron when I said that the concept of relativistic mass was superfluous, and that what was relative in cosmology
was space and timerConot matter.
A hippopotamus doesn't turn into two hippopotamuses just because you
change your frame of reference.
That userrCowho is virulently anti-HachelrCokept telling me the concept
didn't exist, or didn't exist anymore; soon enough, he'll be telling me it never existed at all.
Yeah, right.
And yet, IrCOm reading some brand-new PDFs today that talk all about "relativistic mass" and m=mreC/sqrt(1-Vo-#/c-#).
In short, people still buy into it.
Damn, if IrCOm rightrCoand if we really need to prune away a heap of
useless, difficult, and contradictory conceptsrCothat pruning is going to
be brutal.
I had intended to point out a few contradictions, but IrCOm realizing that
the whole edificerCowith its misunderstandings, its idiotic paradoxes, and
its bogus prescriptionsrConeeds to be completely demolished.

R.H.
--- Synchronet 3.22a-Linux NewsLink 1.2

From Newsgroup: sci.physics.relativity

Le 19/09/2026 |a 14:40, Richard Hachel a |-crit :

An internet user called me a moron when I said that the concept of relativistic
mass was superfluous, and that what was relative in cosmology was space and timerConot matter.
A hippopotamus doesn't turn into two hippopotamuses just because you change your
frame of reference.
That userrCowho is virulently anti-HachelrCokept telling me the concept didn't
exist, or didn't exist anymore; soon enough, he'll be telling me it never existed
at all.
Yeah, right.
And yet, IrCOm reading some brand-new PDFs today that talk all about "relativistic mass" and m=mreC/sqrt(1-Vo-#/c-#).
In short, people still buy into it.
Damn, if IrCOm rightrCoand if we really need to prune away a heap of useless,
difficult, and contradictory conceptsrCothat pruning is going to be brutal.
I had intended to point out a few contradictions, but IrCOm realizing that the
whole edificerCowith its misunderstandings, its idiotic paradoxes, and its bogus
prescriptionsrConeeds to be completely demolished.

R.H.

There are three different claims here, and you keep sliding from
one to another.

1. DID "RELATIVISTIC MASS" EXIST?

Yes.

Of course it did.

The notation

m_rel = gamma*m0
= m0/sqrt(1-v^2/c^2)

was widely used historically and can still be found in books,
papers and teaching material.

Anyone claiming that the concept "never existed" would simply be
wrong.


2. IS IT NECESSARY?

No.

Modern relativistic mechanics normally keeps mass invariant:

m = invariant mass

and writes

p = gamma*m*v

E = gamma*m*c^2

with

E^2 = p^2*c^2 + m^2*c^4.

Nothing requires us to say that the object itself has acquired
more "mass".

So your hippopotamus may relax.

At 0.8c it remains one hippopotamus, not 1.6667 hippopotamuses.

Its invariant mass remains the same.


3. DID HACHEL DISCOVER THAT RELATIVISTIC MASS IS UNNECESSARY?

No.

And this is the important historical point.

The abandonment of velocity-dependent "relativistic mass" in
favour of invariant mass is not a Hachelian correction to
relativity.

It is a standard way of FORMULATING relativity.

So finding a new PDF which uses

m = m0/sqrt(1-v^2/c^2)

does not establish that modern physics requires relativistic mass.

It establishes that you found an author using that convention.

Both notations can describe the same physics.

For example, your

p = m*Vr

with

Vr = gamma*v

gives

p = gamma*m*v,

which is precisely the standard relativistic momentum when m is
the invariant mass.

So there is nothing here requiring the demolition of SR.


And this illustrates a more general problem with your recent
conclusions.

There is a very large logical distance between:

"I dislike this formulation"

and

"this formulation is unnecessary"

and

"this formulation is mathematically contradictory"

and

"experiments show that the underlying theory is wrong."

Those are four different statements.

Relativistic mass is a nice example:

historically used? YES
still occasionally used? YES
necessary? NO
preferred modern formulation? generally NO
contradiction in SR? NO
discovery requiring RH? NO

So prune "relativistic mass" from your booklet if you like.

A great many relativity textbooks have already done the gardening.

No demolition crew required.
--- Synchronet 3.22a-Linux NewsLink 1.2

From Newsgroup: sci.physics.relativity

Richard Hachel wrote:

lled me a moron when I said that the concept of relativistic mass was superfluous, and that what was relative in cosmology was space and
timerConot matter.

well, your matter lives in space and time, idiot, aka the its amplitude probabilistic distribution has to adapt during the relativistic effects. Idiot. It looks like the relativistic effects are more fundamental than
space and time, which are only a configuration.
--- Synchronet 3.22a-Linux NewsLink 1.2

From Newsgroup: sci.physics.relativity

Le 19/09/2026 |a 17:28, Cletus Mikhailetibus Succius Omnibus a |-crit :

Richard Hachel wrote:

lled me a moron when I said that the concept of relativistic mass was
superfluous, and that what was relative in cosmology was space and
timerConot matter.

well, your matter lives in space and time, idiot, aka the its amplitude probabilistic distribution has to adapt during the relativistic effects. Idiot. It looks like the relativistic effects are more fundamental than space and time, which are only a configuration.

Tais toi donc, h|-, bouffon.

Guignol.

Mais c'est pas vrai, merde!

R.H.
--- Synchronet 3.22a-Linux NewsLink 1.2

From Newsgroup: sci.physics.relativity

On Sat, 19 Sep 26 12:40:35 +0000, Richard Hachel wrote:

An internet user called me a moron when I said that the concept of relativistic mass was superfluous, and that what was relative in
cosmology was space and timerConot matter.
A hippopotamus doesn't turn into two hippopotamuses just because you
change your frame of reference.
That userrCowho is virulently anti-HachelrCokept telling me the concept didn't exist, or didn't exist anymore; soon enough, he'll be telling me
it never existed at all.
Yeah, right.
And yet, IrCOm reading some brand-new PDFs today that talk all about "relativistic mass" and m=mreC/sqrt(1-Vo-#/c-#).
In short, people still buy into it.
Damn, if IrCOm rightrCoand if we really need to prune away a heap of
useless, difficult, and contradictory conceptsrCothat pruning is going to
be brutal.
I had intended to point out a few contradictions, but IrCOm realizing that the whole edificerCowith its misunderstandings, its idiotic paradoxes, and its bogus prescriptionsrConeeds to be completely demolished.

Dead right...Sr is the greatest scam since jesus christ.

R.H.

--- Synchronet 3.22a-Linux NewsLink 1.2

From Newsgroup: sci.physics.relativity

Richard Hachel <r.hachel@tiscali.fr> wrote:

An internet user called me a moron when I said that the concept of relativistic mass was superfluous, and that what was relative in cosmology was space and timerConot matter.
A hippopotamus doesn't turn into two hippopotamuses just because you
change your frame of reference.
That userrCowho is virulently anti-HachelrCokept telling me the concept didn't exist, or didn't exist anymore; soon enough, he'll be telling me it never existed at all.

The existence of even dumber morons
is never a good argument for not being one.

Yeah, right.
And yet, I'm reading some brand-new PDFs today that talk all about "relativistic mass" and m=m?/sqrt(1-Vo?/c?).
In short, people still buy into it.

Of course, but nowadays people generally prefer to call it:
the time-component of the Energy-Momentum 4-vector.
Impressionable students are nowadays told from the start
that it is always a very bad idea
to confuse scalars and components of vectors.

Damn, if I'm rightrCoand if we really need to prune away a heap of
useless, difficult, and contradictory conceptsrCothat pruning is going to
be brutal.

Not at all, but your problem is that you are -way- behind the times.
You are still stuck with coordinates and reference frames.
Real physicists understood long ago that everything must be formulated
in a coordinate independent way, in terms of 4-vectors.

I had intended to point out a few contradictions, but I'm realizing that
the whole edificerCowith its misunderstandings, its idiotic paradoxes, and its bogus prescriptionsrConeeds to be completely demolished.

Introspection is the way to go, for you,

Jan


--- Synchronet 3.22a-Linux NewsLink 1.2

From Newsgroup: sci.physics.relativity

Le 20/09/2026 |a 01:03, HenryWilson a |-crit :

On Sat, 19 Sep 26 12:40:35 +0000, Richard Hachel wrote:

An internet user called me a moron when I said that the concept of
relativistic mass was superfluous, and that what was relative in
cosmology was space and timerConot matter.
A hippopotamus doesn't turn into two hippopotamuses just because you
change your frame of reference.
That userrCowho is virulently anti-HachelrCokept telling me the concept
didn't exist, or didn't exist anymore; soon enough, he'll be telling me
it never existed at all.
Yeah, right.
And yet, IrCOm reading some brand-new PDFs today that talk all about
"relativistic mass" and m=mreC/sqrt(1-Vo-#/c-#).
In short, people still buy into it.
Damn, if IrCOm rightrCoand if we really need to prune away a heap of
useless, difficult, and contradictory conceptsrCothat pruning is going to
be brutal.
I had intended to point out a few contradictions, but IrCOm realizing that >> the whole edificerCowith its misunderstandings, its idiotic paradoxes, and >> its bogus prescriptionsrConeeds to be completely demolished.

Dead right...Sr is the greatest scam since jesus christ.

J|-sus-Christ n'est pas une arnaque.

M|-me si J|-sus-Christ n'est rien du tout, sa doctrine a fait grand
bruit.

Ce n'est pas qu'il est d|-pass|-, c'est que jamais il n'a |-t|- rejoint.

Ce qui est une arnaque, c'est Saint Paul, l'Antichrist.

"Petits enfants m|-fiez-vous l'Antichrist vient, et il crachera sur moi".

"Il est d|-j|a de ce monde" : donc il fait partie de ce premier si|?cle romain.

"Il prendra la citadelle de l'int|-rieur pour s'asseoir sur le tr||ne de Dieu" : donc il y |-crira des |-pitres.


R.H.


--- Synchronet 3.22a-Linux NewsLink 1.2

From Newsgroup: sci.physics.relativity

On Sun, 20 Sep 26 13:28:01 +0000, Richard Hachel wrote:

Le 20/09/2026 |a 01:03, HenryWilson a |-crit :

On Sat, 19 Sep 26 12:40:35 +0000, Richard Hachel wrote:

An internet user called me a moron when I said that the concept of
relativistic mass was superfluous, and that what was relative in
cosmology was space and timerConot matter.
A hippopotamus doesn't turn into two hippopotamuses just because you
change your frame of reference.
That userrCowho is virulently anti-HachelrCokept telling me the concept
didn't exist, or didn't exist anymore; soon enough, he'll be telling
me it never existed at all.
Yeah, right.
And yet, IrCOm reading some brand-new PDFs today that talk all about
"relativistic mass" and m=mreC/sqrt(1-Vo-#/c-#).
In short, people still buy into it.
Damn, if IrCOm rightrCoand if we really need to prune away a heap of
useless, difficult, and contradictory conceptsrCothat pruning is going
to be brutal.
I had intended to point out a few contradictions, but IrCOm realizing
that the whole edificerCowith its misunderstandings, its idiotic
paradoxes, and its bogus prescriptionsrConeeds to be completely
demolished.

Dead right...Sr is the greatest scam since jesus christ.

J|-sus-Christ n'est pas une arnaque.

He personally was OK, He tried to freform the ruthless Roman empire. It
was what they turned him into that was a huge scam. Selling seats in a non existent afterlife...and it is still happening all over the world.
Einstein's constant OWlS universe is no better.

M|-me si J|-sus-Christ n'est rien du tout, sa doctrine a fait grand
bruit.

Ce n'est pas qu'il est d|-pass|-, c'est que jamais il n'a |-t|- rejoint.

Ce qui est une arnaque, c'est Saint Paul, l'Antichrist.

"Petits enfants m|-fiez-vous l'Antichrist vient, et il crachera sur
moi".

Little children, beware of any religious preacher. Chances are they are a paedophile.

"Il est d|-j|a de ce monde" : donc il fait partie de ce premier si|?cle romain.

"Il prendra la citadelle de l'int|-rieur pour s'asseoir sur le tr||ne de Dieu" : donc il y |-crira des |-pitres.

R.H.

--- Synchronet 3.22a-Linux NewsLink 1.2

From Newsgroup: sci.physics.relativity

Richard Hachel wrote:

[...] the concept of relativistic mass was superfluous,

It is; it is also misleading. Which is why Einstein (who did not
introduce it) had deprecated it in 1948 already, why it was critized by
Okun, Aron, Taylor, and Wheeler in the late 1980s and 1990s, and why it
has vanished as part of the standard description from university physics
by the late 2010s at the latest (BTST).

<https://en.wikipedia.org/wiki/Mass_in_special_relativity#Relativistic_mass_2>

and that what was relative in cosmology was space and timerConot matter.

That is nonsense because matter is not a quantity. What is absolute,
i.e. frame-independent, indeed, is _mass_, and not (just) in (general-relativistic) cosmology, but in physics as a whole.

A hippopotamus doesn't turn into two hippopotamuses just because you
change your frame of reference.

Correct reasoning.

And yet, IrCOm reading some brand-new PDFs today that talk all about "relativistic mass" and m=mreC/sqrt(1-Vo-#/c-#).

Cite evidence.

In short, people still buy into it.

There are old professors who learned it when they were students, so they continue to teach it; some continue to teach it in introductory classes
because they think it is still useful, and there are many more engineers
and laypeople who simply do not have a clue.

See also:

Fermilab: Is relativistic mass real? <https://youtu.be/LTJauaefTZM?si=qsHf6MFFU5BKNO2K>

from my "Special Relativity" public playlist:

<https://www.youtube.com/playlist?list=PL41EYJuJ5YuAb924jH_kYW5vszLfNaPWI>
--
PointedEars

Twitter: @PointedEars2
Please do not cc me. / Bitte keine Kopien per E-Mail.
--- Synchronet 3.22a-Linux NewsLink 1.2

From Newsgroup: sci.physics.relativity

HenryWilson wrote:

Dead right...Sr is the greatest scam since jesus christ.

You do not know what you are talking about. See my other follow-up for details.
--
PointedEars

Twitter: @PointedEars2
Please do not cc me. / Bitte keine Kopien per E-Mail.
--- Synchronet 3.22a-Linux NewsLink 1.2

From Newsgroup: sci.physics.relativity

Le 21/09/2026 |a 00:44, Thomas 'PointedEars' Lahn a |-crit :

Richard Hachel wrote:

A hippopotamus doesn't turn into two hippopotamuses just because you
change your frame of reference.

Correct reasoning.Yet it was quite obvious that what was relative in the equation p=mv was the velocity, not the mass.

I have always been astounded by a certain kind of human stupidity.

The correct way to write it was p=m-+[vreC/sqrt(1-vreC-#/c-#)], not p=[m/sqrt(1-vreC-#/c-#)]-+vreC, nor p=[1/sqrt(1-vreC-#/c-#)]-+m-+vreC.
I was saying this more than forty years ago.

R.H.
--- Synchronet 3.22a-Linux NewsLink 1.2

From Newsgroup: sci.physics.relativity

The correct way to write it was

p = m*[v0/sqrt(1-v0^2/c^2)],

not

p = [m/sqrt(1-v0^2/c^2)]*v0,

nor

p = [1/sqrt(1-v0^2/c^2)]*m*v0.

Richard...

These THREE expressions are exactly the same equation.

Let

gamma = 1/sqrt(1-v0^2/c^2).

Then your three allegedly different formulas are:

p = m*(gamma*v0)

p = (gamma*m)*v0

p = gamma*m*v0.

Multiplication is associative and commutative.

All three give:

p = gamma*m*v0.


What differs is not the physics.

It is the INTERPRETATION of the factors.

Modern relativity normally says:

m = invariant mass
gamma*v = proper velocity
p = m*gamma*v.

Older terminology sometimes defined:

m_rel = gamma*m

and therefore wrote:

p = m_rel*v.

Same momentum.
Same numerical prediction.
Different terminology.

I was saying this more than forty years ago.

Then for more than forty years you have apparently been presenting

m*(gamma*v) = (gamma*m)*v = gamma*m*v

as three different physical equations.

The hippopotamus was never the problem.

The parentheses were.
--- Synchronet 3.22a-Linux NewsLink 1.2

From Newsgroup: sci.physics.relativity

Le 21/09/2026 |a 10:47, Python a |-crit :

The correct way to write it was

p = m*[v0/sqrt(1-v0^2/c^2)],

not

p = [m/sqrt(1-v0^2/c^2)]*v0,

nor

p = [1/sqrt(1-v0^2/c^2)]*m*v0.

Richard...

These THREE expressions are exactly the same equation.

Yes.

Yesssss!!!

That's what I said.

But... it is not ze same concept.

Ce sont les vitesses qui sont relatives par changement de r|-f|-rentiel,
pas les masses. Il faut dire les choses.

Tu connais toi-m|-me la loi d'additions g|-n|-rales des vitesses
observables, tu vois bien que ce n'est pas newtonien.

En relativit|-, les horaires (tel |-v|-nement n'existera que dans le
futur), les dur|-es (chronotropies), les distances, les longueurs,
et les vitesses sont relatifs.

Les masses, les charges, les particules ne le sont pas.

Il faut |-tre clair avec les choses.

R.H.
--- Synchronet 3.22a-Linux NewsLink 1.2

From Newsgroup: sci.physics.relativity

But... it is not ze same concept.

Yes.

And THAT is a perfectly reasonable point.

You prefer:

p = m*(gamma*v)

with

m invariant mass
gamma*v proper velocity.

So do many modern treatments of relativity.

What was ridiculous was presenting

m*(gamma*v)

and

(gamma*m)*v

as though one were mathematically "the correct way to write it".

They are the same formula.

The distinction is terminology and interpretation.

Ce sont les vitesses qui sont relatives par changement de
r|-f|-rentiel, pas les masses.

With invariant mass, yes.

Congratulations: you have arrived at the modern convention.

But there is a small historical problem with the triumphal
"I was saying this more than forty years ago":

physicists did not wait for Richard Hachel to distinguish
invariant mass from the old "relativistic mass" gamma*m.

So on this particular subject, there is no RH revolution at all.

There is:

old terminology: m_rel = gamma*m

modern terminology: m is invariant,
p = gamma*m*v

Hachel terminology: Vr = gamma*v,
p = m*Vr

Same momentum.
Same physics.

For once, Richard, you are not overthrowing relativity.

You are explaining it.
--- Synchronet 3.22a-Linux NewsLink 1.2

From Newsgroup: sci.physics.relativity

Le 21/09/2026 |a 13:27, Python a |-crit :

Hachel terminology:
p = m*Vr

Il y a une loi physique que les lyc|-ens appliquent dans leurs devoirs.

p=mv.

Il n'y a aucun probl|?me pour penser que cette loi est invariante.

"Un hippopotame ne devient pas deux hippopotame par changement de r|-f|-rentiel".

La vitesse monte, on continue avec la m|-me loi. On n'|-crit pas p=(6mv-5)+p'-3p".

Si la vitesse double, la quantit|- de mouvement double comme chez
Newton.

Si elle triple, la quantit|- de mouvement triple.

C'est aussi simple que |oa.

Il n'y a pas, chez Hachel, de moment o|| la vitesse devenant plus forte,
la droite p=mv se casse et devient autre chose.

La quantit|- de mouvement d'un |-lectron, c'est tout simplement sa masse invariante par sa vitesse r|-elle. Point final.

Il y a, parfois, chez les physiciens, une sorte de d|-go|+t lorsqu'on
leur dit que la vitesse observable Vo, du fait de l'|-tat m|-me de l'espace-temps, ce n'est pas Vr, ce n'est pas la r|-alit|- des choses mais
un leurre impos|- par la structure relativiste du monde.

La formule p=mv est invariante si on utilise la bonne vitesse, la vraie vitesse.

M|-me |a tr|?s haute vitesse p=mVr.

Une question se pose : Et pour les |-nergies?

Pourquoi n'a-t-on pas E=mVr-#? La r|-ponse est tr|?s simple, parce que l'|-nergie, c'est autre chose, et qu'une particule n'a pas seulement une |-nergie de mouvement dans l'espace, elle |a une |-nergie de masse, qui correspond |a son passage dans le temps.

Soit E1=mVr-# et E2=mc-#

Il faut |-videmment additionner ses deux |-nergies pour avoir ce que les physiciens appellent Eg : l'|-nergie globale.

Or, comment peut-on additionner deux |-nergies qui ont des vecteurs diff|-rents, l'un dans l'espace, l'autre dans le temps.

Une simple addition longitudinale n'est pas licite.

Il faut utiliser Pythagore, bien s|+r.

On obtient alors Eg=sqrt(mc-#+mVr-#)

Je vous laisse d|-river jusque E=mc-#/sqrt(1-Vo-#/c-#). C'est facile.
La m|-canique hachelienne peut (et devrait) |-tre introduite et expliqu|-e
au lyc|-e d|?s 15 ans.

C'est plus facile que la RR, et |a l'arriv|-e, plus juste.

Chez Hachel x=Vapp.Tapp, la distance parcourue par un mobile dans le r|-f|-rentiel d'un observateur c'esz sa vitesse apparente par le temps apparent du mouvement.

Soit aussi x=Vapp.Tr (Tr |-tant le temps propre de l'observateur).

Si Vapp=4c, Tr=9 ans, Stella observe la terre revenir vers elle sur
36al.

Ce que ne contredit pas la transformation de Lorentz qui conduit logiquement (niveau lyc|-e) |a un pythagorisme g|-n|-ral et |a :
D'=D.(1+cos+#.v/c)/sqrt(1-v-#/c-#) qui est la simple notion de distance
par changement de r|-f|-rentiel.

On voit aussi que si, dans cette histoire d'aberration de la POSITION
des |-toiles (et non de leur lumi|?re, terme bizarre ici)
au z|-nith, non seulement l'|-toile vire d'un angle ++, mais sa distance augmente et son temps observable de transfert d'information aussi.

Elle ne se trouve plus |a 15 al, mais |a 41 al. L'espace est un
||mollusque de r|-f|-rence.

L'|-v|-nement qui sur terre avait eu lieu il y a 15 ans (temps
observable), a eu lieu il y a 41 ans pour l'autre observateur qui compte
avec sa propre chronotorpie.

Encore que les trois |-v|-nements soient, en r|-alit|-, simultan|-s.
1. L'explosion l|a bas.
2. L'instant o|| je la per|oois.
3. L'instant o|| la fus|-e la per|ooit.

Tout cela est en r|-alit|- simultan|-.

Or, la RR ne l'explique pas tr|?s clairement. Ou pas du tout.

Same momentum.
Same physics.

For once, Richard, you are not overthrowing relativity.

You are explaining it.

Oui, j'explique beaucoup mieux les choses que ce que l'on peut voir dans certaines vid|-os qui reprennent sans cesse les m|-mes
banalit|-s ou les m|-mes erreurs de concept.

R.H.


--- Synchronet 3.22a-Linux NewsLink 1.2

From Newsgroup: sci.physics.relativity

[Something might be wrong with NemoWeb which you are using as the
beginning of your reply was on the same line as my text that you quoted.
I recommend to press Return twice after a quote in order to avoid that
(this works in Betterbird/Thunderbird because it also uses markup for formatting).]

Richard Hachel wrote:

Le 21/09/2026 |a 00:44, Thomas 'PointedEars' Lahn a |-crit :

Richard Hachel wrote:

A hippopotamus doesn't turn into two hippopotamuses just because you
change your frame of reference.

Correct reasoning.
Yet it was quite obvious that what was relative in the

equation p=mv was the velocity, not the mass.

This formula is wrong; the correct formula (in Minkowski space[time],
and for an object with non-zero mass m) is

p = +|(v) m v = m vreoreU(1 reA v-#reoc-#),

where p is ([the magnitude of] the linear 3-)momentum and v is the
relative (3-)velocity (or [3-]speed). Watch the video (which also
explains why p = m v works at small enough speeds).

[The derivation is not trivial, and it is not in the video, so I will
give a possible one here (again). One may start from the Minkowski metric

ds-# = reAdt-# + dx-# + dy-# + dz-#,

where we assume c = 1 for simplicity.

One defines the proper time -a as the time that elapses (and thus is
measured by a clock) at relative rest, dx = dy = dz = 0. It must be
equal to the spacetime interval (aside from the sign and the factor c)
because the Minkowski norm is Lorentz-invariant:

ds-# = reAd-a-#,

so also

reAd-a-# = reAdt-# + dx-# + dy-# + dz-#
= reAdt-# (1 reA [(dx/dt)-# + (dy/dt)-# + (dz/dt)-#])
= reAdt-# (1 reA V -+ V)
= reAdt-# (1 reA v-#),

where by capital letters I mean 3-vectors (the vectors that we were
familiar with before special relativity), and lowercase letters their magnitude/Euclidean norm, therefore

dt/d-a = 1/reU(1 reA v-#) = 1/reU(1 reA v-#/c-#) = +|(v).

(I for one always find it amazing that the Lorentz factor +|
can /literally/ be /derived/ from the Minkowski metric (it is a
derivative ;-)). But if you think about it, the Minkowski metric
comes from considering the motion of a light pulse or piece of
information through space, and how to calculate the spatial
distance that it traverses between events, so it should not be
too surprising.)

Then we find the 4-position (i.e. the position of an event in spacetime)
to be (described by) the vector

xb|a reo (t, x, y, z)b|C,

and the 4-velocity its derivative with respect to proper time:

ub|a reo dxb|areod-a = dxb|areodt (dtreod-a); [chain rule]
= (dtreod-a) dxb|areodt; [commutativity]
= +|(v) (1, dx/dt, dy/dt, dz/dt)b|C
= +|(v) (1, v_x, v_y, v_z )b|C
reo +|(v) (1, V)b|C.

For the 4-momentum, if the mass of the object is non-zero, we may assume (Lagrangian mechanics shows this to be correct), that we just need to
multiply the 4-velocity by that mass as we (Newton) did with the
3-velocity for obtaining/defining the 3-momentum in Newtonian mechanics:

pb|a = m ub|a = m +|(v) (1, V)b|C = +|(v) m (1, V)b|C = [+|(v) m, +|(v) m V]b|C.

Therefore, contrary to what Newtonian mechanics says (and Newton assumed/defined), the 3-momentum of an object with non-zero mass m and (3-)velocity V is _actually_

P = +|(v) m V. (QED.)]

I have always been astounded by a certain kind of human stupidity.

So am I:

The correct way to write it was p=m-+[vreC/sqrt(1-vreC-#/c-#)],

vreC is not defined, presumably one of your pseudoscientific fantasies.

not p=[m/sqrt(1-vreC-#/c-#)]-+vreC, nor p=[1/sqrt(1-vreC-#/c-#)]-+m-+vreC.

These equations are all mathematically equivalent because standard
scalar multiplication (-+) is commutative and parentheses are optional in
this case:

p = m -+ [vreCreoreU(1 reA vreC-#reoc-#)]

= m -+ vreCreoreU(1 reA vreC-#reoc-#)
= m -+ vreC -+ 1reoreU(1 reA vreC-#reoc-#)
= vreC -+ m -+ 1reoreU(1 reA vreC-#reoc-#)
= m -+ 1reoreU(1 reA vreC-#reoc-#) -+ vreC
= mreoreU(1 reA vreC-#reoc-#) -+ vreC

= [mreoreU(1 reA vreC-#reoc-#)] -+ vreC

= m -+ 1reoreU(1 reA vreC-#reoc-#) -+ vreC
= 1reoreU(1 reA vreC-#reoc-#) -+ m -+ vreC

= [1reoreU(1 reA vreC-#reoc-#)] -+ m -+ vreC.

So if the first one is true, then are are _all_ true. But probably they
are all _physically_ false because vreC is just one of your
pseudoscientific fantasies.

I was saying this more than forty years ago.

So you failed basic algebra then already, and have not learned it since?
--
PointedEars

Twitter: @PointedEars2
Please do not cc me. / Bitte keine Kopien per E-Mail.
--- Synchronet 3.22a-Linux NewsLink 1.2

From Newsgroup: sci.physics.relativity

Le 22/09/2026 |a 09:36, Thomas 'PointedEars' Lahn a |-crit :

p = m -+ [vreCreoreU(1 reA vreC-#reoc-#)]

= m -+ vreCreoreU(1 reA vreC-#reoc-#)
= m -+ vreC -+ 1reoreU(1 reA vreC-#reoc-#)
= vreC -+ m -+ 1reoreU(1 reA vreC-#reoc-#)
= m -+ 1reoreU(1 reA vreC-#reoc-#) -+ vreC
= mreoreU(1 reA vreC-#reoc-#) -+ vreC

= [mreoreU(1 reA vreC-#reoc-#)] -+ vreC

= m -+ 1reoreU(1 reA vreC-#reoc-#) -+ vreC
= 1reoreU(1 reA vreC-#reoc-#) -+ m -+ vreC

= [1reoreU(1 reA vreC-#reoc-#)] -+ m -+ vreC.

Toutes donnent le m|-me r|-sultat.

Mais c'est pas de |oa que je parle, je parle du CONCEPT.

Dire que p = m-+[VreC reo reU(1 reA VreC-#reoc-#)], cela donne le m|-me r|-sultat que p = [m/ reU(1-VreC-#/c-#)].VreC, je le veux bien.

Mais dans le premier le concept est implicite : "la masse est relative".

Un hippopotame devient deux hippopotames si on le fait courir tr|?s vite.

Dans le second cas, c'est l'espace et le temps qui sont relatif, et la vitesse, qui utilise ces deux bases est relative.

A noter qu'il ne faut pas confondre vitesse r|-elle (Vr) et vitesse observable (Vo).

C|-l|-rit|- et vitesse observable classique.

Vr=Vo/sqrt(1-Vo-#/c-#), et Vo=Vr/sqrt(1+Vr-#/c-#).

R.H.





--- Synchronet 3.22a-Linux NewsLink 1.2

From Newsgroup: sci.physics.relativity

On 09/22/2026 12:36 AM, Thomas 'PointedEars' Lahn wrote:

[Something might be wrong with NemoWeb which you are using as the
beginning of your reply was on the same line as my text that you quoted.
I recommend to press Return twice after a quote in order to avoid that (this works in Betterbird/Thunderbird because it also uses markup for formatting).]

Richard Hachel wrote:

Le 21/09/2026 |a 00:44, Thomas 'PointedEars' Lahn a |-crit :

Richard Hachel wrote:

A hippopotamus doesn't turn into two hippopotamuses just because you
change your frame of reference.

Correct reasoning.
Yet it was quite obvious that what was relative in the

equation p=mv was the velocity, not the mass.

This formula is wrong; the correct formula (in Minkowski space[time],
and for an object with non-zero mass m) is

p = +|(v) m v = m vreoreU(1 reA v-#reoc-#),

where p is ([the magnitude of] the linear 3-)momentum and v is the
relative (3-)velocity (or [3-]speed). Watch the video (which also
explains why p = m v works at small enough speeds).

[The derivation is not trivial, and it is not in the video, so I will
give a possible one here (again). One may start from the Minkowski metric

ds-# = reAdt-# + dx-# + dy-# + dz-#,

where we assume c = 1 for simplicity.

One defines the proper time -a as the time that elapses (and thus is
measured by a clock) at relative rest, dx = dy = dz = 0. It must be
equal to the spacetime interval (aside from the sign and the factor c) because the Minkowski norm is Lorentz-invariant:

ds-# = reAd-a-#,

so also

reAd-a-# = reAdt-# + dx-# + dy-# + dz-#
= reAdt-# (1 reA [(dx/dt)-# + (dy/dt)-# + (dz/dt)-#])
= reAdt-# (1 reA V -+ V)
= reAdt-# (1 reA v-#),

where by capital letters I mean 3-vectors (the vectors that we were
familiar with before special relativity), and lowercase letters their magnitude/Euclidean norm, therefore

dt/d-a = 1/reU(1 reA v-#) = 1/reU(1 reA v-#/c-#) = +|(v).

(I for one always find it amazing that the Lorentz factor +|
can /literally/ be /derived/ from the Minkowski metric (it is a
derivative ;-)). But if you think about it, the Minkowski metric
comes from considering the motion of a light pulse or piece of
information through space, and how to calculate the spatial
distance that it traverses between events, so it should not be
too surprising.)

Then we find the 4-position (i.e. the position of an event in spacetime)
to be (described by) the vector

xb|a reo (t, x, y, z)b|C,

and the 4-velocity its derivative with respect to proper time:

ub|a reo dxb|areod-a = dxb|areodt (dtreod-a); [chain rule]
= (dtreod-a) dxb|areodt; [commutativity]
= +|(v) (1, dx/dt, dy/dt, dz/dt)b|C
= +|(v) (1, v_x, v_y, v_z )b|C
reo +|(v) (1, V)b|C.

For the 4-momentum, if the mass of the object is non-zero, we may assume (Lagrangian mechanics shows this to be correct), that we just need to multiply the 4-velocity by that mass as we (Newton) did with the
3-velocity for obtaining/defining the 3-momentum in Newtonian mechanics:

pb|a = m ub|a = m +|(v) (1, V)b|C = +|(v) m (1, V)b|C = [+|(v) m, +|(v) m V]b|C.

Therefore, contrary to what Newtonian mechanics says (and Newton assumed/defined), the 3-momentum of an object with non-zero mass m and (3-)velocity V is _actually_

P = +|(v) m V. (QED.)]

I have always been astounded by a certain kind of human stupidity.

So am I:

The correct way to write it was p=m-+[vreC/sqrt(1-vreC-#/c-#)],

vreC is not defined, presumably one of your pseudoscientific fantasies.

not p=[m/sqrt(1-vreC-#/c-#)]-+vreC, nor p=[1/sqrt(1-vreC-#/c-#)]-+m-+vreC.

These equations are all mathematically equivalent because standard
scalar multiplication (-+) is commutative and parentheses are optional in this case:

p = m -+ [vreCreoreU(1 reA vreC-#reoc-#)]

= m -+ vreCreoreU(1 reA vreC-#reoc-#)
= m -+ vreC -+ 1reoreU(1 reA vreC-#reoc-#)
= vreC -+ m -+ 1reoreU(1 reA vreC-#reoc-#)
= m -+ 1reoreU(1 reA vreC-#reoc-#) -+ vreC
= mreoreU(1 reA vreC-#reoc-#) -+ vreC

= [mreoreU(1 reA vreC-#reoc-#)] -+ vreC

= m -+ 1reoreU(1 reA vreC-#reoc-#) -+ vreC
= 1reoreU(1 reA vreC-#reoc-#) -+ m -+ vreC

= [1reoreU(1 reA vreC-#reoc-#)] -+ m -+ vreC.

So if the first one is true, then are are _all_ true. But probably they
are all _physically_ false because vreC is just one of your
pseudoscientific fantasies.

I was saying this more than forty years ago.

So you failed basic algebra then already, and have not learned it since?

These above are "the Lorentzians", about Lorentzian-invariance,
and anything fulfilling them is "a model of relitivity of uniform
motion", just like anything fulfilling "the Galileans" (the vector
addition) about Galilean-invariance gives "a model of uniform motion".

Then "the indefinite-ness of ds^2", as Levi-Civita puts it,
has also that all these d's-for-differential are also _partial_,
besides that also they happen to be as _raw_.

Then, what's in "Levi-Civita's Absolute Differential Calculus"
happens to be a bit beyond "failed basic algebra", these are
called "implicits" then that algebra is the "blissfully ignorant",
then as besides where numerical methods have "error terms" in the
stack of derivations where they are, like small-angle approximation
one may aver, about what's said to give the "metric" vis-a-vis
the _norm_, which is another frame's metric, about small-angle
approximation and Cauchy-Schwarz/triangle-inequality, which one
may find invoked once for metric and once for norm in "the usual
formalism's usual derivation".


Then accounts of what acceleration does involve framing things
back in energy, then about mass/energy equivalence, then for about
that whether momentum is the derivative or energy is the
anti-derivative, have that _energy_ is the conserved quantity,
not momentum.


--- Synchronet 3.22a-Linux NewsLink 1.2

From Newsgroup: sci.physics.relativity

On 09/22/2026 04:54 AM, Richard Hachel wrote:

Le 22/09/2026 |a 09:36, Thomas 'PointedEars' Lahn a |-crit :

p = m -+ [vreCreoreU(1 reA vreC-#reoc-#)]

= m -+ vreCreoreU(1 reA vreC-#reoc-#)
= m -+ vreC -+ 1reoreU(1 reA vreC-#reoc-#)
= vreC -+ m -+ 1reoreU(1 reA vreC-#reoc-#)
= m -+ 1reoreU(1 reA vreC-#reoc-#) -+ vreC
= mreoreU(1 reA vreC-#reoc-#) -+ vreC

= [mreoreU(1 reA vreC-#reoc-#)] -+ vreC

= m -+ 1reoreU(1 reA vreC-#reoc-#) -+ vreC
= 1reoreU(1 reA vreC-#reoc-#) -+ m -+ vreC

= [1reoreU(1 reA vreC-#reoc-#)] -+ m -+ vreC.

Toutes donnent le m|-me r|-sultat.

Mais c'est pas de |oa que je parle, je parle du CONCEPT.

Dire que p = m-+[VreC reo reU(1 reA VreC-#reoc-#)], cela donne le m|-me r|-sultat que p =
[m/ reU(1-VreC-#/c-#)].VreC, je le veux bien.

Mais dans le premier le concept est implicite : "la masse est relative".

Un hippopotame devient deux hippopotames si on le fait courir tr|?s vite.

Dans le second cas, c'est l'espace et le temps qui sont relatif, et la vitesse, qui utilise ces deux bases est relative.

A noter qu'il ne faut pas confondre vitesse r|-elle (Vr) et vitesse observable (Vo).

C|-l|-rit|- et vitesse observable classique.

Vr=Vo/sqrt(1-Vo-#/c-#), et Vo=Vr/sqrt(1+Vr-#/c-#).

R.H.

Einstein distinguishes, if quietly, "spacial" for SR and "spatial" for
GR, giving them two different definitions, c.f. "Out of My Later Years".

C'est a dire, "le spacieau" et "le spatieau", ou comme on les dits,
ils divergent, ils sont speciees. (Ou comme on dit.)




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