Bunch of corrections (multipart message)


It may be nice to correct some serious misunderstandings on recent
postings where I am being directly alluded. My time is very limited
now, therefore I will submit by pieces and will not reply neither to
new misunderstandings nor to questions I already asked before, my
apologies.


####
####
#### About potential energies once again (and the latter) ####
####

On Jul 13, 6:39 pm, "Pmb" <some...@xxxxxxxxxxxxx> wrote:

I feel obliged for Juan's sake to confirm that he knows what he's saying.
Avoid reading anything by Bilge or you're destined to get it all mixed up.

I very much agree with this advice by Pmb but I would extend it to
other folks.

In his last posting on the thread about potential energies, Bilge
seems to unnotice basic differences between Lagrangian and Hamiltonian
formulations of dynamics and seems to confound now U with V or maybe
directly with H, who knows?

Bilge also appears to be unaware that zero component of four momentum
leads to interactions energies of type U as in the Lagrangian
formulation. It seems he never wrote P^0, expanded the term containing
the vector potential A and reorganized the full Hamiltonian into free
(usually denoted by H_0) and interaction components. This is done with
detail in many textbooks, and for both classical and quantum level of
theory.

Any basic course in QFT shows that interaction energy in quantum
electrodynamics is a product involving four vectors. For instance I
remember Weinberg likes to write the interaction energy density for
field QED (Weinberg uses notation H = H_0 + V) like

V = {J^0 * A^0} - {J * A}

Others authors like to _rewrite_ the above interaction in full
covariant form,

{J^a * A_a}.

This is Landau prefered way (Landau also uses greek notation and
matter current four density instead charge current four density: "e*j
= J").

Therefore, Bilge last comment about energy being not product of two
four-vectors has really no sense.

Now I will reply the recurrent misunderstandings by Gisse, Hobba,
Bilge, and Karandash2. The thread about relativistic potential
energies is too large, full of insults to several people, and contains
several off-topic comments, therefore, I summarize here most of it,
add some new references (I do not copy all references I used in the
other thread), and last comments.

Goldstein calls to U(x,v) a "generalized potential" for
differentiating from the 'ordinary' potential energies U(x) of the non-
relativistic theory. See his well-known textbook on mechanics.

Goldstein does not write the word energy when naming the U. Goldstein
writtes

{BLOCKQUOTE
We shall preferably use the name "generalized potential,"
including within this designation also the ordinary potential
energy,
a function of position only.
}

Also Goldstein writes "ordinary potential energy" not just "potential
energy" and this may be another source of confusion for beginners.

From dimensional analysis it is very easy to see that "U" in {L = T -
U} has units of energy, because "T" has units of energy. Otherwise the
difference (T - U) has no meaning. However, Bilge still maintain in
his last posting that U cannot be an energy.

Authors of other textbooks do not asume their readers can complete a
dimensional calculus test. An example is textbook on mechanics [1],
where U(x,v) in {L = T - U} is explicitely called the "generalized
potential energy". That avoids confusion.

Just compare with Hobba thoughts:

{BLOCKQUOTE [Bill Hobba]
Otherwise it can not be interpreted as potential energy.
}

The term "generalized" in generalized potential energy [1] is usually
droped in modern literature and you can call to U simply the
"potential energy". It is trivial that a generalized potential energy
is a potential energy. This is a usual convention in several physics
and chemistry disciplines. This is also a popular convention used in
mathematics. From Mathpages:

{BLOCKQUOTE [5]
We might hypothesize that the potential energy is a
function not only of position but also of velocity.
}

Now compare with

{BLOCKQUOTE [Bill Hobba]
Now, the question is, how can a function containing
velocity be only a function of position as required
by a term that is potential enrergy?
}

What is the problem? The problem is that Bill Hobba, Gisse, Bilge and
Karandash2 never studied physics (they claim the contrary). Then they
got the definition of potential energy from some non-relativistic
basic textbook as the Landau (i.e. the definition of non-relativistic
potential energy) and next misreaded and mixed up all.

Of course, Lagrangians containing a relativistic potential energy
U(x,v) are relativistic *invariant*. This is valid for both classical
and quantum level of theory.

Since Hobba, Karandash2, Eric Gisse, and Bilge will try to mix every
again I reproduce one of most clear quotes about the role of potential
energy in relativity I have found in literature. It is extracted from
"the ABC of relativity" and read as follows,

{BLOCKQUOTE [2]
The Newtonian ideas of kinetic and potential energy can without
much difficulty be adapted to the special theory of relativity.
}

It is interesting to compare [2, 1, 5] with next misunderstandings

{BLOCKQUOTE [Bill Hobba]
Potential energy is a classical concept not applicable
to relativity because the potential function depends
on spatial coordinates
}

{BLOCKQUOTE [karandash2]
What in the explanation that you received earlier about
the inaplicability of potential energy in relativity
is that you don't understand?
}

{BLOCKQUOTE [Bill Hobba]
Sine there is no such thing as relativistic potential energy
what you wrote above is obviously nonsense.
}

And a large collection of similar wrong statements.

Compare is being said by them with an online preprint on gr-qc

{BLOCKQUOTE [18]
The total energy is thus the familiar rest energy mc2 plus
the relativistic potential energy.
}

In the Physical Review D (one of more respected and rigorous journals
of physics), authors write,

{BLOCKQUOTE [19]
If the energy levels are kept fixed, the relativistic potential
energy
must then exceed the nonrelativistic potential energy.
}

Therefore, notice the irony. The authors of [19] write about
relativistic potential energies and compute its magnitude. They submit
the paper to Physical Review, the referres aprove the paper and the
editor decides to publish it. The paper is published and none
physicist writtes a rebutal paper; I mean nobody wrote a hangry letter
to the journal writing stuff like

{BLOCKQUOTE [karandash2]
There is no potential energy in
relativity, cretin.
}

The irony is that Hobba, Karandash2, Eric Gisse, and Bilge claiming to
know relativistic physics decided to insult me and others. They would
go to university and learn a bit of physics before posting nonsense
and insults at this newsgroup.

I also said that the concept of relativistic potential energy is used
in another meaning in chemical physics and physical chemistry.
Chemists and physicists also use the term "relativistic potential
energy" for relativistic generalizations of molecular PES.

Once more again just compare

{BLOCKQUOTE [Bill Hobba]
Sine there is no such thing as relativistic potential energy
what you wrote above is obviously nonsense.
}

with the title of the published paper [21]: "Relativistic potential
energy surfaces of XH_2 (X=C, Si, Ge, Sn, and Pb) molecules: Coupling
of 1A_1 and 3B_1 states".

Funny, true?

I also cited a sci.physics.research trend. They decided do not read,
and continued to insult people and countries and to submit more
nonsense about potential energies and relativity. The more interesting
thing is that they claim here often they know physics, and Eric Gisse
fantasizes about him studying physics in the University!!!!

I reproduce parts of the messages (the original queries and two
replies from two diferent epople) on the sci.physics.research
newsgroup [20]. Messages are so obvious...

{BLOCKQUOTE [Query]
How do we deal with potential energy and forces
in special relativity?
}

{BLOCKQUOTE [reply]
Same way as in classical mechanics except that now
you can't assume that the force is independant of
velocity as you usually could in classical mechanics.
}

{BLOCKQUOTE [Query]
Is the concept of potential energy still useful in relativity?
}

{BLOCKQUOTE [reply]
Yes, it is useful. The energy still exists in relativity,
it continues to be conserved, and it has various
contributions just like in classical mechanics.
}

{BLOCKQUOTE [reply2]
It's as useful in relativity as it was in Newtonian mechanics,
i.e. it's a constant of motion for a given frame of referance
when the system is conservative in that frame.
}

Now you can compare above replies in sci.physics.research (moderated
newsgroup) with next messages in sci.physics.relativity (no moderated)

{BLOCKQUOTE [Bill Hobba]
Potential energy is a classical concept not applicable
to relativity because the potential function depends
on spatial coordinates
}

{BLOCKQUOTE [karandash2]
What in the explanation that you received earlier about
the inaplicability of potential energy in relativity
is that you don't understand?
}

{BLOCKQUOTE [karandash2]
There is no potential energy in
relativity, cretin.
}

{BLOCKQUOTE [karandash2]
NO, they are NOT.

They are _components_ of the Lagrangian but
they are not energies. It was also already pointed
out to you that L = T - V is not true in
relativity. Which was the whole goddamn point.
}

Of course, they will never aceppt they have no idea of physics. They
will insult again. They think that they are completely right and that
the people who replied in sci.physics.research is wrong. They will
also insult the moderators on sci.physics.research. For instance,
karandash2 (who never studied physics) want to write a mail to
moderators kevin (at Caltech) and helbig saying them

{BLOCKQUOTE [karandash2]
There is no potential energy in
relativity, cretin.
}

Ups!


I have been kindly informed that now Eric Gisse is adding a new
misunderstanding to the large list. The warning is as follows,

Juan - Before I begin Eric Gisse is now claiming that what Bilge is doing is
proving that Potential energy is not invariant.

Well, Gisse already proved his difficulties to understand invariances
in the thread about temperatures. And we know both have difficulties
with dimensional analysis. They continue to claim that U in
relativistic L = T - U has not units of energy.

The authors of the monograph on relativistic dynamics [4] already
predicted puzzled folks never studied physics would get confussion
about invariances. Therefore for avoiding any ambiguity or misreading
they wrote an entire section on that, the "4.2.4 The invariant
potential".

{BLOCKQUOTE [4]
identifiable like the invariant kinetic energy T
and the invariant potential energy V.
}

By invariance they explicitely mean "Lorentz-invariant terms".

Of course the relativistically *invariant* V on equations (4.36),
(4.37), (4.38), and (4.39) of monograph [4] is not simply the non-
relativistic potential V that you can find in textbooks on non-
relativistic mechanics.

The invariance of U is also proven with detail in many textbooks.

I will not comment adittional misunderstandings about this issue.


Karandash2 was also very confused about Einstein original papers.
Einstein uses electromagnetic potential energy concept in 1905.
Einstein also discusses about gravitational potential energies in
posterior works on relativity,

{BLOCKQUOTE [3]
It thus proves that for the fulfilment of the principle of energy
we have to ascribe to the energy E, before its emision in S_2,
a potential energy due to gravity, which correspond to the
gravitational mass E/c^2. Our assumption of the equivalence of K
and K' thus removes the difficulty mentioned at the beginning of
this paragraph which is left unsolved by the ordinary theory of
relativity.
}

However, today it is accepted that Einstein discussion about gravity
was naïve. The famous problem of energy in *general* relativity
remains unsolved.



In the other thread i received only 4 1-stars (imagine what four folks
voted against me). Since this thread will be of no interest to many
'relativists' because says stuff they do not like, I wait this time to
receive at least 80 1-stars. Thanks by votes!

.

Relevant Pages

  • Re: Bunch of corrections (multipart message)
    ... Also Goldstein writes "ordinary potential energy" not just "potential ... {BLOCKQUOTE [Bill Hobba] ... Karandash2 never studied physics. ... energy in relativity I have found in literature. ...
    (sci.physics.relativity)
  • Re: Planetray precession in flat space
    ... Bill Hobba wrote: ... Potential energy function in relativity? ... particle and immediately its potential energy and hence force ... Galileo's relativity principle. ...
    (sci.physics.relativity)
  • Re: Relativistic Lagrangian and limitations of field theory
    ... Potential energy in Einstein's 1905 Relativity ... mass concept. ... In his work about _Gravitation and Light_, ...
    (sci.physics.relativity)
  • Re: Potential energy in Einsteins 1905 Relativity
    ... relationship from the Principle of Relativity (PoR, ... Jun 30 paper) and the Principle of Energy (PoE, ... measuring rest mass its potential energy. ... inaplicability of potential energy in relativity is that you don't ...
    (sci.physics.relativity)
  • Re: Potential energy in Einsteins 1905 Relativity
    ... relationship from the Principle of Relativity (PoR, ... Jun 30 paper) and the Principle of Energy (PoE, ... measuring rest mass its potential energy. ... inaplicability of potential energy in relativity is that you don't ...
    (sci.physics.relativity)