Hendrik van Hees wrote in message
...
greywolf42 wrote:


They are consistent with QM because moving into the quantum domain we
move from the category of continuous or even smooth fiber bundles
to the category of measurable functions and operator algebras.

I was under the impression we were discussing the physical universe, not
arbitrary mathematics.. Maxwell's equations are continuous approximations
in Maxwell's original derivation.

I don't know of any mathematical or physical reason which forbids
magnetic monopoles in electrodynamics (neither in classical nor in
QED).

Maxwell's original, physical derivation of "Maxwell's equations" was "On
Physical Lines of Force", 1861. (The reference was snipped by Arkadiusz.)
These derivations are based on a physical model. Maxwell's physical
derivation *cannot* support magnetic monopoles. This is purely classical,
and the limit is physical -- not mathematics. In other words, one can
'insert' monopoles in to 'Maxwell's equations'. But one cannot derive any
form of Maxwell's equations from Maxwell's physical theory that contain
monopoles.

Now you know one physical reason in classical electrodynamics, provided by
Maxwell.


There are two famous papers by Dirac about the subject:

P. A. M. Dirac, Quantised Singularities in the Electromagnetic Field, Proc.
Roy. Soc. A133 60 (1931)

P. A. M. Dirac, Theory of Magnetic Poles, Phys. Rev. 74 817 (1948)

A more modern approach:

T. T. Wu and C. N. Yang, Concept of nonintegrable phase factors and global
formulation of gauge fields, Phys. Rev. D12 3845 (1975)

If you understand German there is a little workout of a seminar I had to
give in the theory student seminar (TH Darmstadt):

http://theory.gsi.de/~vanhees/faq/magmon/magmon.html

The more modern 'pure math' approaches, above, do not address either
physical limitations, or the point under discussion.

greywolf42
ubi dubium ibi libertas

Maxwell's electrodynamics have come down to us via Lorentz as F=dA and
d*F=J. The fields and currents are continuous distributions and at
complete variance with the observed quanta of electrons and photons.
Dirac's introduction of magnetic monopoles did two things: 1) it
quantized charge as alluded to above and 2) filled a gaping hole in
Maxwell's equations. This to my knowledge is the only serious attempt
to get quantised charges and that desire has given the magnetic
monopole its only credibility. With magnetic current densities Jm, the
"electromagnetic" field equations would read dF=*Jm and d*F=J. Some
years ago Misner and Wheeler in "Classical Physics as Geometry", (Ann
Phys (NY), vol 2,pp 525-603,1957)introduced de Rham cohomology theory
to the physics community and suggested that mass and charge were the
result of closed forms that were not exact. These topological masses
and charges were still continuous variables, but emerged from a
non-trivial topology. They argued that the currents were just averages
over the source free fields that dressed the missing points, and the
fundamental equations would be dF=0, d*F=0.(Here I put words in their
mouth as they said nothing about dF=0)These latter equations allow the
monopole of Wu and Yang because F is closed and not exact and electric
charges because *F is closed and not exact. The global vector
potential A of Maxwell's equations removes the magnetic monopole
completely. The gap that Dirac filled in Maxwell's equations may be
there for a reason.

Ralph Hartley wrote in message
...
greywolf42 wrote:
Hendrik van Hees wrote:

I don't know of any mathematical or physical reason which forbids
magnetic monopoles in electrodynamics (neither in classical nor in
QED).

Maxwell's original, physical derivation of "Maxwell's equations"

Maxwell's derivation was, as are all derivations, mathematical. I don't
even know what it means for a derivation to be "physical".
In any case, the way in which the equations were first derived is a
*historical* matter, not physical.

A physical derivation is one that is based on a physical model. Thus, any
mathematics are limited by the physical properties of the model. The
derivation of Maxwell's equations was from a physical model.

The equations can be arrived at in many
ways. It is a historical accident that the equations were derived by the
route they were. If Maxwell had died in childhood, the original derivation
of the equations might be very different, and might provide for monopoles
(by now those terms would often be omitted because monopoles are never
seen).

An amusing speculation. But such speculation is outside the guidelines of
this N.G, and I choose not to be led down that path.

However, Maxwell's equations were very definitely first derived from a
physical, fluid aether.

These derivations are based on a physical model. Maxwell's physical
derivation *cannot* support magnetic monopoles. This is purely
classical,
and the limit is physical -- not mathematics. In other words, one can
'insert' monopoles in to 'Maxwell's equations'. But one cannot derive
any
form of Maxwell's equations from Maxwell's physical theory that contain
monopoles.

Why would anyone want to?

Because that is the basis for Maxwell's equations.

His "physical" (I would say "mechanical") model was classical and
non-relativistic. In other words, it is now known to be *wrong*.

There isn't a single experiment or theory that requires Maxwell's model to
be 'wrong.' Einstein merely said Maxwell's model (an aether) wasn't
'necessary.' First off, Maxwell's equations (from Maxwell's model)
explicitly require SR. That is, Einstein explicitly used Maxwell's
equations as the basis for his postulates (see the first sentence of
Einstein's 1905 paper). Hence, if you disprove Maxwell's equations, you
disprove SR. If you don't disprove Maxwell's equations, you can't disprove
Maxwell's model.

I.O.W. Maxwell's model providuced relativity. Your claim that Maxwell's
model was non-relativisitic is ludicrous.

That isn't
to say that Maxwell was wrong to use it, it worked at the time, it was a
good heuristic, and was consistent with the information he had.

And -- until Maxwell's equations are disproved in a manner outside of
Maxwell's model -- Maxwell's model is consistent with all the information we
have today.

It is the luminiferous aether that is unphysical.

Nonsense. The luminiferous aether is most definitely physical. Or do you
simply mean you haven't detected it, yet?

Now you know one physical reason in classical electrodynamics, provided
by
Maxwell.

Now I know one historical reason.

It's also physical.

I know of exactly one valid reason to believe there are no magnetic
monopoles: none have been observed.

Absence of evidence is not evidence of absence. We haven't observed any
'gravitational waves' yet, either. Is that a valid reason to belive that
there are no graviational waves?

That's a good enough reason for now. Not everything that could exist does.
There is no physical or biological reason that there can't be a horned
horse, but I won't believe in unicorns until I see one.

How recently have you seen a virtual particle -- which by definition cannot
be directly observed?

greywolf42
ubi dubium ibi libertas

On Thu, 21 Aug 2003 20:48:02 +0000, greywolf42 wrote:

Ralph Hartley wrote in message
...
[snip]
His "physical" (I would say "mechanical") model was classical and
non-relativistic. In other words, it is now known to be *wrong*.

There isn't a single experiment or theory that requires Maxwell's model to
be 'wrong.'

This is untrue. Maxwell's equations coupled to a Dirac electron do not
give the correct value for the magnetic moment of the elctron. QED
predicts many effects, which have been observed, that are not predicted by
classical E&M. One loop corrections to Bhabba scattering, to pick one
example. There are hundreds of others (see the many articles in
Kino****a's book "Quantum Electrodynamics").

Einstein merely said Maxwell's model (an aether) wasn't
'necessary.' First off, Maxwell's equations (from Maxwell's model)
explicitly require SR. That is, Einstein explicitly used Maxwell's
equations as the basis for his postulates (see the first sentence of
Einstein's 1905 paper). Hence, if you disprove Maxwell's equations, you
disprove SR.

That's false. I could equally well say "if you disprove hole theory,
you've disproven the Dirac equation". That's not true either.

If you don't disprove Maxwell's equations, you can't disprove
Maxwell's model.

Again, QED has "disproven" Maxwell's equations. There are things,
predicted by QED, that are not predicted by classical E&M (the Lamb shift,
for example).

I.O.W. Maxwell's model providuced relativity. Your claim that Maxwell's
model was non-relativisitic is ludicrous.

I'd imagine that he means the particles in Maxwell's ether obeyed
non-relativistic Newtonian mechanics. So in that sense, his claim is not
ludicrous. And, since particles do obey the laws of SR (even neutral ones
like \pi^{0}s) that shows Maxwell's model to be misguided.

That isn't
to say that Maxwell was wrong to use it, it worked at the time, it was a
good heuristic, and was consistent with the information he had.

And -- until Maxwell's equations are disproved in a manner outside of
Maxwell's model -- Maxwell's model is consistent with all the information we
have today.

It is not consistent with quantum mechanics, and not consistent with
quantum electrodynamics.

--
Matthew Nobes
c/o Physics Dept. Simon Fraser University, 8888 University
Drive Burnaby, B.C., Canada
webspace -- http://burbland.phys.sfu.ca/~matt
PGP key -- http://burbland.phys.sfu.ca/~matt/pgpkey.txt

In article ,
greywolf42 wrote:

How recently have you seen a virtual particle -- which by definition cannot
be directly observed?

I'm seeing a bunch right now! As has occasionally been noted on
this newsgroup, any photon that gets absorbed by a charged particle
is "virtual" - and this includes all the light we ever see.

But every charged particle that emits a photon is also virtual.
So, I'm made of virtual particles myself! And so are you.

Actually, a deeper look at this issue reveals that the
concept of "virtual particle" only makes sense as a mathematical
construct within Feynman diagram calculations, which are good
for pertubative scattering theory but not for studying bound
states like you and me. So, it doesn't really *make sense* to
ask if the light we see consists of virtual or real photons -
or if any of the particles we ever observe are real or virtual.

John Baez wrote in message
...
In article ,
greywolf42 wrote:

How recently have you seen a virtual particle -- which by definition
cannot
be directly observed?

I'm seeing a bunch right now! As has occasionally been noted on
this newsgroup, any photon that gets absorbed by a charged particle
is "virtual" - and this includes all the light we ever see.

But the 'virtual photon' is not the 'physical photon' that does the
travelling from point A to point B. By definition, a 'virtual photon'
cannot itself be observed. (It may get 'absorbed', but we can't observe
it.)

But every charged particle that emits a photon is also virtual.
So, I'm made of virtual particles myself! And so are you.



Actually, a deeper look at this issue reveals that the
concept of "virtual particle" only makes sense as a mathematical
construct within Feynman diagram calculations, which are good
for pertubative scattering theory but not for studying bound
states like you and me. So, it doesn't really *make sense* to
ask if the light we see consists of virtual or real photons -
or if any of the particles we ever observe are real or virtual.

That quantum mechanics cannot provide the answer does not mean the question
cannot be asked. Of course, that is why you found it necessary to mix up
the QM distinction between 'observe' and 'absorb'.

greywolf42
ubi dubium ibi libertas