In message , I wrote
| [[Mod. note -- There's a famous argument by (I think) Dirac
| (it's summarized in Jackson's E&M textbook) that the existence of
| even a single magnetic monopole in the universe would explain
| (require for consistency) the quantization of electric charge.
| -- jt]]

In article ,
greywolf42 wrote:
On the other hand, the existence of magnetic monopoles would contradict
Maxwell's original derivation of "Maxwell's equations", in "On Physical
Lines of Force", 1861. MM's were "added" to Maxwell's equations in the name
of "symmetry" in the '60's
============

Dirac's papers on this were published in 1931 and 1948. The argument
is described (and full citations to Dirac's papers are given) in
sections 6.11 and 6.12 of the book I mentioned before,

@Book{Jackson99,
author = "John David Jackson",
title = "Classical Electrodynamics",
edition = "3rd"
publisher = "Wiley",
address = "New York",
year = "1999",
isbn = "0-471-30932-X"
}

Quoting from the opening paragraph of section 6.11,

"Dirac's argument, outlined below, is that the mere existence
of one magnetic monopole in the universe would offer an
explanation of the discrete nature of electric charge."

ciao,

--
-- "Jonathan Thornburg (remove -animal to reply)"
Max-Planck-Institut fuer Gravitationsphysik (Albert-Einstein-Institut),
Golm, Germany, "Old Europe" http://www.aei.mpg.de/~jthorn/home.html
"Washing one's hands of the conflict between the powerful and the
powerless means to side with the powerful, not to be neutral."
-- quote by Freire / poster by Oxfam

Jonathan Thornburg wrote in message
...

In message , I wrote
| [[Mod. note -- There's a famous argument by (I think) Dirac
| (it's summarized in Jackson's E&M textbook) that the existence of
| even a single magnetic monopole in the universe would explain
| (require for consistency) the quantization of electric charge.
| -- jt]]

In article ,
greywolf42 wrote:
On the other hand, the existence of magnetic monopoles would contradict
Maxwell's original derivation of "Maxwell's equations", in "On Physical
Lines of Force", 1861. MM's were "added" to Maxwell's equations in the
name
of "symmetry" in the '60's

============

Dirac's papers on this were published in 1931 and 1948. The argument
is described (and full citations to Dirac's papers are given) in
sections 6.11 and 6.12 of the book I mentioned before,

@Book{Jackson99,
author = "John David Jackson",
title = "Classical Electrodynamics",
edition = "3rd"
publisher = "Wiley",
address = "New York",
year = "1999",
isbn = "0-471-30932-X"
}

Quoting from the opening paragraph of section 6.11,

"Dirac's argument, outlined below, is that the mere existence
of one magnetic monopole in the universe would offer an
explanation of the discrete nature of electric charge."

There was no need for you to snip the essence of my post, and you should not
snip without marking same. The rest of my sentence was:

", and were big in the '70's -- including a few claims of observation.
Those observations were proven incorrect, and the fad has since died down."

While I was unaware that Dirac was the first to bring up magnetic monopoles
in the interests of symmetry, the faddish years were definitely the 60's and
70's. And despite Dirac, symmetry, and 20 years of effort -- magnetic
monopoles remain fictional. Constistent with Maxwell's derivation -- and
inconsistent with QM and Dirac.

greywolf42
ubi dubium ibi libertas

On Mon, 14 Jul 2003 18:56:08 +0000 (UTC), "greywolf42"
wrote:


(snip)


While I was unaware that Dirac was the first to bring up magnetic monopoles
in the interests of symmetry, the faddish years were definitely the 60's and
70's. And despite Dirac, symmetry, and 20 years of effort -- magnetic
monopoles remain fictional. Constistent with Maxwell's derivation -- and
inconsistent with QM and Dirac.

greywolf42
ubi dubium ibi libertas


Another view is that magnetic monopoles are incosistent with Maxwell
equations but consistent with QM and Dirac. They are inconsistent
with Maxwll equations if Maxwell equations contain dF=0.

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. In QM
dF=0 needs to hold only "almost everywhere", and this leads to the
possibility of having an infinite number of monopoles in the universe.

ark
--

Arkadiusz Jadczyk
http://www.cassiopaea.org/quantum_future/homepage.htm

--

In article ,
Steve Willner wrote:

1. Is there sound reason for ruling out the existence of magnetic
monopoles? I know of some upper limits on their abundance, but is
there an argument that none at all can exist?

Not that I know of, but I'm certainly not an expert.

2. Has there ever been a satisfactory explanation of the "Valentine's
Day Event?" Could it have been a genuine (but _very_ lucky!)
monopole detection?

(In response to one comment, subsequent non-detections in more
sensitive experiments do not rule out a true detection by Cabrerra.
They only confirm he had to have been lucky.)

Every time an experiment with better sensitivity fails to detect
monopoles, and therefore sets a better upper limit on the number
of monopoles, the probability that the Valentine's Day monopole
was real gets lower and lower. By now, it's extremely low.

As far as I can tell, your question is essentially "Is this probability
exactly zero or merely very tiny?" I'd say the answer is "merely very
tiny." But that's true for pretty much any statistical statement
in science. Hypotheses are essentially never ruled out with
strictly 100% probability.

If I've misinterpreted what you're asking, I apologize, but I can't
figure out any other way to interpret it.

-Ted





--
[E-mail me at , as opposed to .]

"I think the burden is on those people who think he didn't have weapons
of mass destruction to tell the world where they are." --Ari Fleischer

Arkadiusz Jadczyk wrote in message
. ..
On Mon, 14 Jul 2003 18:56:08 +0000 (UTC), "greywolf42"
wrote:


(snip)


While I was unaware that Dirac was the first to bring up magnetic monopoles
in the interests of symmetry, the faddish years were definitely the 60's and
70's. And despite Dirac, symmetry, and 20 years of effort -- magnetic
monopoles remain fictional. Constistent with Maxwell's derivation -- and
inconsistent with QM and Dirac.

greywolf42
ubi dubium ibi libertas


Another view is that magnetic monopoles are incosistent with Maxwell
equations but consistent with QM and Dirac. They are inconsistent
with Maxwll equations if Maxwell equations contain dF=0.

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. In QM
dF=0 needs to hold only "almost everywhere", and this leads to the
possibility of having an infinite number of monopoles in the universe.

ark

But what if dipoles were an inherent property of electric charges?
Then what? Then you could not have monopoles and electromagnetism at
the same time.

I believe that all charges have dipole analogies to them. For
electricity, there is magnetism. In some cases I've heard of people
referring to something called 'gravitomagnetism'. You could extend
this logic to the weak force (gaugomagnetism) and the color force
(chromomagnitism).

This is a bit speculative, but I'm not claiming these things as fact.
They are simply possibilities, and in my opinion, likely ones, since
nature has a tendency to recycle the same physics over and over again.

(...Starblade Riven Darksquall...)

In article ,
writes:
As far as I can tell, your question is essentially "Is this probability
exactly zero or merely very tiny?" I'd say the answer is "merely very
tiny." But that's true for pretty much any statistical statement
in science. Hypotheses are essentially never ruled out with
strictly 100% probability.

Thanks, Ted.

I guess I was trying to ask whether magnetic monopoles are in the
same category as, say, a fourth lepton family: ruled out unless we
have a lot of physics wrong. As I understand your reply, that is not
the case. Upper limits show that monopoles must be very rare, but
there is no reason to rule out their existence.

The question about the Cabrerra experiment was whether anyone had
identified an instrumental flaw that could explain the one detection.

--
Steve Willner Phone 617-495-7123
Cambridge, MA 02138 USA
(Please email your reply if you want to be sure I see it; include a
valid Reply-To address to receive an acknowledgement. Commercial
email may be sent to your ISP.)

Steve Willner wrote in message
...
In article ,
(Jonathan Thornburg) writes:
Dirac's papers on this were published in 1931 and 1948. The argument
is described (and full citations to Dirac's papers are given) in
sections 6.11 and 6.12 of the book I mentioned before, [Jackson]

Thanks. The section numbers may not be the same in other editions,
but a glance at the index will locate the topic.

Can anyone answer my earlier questions? (If there has been an answer,
I apologize, but I missed it.) I have rephrased the first question
slightly.

1. Is there sound reason for ruling out the existence of magnetic
monopoles? I know of some upper limits on their abundance, but is
there an argument that none at all can exist?

Yes. Magnetic monopoles violate the physical derivation of Maxwell's
equations. See "On Physical Lines of Force", 1861. One can find related
mathematical derivations that avoid any physical cause, and come up with
similar math statements. However, these have no basis in the physical
world.

2. Has there ever been a satisfactory explanation of the "Valentine's
Day Event?" Could it have been a genuine (but _very_ lucky!)
monopole detection?

(In response to one comment, subsequent non-detections in more
sensitive experiments do not rule out a true detection by Cabrerra.
They only confirm he had to have been lucky.)

I recall it was later determined to be a cosmic ray hit. However, the main
problem is that the predicted abundances kept having to be "recalculated".
"How lucky" had to keep being increased. Once you get to 1 in a billion
chance (and I don't recall the actual numbers), you've essentially reached a
non-confirmation. Science requires repeatable measurements.

greywolf42
ubi dubium ibi libertas

Arkadiusz Jadczyk wrote in message
...
On Mon, 14 Jul 2003 18:56:08 +0000 (UTC), "greywolf42"
wrote:


(snip)


While I was unaware that Dirac was the first to bring up magnetic
monopoles
in the interests of symmetry, the faddish years were definitely the 60's
and
70's. And despite Dirac, symmetry, and 20 years of effort -- magnetic
monopoles remain fictional. Constistent with Maxwell's derivation -- and
inconsistent with QM and Dirac.

Another view is that magnetic monopoles are incosistent with Maxwell
equations but consistent with QM and Dirac. They are inconsistent
with Maxwll equations if Maxwell equations contain dF=0.

And Maxwell's equations DO contain dF=0.

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.

In QM
dF=0 needs to hold only "almost everywhere", and this leads to the
possibility of having an infinite number of monopoles in the universe.

But there is no physical basis for dF0. Again, (as per the prior
statements and history that you snipped) your view was popular in the 60's
and 70's. And a great deal of effort was spent looking for such things.
And nothing was found. To orders of magnitude lower incidences than
theorists expected. Certainly, absence of evidence is not evidence of
absence. However, when theorists have to keep "moving the goalposts" after
each "not found," one can infer a major flaw in the theory.

greywolf42
ubi dubium ibi libertas

On Thu, 31 Jul 2003 21:46:14 +0000 (UTC), "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.

The mathematics here is not "arbitrary" - as you call it. The
mathematics here is the one that helps us to describe and predict
physical phenomena of interest.


In QM
dF=0 needs to hold only "almost everywhere", and this leads to the
possibility of having an infinite number of monopoles in the universe.

But there is no physical basis for dF0.

There may be one. We do not know. Quantum theory is not yet completely
understood. Let me quote from J. A. Wheeler: " No prediction lends
itself to a more critical test than this, that every law of physics,
pushed to the extreme, will be found to be statistical and approximate,
not mathematically perfect, precise."


Again, (as per the prior
statements and history that you snipped) your view was popular in the 60's
and 70's.

Popularity of some view is one thing, discussion of unpopular views can
also be revealing. Alpher and Herman predicted background radiation
already in 1948. As Herman wrote: " There was no doubt in our mind that
we had a very interesting result, but the reaction of the astronomical
community ranged from skeptical to hostile." So, perhaps, it is good to
be open-minded?

And a great deal of effort was spent looking for such things.
And nothing was found. To orders of magnitude lower incidences than
theorists expected.

Maybe people were looking at wrong places? Maybe the theory is not
ready? Maybe the theory needs a major re-thinking and re-writing? Or
maybe we will find something else - which will also be interesting. And,
we do not know that "nothing has been found". Perhaps something has
been found but the phenomenon is "elusive".

Certainly, absence of evidence is not evidence of
absence. However, when theorists have to keep "moving the goalposts" after
each "not found," one can infer a major flaw in the theory.


And yet theorists predicted antimatter. P.A.M. Dirac wrote:

"The pure mathematician who wants to set up all his work with absolute
accuracy is not likely to get very far in physics".

But he also wrote:

"There are, at present, fundamental problems in theoretical physics the
solution of which will presumably require a more drastic revision of our
fundamental concepts than any that have gone before. Quite likely, these
changes will be so great that it will be beyond the power of human
intelligence to get the necessary new ideas by direct attempts to
formulate the experimental data in mathematical terms. The theoretical
worker in the future will, therefore, have to proceed in a more direct
way. The more powerful method of advance that can be suggested at
present is to employ all resources of pure mathematics in attempts to
perfect and generalize the mathematical formalism that forms the
existing basis of theoretical physics, and after each success in this
direction, to try to interpret the new mathematical features in terms of
physical entities."

Of course we do not have to agree with all that Dirac wrote but, at
least, we should acknowledge that he may have had a point....

ark
--

Arkadiusz Jadczyk
http://www.cassiopaea.org/quantum_future/homepage.htm

--

greywolf42 wrote:


And Maxwell's equations DO contain dF=0.

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).

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



--
Hendrik van Hees Fakultät für Physik
Phone: +49 521/106-6221 Universität Bielefeld
Fax: +49 521/106-2961 Universitätsstraße 25
http://theory.gsi.de/~vanhees/ D-33615 Bielefeld