Half-Integer Fractional Dirac Magnetic Monopole Charges

[guest1202]

Mr. Yablon,

I get the impression from your lengthy Dec. 6 post that your
paper uses single-valued wave functions. If this is a wrong impression,
then please disregard the following, and state clearly that your wave functions
are multiple valued, or that they are single-valued in such-and-such
clearly specified context, and multiple-valued in some other clearly specified
contexts. It is impossible to discuss your paper when the meanings of
the symbols are not clearly specified.

The following will discuss the following points. The first
is the most important, and hasn't yet been raised explicitly.

(1) I think there may be a fundamental misunderstanding of what it means
to say that
`

[from your paper, attributed to Misner, Thorne, and Wheeler]

"...a spinor will reverse sign after any 2p = 360 degree rotation,
and will only regain its original sign after a
4p = 720 degree rotation."

The way you interpret this is not the way I interpret it.

(2) I think that your equation (4.8) definition of e_0 is circular,
and therefore not a valid definition. I do not know what your symbol
e_0 represents. A typo in my original analysis
prevented this from being as clear as it should have been.


BEGIN DISCUSSION OF POINT (1):

There are at least two conceivable meanings for

"a spinor will reverse sign after any 360 degree rotation:

(i) This could happen if the spinor wave function were multiple-valued.
But in my understanding of your paper, you don't assume
that it is.

(ii) This will require a bit of explanation, so please bear with me.

In describing a physical system, whether classically or quantum-
mechanically, one needs to first specify a coordinate system.
The description will depend on the coordinate system. Two descriptions
corresponding to two different coordinate systems will be related by
some transformation law.

Suppose we have a quantum mechanical system described in part by a wave
function \psi , and we want to ask what the wave function would look like
if we used a coordinate system rotated by a small angle, say 5 degrees,
about some axis relative to the original system.

If the wave function is a two-component spinor,
there are two possible answers. either U(5)\psi or U(365)\psi,
where U(angle) is a unitary operator (a 2x2 unitary matrix), and

U(365) = - U(5) .

It is a peculiarity of spinor representations that U(365) is not the
same as U(5). However, U(365)\phi does represent the same quantum state
as U(5)\phi. This is because when quantum states are represented by
wave functions, two (unnormalized) wave functions are considered the "same" if
each is a nonzero complex multiple of the other.

If we are considering a rotation through a very small angle,
it seems more natural to represent the wave function as seen in the
rotated coordinate system by U(5)\psi instead of U(365)\psi = - U(5)\psi,
because we would like for the wave function as seen from a slightly
rotated system to be close to the wave function as seen in the original
coordinate system.

Notice that WHAT IS BEING ROTATED IS THE COORDINATE SYSTEM.
The wave function never changes, only its mathematical representation
changes. An analogy is a classical particle not acted on by any forces.
We can find a coordinate system in which its momentum is constantly
zero or anything we please. The particle itself is always the same,
only its mathematical description changes as we change from one coordinate
system to another.

Now consider how our original wave function \psi will look in
a coordinate system rotated by 360 degrees from the original coordinate
system. Of course, it shouldn't change in any physically observable way,
because rotating a coordinate system by 360 degrees brings us back to
the original coordinate system. Remember, we are not performing some
kind of physical rotation; we are only changing coordinate systems.

However, if we conceive of performing the 360 degree coordinate
rotation as a succession of tiny rotations, say 72 rotations of five degrees
each, the resulting wave function will be described by

U(5)U(5) ... U(5) \psi = U(5)^72 \psi = U(360)\psi = - \psi .

The last equation U(360)\psi = -\psi is because of the two-valued nature
of spinor representations: U(angle + 360) = - U(angle)
for all angles including angle 0.

But -\psi represents the same quantum state as \psi because
in representating quantum states as wavefunctions, there is always
the ambiguity that for any nonzero complex constant *c*,
c \psi represents the same quantum state as \psi, even though considered
as functions, c \psi is different from \psi.

Physically, the above picture of rotating coordinate systems is
completely different from taking a wavefunction \psi = \psi(x) and
following its values as *x* traverses a small loop generated by a 360 degree rotation.
For single-valued \psi (which you seem to be assuming), the value \psi(x)
after traversing the loop will be the same as the value at the start of the
loop: the spinor function \psi DOES NOT CHANGE SIGN from the start to
the end of the rotation loop. If it's single-valued, it can't change sign!

I don't have Misner, Thorne, and Wheeler (MTW) at hand, but I
would bet that their interpretation of

"a spinor will reverse sign after any 360 degree rotation"

is (ii) rather than (i). I think this is the standard interpretation.
For example, the first paragraphs of the Wikipedia article on "Spinors"
unequivocally specifies this interpretation.

[Normally, I don't like to cite Wikipedia because some of its
articles are just plain wrong, but I don't have any better
reference at hand, and at least this reference shows that
my interpretation is a common one. If you rewrite
the Wikipedia article to change to interpretation (i), you
will probably generate howls of protest.]

I would bet that your paper was never read in any meaningful way
by Phys. Rev. D. I would also bet that if it ever *is* read carefully
by any knowledgeable referee for any mainstream journal,
he will cite the above apparent misunderstanding as reason to reject the paper.

END DISCUSSION OF POINT (1)

BEGIN DISCUSSION OF POINT (2):

This will be essentially the same as the original discussion of
your equations (4.7) and (4.8), with a silly typo corrected.


The paper's equation (4.7) states the "Dirac Quantization Condition":

(4.7) 2eg = n .

Here *e* is the electronic charge, *g* the monopole's "magnetic charge",
and *n* an arbitrary nonzero integer. The paper goes on:

"From (4.7), defining the n=1 charge units as e_0 = 1/2g
and g_0 = 1/2e, we see that the respective electric
and magnetic charge strengths are reciprocally quantized by

(4.8) e = n/2g = n e_0
g = n/2e = n g_0 . "

[In the original, g = n/2e was replaced by g = n/23.]

This seems to be circular logic: e is defined in terms of g while
g is defined in terms of e. Morever, I think that the preceding sentence
should read:

e_0 = 1/2g_0 and g_0 = 1/2 e_0 .

The effect is that neither e_0 nor g_0 are actually defined,
making it impossible to follow later discussion which references them.

END DISCUSSION OF POINT (2)


Some of the posts in this group have been viewed thousands of times,
which suggests that there could be hundreds of members. I have to wonder
if there is *no one* in the group sufficiently knowlegeable about spinors
to comment on whether interpretation (i) or (ii) above is the standard
interpretation. So far, no one other than I has volunteered any
substantive comment on your paper.

You want to avoid rejection for cause (e.g., incorrectness
or unclarity) because that will impact your credibility with the journal
for further submissions. Your future papers could be editorialy rejected
without even being refereed. Indeed, I suspect that this may have been
the case with Phys. Rev. D.

In my opinion, the paper is probably incorrect and surely unclear.
But I am only one fallible individual.

You can submit with more confidence if you can find even one qualified
person who will publicly assert that the paper is clearly written and
conceivably correct. If you can't find such a person in
sci.physics.founations, you might try sci.physics.research, which is
a moderated discussion group accessible through Google groups.

At one time, that group hosted many high-level discussions
read by many physicists and mathematicians. It used to be a reliable
source of inspiration for me. Of late, it has fallen on hard times,
with few posts, and fewer knowledgeable ones. But it may still be read
occasionally by competent people. The moderators are competent and
might well give reliable opinions on issues as straightforward as
the meaning of spinor sign reversals.

[Yablon]

To guest 1202 and all:

The rendering now works, so I have updated my post from yesterday to render the equations properly, visually.

I will have limited time these next two weeks, but do want to reply to our guest's latest post. I will just pick out one point right now which is this:

I may have been not precise enough when I said that the number c in must have a magnitude of 1. As our guest sort of pointed out in passing, a wavefunction is determined up to a normalization constant. And, the normalization is generally conducted by requiring that the total probability of the electron being somewhere must be equal to 1. This is often done in a covariant fashion, to account for the Lorentz contraction of the physical spaces involved in the circumstance where there is relativistic motion involved. Yet, it seems to me that if the magnitude of c is something other than 1, we will end up transforming the total probability so the electron to be somewhere, to some number other than 1. So it still seems to me, even with the caveat that the magnitude of a wavefunction is undetermined until one normalizes the probability, that allowing a transformation will mess with the probabilities in a way that makes no sense.

I do not have a strong opinion about this and can be persuaded otherwise, but in any event, none of what I am doing in my paper involves anything other than using unitary transformations.

I wish I could write more; but I have to leave for a meeting that will take most of the rest of the day.

Jay

[Ben6993]

Hi Jay

(I know you are busy and I do not expect a reply to this. I am always grateful to read your explanations wherever and whenever ... )

Thanks very much for your latest post with explanations. They helped me a lot and I think they have helped me to try to start to try to get a first glimpse of the magnetic monopole in a preon model.

I did not think that you were using 'strong' to mean a gluon but was not sure simply because you used that word.
So the photon is the electric force boson and is also the magnetic force boson. With the inverse relationship between the electric coupling constant and the magnetic coupling constant meaning that if one force is relatively weaker than some norm then the other force is stronger than that norm. The photon carries no net electric charge nor net magnetic charge which is nice and symmetric between the two forces.

OK, I will forget about quarks (at least for this paragraph!) but I am still not very clear as to what is the monopole when an electron traverses a magnetic monopole in tidal lock. You mention an electron and a positron. I can imagine an electron and positron interacting and annihilating. In my preon model their preons still exist after annihilation and could reform into two new particles, say a magneto-electron and a magneto-positron. In my model the preons in an electron-positron pair can be reformed into many different particle pairs eg neutrino & antineutrino, or red up quark & antired antiup quark [sorry, those pesky quarks get everywhere, but I am not going to use them here]. So the e-/e+ pair could possibly be reformable into two magneto- particles. Then take the magneto-positron and let an electron traverse the magneto-positron in a tidal lock at near 0 degrees K.

In my preon model, the electric charge of an electron is not a fundamental property, it is derived from the net amount of colour tone (QCD white tone= negative electric charge and QCD black tone = positive electric charge) in the preons making up the electron. So as the electric charge is not, in my model, a fundamental property of a particle, nor of a preon, so magnetic charge does not need to be added to the fundamental properties of a preon. But I need to find out how QCD colour charges can determine magnetic charges.

I ought to add that the relationship between QCD colours in preons is different to that in quarks (else I would be seen immediately as wrong because a red quark can be either positive of negative in electric charge). A coloured (sub-)preon is always negatively charged and an anticoloured sub-preon is always positively charged. Also, the colour additions for the quarks are interrelated, as in a geometric algebra, or in the primary colour wheel eg red+green = antiblue.

However, in my model there is no primary colour wheel relationship between preon colours. Say capitals for quark colours and anticolours (R, G, B, R', G' and B') and lower case for preon colours and anticolours (r, g, b, r', g' and b').
In my model the quark colours are made from preon colours as:
R = r g' b'
G = r' g b'
B = r' g' b
R' = r' g b
G' = r g' b
B' = r g b'
(This is a slightly simplified version.)

So red + green = R + G = r g' b' + r' g b' , which after rearranging terms = (r g b') + (r' g' b') = B' + black.
The black term shows how colour tone interferes with a simple explanation of electric charge being derived from colour tone.

A first idea for magneto-colours is to rearrange, at a 0 degree K interaction, the subpreons into rg, rb, gb, r'g', r'b' and g'b' in the magneto-electron instead of r, g, b, r', g' and b' in the electron.
An analogy is that r represents a spinor (or bivector?) wrt a red brane while rg represents a spinor (or trivector?) wrt the red and green branes simultaneously. Though I suggested it above, I cannot be sure that preon colours do not obey a primary colour wheel relationship, it would be useful if they did as follows. The electron has r, g and b subpreons. These could be recast as g'b', r'b' and r'g' respectively using a colour wheel relationship.This could mean that the electron preons get used in the magneto-positron monopole.

Another point is about tidal lock. Although I like the idea in relation to the great forces for the magnetic monopole, in general wavelength get very large at zero degrees (or is that ony for bosons, as in Penrose's CCC end of cycle or in cold end of universe?) Do not long wavelengths sit uncomfortably in a very naive sense with tidal lock?

I hope the interesting discussion about single value/ multi-value is not continued in camera, or if it is that we get a summary of the outcomes later?

(Sorry to go on about preons but I see almost everything in those terms.)

[Yablon]

...Another point is about tidal lock. Although I like the idea in relation to the great forces for the magnetic monopole, in general wavelength get very large at zero degrees (or is that ony for bosons, as in Penrose's CCC end of cycle or in cold end of universe?) Do not long wavelengths sit uncomfortably in a very naive sense with tidal lock?

Hi Ben, quick reply:

Fermions obey Exclusion, so even right above 0K there are some energies retained because some fermions are forced into higher energy states to satisfy exclusion.

Your observation about the wavelength is astute, and leads me to outline the thermodynamic connection I will develop in the coming weeks. Plank's law merged Rayleigh-Jeans' and Wein's laws to cover both ends of the wavelength / frequency spectrum. What I will do is use the integration over frequencies of Plank's law into the Stefan Boltzmann law to obtain a probability density function that integrates to 1, which includes a dimensionless scalar spectral blackbody function that is equal to zero if T=0K and larger than zero if T>0K. I will show the generalization to greybodies, but use the blackbody spectrum as an idealized illustration. That spectral function is the monopole residue charge so that when T=0K and monopoles exist you have the Dirac Quantization Condition, and when T>>0K and the monopoles are all melted the thermal charge takes over where the monopoles left off. This charge is closely related to the statistical mechanics partition functions, so when you start taking derivatives you come across internal heat energy and entropy and all these other things we see in thermodynamics. This hooks into the monopoles because in all the Dirac derivations the charges e and g are idealized to be constant, even though in the natural world they must run even if ever-so-slightly, and , when you raise the temperature. There is then a direct relationship that will be demonstrated between the running of these electric and magnetic charge strengths and the thermal blackbody scalar charge residue, and this is the umbilical cord that unifies electrodynamics and thermodynamics. Perhaps the most plainly I can put it is that the answer to the question "in what ways do we observe magnetic monopoles in our daily life?" is that "we observe them -- and really their melted residues -- through the very existence of heat and associated thermodynamic processes." Briefer: thermodynamics is the way in which we experience the existence of magnetic monopoles on a daily basis.

Background for Plank's law et al. is at https://en.wikipedia.org/wiki/Planck's_ ... tzmann_law, and for partition functions is at https://en.wikipedia.org/wiki/Partition ... chanics%29.

I hope the interesting discussion about single value/ multi-value is not continued in camera, or if it is that we get a summary of the outcomes later?

So far nobody's antics have scared off our new guest. Let's keep it that way.

Jay

[guest1202]

Mr Yablon,

My last post discussed two points:

(1) It seems to me that your interpretation of spinor sign reversal
under 360 degree rotations is not the usual one;

(2) I thought that the discussion around equations (4.7) and (4.8)
in your paper was mathematically incorrect.

I still opine (1), but I think I see a way to make sense
of (4.7) and (4.8). The paper's exposition was unclear to me,
though I'm not sure everyone would find it unclear. Now that I think
I understand it, it certainly seems clearer.

Following is my present understanding. I start by
quoting my previous post:

"The paper's equation (4.7) states the "Dirac Quantization Condition":

(4.7) 2eg = n .

Here *e* is the electronic charge, *g* the monopole's "magnetic charge",
and *n* an arbitrary nonzero integer. The paper goes on:

"From (4.7), defining the n=1 charge units as e_0 = 1/2g
and g_0 = 1/2e, we see that the respective electric
and magnetic charge strengths are reciprocally quantized by

(4.8) e = n/2g = n e_0
g = n/2e = n g_0 . "

[In the original, g = n/2e was replaced by g = n/23.]

This seems to be circular logic: e is defined in terms of g while
g is defined in terms of e. Morever, I think that the preceding sentence
should read:

e_0 = 1/2g_0 and g_0 = 1/2 e_0 .

The effect is that neither e_0 nor g_0 are actually defined."

I think you may be saying that *given* a monopole with
magnetic charge *g* (so that *g* is already defined), the charge *e*
of an electrically charged particle is quantized by (4.7). The smallest
possible electric charge corresponds to n=1, and you denote this by
e_0. Then the first line of (4.8) becomes correct. Similar remarks
apply if some electric charge *e* is given, leading to quantization of
*g* according to the second line of (4.8)

This is a minor point, which doesn't affect the mathematical
correctness of the paper, and the exposition could easily corrected.
But as written, I certainly did find it puzzling. This underscores
why I think it would be to your advantage to have the paper read
and approved informally by some knowledgeable person before formal
submission to a journal.

That could help you iron out kinks in the exposition
which might trip up a referee. I can see how from your point of view,
knowing what you want to say, the exposition might seem clear.
For this particular example, I would hesitate to say unequivocally
that it is not clear, but it took me quite a bit of thought to discern
your meaning (assuming that my present understanding is correct).

While on the subject, I'll make a few further remarks.


REMARK 1:

The impression I got from your lengthy December 6 post
is that your paper assumes single-valued wave functions. But on
further consideration, it seems to me that the mathematics is more
likely to hold together if instead you assume multiple-valued wave functions
(as does Dirac). I won't go into the reasons for this, but I think
it would be to your advantage if the paper clearly specified the
underlying framework which it assumes.

REMARK 2:

If I understand the paper's argument correctly, it basically
says that Dirac's analysis was wrong because he failed to take into
account that (according to your interpretation which I question)
the electron wave function is double-valued and changes by a factor (-1)
as one goes around a loop generated by a 360 degree rotation.

If your interpretation is correct, this is an astonishing
insight. Dirac invented the wave function of the electron (before
publishing his quantization paper) but never noticed this!
Moreover, no one before you has noticed this error for about 75 years!

This is certainly possible (I know of a similar case), but
you will find it a very hard sell. To get people to believe it,
(and many won't no matter what you do), you will have to explain
it in a way that is crystal clear. As currently written, I would be
surprised if anyone would characterize the paper as crystal clear.
It will be to your advantage to induce someone knowledgeable to read the paper
carefully and point out places where the exposition might be improved.
You can't expect a referee to do this.

Of course, this assumes that the paper is correct to start with.
I have my doubts, but I have to consider the possibility that the
sticking points for me are as trivially overcome as those around the paper's
equations (4.7) and (4.8).

[Yablon]

...I think you may be saying that *given* a monopole with magnetic charge *g* (so that *g* is already defined), the charge *e* of an electrically charged particle is quantized by (4.7). The smallest possible electric charge corresponds to n=1, and you denote this by e_0. Then the first line of (4.8) becomes correct. Similar remarks apply if some electric charge *e* is given, leading to quantization of *g* according to the second line of (4.8).

This is a minor point, which doesn't affect the mathematical correctness of the paper, and the exposition could easily corrected. But as written, I certainly did find it puzzling. This underscores why I think it would be to your advantage to have the paper read and approved informally by some knowledgeable person before formal submission to a journal.

That could help you iron out kinks in the exposition which might trip up a referee. I can see how from your point of view, knowing what you want to say, the exposition might seem clear. For this particular example, I would hesitate to say unequivocally that it is not clear, but it took me quite a bit of thought to discern your meaning (assuming that my present understanding is correct).

First, I will say that this issue does not affect the correctness of the paper, and am glad you see that also. But I agree that it is worth my going back to Dirac's original work and some later expositions of his work to clean up anything that possibly could throw a reader off track. The way I view the DQC is that it contains an absolute reciprocity between e and g, and therefore presents a chicken and egg when it comes to the units of charge and . You can pick out either as a quantum of electric charge or as the quantum of magnetic charge, which is what I showed at (4.8). But -- it may be that you may do one or the other but not both, i.e., that doing both creates a tautology. That is what I will review and ponder and try to answer explcitly in my next revision of the paper.

REMARK 1: The impression I got from your lengthy December 6 post is that your paper assumes single-valued wave functions. But on further consideration, it seems to me that the mathematics is more likely to hold together if instead you assume multiple-valued wave functions (as does Dirac). I won't go into the reasons for this, but I think it would be to your advantage if the paper clearly specified the underlying framework which it assumes.

Agreed, and I am studying single versus multi-valuedness much more directly now. Whether my paper sinks or swims will depend on properly handling this issue and it is not a trivial issue.

REMARK 2: If I understand the paper's argument correctly, it basically says that Dirac's analysis was wrong because he failed to take into account that (according to your interpretation which I question) the electron wave function is double-valued and changes by a factor (-1) as one goes around a loop generated by a 360 degree rotation.

If your interpretation is correct, this is an astonishing insight. Dirac invented the wave function of the electron (before publishing his quantization paper) but never noticed this! Moreover, no one before you has noticed this error for about 75 years!

This is certainly possible (I know of a similar case), but you will find it a very hard sell. To get people to believe it, (and many won't no matter what you do), you will have to explain it in a way that is crystal clear. As currently written, I would be surprised if anyone would characterize the paper as crystal clear. It will be to your advantage to induce someone knowledgeable to read the paper carefully and point out places where the exposition might be improved. You can't expect a referee to do this.

Of course, this assumes that the paper is correct to start with. I have my doubts, but I have to consider the possibility that the sticking points for me are as trivially overcome as those around the paper's equations (4.7) and (4.8).

Au contraire. Actually, I am not saying that Dirac's analysis was wrong. It was right. But it contained an assumption that nobody seems to have pointed out, or tracked down the consequences if that assumption were to be changed. There is no reason why an electron wavefunction being loop-transported around a magnetic monopole to detect the field strength a.k.a. gauge curvature which contains the Coulomb magnetic field B must also be rotated in a tidal lock at the same time. In fact, the natural assumption would be that there is no rotation which is the assumption that Dirac and others have used. Given that assumption, Dirac and everybody else has been perfectly correct. If I did not make myself clear, the whole point of sections 1 through 4 was to demonstrate what Dirac did and why he was correct given his implied assumption that the electron was not rotating while making the loop.

What I am claiming, is that nobody appears to have studied the double-valued nature of the wavefunction which changes its coefficient from +1 to -1 after a single rotation, and also studied the way in which Dirac quantization is derived by having a wavefunction orbit a Coulomb magnetic field, and based on those studies, asked the question: what would happen to the Dirac condition, if anything, if during its orbit, the electron also rotated in a tidal lock and so reversed sign? If the equation in https://www.encyclopediaofmath.org/inde ... c_monopole that reads:



and the condition stated on the next line that "The wave function is single valued" still applies in the same form when the rotation is synchronized to the orbit and so a sign has flipped, then the identity which brings in the quantization changes to the identity (see my (6.1)) in order to absorb that sign change, and (a3) changes to my half-integer charge condition (5.14), namely:

(5.14)

I am not claiming that anybody made an error. I am claiming that they made an valid albeit inexplcitly-stated assumption, and that nobody appears to have made a different assumption and then followed though its logical consequences. If part of what you are saying is that the valuedness conditions applied to the wavefunctions are critical whether to all of this works, you will get no disagreement from me.

If it does work, then one must still answer Weinberg's implied critique -- not of the method but of the result -- that the wavefunction would have to be affecting the magnetic potential which we do not do in classical theory. That, I have explained in this thread already, as a quantum phenomenon in which the nature of the detecting wavefunction does indeed induce a quantum transition in that which it is detecting. I will also note that while there is a prevailing theoretical explanation for odd-fractional FQHE charges which I intend to eventually overthrow, there is, to date, no explanation of the half integer charges. So the fact that this line of inquiry explains something observed that has no other explanation does work, long-term, in my favor.

One other set of comments before I go. Perhaps somebody between 1931 and the 1980s who knew Dirac monopoles and knew SU(2) double covers did look at what I have proposed and concluded that it would lead to half-integer charge quanta and decided that this was a throwaway because there are no half integer charges (and so missed to opportunity to predict them before they were observed). But once those charges became observed, they needed an explanation. Yet, by that time condensed matter physics had matured into a certain direction and was using macroscopic collective systems of quasi- / pseudo- particles to explain things. Sometimes, the explanation for why something has been overlooked is more sociological than logical. So, there may not have been any motivation for someone to go back to Dirac's condition to look for a microscopic explanation that at low temperatures, electrons simply condense into magnetic monopoles on a one-by-one basis and that quantum electrodynamics then starts to show fractional charge quanta as well as integer charge quanta as part of its fundamental character under those fundamental thermodynamic conditions. If electrons do condense to magnetic monopoles near 0K and duality symmetry takes over and dominates everything near 0K, all sort of funky new things would naturally happen with the magnetic fields and the electric currents which everybody at present is trying to explain instead with funky collections of ordinary electrons. That is why I see a unification between the two major physics disciplines of electrodynamics and thermodynamics taking place in the high-symmetry environment near 0K.

Jay

[Ben6993]

Hi Jay

I have just been reading, in relation to cold temperature physics, this excellently readable article: http://cerncourier.com/cws/article/cern/63157
about the works of Nambu.

So may I ask you is the Meissner effect (superconductors repel external magnetic fields) caused by the superconductors containing magnetic monopoles? (Which can repel [or attract and bind up?] external magnetic fields.)

Also, the article mention the charge symmetry breaking at low temperatures leading to a photon with mass plus a neutral, scalar particle. I have not read anywhere that the mass of this heavy photon has been measured (unless these are simply the Z and higgs again?). But has anyone measured the mass of the heavy photon under near 0K conditions, to see if this heavy photon is not the Z?

Also, does 'your' magnetic monople also have electric charge = -0.5? That seems to be an asymmetry in that the entity would have a magnetic monopole plus an electric monopole. Or is this an effect of being not quite at 0K temperature? I thought a duality was either magnetic or else electric, but is it right for a single 'electron' to have both types of monopole simultaneously?

[FrediFizzx]

Hi Jay,

I am wondering if this might be relevant to your research?

http://phys.org/news/2015-12-physicists ... anics.html

[Yablon]

Hi Fred and Ben,

Thank you for your posts these last couple of days. I am in the middle of a brief vacation in Florida following a trip down to attend a wedding, and I am indisposed to be able to prepare a proper reply. But I always appreciate having new things drawn to my attention, and will carefully review everything and reply once I am back home and situated.

Best regards,

Jay

[Yablon]

Hi Jay,

I am wondering if this might be relevant to your research?

http://phys.org/news/2015-12-physicists ... anics.html

"Fundamental monopoles are hypothetical, but there has recently been much research on constructing condensed matter systems consisting of quasi-particles which have properties similar to monopoles," said coauthor Suddhasattwa Brahma.

Fred,

I am sitting here while my wife Debbie is shopping for dresses, so maybe I will take a few minutes to reply.

The quote above is an example of people beating around the bush without cutting to the chase. People are sniffing out that phenomena of low temperature physics have properties which resemble those of magnetic monopoles. This is similar to how people are sensing that forces within the proton and neutron resemble those of monopoles and magnetic flux tubes.

The reason they are sensing this is not because the properties are "similar." It is because in fact we are observing real, physical magnetic monopoles themselves. In nuclear physics, when we are observing protons and neutrons we are in fact observing non-abelian magnetic monopoles. And in condensed matter physics near 0° Kelvin, we are not merely observing things that resemble magnetic monopoles, but are in fact observing magnetic monopole themselves as well as the effects of large aggregates of said monopoles.

I have said it before and I will say it again and again and again until people listen and realize that I am right: The road to unification in physical science resides in properly understanding magnetic monopoles fully and completely in their abelian and non-abelian forms. Once that realization occurs, physicists will be able to tremendously simplify and the economize their understanding of the natural world amongst what are presently understood only to be separate ununited disciplines of physics.

As I conclude this post, Debbie has finished her shopping, and I am back on the deck of our resort overlooking the Gulf of Mexico on a clear star-filled night. At the 8 o'clock position and on the rise is the constellation of Orion the Hunter who has guided and will guide the travels of southern wanderers for millennia past and still to come. Once again I am in awe of how the creations of nature far exceed any and all imitations within the reach of mankind by leaps and bounds.

Jay

[Q-reeus]

...So, there may not have been any motivation for someone to go back to Dirac's condition to look for a microscopic explanation that at low temperatures, electrons within said volume element simply condense into magnetic monopoles on a one-by-one basis and that quantum electrodynamics then starts to show fractional charge quanta as well as integer charge quanta as part of its fundamental character under those fundamental thermodynamic conditions. If electrons do condense to magnetic monopoles near 0K and duality symmetry takes over and dominates everything near 0K, all sort of funky new things would naturally happen with the magnetic fields and the electric currents which everybody at present is trying to explain instead with funky collections of ordinary electrons.

Jay, just to be real clear on what that passage seems to be obviously claiming.....
Take some small volume element, for which there is zero flux of matter and/or charge across the bounding surface. At a certain transition temperature, electrons condense 1:1 into magnetic monopoles. Presumably, such that invariably say e- -> g- (or g+), but not BOTH g- and g+. In which case, div E and div B both abruptly change i.e. a simultaneous violation of electric and magnetic charge conservation has taken place.
If above is not what you are claiming, a simple, dumbed-down explanation-by-way-of-specific-scenario of just what you are claiming would be appreciated.

Many years ago I discovered by a 'naive' direct application of fully relativistic (Lienard-Wiechert) EM field equations, for certain, even steady-state current distributions, one of the four ME's directly failed - the Maxwell-Ampere curl one. On the surface an illogical contradiction, but it's there nonetheless, not owing to any careless maths blunder. Depending on what one adopts as a truly fundamental definition for E and B, it can be argued the Maxwell-Faraday one for curl E might also fail - but any such failure only showing under special circumstances involving superconducting circuits. Point here though is, found not a single case where the other two - the div ones, ever failed. Which makes your claims all the more 'remarkable', to put it mildly.

Will just add that I'm not a fan of Dirac's original reasoning which relied heavily on conservation of angular momentum. For me it's bleeding obvious the so-called Feynman disk paradox (actually originally owing to J.J.Thompson ca early 1900's) has been given the wrong interpretation. Ascribing a physically real 'stored field momentum' to crossed static and *independent* E & B fields.

[Yablon]

Jay, just to be real clear on what that passage seems to be obviously claiming.....
Take some small volume element, for which there is zero flux of matter and/or charge across the bounding surface. At a certain transition temperature, electrons condense 1:1 into magnetic monopoles. Presumably, such that invariably say e- -> g- (or g+), but not BOTH g- and g+. In which case, div E and div B both abruptly change i.e. a simultaneous violation of electric and magnetic charge conservation has taken place.
If above is not what you are claiming, a simple, dumbed-down explanation-by-way-of-specific-scenario of just what you are claiming would be appreciated.

Hi Q-reeus: Actually, one would think so, but no. The reason is that at the transition temperatures near but somewhat above 0K where the magnetic charges of electrons and protons dissolve, the magnetic charges smoothly migrate over into thermal charges. This is what I mean when I say that the magnetic charges dissolve into a thermal residue. Put another way, it is thermodynamics itself which smooths out what would otherwise appear superficially to be the abrupt introduction (or dissolving) of magnetic monopoles. This is a form of spontaneous symmetry breaking, albeit at very low temperatures. Keep in mind also that the electric charges remain as is; they are simply supplemented with magnetic charges near 0K via the condensation of thermal charges into magnetic charges, sort of like solidifying heat energy into magnetic charges. These thermal charges are dimensionless scalar numbers just as are e and g (in units), and they are very closely related to the partition functions of thermodynamics insofar as taking their derivatives leads to to the various laws of thermodynamics. These magnetic charges may also be seen as thermal potentials: while the potentials in electrodynamics are vectors with a local invariance under transformations using a scalar phase angle (gauge symmetry), the potentials in thermodynamics are these scalar thermal charges which "fill in" the indeterminacy of the scalar phase. Put another way, the laws of electrodynamics emerge from differentiating a vector potential; those of thermodynamics emerge from differentiating a scalar potential which is tied to partition functions and is a dissolved monopole residue. For basic background see https://en.wikipedia.org/wiki/Partition ... chanics%29.

I am trying to develop and present this on several fronts right now. First, I do want to establish that I am correctly handling the single valuedness problem which I discussed with guest1202 recently in this thread. I am using a parallel transport around a closed loop approach to do so; that is why I asked earlier today for an off-the-shelf derivation of the Lorentz force law from varying an action, if somebody has one. Second, I want to update my paper to thoroughly answer why Weinberg's objection stands under a classical analysis but can be overcome under a quantum analysis. Finally, I want to show all these thermodynamics connections.

For a preview of the approach to the thermodynamics connections, look at section 2 of http://vixra.org/pdf/1503.0054v1.pdf, and also http://vixra.org/pdf/1501.0070v2.pdf. Keep in mind that the details in both of these papers have errors and will be superseded, and that what I intend to develop this coming season will essentially correct the development of these ideas the thrust of which is correct IMHO, but which ideas were nonetheless incorrectly implemented in these earlier papers. The latter paper especially was a rather naive first attempt to connect to thermodynamics which was never a wheelhouse for me; but in the past year I have learned what I need to know about thermodynamics to do this correctly going forward.

Jay

[Q-reeus]

...The reason is that at the transition temperatures near but somewhat above 0K where the magnetic charges of electrons and protons dissolve, the magnetic charges smoothly migrate over into thermal charges. This is what I mean when I say that the magnetic charges dissolve into a thermal residue...

Well Jay, 'thermal charge' has now been added to my lexicon. I'm guessing said migration/dissolution magnetic charge <-> thermal charge invariably always involves only g-/g+ pairs. Such that there is never a definable bounding surface where div B alters sans a corresponding monopole current. Best over Xmas/NY.

[Yablon]

...The reason is that at the transition temperatures near but somewhat above 0K where the magnetic charges of electrons and protons dissolve, the magnetic charges smoothly migrate over into thermal charges. This is what I mean when I say that the magnetic charges dissolve into a thermal residue...

Well Jay, 'thermal charge' has now been added to my lexicon. I'm guessing said migration/dissolution magnetic charge <-> thermal charge invariably always involves only g-/g+ pairs. Such that there is never a definable bounding surface where div B alters sans a corresponding monopole current. Best over Xmas/NY.

Thanks Q-reeus. Actually my Xmas will be with some good friends near Boston whom we met in Israel about 5 years ago. What we call a Jewish Christmas.

I do want to talk a bit more about all of this. There are two issues involved I wish to articulate and develop right now. First, is the simple physical fact (or more precisely, what I am planning to get everyone to realize is a simple physical fact) that on a microscopic basis, when the temperature approaches absolute zero, individual electrons take on a magnetic charge in addition to their electric charge which represents a migration of higher-temperature thermal partition charges into lower-temperature magnetic charges. Second, is the question of how one models what then happens when we observe large collections of these electrons-turned-monopoles near 0K. Keep in mind, per Dirac, that the Coulomb magnetic interaction between two such monopoles is times as large as the Coulomb electric interaction between them. So for like charges this is a very strong repulsion, and for opposite charges it is a very strong attraction. For attracting monopoles, this is what creates the tidal force bulge that then creates a tidal lock that then spawns half-integer charge fractions.

Now, in some earlier posts in this thread, I suggested using an electron / positron model for two attracting magnetic charges. This is a modelling assumption. On further thought, I think it best to work from the prevailing understanding of how matter holds together in the first place: atoms contain large numbers of negative electric charges that do repel one another, but they do not come flying out of the atoms because there are also counterbalancing positive proton charges which keep electrons in the system. Protons of course confine two up quarks and one down quark with Q=+2/3 and Q=-1/3 charges, respectively. So rather than invent something new that involves positrons, I think we take matter as we already understand it, and build on that. Consequently, near 0K, electrons take on negative magnetic charges -1, up quarks take on positive magnetic charges +2/3, down quarks take on negative magnetic charges -1/3, and protons therefore take on an aggregate magnetic charge of +1. So we model the atoms and the bulk materials formed from atoms in exactly the same way that we always do, with one exception that simply scales up the Coulomb interaction strengths tremendously: Now, protons will attract electrons times a strongly, protons will repel one another more strongly by the same factor, and electrons will also repel one another more strongly by the same factor. In other words, take whatever model one uses for a bulk system of matter, but make all attractive and repulsive electrical forces approximately 4693.25 as large. And that is your so-called "condensed matter" system. Very simple, nothing more required. (Of course, there are still the usual electric versus magnetic features that must be accounted, but now the electric fields are just high-order corrections to the magnetic fields which dominate the physics.) What now happens when we do this?

First, if we assume (and I am assuming) that the strong force of QCD remains substantially unchanged near OK, then protons will magnetically repel one another 4693.25 times as strongly, so that the nuclei will actually expand, not condense their spatial volume. Secondly, the protons will magnetically attract the electrons 4693.25 times as strongly, so the atomic shell layers will indeed condense their spatial volume. Finally, the electrons will magnetically repel one another 4693.25 times as strongly. So, for example, take two the two electrons in the 1s shell of a helium atom. The probability clouds for these two electrons will "push apart" much more strongly than they do at higher temperatures, which if you think through the physics of this, means that the electron systems will become "flatter," i.e., electrons ordinarily filling a three-dimensional surface will flatten out and be much more restricted to two dimensions owing to a much stronger mutual repulsion. And you will see it often said that the FQHE physics involves condensed two-dimensional systems of electrons. This is why: although the protons still hold the electrons in place (and do so with much greater strength), the electrons themselves form much flatter systems due to their much stronger mutual repulsion. These systems are "condensed" because the protons pull in the electrons with much greater strength, and they are two dimensional because the electrons repel one another with much greater strength. But, the nuclear core of these systems is expanded, not condensed, because the protons will push one another apart with much greater strength. This final aspect of an expanded nuclear core near 0K -- which I hereby make as a prediction -- may be something that some clever experimental physicists can observe in their low temperature experiments. Finally, within each proton, the two up quarks will repel one another and the down quark will attract the two up quarks with much greater strength. Similarly for neutrons, just flip over to two down quarks and one up quark. So each individual proton or neutron will also tend to elongate, so that they will model much less as "round" balls, but instead as elongated ovoids (colloquially, elongated eggs). This is the per-nucleon manifestation of the flat electron systems near 0K. So here is another prediction: near 0K, each nucleon should be detected to be much more elongate than otherwise.

Let me conclude by stating that one of the very nice things that happened while I was in Florida last week is that Fred Diether, in this thread, pointed out to me the link http://phys.org/news/2015-12-physicists ... anics.html which also links to http://phys.org/news/2015-04-physicists ... .html#nRlv and http://phys.org/news/2009-07-physicists ... poles.html, all of which I will cite in the next draft of my paper. To me, it is abundantly clear that physicists are observing structures "resembling the magnetic monopole particle" near 0K, not because of some mere "resemblance," but because nature really does have magnetic monopoles near 0K. The pedagogical problem is that so long as physicists continue to not recognize what I am claiming here, they will continue to try to understand low temperature physics by synthetically creating theoretical "monopoles" through various manipulations of the ordinary magnetic fields that come about through the relative motion, including spins, of ordinary electric charges. In a sense, it was really Dirac who first did this in 1931. He showed that you can use ordinary electrons to create a solenoid, and then if you made the solenoid infinitely long and infinitely narrow (hence "string") and kept one solenoid mouth near you and the other mouth out at infinity, the fields coming in and out of the mouth of the solenoid near you would approach the fields of a magnetic monopole. In other words, postulate a solenoid, and then in the limit where your postulate approaches a physical fiction, you will have a magnetic monopole at one end of the solenoid. The same effect can be approximated by a large separation of a north and south magnetic dipole. So if you made all the made all the north and all the south dipoles sit on "opposite sides of the room" in a low-temperature conductor (sort like the boys and girls at the summer camp dances I attended when I was nine years old), you can simulate magnetic monopoles, but only on a synthetic basis. In effect, much of condensed matter physics and the use of quasi particles has been about concocting clever configurations of ordinary electrons to simulate magnetic charges and explain on an approximate basis, much of what is observed. But as Marvin Gaye and Tammi Terrell once sang, "Ain't Nothing Like the Real Thing." Because nature does not merely simulate magnetic monopoles: near 0K, it does contain genuine Dirac monopoles themselves.

Specifically, notwithstanding that he started off by modelling with a solenoid made to approach fictional limits, the most important thing that Dirac found in 1931 was the quantized relationship , and its implied strength factor , because the one thing that you can never get from theoretically synthesized magnetic monopoles, is the strength factor that Dirac uncovered. There is nothing inherent in the magnetic fields of ordinary solenoids carrying ordinary electrons that give the magnetic fields at their mouths some strength increase over the electric fields. There is no such factor emerging from spinning electrons. This strength factor is wholly a feature of real, physical monopoles, and not something that can be concocted by collective configurations of ordinary electrons alone, no matter what you do. So for as long as theorists continue to model matter at low-temperature with synthetic magnetic charges, they may be able to get the magnetic field configurations approximately correct. But they will have no way to introduce the high-strength magnetic forces which are responsible for truly "condensing" the condensed matter, and are physically responsible for the electronic systems becoming two-dimensional, and for the tidal locking that spawns the half integer FQHE charge fractions. Nor will they be able to properly explain the odd-integer fractions which I can also explain downstream using "root of unity" transformations on spinors that I have talked about in some earlier papers shared here, see section 11 of https://jayryablon.files.wordpress.com/ ... or-spf.pdf, wherein the even-integer fractions that are not empirically observed turn out to also be theoretically forbidden by Lorentz symmetry, bringing theory and observation into complete concurrence.

So with that, let me wish a Merry Christmas to my friends who observe that holiday, and a great end of year and a peaceful and prosperous and happy new year to everyone.

Jay

[Q-reeus]

Yablon, the following is not intended to be a party spoiler. Just my attempt at a reality check.
In other threads:
viewtopic.php?f=6&t=51&start=100#p5792 (and further posts there)
viewtopic.php?f=6&t=241
,I attempted to point out a few fundamental issues with models of electron and photon posited by a Randell Mills. Lots of maths there but it only takes a short while to see that such models fail at a basic level. Violating e.g. SR, and/or inherently unstable. Not suggesting by any means you are in the same basket as RM. However in returning to think about your last post here and my one before that, in concentrating on real or apparent monopole charge violation, the attendant issue of energy-momentum conservation was evidently ignored.

As you explicitly claim accordance with that principle, it's extremely hard for me to see how it could hold in given scenario.
Which as per above post, evidently has it that in certain condensed matter systems, as T - > 0 deg K, all electrons, and all protons (further; all up and down quarks) take on magnetic charges of |g| or 1/3 multiples in quark cases. The EM interaction forces rising by the factor 1+(137/2)² ≈ 4700. As you describe it, swelling the nucleus, flattening electronic orbitals, and elongating protons.
This dramatic transformation is clearly taken to be a spontaneous one triggered by an endothermic process - cooling. Extraction of practically all available thermal energy from the system. Yet surely e -> e+(-g) is itself a massively endothermic process, and the nuclear environment equivalent p -> p+g even far more so. Are not massive energy inputs required - somehow? So, can you explain, in straight-forward language, how to reconcile conservation of energy-momentum with something that at least appears to clearly violate it?
There is an obvious balancing process there you have in fact explained but I just haven't noticed?

One further matter. In all your writings there is much reference back to Dirac in particular re monopoles, but wouldn't the most obvious comparison and point of reference be to Julian Schwinger's original 1969 formulation of 'The Magnetic Theory of Matter'? Wherein he coined the term dyon to describe the dual electric/magnetic charge entities of his theory: https://en.wikipedia.org/wiki/Dyon

[Q-reeus]

Last post managed to confuse things a bit by referring to refrigerating as endothermic but strictly speaking exothermic would have been closer to the mark but still askew. I had meant to convey that exothermic processes are energetically favorable and tend to be spontaneous, whereas a system doesn't spontaneously cool below it's environmental temperature. It would have been better to simply say refrigeration extracts what was initially a comparatively meager source of energy.

Main concern remains as to where the enormous gains in rest energy alone could be 'cannibalized' from when electrons & protons (quarks) -> dyons. And further, if there is such an identifiable reservoir, how such a transformation could be thermodynamically favorable i.e.spontaneous and stable against various possible decay processes.