Revised Dirac Monopole Paper

[Yablon]

Dear Friends:

On April 4 I posted a link to my monopole paper at http://vixra.org/pdf/1504.0025v1.pdf and wrote a report here. I had submitted this to PRD on April 2.

On April 16 I received the following rejection of this paper from PRD:

If your manuscript were correct, it should be a simple matter to explicitly present a vector potential whose curl is a Coulomb magnetic field and which has no observable singularities. Given the absence of the explicit presentation of such a vector potential, I still conclude that your manuscript is not suitable for publication in Physical Review D.

I was very encouraged by this rejection, because it was no longer asserting that there was something amiss with my paper. Rather, it was simply challenging me to make a particular presentation which I had not made. I read this to say that if I could successfully make this explicit presentation, the paper could be accepted the next time through.

So, this past week I worked on a revision which does include the explicit presentation that I had been challenged to make, and I resubmitted it to PRD last evening.

This latest version of the paper may be found at http://vixra.org/pdf/1504.0200v1.pdf.

The cover letter I sent last night with the resubmission stated as follows:

In your review of April 16 you stated, simply, that “if your manuscript were correct, it should be a simple matter to explicitly present a vector potential whose curl is a Coulomb magnetic field and which has no observable singularities.”

I very much appreciate this wisdom. It was spot-on, and is precisely the type of feedback I would have been hoping to obtain from a thesis advisor if I was some 30 years younger studying at Columbia or my alma mater MIT or a similar institution. Thank you!

The revised manuscript I am submitting today – please note revised title and abstract – does exactly what you suggest. Sections 2, 3 and 4 do explicitly present a vector potential whose curl is a Coulomb magnetic field, and they show how using the standard DQC, this leads to no observable singularities. The rest of the paper goes on to show how the standard DQC can be extended to the fractional Dirac-Wu-Yang charges I have been writing about for the past five months or so, also without observable singularities.

I believe that this revision overcomes all prior objections, and may finally be at a point of development where it is suitable for publication in Phys. Rev. D.

I am keeping my fingers crossed that this will finally do the trick. I will keep you apprised.

Jay

[Q-reeus]

On April 16 I received the following rejection of this paper from PRD:

If your manuscript were correct, it should be a simple matter to explicitly present a vector potential whose curl is a Coulomb magnetic field and which has no observable singularities. Given the absence of the explicit presentation of such a vector potential, I still conclude that your manuscript is not suitable for publication in Physical Review D.

Jay, that criticism by a referee was just what was being hinted at in the currently last post here: viewtopic.php?f=6&t=149
[it would be so helpful if POST NUMBERING were implemented here at SPF!]
So much of your math is above my level, but trying to discern the underlying implications & consequences, that's what stood out for me. Noticing in your reply you claim to have achieved such a feat, perhaps you could summarize it to one of the following two:
1: There is a physical singularity, but it's unobservable.
2: There is no physical singularity - it's a genuine Coulomb type field. Derived from the curl of a vector potential!

[Yablon]

. . .Jay, that criticism by a referee was just what was being hinted at in the currently last post here: viewtopic.php?f=6&t=149

Q-reeus: Yes, I see that now. I did not quite get what you were asking about, but now I do. It took the PRD Chief Editor to ask the question you were asking in the way he asked it before it dawned on me what you both were asking about. Good insight!

[it would be so helpful if POST NUMBERING were implemented here at SPF!]

Fred? He is our technical guru at SPF.

So much of your math is above my level, but trying to discern the underlying implications & consequences, that's what stood out for me. Noticing in your reply you claim to have achieved such a feat, perhaps you could summarize it to one of the following two:
1: There is a physical singularity, but it's unobservable.
2: There is no physical singularity - it's a genuine Coulomb type field. Derived from the curl of a vector potential!

Answer: 2. The singularity is an artifact of using a polar coordinate system on a closed surface (for symmetry and simplicity, a sphere) and the fact that longitude is undefined at the north and south pole. In other words, is Santa Claus at Greenwich Mean Time or Eastern Time or Pacific Time etc.? In fact, Santa's time zone is indeterminate.

Here is an excellent link that I found shortly after April 16: http://www.encyclopediaofmath.org/index ... c_monopole. This link was very helpful to me in thinking about and then developing the first several sections of the revised paper.

Jay

[Q-reeus]

Q-reeus: Yes, I see that now. I did not quite get what you were asking about, but now I do. It took the PRD Chief Editor to ask the question you were asking in the way he asked it before it dawned on me what you both were asking about. Good insight!

I learn from that it's best to be more direct at times.

Fred? He is our technical guru at SPF.

Yes and pardon If I seemed to be directing that at you. It was let's say 'a general remark' aka grumble.

Answer: 2. The singularity is an artifact of using a polar coordinate system on a closed surface (for symmetry and simplicity, a sphere) and the fact that longitude is undefined at the north and south pole. In other words, is Santa Claus at Greenwich Mean Time or Eastern Time or Pacific Time etc.? In fact, Santa's time zone is indeterminate.

Thanks for clearing that up. Yes the 'north pole' issue comes up a lot more so in GR it seems.

Here is an excellent link that I found shortly after April 16: http://www.encyclopediaofmath.org/index ... c_monopole. This link was very helpful to me in thinking about and then developing the first several sections of the revised paper.

Will try and make time to read through your revised paper. Hope your admirable persistence pays off soon.

[Ben6993]

Hi Jay

I have just spent two to three hours reading your paper. It is fantastic. Its like a best seller that you can't put down until it is read to the end!
I commented on your previous version of the paper but did not read that version as avidly.

Hope you don't mind me pointing out just one very small thing that you might review, on the line below eqn 6.4 you write: (i4 πkeg) = (i4 πeg)^k
which is an obvious shorthand for what you mean but is technically incorrect as an equation in isolation.
Should it be replaced by exp(i4πkeg) = exp(i4πeg)^k ? Or alternatively write it without making it look like a new equation?

Good luck with publication.

[lcwelch]

"I very much appreciate this wisdom. It was spot-on, and is precisely the type of feedback I would have been hoping to obtain from a thesis advisor if I was some 30 years younger studying at Columbia or my alma mater MIT or a similar institution. Thank you!"

I think you hurt your cause by such personal (as opposed to professional) observations.

[Yablon]

Hi Jay

I have just spent two to three hours reading your paper. It is fantastic. Its like a best seller that you can't put down until it is read to the end!
I commented on your previous version of the paper but did not read that version as avidly.

Thanks Ben, I very much appreciate that!

Hope you don't mind me pointing out just one very small thing that you might review, on the line below eqn 6.4 you write: (i4 πkeg) = (i4 πeg)^k
which is an obvious shorthand for what you mean but is technically incorrect as an equation in isolation.
Should it be replaced by exp(i4πkeg) = exp(i4πeg)^k ? Or alternatively write it without making it look like a new equation?

Yes, good catch. Thanks!

Good luck with publication.

Thanks again, Ben.

[Yablon]

"I very much appreciate this wisdom. It was spot-on, and is precisely the type of feedback I would have been hoping to obtain from a thesis advisor if I was some 30 years younger studying at Columbia or my alma mater MIT or a similar institution. Thank you!"

I think you hurt your cause by such personal (as opposed to professional) observations.

You are probably right. Usually I resist the temptation to say such things in formal correspondence, but I guess I succumbed here. The only reason I did so, is that I did meet the E. Weinberg last year and we talked for an hour and a half, so I am not unknown to him as a person. But I think that on balance you are right; back to being more disciplined!

[Yablon]

Well, it took less than a day for PRD to reject this latest paper at http://vixra.org/pdf/1504.0200v1.pdf

Taking an electron around a 2pi circuit in phi shows that the vector potential in Eq. (5.4) is unacceptable unless m=1. The fact that this would not be detected by a different experiment in which the electron went through m such circuits in succession is irrelevant.

I simply do not agree with this, but it is clear that this is as far as this paper will go at PRD.

Electrons reverse sign in SO(3) and do not recover their sign until you bring the electron through a 4pi circuit. To effectively assert that any enlarged domain on SO(3) is irrelevant is what is wrong, IMHO.

I have already submitted this paper for review elsewhere, at another equally-reputed journal; this needs at least a second opinion.

Jay

[Yablon]

I have been thinking about the 2pi-ers (people who believe that the domain beyond phi = 2pi is irrelevant), and how to explain an electron with 4pi or 6pi etc.

Then it just hit now me that I have uncovered another weird aspect of quantum theory which is this:

An electron has 2 versions based on orientation / entanglement. These versions also correlate to spin up and spin down The probability of finding an electron somewhere must be 1, and normally, classically, for a probability density p we would take the integral:

$$$ p dr dphi dtheta =1

and this would be taken be from r=0 to oo, phi =0 to 2pi, theta = 0 to pi.

But for a 4pi cover electron with a half unit of charge (which condensed matter folks find in the FQHE), the total probability of finding an electron from phi = 0 to 2pi is 1/2! You need a 4pi sweep to get the probability of finding the electron somewhere to be equal to 1. So my next paper will have a probability which = 1 only when you use a 4pi sweep. (or 6pi, 8pi, 10pi... sweep for higher roots of unity.)

You can think of it like a radar that sweeps through 2pi, and then another 2pi, etc., and only detects the electron every other sweep. Thought of differently, Stern Gerlach says that we have a 50-50% probability of finding a spin up electron versus a spin down electron. But say I am looking only for spin up electrons. Then to detect a spin up electron, I need to go through 4pi. My chance of finding that on a 2pi radar sweep is only 50%. Thought of another way, Alice is 0 to 2pi and Bob is 2pi to 4pi. Joy Christian, does this ring any "Bells" for you?

In any event, this electron hiding every other sweep is the quantum “weird” result that I have now realized my approach implies. And since we only see the half unit monopole charges near 0K, I would characterize this as something that would show up only at low temperature.

Then, for 1/3, 1/5, 1/7, 1/9... fractional charges, the radar only picks up the electron every 3, 5, 7, 9... sweeps.

Does this sort of weird quantum electron behavior ring a bell with anything anybody knows about about, either in condensed matter physics, or anywhere else for that matter?

Jay

[Yablon]

So I guess what I am asking below is this:

If I write a probability equation for an electron in the field of a monopole with reads:



with depending on the monopole charge fraction, and the related:



which seems to be a consequence of what I am proposing, will people laugh, or will people come to understand this as yet another weird aspect of quantum reality? And, are there some observations already known which either support this or exclude this?

Jay

[Ben6993]

Hi Jay

I had a number of questions previously that I was reluctant to ask as they would make me look even less like a physicist than usual. But while you have asked for ideas:

You did not mention 0 deg K in the paper, as far as I remember, so is all the work in the paper applicable at any temperature? Some effects such as FQHE only apply at 0K which you dealt with in a previous [thermodynamics] paper which had T as a variable. And the exact counterpart to FQHE is shell energy states at normal T.

What 'rotation' of the electron or electron potential is implied in an integration around 2 pi? None presumably implied by the integration itself but, as you note in the post, the electron has 50% chance of appearing in a 2pi sweep so you would need a 4pi sweep to ensure finding it with certainty. BTW I assume you are integrating over normal space? This reminds me of my puzzlement in the Bell experiments as to why the detector magnets are only rotated through 2pi rather than 4pi. I mentioned this in a Bell post somewhere nearby and was met with zero acceptance. I thought this was strange when Joy is trying to get the 4pi orientation of macro objects recognised yet noone seems to care that the magnets are only used in a mod 2pi sweep. For example if particle 1 is detected in a range of 0 to 2 pi but the paired particle 2 is detected in a range of 2pi to 4pi, won't this adversely affect the correlations? I was left assuming that I am wrong but do not yet understand why. (NB if the magnet is set at 355 deg and needs to be re-set at 5 deg, do experimenters just move the magnet on through 10 degrees, rather than back through 350 deg, so putting the two readings in different 2pi sweeps?)

In my preon model there is a LH electron and a RH electron and ditto for the positron. My LH and RH electrons are different structures (made of different preons) and retain their structure during time of flight between emission and detection. That is what permits a hidden variable to be retained by a say LH electron throughout its time of flight. And the outcome at detection (assuming that there is a detection made, which implies a 4pi integration) is 100% certain, not a 50% chance, if we were to know the hidden variable, which of course we never know in a real experiment as it is hidden. If you tested a LH electron and found it spin 'any', then if it were instead to have been a RH particle then it would have been detected spin 'anti-any'.

I said a 4pi integration in the previous paragraph, but how does that fit in with your 6pi, 8pi, 10pi etc sweeps?

Jay wrote:
Then, for 1/3, 1/5, 1/7, 1/9... fractional charges, the radar only picks up the electron every 3, 5, 7, 9... sweeps.

Is the counterpart to that, at normal temperatures, that every different electron shell state is in its own, unique 2pi sweep?

Kind regards

[Yablon]

Hi Jay

I had a number of questions previously that I was reluctant to ask as they would make me look even less like a physicist than usual. But while you have asked for ideas:

You did not mention 0 deg K in the paper, as far as I remember, so is all the work in the paper applicable at any temperature? Some effects such as FQHE only apply at 0K which you dealt with in a previous [thermodynamics] paper which had T as a variable. And the exact counterpart to FQHE is shell energy states at normal T. . .

Well, let's start with this. I may need some time to decide if I like what I am doing with the probability or not. I wrote this post within minutes of thinking of this, to have you guys be a sounding board. Because it is radical at some level.

But I thank you for reminding me of my own theory, that yes, at normal temperatures, the 3-cover (6pi rotation) corresponds to total angular momentum 3/2 electron (p shell). So you do not get these states in an electron until the electron is part of an atom. 10 pi is 5-cover and spin 5/2 (d shell), etc. Free electrons are always 1-cover. And when the monopoles show up near 0K, then those angular momentum numbers migrate their role and manifest as the charge fraction. An important piece of this is that "total angular momentum" is taken about the azimuth. But what does an electron angular momentum really mean? The old Bohr model of an electron going round the nucleus like a planet is of course long defunct. So I am looking for a way to understand electronic angular momentum that makes sense with wavefunctions which are probabilistic. And that is why I though of this. Now I have to make sure all is consistent on all fronts; but I'd say that yes, an electron which picks up an orbital quantum number by going into an atom essentially gets 4pi added to the domain needed to calculate its probability.

What I like about this -- which I thought of six weeks ago but never wrote up, is this: Look at http://en.wikipedia.org/wiki/Azimuthal_ ... mentum.svg, for example. Electrons are always characterized by the angular momentum on the z-axis. But they can just as well be characterized by area in the x-y plane. If you do it that way, an electron with J=3/2 has 3 times the area as an electron with J=1/2. And J=5/2 has 5 times the area as J=1/2. Try it! So right away, there is an overlooked way to characterize these angular momenta that also has an area with a variation that maps precisely to what I am doing. Maybe this is an alternative to how I am thinking about the probability. Or maybe it is a complement. Need to think it through some more.

Jay

[Ben6993]

Hi Jay, I have looked at the wiki link and the page it comes from. I vaguely follow it, and your interpretation, but only vaguely.

I looked at the dumbell diagrams on the parent webpage and could see a sphere for s and four dumbells for d but could not see three dumbells stated by wiki for p. But, ignoring that, looking at your link I can see that the cone angle changes for each new quantum number. So the slice of 2pi per cone decreases for each new quantum number. And presumably this decrease would fit in with the reduced angle per m th root of unity for increasing m? I am not quite clear where is the [Lx, Ly] area that is increasing with quantum number. The surface area of the cone seems to be increasing but the projection of the cone onto the [Lx,Ly] plane is decreasing.

There was a rumpus in the popular press a few years back when Brian Cox said something like: every electron has a different energy wrt every other electron in the universe. I.e. the exclusion principle does not stay within an atom. In which case there is no such thing as a free electron. It is just that the proximity to a nucleus lets us see the structure more clearly. So you could extend the quantum number, l, to infinity, irrespective of other atoms, to include all electrons in the universe, each in its own, separate 'radar sweep'. In one way that seems silly as it implies FTL communication to enforce the exclusion throughout the universe, but the need for FTL is hopefully illusory.

[Yablon]

After sleeping on the probability approach to the angle I am getting more comfortable with using probability densities and probabilities as I outlined yesterday. But here is the refinement I think is needed. I will show this for which corresponds to the fractional charge and the square root of unity; the generalization to larger roots follows suit. The benefit of using is really political. People are already familiar with electrons having a two-valued nature that is based on the square root of unity. I do not have to make the separate argument that higher roots of unity are also important to consider.

The ket for an electron wavefunction generally decomposes into its two spin up and spin down eigenstates +/- as such (which eigenstates are square roots of unity):



The expansion coefficients are complex numbers, and their magnitude (square modulus) is a probability. In this case for two states:





If we write these as probability density integrated over the entirety of a three-dimensional space using spherical coordinates then we may write:





So by doubling the range we may write:





This means that when we are moving an electron wavefunction around a monopole through a or ... circuit, we are really moving this wavefunction in a particular eigenstate around the monopole. So long as we are doing that, I believe this approach could fly as a way to interpret what it means to make a circuit of more than .

I'd be curious to get some second opinions whether I am somehow missing anything here.

Jay

[Yablon]

...So by doubling the range we may write:

Actually, this is not quite right. Thinking about Stern-Gerlach (SG), the first , if there is a detection, will establish a spin up or spin down eigenstate. Then the second is like a second SG experiment, but now we know that the eigenstate is determined, so the probabilities do not combine in the way shown above.

The correct (I think) way to write this using would be:



Jay

[Q-reeus]

Yablon, this thread in another forum may be of interest: https://www.physicsforums.com/threads/m ... em.681917/
Might even get helpful feedback re your own model by joining in there.

[Yablon]

Yablon, this thread in another forum may be of interest: https://www.physicsforums.com/threads/m ... em.681917/
Might even get helpful feedback re your own model by joining in there.

Thanks Q-reeus.

Quick update, the paper http://vixra.org/pdf/1504.0200v1.pdf I submitted to a journal other than PRD on April 27 -- also one of the top-rated journals in the world -- is still under review there. The referees' reports came in a couple of weeks ago and there is still no decision. I suppose that means that the reports were not terrible, otherwise I'd have heard.

In the mean time I have been working on an update which I believe makes the paper even better, and last night I discovered using SU(2) spinor algebra that the physical mechanism underlying the "root of unity" groups which I am using as the basis for the fractional Dirac charges (which also lead to a thermodynamic and electrodynamic union) is one of a heretofore undiscovered transformation between space and time which is Euclidean rather than Minkowskian, and which supplements the known theory of Dirac fermion rotations and boosts. I should have this next revision ready to unveil in the next ten days.

At the moment, I am spending a lot of time talking to myself to try to convince myself that this type of transformation is real. The math works; but my psyche is still lagging. Because if this is real, then this will give future generations the technological ability to do some very strange and powerful things to alter and manipulate space and time at ultra-low temperatures, which at the moment are only dreamt about in science fiction.

Stay tuned...

Jay

[Yablon]

...In the mean time I have been working on an update which I believe makes the paper even better, and last night I discovered using SU(2) spinor algebra that the physical mechanism underlying the "root of unity" groups . . . is one of a heretofore undiscovered transformation between space and time which is Euclidean rather than Minkowskian, and which supplements the known theory of Dirac fermion rotations and boosts. I should have this next revision ready to unveil in the next ten days.

At the moment, I am spending a lot of time talking to myself to try to convince myself that this type of transformation is real. The math works; but my psyche is still lagging. . .

I am glad I was skeptical and re-did the calculation very carefully; actually there is no space and time transformation of the type I described. So scratch that.

Jay

[Yablon]

I am glad I was skeptical and re-did the calculation very carefully; actually there is no space and time transformation of the type I described. So scratch that.Jay

On third thought, scratch the scratch. The Euclidean space / time transformation is back on. I left a term out of my second calculation. Jay