The Crisis in Physics

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

The Crisis in Physics

Postby Yablon » Sat Aug 24, 2019 4:06 pm

I am starting this new thread in response to a post at viewtopic.php?f=6&t=373#p9772 which cannot be ignored.

Heinera wrote:
gill1109 wrote:People like Sabine Hossenfelder are already preaching that physics is in crisis. I think there is a lot in what she says.

There is no crisis in physics in my opinion. If anything, it's too good, so there has hardly been any progress on the theoretical level since the seventies. Even the LHC couldn't find any significant new empirical stuff that can't be explained by the standard model.

As to “significant new [or old] empirical stuff that can't be explained by the standard model”:

Can somebody please use the standard model (or any model) to explain to me why the various nuclides of the elements in the periodic table have the masses/binding energies/mass defects which they have? And to make it “easier,” let’s just focus on the lightest and simplest nuclides: just tell me about hydrogen, helium, lithium, beryllium, boron, and carbon. The empirical data for these and heavier elements and isotopes has been known since the 1940s. But I have not seen an accepted theoretical explanation of this in the 75 years or so that people have had available to discover one.

Can somebody please use the standard model (or any model) to explain to me why the proton and the neutron have the masses which they have, in relation to the mass of the electron? These three masses have likewise been known for 75 years or longer. This is a question in which I first became interested at the age of 16 when my high school chemistry teacher wrote these three masses down on the blackboard, and I asked him to explain why those masses are what they are, and he said that was just empirical data and nobody knew the answer, and that if I could figure that out it would be a big deal. My chemistry teacher’s uncle, by the way, was J. Robert Oppenheimer.

Can somebody please use the standard model (or any model) to explain to me why the natural world shows us precisely three generations of fermions, and why their left-handed chiral projections mix as they do? Isador Rabi first asked "who ordered this?" about the muon in 1936. No good answer yet.

Can somebody please use the standard model (or any model) to explain to me why the six elementary quarks and the three charged leptons have the masses they do? And can somebody tell us for sure what the masses of the neutrinos actually are, so that we can fine-tune our experiments which are trying to detect these? The empirical data has been there for decades. No good answers.

Can someone please tell me why the half-life of a free neutron is about 15 minutes? We have all had the data for 75 years. No good answer.

I could also ask why somebody has not yet successfully unified even classical electrodynamics with classical gravitation? But that is an entirely theoretical question, not one of having data sitting in our lap that nobody can explain. And although preposterous IMHO, somebody can dismiss that by saying that chasing their unification is like chasing a unicorn. So, I won’t ask that.

And along the lines of pure theory, has anybody yet solved the Yang Mills mass gap problem? But again, I am happy to stick with nothing more than all of the “empirical stuff that can't be explained.”

Now, to be fair, none of these are easy questions. Indeed, they are very hard questions. But, as Einstein once said, “I have little patience with scientists who take a board of wood, look for its thinnest part, and drill a great number of holes where drilling is easy.” And yet, that is precisely what is happening.

So, perhaps you would disagree with the use of the word “crisis,“ but it seems to me that if “professional“ physicists have been sitting around for decades with unexplained empirical data on their lap, and not made a real effort to explain that data, or at least after making effort have not been able to successfully do so, perhaps that is something of a crisis? And if “professional” physicists have been ignoring all this unexplained data out there, and don’t regard that as a problem so long as they get money to “drill a great number of holes where drilling is easy,” might it be that making believe these questions do not really exist, and pretending that the standard model has explained everything necessary for the data we have, constitutes a crisis?

Heinera wrote:
gill1109 wrote:Amateurs actually have repeatedly made enormously important contributions to the field.

Uh...not recently. ;) You would have to go at least 130 years back to find an amateur who contributed to physics in any significant way (but what is the definition of an amateur anyway...)

I did not pick the foregoing examples of unexplained empirical data randomly out of a hat. I picked them because I have personally solved each and every one of these problems, because it is my mission in this life to help pull physics out of the crisis that it is in. And it is indeed in a crisis, especially because most “professional” physicists disregard this crisis and just keep drilling shallow holes. If you have the time and inclination, you ought to study what I have written at the following:

[1] J. R. Yablon, “Why Baryons Are Yang-Mills Magnetic Monopoles,” Hadronic Journal, Vol. 35, No. 4, 2012, pp. 401-468. https://www.researchgate.net/publicatio ... KLsQEDdoiQ (2012)

[2] J. Yablon, “Predicting the Binding Energies of the 1s Nuclides with High Precision, Based on Baryons which Are Yang-Mills Magnetic Monopoles,” Journal of Modern Physics, Vol. 4 No. 4A, 2013, pp. 70-93. doi: 10.4236/jmp.2013.44A010, http://www.scirp.org/pdf/JMP_2013043014242019.pdf (2013)

[3] J. R. Yablon, "System, Apparatus, Method and Energy Product-by-Process for Resonantly-Catalyzing Nuclear Fusion Energy Release, and the Underlying Scientific Foundation" https://patentscope.wipo.int/search/doc ... 0025517277

[4] J. Yablon, "Grand Unified SU(8) Gauge Theory Based on Baryons which Are Yang-Mills Magnetic Monopoles," Journal of Modern Physics, Vol. 4 No. 4A, 2013, pp. 94-120. doi: 10.4236/jmp.2013.44A011. http://www.scirp.org/pdf/JMP_2013043014285020.pdf

[5] J. Yablon, "Predicting the Neutron and Proton Masses Based on Baryons which Are Yang-Mills Magnetic Monopoles and Koide Mass Triplets," Journal of Modern Physics, Vol. 4 No. 4A, 2013, pp. 127-150. doi: 10.4236/jmp.2013.44A013. http://www.scirp.org/pdf/JMP_2013043014410549.pdf

[6] J. R. Yablon, "Theory of Fermion Masses, Mixing, Lagrangian Potentials and Weak Beta Decays, based on Higgs Bosons arising from the Scalar Fields of a Kaluza Klein Theory with Five-Dimensional General Covariance Provided by Dirac's Quantum Theory of the Electron," https://www.researchgate.net/publicatio ... nce_Provid

and

https://jayryablon.files.wordpress.com/ ... .1-spf.pdf

[7] J. R. Yablon, "Filling the Mass Gap: Chromodynamic Symmetries, Confinement Properties, and Short-Range Interactions of Classical and Quantum Yang-Mills Gauge Theory" https://www.researchgate.net/publicatio ... uge_Theory

Finally, I have spent the last 25 years of my life earning my professional living in the patent business, dealing with all sorts of inventors and all types of science and technology, and using the success of my business to give myself the time to work on the aforementioned problems and write the above papers. I have not spent that time as a professor in an academic institution. So while I do not think of myself as a “amateur” physicist, people who have chosen the academic path might very well think of me that way. And I can tell you for certain that arxiv will not post anything I write and has not for years, because I do not have academic affiliation, and it is at that level of superficiality that their screeners accept or reject papers. And then, many “professional” physicists will only consume papers which get posted there. Thank goodness that there are other avenues which have developed in recent years for preprints, which do not engage in scientific censorship using superficial criteria applied in the span of a few hours after a submission is made with no genuine substantive review.

So we have empirical data which has been sitting in everybody’s laps for decades and which poses problems which no “professional” physicist has managed to solve. We have a physics community which pretty much ignores these unsolved problems and acts as if everything is just hunky-dory so long as they are paid to drill shallow holes and occasionally interact with students. I have with great efforts and deep drilling discovered actual solutions to all of these problems of “empirical stuff that can't be explained,” but none of the “professional“ physicists take the time to study these solutions because they were not proposed by themselves or one of their academic colleagues and the prevailing wisdom is that nobody who has chosen a career path outside of academe can possibly offer something of real value. Which, by the way, ties people who seek to advance science to making their money doing science; a toxic mix for what ought to be a noble calling.

You may not call that a crisis. I certainly do. Indeed, it has been and remains my life‘s mission to solve those problems involving a great deal of significant unexplained empirical data, and to help the entire physics enterprise overcome this crisis in physics, which is even more of a crisis because most “professionals“ do not recognize it as such and only listen to themselves.

Jay
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Re: The Crisis in Physics

Postby FrediFizzx » Sat Aug 24, 2019 4:54 pm

Yep, with all the successes of the Standard Model, we still don't know what an electron is or why it weighs what it does. :D
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Re: The Crisis in Physics

Postby gill1109 » Sun Aug 25, 2019 1:29 am

Well said, Jay. Part of the problem is that there is a crisis in academia. Funding and career progression require rapid publication of heaps and heaps of papers which nobody is ever going to read, and of course most of those papers are indeed written by drilling holes in a big plank in the place where the wood is thinnest. Young people (PhD students, postpocs) are merely cannon-fodder for the people who run labs or large research groups. They produce, and they are discarded when they're done. It's a production line, it might as well be AI robots instead of human beings working on them. The few who are selected for the promotion ladder (yet another war of attrition) are selected on their capacity to do what their masters did - write project applications, get media attention, be the boss of a big "team". Look at the mass of new journals specially designed to allow people in developing countries to do just the same. ie "have an academic career". It is so, so sad; such a waste of resources! Oh well, I guess a good climate catastophe will sort a lot of things out. I have the feeling we are living in the last days of the Roman Empire. Bread and circusses for the masses. The elite go to banquets and eat blackbird tongue paté. We are all dying of the lead in the pipes which bring us (those lucky enough to live comfortably in the cities) water. Except it is not the lead in water but the platinum in the expensive catalyser thing which cleans the exhaust fumes of your car. Oh well we'll go electric ... then we will run out of rare metals in no time. The amazon is burning and the tundra is melting and farting methane in enormous quantities.
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Re: The Crisis in Physics

Postby Jarek » Sun Aug 25, 2019 2:03 am

FrediFizzx wrote:Yep, with all the successes of the Standard Model, we still don't know what an electron is or why it weighs what it does. :D .

First of all: why charge is quantized - why Gauss law allows only for integer charges? Then the lightest nonzero charge is electron.
The main problem here is blind belief that electron is perfect point - looking for experimental evidence for this belief, it seems there is only Dehmelt's 1988 extrapolation by fitting parabola to two points(!): https://physics.stackexchange.com/quest ... of-electro
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Re: The Crisis in Physics

Postby Heinera » Sun Aug 25, 2019 5:57 am

FrediFizzx wrote:Yep, with all the successes of the Standard Model, we still don't know what an electron is or why it weighs what it does. :D
.


Since the beginning of civilization, the available knowledge has always stopped somewhere. So if the criterion for a crisis is that there are things we still have no explanation for, then science has always been in a crisis.

There are 25 free (or "unexplained") parameters in the standard model (if we include massive neutrinos). Ok. Some think that is too many, and gives the theory an "ad hoc" flavor. But what would be a suitable number? Ten? One? Zero? When should we be satisfied and say "now we understand everything"? I'm pretty sure that will never happen.
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Re: The Crisis in Physics

Postby Yablon » Sun Aug 25, 2019 7:01 am

Yablon wrote:I could also ask why somebody has not yet successfully unified even classical electrodynamics with classical gravitation? But that is an entirely theoretical question, not one of having data sitting in our lap that nobody can explain. And although preposterous IMHO, somebody can dismiss that by saying that chasing their unification is like chasing a unicorn. So, I won’t ask that.

I should note, however, that I have solved this problem as well, and in the process obtained a Dirac equation which is modified just enough to directly account for the magnetic moment anomaly without the need for renormalization because the infinities which are customarily renormalized away, never appear to begin with. Very fundamentally, I generalize the special and general relativistic connections between energy content and time dilation, into electromagnetism, which is highly suggestive of a universal connection between energies and time dilations. That is: draw a field map of energy. You can equate that on a one-to-one basis with a field map of time dilations. And in Part V, I do propose several realistic empirical tests:

J. R. Yablon, Quantum Theory of Individual Electron and Photon Interactions: Geodesic Lorentz Motion, Electromagnetic Time Dilation, the Hyper-Canonical Dirac Equation, and Magnetic Moment Anomalies without Renormalization, (2018) https://www.researchgate.net/publicatio ... enormaliza
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Re: The Crisis in Physics

Postby Yablon » Sun Aug 25, 2019 10:35 am

Jarek wrote:
FrediFizzx wrote:Yep, with all the successes of the Standard Model, we still don't know what an electron is or why it weighs what it does. :D .

First of all: why charge is quantized - why Gauss law allows only for integer charges? Then the lightest nonzero charge is electron.
The main problem here is blind belief that electron is perfect point - looking for experimental evidence for this belief, it seems there is only Dehmelt's 1988 extrapolation by fitting parabola to two points(!): https://physics.stackexchange.com/quest ... of-electro

Dirac actually solved the charge quantization problem in his 1931 paper Quantised Singularities in the Electromagnetic Field: http://users.physik.fu-berlin.de/~klein ... ac1931.pdf.

The problem with this paper is its finding that if magnetic charges exist anywhere in nature, then electric charge is quantized in the fashion we observe, coupled with the empirical data that we have never observed magnetic charges. Plus, one could argue that the later 1954 advent of Yang-Mill gauge theories and its diagonalized matrix generators provides a theoretical underpinning for charge quantization which does not require Dirac monopoles.

However, my paper:

J. R. Yablon, Fractional Dirac Magnetic Monopole Charges without Observable Singularities, 2015 https://www.researchgate.net/publicatio ... gularities

eliminates this barrier to Dirac's monopole theory. Here, I show how the existence of Dirac monopoles actually lead not only to charge quantification, but also, to fractional charges n/d with an even denominator d=2, and thereafter, only odd denominators 3, 5, 7, 9..., with n being an integer and n<d. But these are the precise fractional charges observed in the quantum and fractional quantum Hall effects. As such, with this understanding, we come to understand that Dirac monopoles actually do exist, but only near ultra-low temperatures close to 0K. These monopoles are responsible for all the funky magnetic behaviors of low-temperature superconductors, at which temperatures Maxwell's equations really do have electric / magnetic symmetry. When, we break this symmetry a few degrees above 0K, the monopoles "evaporate" and their residue is what we experience as thermal heat, while the electric charges retain their familiar, observed integer quantization.

Related to some of the above, take a look at this:

J. R. Yablon Classical Thermodynamics Entropy Laws as a Consequence of Spacetime Geometry, (2015) https://jayryablon.files.wordpress.com/ ... cs-2.4.pdf

You can get the gist of this from just reading the very last paragraph. To sum it up: applying exterior calculus, a scalar potential is to thermodynamics what a vector potential is to electrodynamics.
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Re: The Crisis in Physics

Postby Jarek » Sun Aug 25, 2019 10:52 am

Faber also has started with Dirac, using dual E<->B formulation: changing magnetic monoples into electric (charges): https://www.dropbox.com/s/aj6tu93n04rcgra/soliton.pdf
But generally trying to talk about it, "everybody knows that electron is perfect point" ending discussion ...

Regarding unification of classical EM and gravity, see https://en.m.wikipedia.org/wiki/Gravitoelectromagnetism
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Re: The Crisis in Physics

Postby Yablon » Sun Aug 25, 2019 11:18 am

Jarek wrote:Regarding unification of classical EM and gravity, see https://en.m.wikipedia.org/wiki/Gravitoelectromagnetism

In GR/EM unification it is IMHO essential to show how the Lorentz force motion is geodesic motion irrespective of the charge-to-mass ratio. In GR you do not have that problem because of the equivalence of gravitational and inertial mass. In EM, "electrical mass" aka charge is independent of, i.e., inequivalent to, inertial mass. The only way to succeed in deriving the Lorentz motion as geodesic motion using a variational least action principle in the same way that Einstein did to obtain the gravitational motion, is to have there be electromagnetic time dilations in the natural world.

That is the foundation of my paper at https://www.researchgate.net/publicatio ... enormaliza, laid in sections 2 through 6 (less than 20 pages). The rest of the paper builds out the consequences of this. One of which is that you eliminate the need for renormalization in Dirac theory in order to explain magnetic moment anomalies.
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Re: The Crisis in Physics

Postby Jarek » Sun Aug 25, 2019 1:37 pm

Gravitoelectromagnetism (approximation of GR) is nearly identical as EM, differs by: attraction for the same, and lack of mass quantization.
This way they can be simply unified - in this dual Dirac picture, dynamics of 3D space rotations leads to electromagnetism, analogously tiny rotations in 4-th dimension can recreate gravitomagnetism. Only the former are topological - quantized.
For time dilation, it requires slowing down information propagation of EM. If they are coupled, strong gravity could cause such slowing down.
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Re: The Crisis in Physics

Postby Yablon » Mon Aug 26, 2019 3:37 pm

Heinera wrote:Since the beginning of civilization, the available knowledge has always stopped somewhere. So if the criterion for a crisis is that there are things we still have no explanation for, then science has always been in a crisis.

The crisis is not that there are things we still cannot explain. The crisis is that there is a lot of data on the table that we still cannot explain which has been there for decades, coupled with most of the professional community ignoring the presence of that unexplained data and at the same time looking for money to build more instrumentation with the claim that they need this to acquire even more data. As I tell my grandsons when they have a full plate and ask for more food: eat what is already there first!
Heinera wrote:There are 25 free (or "unexplained") parameters in the standard model (if we include massive neutrinos). Ok. Some think that is too many, and gives the theory an "ad hoc" flavor. But what would be a suitable number? Ten? One? Zero? When should we be satisfied and say "now we understand everything"? I'm pretty sure that will never happen.

Do not let the perfect be the enemy of the good. Let's roll with the 25 free parameters, which are a good example. These are:

6 quark masses + 6 lepton masses =12
4 quark mixing angles + 4 lepton mixing (neutrino oscillation) angles = 8
Higgs mass = 1
electromagnetic coupling + electroweak mixing angle + strong coupling + Fermi Constant = 4 (there are other way to represent these, but it is still 4).
Total: 25
I also like to include the Newton gravitational constant even though it is not in the standard model, because we know very well that it will have to be included in any more advanced standard model.
So I will start with 26.

Now look at my paper at https://www.researchgate.net/publicatio ... nce_Provid.

In summary, which I review at (21.15), I have removed 11 of these unexplained parameters -- that is all of the fermion masses less one new parameter -- and so squeezed 26 down to 15. And in the process, I did use the gravitational constant, because you have to use it to get to the neutrino masses, as many who have studied neutrino physics intuitively believe. In particular, it is from which you get the large numeric ratio between the quark and charged lepton masses, versus the neutrino masses, see (20.2).

Is there always more to do and learn? Sure! But when we take 26 free parameters and turn them into 15 free parameters, we are making very real progress moving human knowledge forward. Crisis is when you are stuck and not moving and not even recognizing that you are stuck, or being stuck and using that an excuse to ask for more money so you can purportedly get unstuck.
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Re: The Crisis in Physics

Postby FrediFizzx » Mon Aug 26, 2019 4:27 pm

Yablon wrote:...
I also like to include the Newton gravitational constant even though it is not in the standard model, because we know very well that it will have to be included in any more advanced standard model.

Here is another way to include in the Standard Model.

https://arxiv.org/abs/1705.06036

https://www.prespacetime.com/index.php/ ... /view/1584
.
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Re: The Crisis in Physics

Postby gill1109 » Mon Aug 26, 2019 11:38 pm

FrediFizzx wrote:
Yablon wrote:I also like to include the Newton gravitational constant even though it is not in the standard model, because we know very well that it will have to be included in any more advanced standard model

Here is another way to include in the Standard Model.

https://arxiv.org/abs/1705.06036

https://www.prespacetime.com/index.php/ ... /view/1584

Isn't it possible that all these "constants" actually are the result of irreducible randomness in the very very early quantum universe at the stage when space-time itself is being born out of entangled quantum fluctuations in the initial singularity? The anthropological principle explains why they are all more or less finely tuned so as to allow the existence of sentient beings (at least, they think they are sentient beings, but how can they be sure?) walking about on classical planets in classical solar systems in classical galaxies and asking the questions: Why are we here? Where do we come from? Where are we going to? ie it is a post-selection effect. My answer to those "sentient" beings' question would be: dust to dust, ashes to ashes. That's all there is. There is nothing behind it all. Better make the best of what you have now.

Congratulations on your paper. I'm afraid it is too difficult for me to absorb much from it.

The journal "Prespacetime of QuantumDream, Inc.", https://prespacetime.com/, is a bit obscure: "PSTJ employs a three-tier due diligence process in selecting submissions for publication. First, all submissions are screened by the Editor to determine whether the contents and/or forms are suitable for publication in PSTJ; and unsuitable submissions will be declined without reviews. Second, the remaining submissions will be reviewed by the Editor; and submissions passes Editor's review will be accepted for publications. Third, the still remaining submissions will be sent to one or more PSTJ Advisors or outside reviewers for further reviews or sent back to the authors for revisions; and final decisions will be made by the Editor based on PSTJ Advisors' or outside reviewers' reviews and/or revisions made the authors. The Editor will also solicit certain articles for publication or invite some authors for submissions which will then be put through the said due diligence. Commentaries to articles published in PSTJ and replies from authors are welcomed; and they will be subjected to the said due diligence before acceptance or refusal. There is also a Prespacetime Forum available for discussing issues related to prespacetime & other fundamental questions of physics."

Does anyone know who is "The Editor"? Who are the "PSTJ Advisors"? Governance, transparency? The website gives no clue. So we have to guess. I'm confidently guessing that the editor is the only person who so far posted in the forums, one "hu_huping". One can read all about his career here: https://www.neuroquantology.com/index.php/journal/article/viewFile/84/84. Certainly, a very enterprising and ambitious fellow, and a New York lawyer! Maybe Jay knows him? "He is also the founder of Scientific God Institute aimed at scientific inquiry on God and Science Association for the New Millennium aimed at a new paradigm of science." Not a bad idea - figure out some new paradigms of science. I have some sympathy for these sentiments. I'm concerned that not many people are going to take this journal seriously. So the impact of papers published there will be low.
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Re: The Crisis in Physics

Postby FrediFizzx » Tue Aug 27, 2019 12:00 am

gill1109 wrote:Congratulations on your paper. I'm afraid it is too difficult for me to absorb much from it.

The essay shouldn't be that hard to understand. The existence of matter is proof that gravitational torsion exists. If that is too hard to understand, then Jay's paper is going to be really hard.
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Re: The Crisis in Physics

Postby gill1109 » Tue Aug 27, 2019 12:43 am

I know in advance that I won’t understand Jay’s paper! I know it will contain too many long computations which I no longer have the patience or time to check, and I would make too many small errors anyway. Sorry about that. I’m interested (among other things) in mathematical structures, algebra, logic, geometric algebra, Clifford algebras, division algebras. I’m most deeply interested in Truth and in Justice. I want to see the Big Picture. As a mathematician, I don’t check other people’s computations. I look for ways to see the answer without tedious computations. “Replace calculations by ideas!” (Dirichlet, I believe).

Fortunately, Science is a collaborative venture of humanity, to which everyone can contribute, and where nobody needs to know “everything”. And nobody *can* know everything!

Now here’s a link which should interest many people here: Lee Smolin on Bohmian mechanics. “Space is dead: A challenge to the standard model of quantum mechanics”. https://bigthink.com/videos/lee-smolin-space.amp.html
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Re: The Crisis in Physics

Postby Jarek » Wed Aug 28, 2019 12:02 am

gill1109 wrote:Space is dead

Indeed - as long as one insists on fundamental time/CPT asymmetry.
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Re: The Crisis in Physics

Postby Yablon » Mon Sep 09, 2019 4:26 pm

gill1109 wrote:I know in advance that I won’t understand Jay’s paper! I know it will contain too many long computations which I no longer have the patience or time to check, and I would make too many small errors anyway. Sorry about that. I’m interested (among other things) in mathematical structures, algebra, logic, geometric algebra, Clifford algebras, division algebras. I’m most deeply interested in Truth and in Justice. I want to see the Big Picture. As a mathematician, I don’t check other people’s computations. I look for ways to see the answer without tedious computations. “Replace calculations by ideas!” (Dirichlet, I believe).

Actually, for Richard or anybody else who might be interested, as complex as it may seem on the surface, the mathematical skeleton of my paper which explains the quantum Hall and fractional quantum Hall effects, using Dirac monopoles, at:

https://www.researchgate.net/publicatio ... gularities,

can actually be summarized very simply:

The Dirac quantization condition which leads to integer electrical charges, is obtained by moving a wavefunction around a closed curve in such a way as to avoid singular behavior when it is returned to its starting point. The Dirac quantization of charges in units, comes from the mathematical relation . This comes about when we do not rotate a wavefunction, but simply move it in closed curves about a monopole and apply gauge theory and insist on no singularities. See, e.g., (4.9). Let's just say that this solution is based on the first root of 1, that is, the number 1 itself.

If you tidally lock the electron with the monopole, which is to say to rotate it as you go around just like the moon orbits the earth, then it turns out that this solution is based on the square root of 1, and this gives you half-integer charges. Hall effect. Section 5.

Then, having obtained these basic charges from first and square roots of 1, we take a look at the generalization to all roots of unity. Central to this, in mathematical terms, is the Euler relation:

. See (6.1)

From this, you can avoid singularities with any fractional charge n/m where n and m are both integers.

But, in section 11, I show how even though this is so, the even-number denominators violate Lorentz symmetry, while the odd-numbers do not. So this now imposes an added restriction which only permits odd-denominator fractions. See (11.1) through (11.9).

So all in all, with Dirac monopoles, we can have integer charges as Dirac found. But we can also have a half unit m=2 of charge based on a tidal lock which is a square root of unity, and m=3,5,7,9... odd denominator fractional charges consistent with Lorentz symmetry based on odd roots of unity. The even roots other than 2 are kicked out because they violate Lorentz symmetry. And this is precisely the fractional charge behavior empirically observed near 0K, which disappears as soon as you heat things up at all.

So as I conclude in section 14:

"Knowing that this is exactly the same pattern of charges experimentally observed in the Fractional Quantum Hall Effect (FQHE), it is difficult not to suspect that these fractional Dirac charges are in fact being observed in the FQHE at ultra-low-temperatures near 0K."

So when we see all of these funky superconducting and fractional charge behaviors in condensed matter physics near 0K, it is because something very odd is going on with the magnetic fields: we are actually observing the effects of true, real magnetic monopoles in the sense of Maxwell. Maxwell electric / magnetic duality does hold near 0K. But these monopoles -- and the fractional charges they enable -- evaporate as soon as you apply any modicum of heat. All we are then left with are integer charges, and heat which is a dissolved monopole residue. And there is a unification of electrodynamics and thermodynamics which stems from this.

Interestingly, as I also point out, the same root of unity patterns map into atomic shell structures. See section 12.
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