anonymous is Me : Amazigh, M. H.,
What Is the Meaning of Fractional Electric Charge? by Peter Rowlands
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Dear Dr. Rowland,
A vert nice essay. I especially like the idea from Laughlin that fractional chrges may be an emergent feature a la fractional quantum Hall effect.
I recall that the Han-Nambu model was equivalent to the standard quark picture, but I thought that the R-ratio might provide a way to distinguish teh two? Briefly the R-ratio is
R= sigma(e+e- --> q q-bar) / sigma (e+e- --> mu+ mu-)
i.e. it was the ratio of the total cross section of electron, positron to quark,anti-quark divided by the total cross section for electron, positron to mu-, mu+. This ratio then provides a glimpse into the charge and color assignments. In the standard quark picture for a single quark, anti-quark (u-quark say)
R= N_c (q_u)^2
where N_c is the number of colors and q_u is the electric charge of the up-quark. In scatterinng experimetns up to the s-quark mass (but below c-quark) one finds (to tree level)
R=3(4/9+1/9+1/9) = 2
Everytime a new energy is reached where a new quark can be created the R-ration jumps so for exmaple when one has an energy to include the c-quark this becomes
R=3(4/9+1/9+1/9+4/9)=10/3
This relationship for R (and the first order log corrections) has been tested nd confirmed. What does the Han-Nambu model give for the R-ratio? This might be a tricky test since it depends on the square of the charges and the average of the square is not always the square of the average. In any case it would be a good test of the Han-Nambu model.
One should also check if the chiral anomaly cancellation of the Standard Model works since this relates the various charges of leptons with quarks in order that the anomaly cancel. However even thhough I did not check this my feeling is that the Han-Nambu model will work for this since in the anomaly (at least to one-loop) the anomaly depends linearly on the various charges rather than quadratically as for the R-ratio.
Best,
Doug
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Dear Ben
Thank you for this. I am not sure that I said charge was an emergent concept in itself, but that fractional charges were.
Best wishes
Peter
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Dear Sergey
I think it is a valid idea that quarks are quasi-particles rather than actual particles, and I have worked out a quantum mechanical theory of baryon / meson structures which effectively requires this, though I don't yet know how this would relate to what you are suggesting. It is described in my book Zero to Infinity (World Scientific, 2007). I am interested in your ideas on how all the relevant masses, etc, work out and will read this closely.
Best wishes
Peter
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Dear Lawrence
Thank you for this. You may be interested in the quantum mechanical aspects of the ideas I have been investigating, which are in my book Zero to Infinity (World Scientific, 2007) and are also outlined in an arXiv paper of 2010 (the only one I published on arXiv that year). Here there is some mathematical development related to QCD fluxes, etc. Maybe this will generate some ideas that you can connect with yours. You may remember that we have met (Berkeley, 2000) and discussed string / brane versions of what I then presented, which I think you subsequently referred to in your Quantum Fluctuations of Spacetime.
Are you still based in Budapest? I will probably be visiting next year, and maybe we could meet up again to discuss the possibilities.
Best wishes
Peter
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Dear Doug
Thank you for this. My quick answer to your question is that I believe any QED measurements will be the same in both representations because the prefect gauge invariance observed in QCD and the massless nature of the gluons means that all possible phases of the QCD exist simultaneously, which means that any particular electric charge structure is only in place for one third of the time, though that third can, of course, never be identified. So, I think that it is the properties of the strong interaction that determine the QED for quarks, just as it is the weak interaction that determines the QED for electrons in the fractional quantum Hall effect.
Best wishes
Peter
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Dear M. H. Amazigh
Thank you for your comments. I think it is a perfectly valid thing to look for simple ratios and to expect them to occur in certain circumstances. For example, I have an article somewhere on arXiv about the physical significance of the factor 2 and have written about it also in my book Zero to Infinity (World Scientific, 2007). Numerical factors sometimes emerge from something simpler and more fundamental than the physical thing one is looking at, often some deep symmetry or duality. My own belief is that two numbers occur again and again in physics (and in some other areas of science), and these are 2 and 3. The first usually signifies duality and the second anticommutativity. So, I think the 0.25 for electroweak is probably a number of this kind. I have read through your article and will study it more closely to see how it may relate to this way of thinking.
Best wishes
Peter
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I am still affiliated with AIAS at U. Budapest, but I have not been in Europe for over 6 years. That position is an ingratis position, so I have to work outside of there. I was working for some time doing work on photovoltaic physics, but that whole industry has gone completely into the tank.
Gravity is in a sense the square of gauge theory, and in particular in the AdS setting it is the square of SU(3) and SU(4) ~ SU(2,2), which is a "type of QCD" in a twistor framework Two gluons in an entanglement that are color neutral define a spin = 2 particle that has a graviton amplitude. The LHC is going to ramp up the heavy ion work next year at 7 TeV and it will be interesting to see if there are more of these signatures of AdS/black hole-like scattering amplitudes.
I have though for some time that fractional quark charges are some manifestation of the quantum Hall effect. It may be due to the incidence of a gauge 4-form on the D3-brane, similar to a magnetic field across a material or graphene.
Cheers LC
Dear Peter Rowlands,
The noumenon that describes Color confinement of quarks indicates that the fundamental matters are string like structures rather than point like particles, in that eigen-rotation of mason is demonstrable to validate a Coherently-cyclic cluster-matter paradigm of universe.
With best wishes,
Jayakar
Dear Peter,
Thanks for your comment.
You are right, the number 2 indicates something fundamental in the functioning of the Universe.
These numbers, ratios, these constants we challenge and sharpen our curiosity to get the laws behind them.
I read your article on arxiv about the significance of the factor 2. I find it interesting and you bring an original perspective.
I'm working too on the duality of nature and I think we're both on the right way.
I am preparing to release a book on a comprehensive theory of how the universe and nature works. And I can tell you that I use excessively the duality.
All the best with your essay
[deleted]
Dear Jataker
Experiment is the final arbiter, and experiment seems to suggest that quarks are point like particles. The string idea was not a description of the quarks but an early way of describing the strong force before the more sophisticated QCD theory was created. If someone comes up with a new type string theory of the particles involved, that is not relevant to the level of observation I was discussing in my essay. I kept any discussion about exotic models of quarks out of my essay, as it was concerned only with the interpretations of observations involving the Standard Model.
Best wishes
Peter
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Dear Hải.Caohoàng
I think your post should have concentrated on making comments on my essay, rather than promoting an alternative theory, which you have every opposrtunity to do in your own essay. You can, of course, refer to this, but the main thrust of your comments should be on what I have written. In any case, I think the results of experiments recently carried out at CERN seem to be against you. There is every probability now that the Higgs boson really does exist, and such experiments are the only sure way we have of testing out the vailidity of our assumptions. My own essay concerns the Standard Model, which has been tested successfully many times over, and does not seek to contradict this. In view of the massive evidence already accumulated in its favour, I think ideas which cannot incorporate the Standard Model are unlikely to add significantly to our knowledge.
Best wishes
Peter Rowlands
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Meaning of Fractional Electric Charge yo can read i my old essay
http://www.fqxi.org/community/forum/topic/946
After studying about 250 essays in this contest, I realize now, how can I assess the level of each submitted work. Accordingly, I rated some essays, including yours.
Cood luck.
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Dear Sergey
Thank you for this. I am impressed that you have managed to read so many essays.
Best wishes
Peter
If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is [math]R_1 [/math] and [math]N_1 [/math] was the quantity of people which gave you ratings. Then you have [math]S_1=R_1 N_1 [/math] of points. After it anyone give you [math]dS [/math] of points so you have [math]S_2=S_1+ dS [/math] of points and [math]N_2=N_1+1 [/math] is the common quantity of the people which gave you ratings. At the same time you will have [math]S_2=R_2 N_2 [/math] of points. From here, if you want to be R2 > R1 there must be: [math]S_2/ N_2>S_1/ N_1 [/math] or [math] (S_1+ dS) / (N_1+1) >S_1/ N_1 [/math] or [math] dS >S_1/ N_1 =R_1[/math] In other words if you want to increase rating of anyone you must give him more points [math]dS [/math] then the participant`s rating [math]R_1 [/math] was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process.
[deleted]
Dear Sergey
Thank you for this. I don't understand it either. It seemed to happen overnight. I don't have any idea how these things are organized but it seems strange to me that contestants are allowed to rate other contestants' essays.
It would be better if an independent panel simply read all the essays from the outset.
Best wishes
Peter
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From an experimentalists' point of view, which is my perspective, this essay raises a number of interesting points, all of which have a bearing on what is now the main thrust of Particle Physics and therefore all of which are of importance and significance.
The SM has grown up to be the triumphal edifice that it is because experiment has verified many of its predictions with remarkable precision. These predictions depend on the acceptance that all the degrees of freedom with their defined properties in field theory dynamics, work - together (and this is the point) - in calculations for specific measurements which test only some (the rest of the point!) aspects of the SM at once.
An example, relevant to the author's essay, is quark charge where there have been many tests with experimental data demonstrating that the calculations are correct in assuming the SM assignments of charge 2/3 and -1/3 to the Dirac fermion degrees of freedom, the quarks. Periodically in the last three or more decades claims have been made to rule out integer charged quarks. Though always first claimed to be definitive, in the fullness of time it has been realised that it is possible within the framework of the principles underpinning the SM to adjust properties of the degrees of freedom and/or to alter aspects of the SM calculations in acceptable ways which render the hitherto definitive tests to be less than conclusive. In short in terms of this example, we have plenty of corroborative evidence that measured observables are consistent with the SM fractional quark charges, but we to date have never been able to measure directly the charge on a quark, or indeed even just to observe directly quarks. A latter day JJ Thomson and/or R Millikan have yet to manage to make this measurement definitively for very good reason.
That this is the case is no criticism of physics, experimental or theoretical, rather it exemplifies the way science always progresses.
Rowlands is in essence highlighting this truism, but in a way that we should take on board. It requires the humility to be open minded about what humanity has achieved in understanding the physics of the Universe, and in taking advantage of that understanding. He is saying that we should always be aware of the danger of accepting of necessity the assumptions, in his case the degrees of freedom and their numerology in the always rigorous theoretical approach which is essential for meaningful prediction. Our humility should be such as to recognise that to date we may have been unable to identify from a myriad of possibilities that what we use so far works because someone, for example Gell-Mann and Zweig, demonstrated out of luck, good judgement or serendipity, that their SU3-flavour group structure worked for spin1/2 fermions with fractional charges. We never can rule out other possibilities for certain because we haven't chanced upon, or conceptualised, them yet.
I find this essay to be very thought-provoking, and also innovative. We ignore it at our peril if we really deep-down are driven by a wish to understand what makes the world work, and not by other extraneous, misplaced, and in many ways totally irrelevant, criteria. For I am haunted by many decades ago my supervisor saying to me that of course quarks are infinitely massive and very tightly bound in hadronic matter because they have never been, and will never be, observed directly. I now see quarks every day as I look at events from the LHC and the jets that are so beautifully apparent. My supervisor, and myself at the time, had completely the wrong perspective of the nature of quark degrees of freedom, their properties, and the present day perspective of confinement in a non-abelian quantum field theory. Rowlands is just saying this all over again in the present-day context of the SM, and we should be humble enough to take him to task and ask him for further predictions when he has them, for we will measure alpha_EM at the scale of his distinct prediction sooner rather than later! If I could vote (how does one?) I would vote for this submission.