The Amazing Effectiveness and Usefulness of Mathematical Models in Physics by Ed Unverricht

Dear Ed Unverricht,

As can be expected from someone programming computer animated motions based on particles and forces, your essay provides clear illustrations with required explanations that any one can comprehend what the physicists are saying about the particles of the standard model. The picture is thus very clear, the mathematics is right. But the whole thing is founded on wave-particle duality. If wave-particle duality is correct, then the standard model is correct. As argued in my essay, the interpretation based on mathematical relation can be tricky; the wave-particle duality is a wrong interpretation; bodies cannot remain in two forms at any given instant.

The model proposed by me (not explained in my essay) views light as streams of particle-pairs; the pair rotates as it moves forward, thus path of each particle is a helix. The axis of the helix is circular and the pair is thus confined to circular path of very large radius. Such a motion creates small variations in their speeds, and this creates a varying charge in them, and hence a varying electromagnetic field. I think, based on how you explained the models in the essay, that you would have got a clear mental picture of my model. It is another mathematical model, but devoid of the meaningless concept of duality. Please visit my site: finitenesstheory.com.

Hi Ed,

Thanks for reading my essay, answering one of the questions posed (actually, the one my girlfriend thought I should omit), and watching the Digital Physics movie trailer. To answer your question, the movie will eventually be available over the internet, but I'm hoping to have some public screenings at film festivals first. Please sign up for the mailing list if you want to be updated.

As for your essay, I wish I had better knowledge of the particle zoo so I could better appreciate your visual model. Do you think your visual model represents the reality of particles more closely, or do believe it just is another "model" that offers a different perspective and perhaps a more intuitive insight?

Related to this thought, I disagreed with one of the quotes you referenced. If two models both fit the data, I would be ok with preferimg one of them to the other if the one was more elegant. This view would go along with Occam's razor and Leibniz's notion that to understand something is to compress the experimental results into a more simple theory. You wouldn't accept a theory that just added each experimental result as an axiom, so to speak, would you?

Jon

Hi Ed,I have forgotten to copy my answer to your blog.

Your essay is excellent. Full of great pictures. You present an approach that I was waiting for. I mean: a visual language, independent, universal and baggage-free description. The last notion is explained in Max Tegmark's very inspiring letter "The Mathematical Universe" (arXiv:0704.0646v2) where he says: "a description to be complete, it must be well-defined also according to non-human sentient entities (say aliens or future supercomputers) that lack the common understanding of concepts that we humans have evolved, e.g., "particle", "observation" or indeed any other English words. Put differently, such a description must be expressible in a form that is devoid of human "baggage".

I think that visual imaging could be the answer.

You say: Usefulness is also high if the model can be represented in a number of different ways and leads to a predictive power. My essay delivers the predictive power that five out of Thurston geometries remain to be uncovered in nature. These are five exotic Riemannian manifolds, which are homogeneous but not isotropic: the geometry of S2 ﾃ-- R, H2 ﾃ-- R, the universal cover of SL(2, R), Nil geometry and Solv geometry. Maybe you could prepare visualizations of these geometries?

Obviously our, humans, problem is that some geometrical structures we are not able to imagine in our brains e.g. S3 and H3. Unfortunately it needs to take a look from R4 perspective. But we can create some projections on R3 or cross-sections. You have tried to help to imagine quarks. It is really interesting... Do not stop in your useful work. Your rating is unfair. You deserve much more.

Regards,

Jacek

Dear Ed,

Greetings. The images are very nice as a visual aid (in so far as they refer to the particle aspect of the quantum object), and we hope to use some of them as teaching aids, as also the videos listed in your references [which we haven't seen yet, but surely will].

When you refer to the Higgs boson as a swirling vortex of energy, what does it really mean? Is it not too classical (non-quantum) a picture?

Thus, we felt a bit concerned that the graphics, while nicely emphasising the particle aspect of wave-particle duality, seemingly omits the wave aspect, which you will agree is an equally important aspect. Thus one could do set up, at least in principle, a double slit interference experiment with a beam of Higgs bosons. A Higgs in flight is a wave, which passes through both the slits, and then eventually collapses to a point after reaching the screen. Once it has collapsed onto the screen, we are comfortable thinking of it as a particle and using your visual aids. But what during the flight - how to form a visual aid, if at all possible?

Thanks again for the instructive graphics.

Regards,

Anshu, Tejinder

Dear Ed,

You have obviously put a lot of effort into trying to put a visual model for quantum phenomena, and the visualizations are very pleasing. Your models remind me a little of DeBroglie's standing wave model, but they are prettier, and the extension to a torus gives your model greater expressive power.

But let me ask you these questions:

1. How do you reconcile your visual model with, say. that of the wavefunction in the position basis of a single particle spread over a region of space? I have the impression that you advocate something like an upward scaling proportional to the wave-length (at least your discussion of photons suggests this), but this way of visualizing quantum objects seems to run into difficulties when the wavelength in question approaches mesoscopic scales. How do you visualise its the process of its collapse to a small region upon a measurement? Is it the reverse scaling process only much faster?

2. Can you derive novel predictions (ideally testable) from your model? Can you predict any particle masses currently not theoretically predictable? Can you predict the neutrino masses?

I enjoyed your visualizations and wish you all the best,

Armin

Dear Ed,

I enjoyed your essay and the beautiful examples and illustrations concerning the standard model.

I particularly enjoyed the quotation in the summary:

When one accepts one theory and rejects another which is equally consistent with the phenomenon in question, it is clear that one has thereby blundered out of any sort of proper physics and fallen into mythology - Epicurus, Letter to Pythocles

Well it does beg the question of how we decide which theory is physics and which theory is mythology. In fact it is quite likely that both theories have merit, for example the theory of gravity as expounded by Newton and Einstein.

I find myself in the difficult position of having a theory (the Spacetime Wave theory) (see Solving the Mystery) which seems at odds with the Satandard Model of particle physics. It treats the fundamental particles (electron, proton and neutron) as looped wave disturbances of spacetime. Further it shows that the idea of a quark does not fit in with this new theory as an independent stable particle.

I am not saying that the standard model is wrong. What I am saying is that it does not provide a good unified description of reality. When we do have such a complete unified description of reality (including all fundamental forces, mass and charge) I expect that it will be possible to explain why the standard model is so effective in using ideas of symmetry to describe the particles whose real nature is described elsewhere.

This must sound like mythology (or even heresy?).

Best regards

Richard

Dear Ed,

I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

Joe Fisher

Hi Ed,

I enjoyed your impressive visualizations of the Pythagorean faith in the logical beauty of nature. "The laws of nature are described by beautiful equations", as Dirac put it, and you are wonderfully showing that. May be, you would be interested to read our essay where we are doing metaphysical conclusions from this primacy of mathematical beauty.

Good luck in this contest!

Alexey Burov.

Dear Ed,

Thanks again for the kind comments of my essay. I finally got to read your interesting and visually impressive essay. I agree it is very useful to find visual models of particles, and that if they are found to contradict reality, should be replaced. Cool movies and animations!

Best wishes,

Cristi

Dear Ed Unverricht,

Your essay is very good. It deserves high score. Perhaps you could help to model the relationship that is important in my essay.

If we define x=classical electron radius / proton Compton wavelength = 2.13252558524. Using this ratio, we can define the following dimensionless value:

DeltaP =2-1 / (2pi * x 2) =1.935060944. The model would help to understand the possible physical significance of DeltaP. I would be very grateful.

Regards,

Branko

Dear Ed Unverricht,

In my search for pieces to the Great Cosmic Puzzle and for mathematical toolsets with which to assemble a Cosmological Model based on a True Understanding. Your paper impresses me as being 100% relevant and MOST useful to Quantum Mechanics. I hope to apply these understandings to my idea of Combinatorial Quantum-wave Mechanics (CQM).

Your paper stands above most in that it clearly lifts up the understanding of anyone who reads it.

You have earned my respect BIG TIME! First, you realized the importance and relevance of the subject matter to have studied it so well! Second, you have presented a clearest and most concise description of Group Theory I've ever seen. Third, and to me the most important, is your description of quarks fits nicely into the 4D Space~Time "framework" of my paradigm called the Cosmic Onion Model. In the context of this model quarks are NOT entities in-and-of themselves but are the geometric interactions of three wave functions interacting with a 4th wavefunction type (wave-icle) which are the root-causes of protons and neutrons. (These interactions manifest as quarks -- that's why neutrons decay into electron, proton and photon energy - NEVER into quarks. The wavefunction of a decaying neutron twists into the wavefunction of a proton plus splits into an electron and anti-neutrino and sometime with gamma ray emission. Not to mention other "bounded" decay modes.)

Just as challenge to anyone reading this, maybe there exists a physicist who can explain the Electromagnetic Wave diagram showing the electric field and magnetic fields perpendicular to each other, yet perfectly in-phase with each other. Why would they propagate one way or the other? (Nature does not include the little arrow.) Without the help of the little arrow what "propels" the wave one way or the other? (My best guess is that the wave is constructed from photons (h*c) (packet of energy in the form of angular momentum moving at c) temporally spaced so that they construct the overall EM wave -- at the photon level there must be a phase shift between E vs. M.)

Not to worry, I don't hold that against you. I only mention it as a challenge to anyone who can offer an better explanation.

Overall, your paper desires more than 4.8 so here is a boost to 5.1.