Saturday, November 28, 2020

A childish topological TOE of mine and what made it unwise

When I achieved some real, important enough realizations about physics, like matrix string theory, I was happy but I slept well. Things suddenly fit together and after a few minutes, one may get pretty much certain that the nontrivial new statements are right. They pass a lot of consistency checks. One may try to deduce many consequences and calculate some other things. But once you know that it works, you may leave it for tomorrow, the day after tomorrow, or someone else. Some fun should be left for the other people, shouldn't it?



It was the ultimately wrong ideas that have prepared several sleepless nights for me when I was a kid (or a teenager). And that may be how I learned that losing your sleep doesn't necessarily increase the depth of the theory. Let's discuss the theory. Sometime in 1987 when I was 14 or so, I decided that I had just found a theory of everything (of all elementary particles). Be ready, it was a theory of a nearly Leo Vyukesque "strawberry TOE" caliber.



OK, I decided that there were just several independent elementary particles and everything was made out of them. Photons and gravitons (let alone Higgs bosons) weren't in my list but I needed electrons, protons (to create nuclei), and neutrinos. My elementary particles of matter were actually electrons, protons, and neutrinos. Neutrons were bound states created out of the three, \(n\approx p e^- \bar \nu\). No attention was paid to heavier generations. I realized that there should be antiparticles for each; but their representation wasn't too clear. The protons were elementary; those who should have promoted quarks and QCD by the mid-to-late 1980s hadn't done a good enough job among the Czechoslovak kids.



But I was obsessed with topology change and wormholes, like those in general relativity (which I understood reasonably well; but I knew no real quantum mechanics at that time), and I decided that those were enough to explain everything. You should get some empathy for the "background of the time". I did understand Einstein's equations but I hated the addition of "matter" as a dull (or perhaps pointlike) stuff to these equations. The conversion of everything to pure geometry would have been so much better! A year later, I saw that Einstein was focusing on this paradigm, too. Geometry (some variation of a smooth 4D spacetime geometry) could be enough to describe everything in the Universe.

Suddenly, a theory looked extremely attractive. There were just three particles of matter and all of them were wormholes of different types. How can you create a wormhole, a topologically nontrivial 3D space? Remove 2 solid 3D regions from the 3D space, \(\RR^3\), and identify their boundaries (the two copies may be mirror images of each other if needed). So if you penetrate into the removed interior of one of the solid bodies, you appear outside the other solid body. Simple.

With these assumptions, the only adjustable characteristic of the wormhole is the topology of the 3D body that you remove. It is pretty much equivalent to the topology of its boundary and such 2D surfaces are classified by their genus \(g\). The simplest example is a sphere. The simplest wormhole is created by removing two balls from \(\RR^3\), followed by the identification of the two spherical \(S^2\) boundaries.



The next wormhole uses two copies of the "solid torus" followed by the identification of their boundaries \(T^2\). If an observer walks into the first solid torus by crossing the first \(T^2\) boundary, he reappears outside the second solid torus, on the corresponding place. Finally, you may have a solid body with two holes whose surface is a \(g=2\) surface.



For this \(g=2\) topology, you may choose the precise shape roughly in this way so that the boundary as well as the 3D region inside it has a \(\ZZ_3\) symmetry. It's nice that even though the genus is just two, the object may behave as an object with "three wings". I loved that observation because the number 3 seemed relevant: some crazy people were writing that there were 3 "quarks" inside a proton. I decided it was not even wrong and the real reason why some people claimed to have the experimental evidence for "3 quarks inside the proton" was that they were seeing this \(\ZZ_3\)-symmetric shape of the wormhole. Imagine how much redundant rubbish all the QCD people were trying to add to physics. In my world view, the likes of Gell-Mann, Zweig, let alone Gross and Wilczek had to be real losers who were dumb as doorknobs (and I only knew proper door handles up to 1997 when I touched my first doorknob in the U.S., a cultural shock).

You can continue to higher genera but I didn't need to study it. Clearly, there would be some extra particles with higher genera waiting to be discovered. I could do well with the three simplest wormholes and those explained the matter we needed, including electrons, protons, and neutrons (recall that the latter were just some bound states of electrons, protons, and neutrinos). Electrons were the connected pairs of \(g=0\) spheres; neutrinos were the tori; protons were the \(g=2\) shapes with the \(\ZZ_3\) symmetry. Aside from the "3-quark misinterpreted experimental fairy-tale", my theory also explained why neutrinos looked like they were spinning. The torus \(T^2\) with \(g=1\) may be spinning around an axis without changing its shape, right? So both sentences include the "spin" in some way so a consistency check was found. All matter was composed of pure geometry, namely these \(g=0,1,2\) wormholes.

Yes, I find it crazy how I could have been excited about this utter stupidity for hours and perhaps for one passionate sleepless night.

Why? Because nothing really works about this theory. The "patterns explained or confirmed" by my theory are so vague and superficial that they should be counted as no confirmation at all. Even more importantly, there are many straightforward observations of matter that instantly show that the theory was wrong. First, there should be antimatter. If elementary particles such as the electron are "pure geometry", the positrons and other particles of antimatter must also be pure geometry! But this would seem to imply that they have to be identical. There is no natural "new geometry" that may be created out of my wormholes by a reflection. So the electron and positron would have to be perfectly identical.

On top of that, they couldn't really annihilate with each other (or be pair-created). A spacetime with two wormholes – two pairs of the removed balls whose spherical surfaces are identified – is more topologically complicated than the empty space, \(\RR^3\).

I didn't have a proper explanation for the bosonic elementary particles. Or for the actual reasons why people thought that quarks existed, like the deep inelastic scattering. I obviously wouldn't have understood the phrase "deep inelastic scattering" at that time. I would have misunderstood many other things like that. Add the problems with the absence of the elementary particles with higher genera. Or topological variations of the spacetime that cannot be obtained by the removal of 2 copies and their identification. The list of problems with my theory would be as long as a textbook on particle physics because literally "almost everything" that particle physics has learned is incompatible with my theory! ;-)

So the excitement of mine – and the sleepless night – was a result of very poor standards. I didn't need too much to become excited! And I didn't have much respect for the body of wisdom – either direct experimental data or theoretical ideas or principles that have been extracted or deduced from diverse experiments – because if I had had respect for them, I would have tried to learn what was known in much more detail. And these "details" should have been explained. They would be much more well-defined details than the vague observation that "the number 3 is seen somewhere around a proton".

In this perspective, the theory looks really stupid. But you should understand that it was one of my first attempts to uncover a "deeper structure inside elementary particles" which should have been embedded to "something like classical general relativity".

The main reason why I wrote this silly story is that there may be many armchair physicists whose thinking is very similar to my reasoning in 1987 (I did abandon the theory during the following day or days). They offer some juicy, strawberry-like ideas that taste yummy to them and that must have the potential to explain a lot, these people believe. But at the end, the belief is based on virtually nothing – except for the creators' overgrown egos.

Why? It's because a lot is known from the experiment. Lots of the numbers have been measured. And the billions of different parts of experiments have been organized into phenomenological theories that are "pretty much proven experimentally as well" although they predict much more than the isolated experiments. The phenomenological theories may interpolate in between the experiments with particular particles at particular energies; and they may extrapolate them to other energies and other collections of particles, too.

In quantum field theory, what specifies the model – or the body of all results from allowed experiments – is the particle spectrum along with the cross sections (or decay rates) describing the probability of any transmutation of initial particles into final particles with certain initial and final momenta. These are the numbers – functions of momenta – that your theory should actually calculate, or at least constrain the form of all these functions. If your theory doesn't do this thing at all, it is describing approximately 0% of the relevant experimental data. And it was the case of my wormhole theory of elementary particles, too. On the contrary, if you can calculate the cross sections for any arrangements of particle species and their momenta, your theory calculates "everything" because all processes in the Universe may be reduced to the elementary processes of this kind. (Green's functions or S-matrices are not the only ways to parameterize "everything in physics", however.)

The previous simpler theory, a theory with pointlike electrons, neutrinos, and others (quarks are better than hadrons) was really better than my wormhole theory. The addition of the wormholes didn't really increasing the explanatory power of physics. I was adding junk but what I got from the theory was less than what you could get from a theory of point-like particles (at least assuming my particular realization of the wormholes and their dynamics). Note that strings are different. You may deduce quantum field theory from string theory at low energies; that also guarantees the UV finiteness of the loop diagrams; it allows you to genuinely unify different particle species into one object because all species are just vibration modes of the same string; it allows you to do many other things. But my wormholes theory didn't really do anything that string theory does. It contradicted almost everything that it should have agreed with. There was no overlap of my theory's predictions with those of quantum field theories (which I hadn't understood by that time).

If you want to have a chance to move the search for a theory of everything forward, you simply need to pay attention to what is known – from experimenters and from theorists or at least phenomenologists (whose wisdom is just very cleverly processed meat from the experiments). You can't get ahywhere if you ignore everything or almost everything. Your belief that you're smarter than everyone else and that's why you may ignore everything that is known is a lame justification for your ignoring the wisdom. It only proves your overgrown ego and arrogance; not your intellectual superiority.

Don't get me wrong. It's often right and extremely important to ignore many things, even most things. It's often very important to focus on the "right subset of insights" that are enough to deduce some new principles of physics – or some new structure inside matter. But the set of observations that you generously pay attention to simply cannot be too small. If it is too small, you are almost certainly naive and your theory is almost certainly childish.

The claim that some structure inside the seemingly point-like elementary particles is physically justified is a huge claim. And as far as proper physics knows as of late 2020, the constructions derived from string theory offer the only "shapes" of elementary particles that are at least as justified as the point-like character of the elementary particles (and indeed, strings are more justified than points by now). Everything else that has been tried – efforts to replace all the point-like elementary particles by something else – may be demonstrated to contradict the experimental facts as soon as your theory is defined sufficiently accurately to be actually capable of predicting "something like the cross sections". Everyone who claims something else is really clueless about modern physics – he or she hasn't subjected his alternative theory to sufficient tests that are mandatory in physics. He hasn't even started to seriously work on the subject, otherwise he would know that his theory doesn't work at all.

You can't really ignore the overwhelming bulk of the known experimental and theoretical physics if you want to help to move the frontier of physics further. Proper physics can't ever become a shouting match between dudes with overgrown egos who ignore each other. Proper physics does depend on quite some attention paid to the experimental facts (often rather subtle patterns in these facts) and phenomenological laws or even deep theoretical principles derived from the experimental data. And once you accept this verdict and tame your ego correspondingly, you will be led to the insight that the picture with the point-like elementary particles (and the conventional quantum field theory) is damn accurate and useful and the only viable alternatives (those that are derived from one formulation of string/M-theory or another) actually end up being extremely similar to the point-like elementary particles in very many respects.

There may be a way to describe all the matter as "some kind of wormholes", some configurations that are locally (either in our 3D space or in another space) equivalent to the empty space with nothing in it (not even strings). But you need to fix all the problems discussed above – you need to allow the topology change that is involved in annihilation; you need to interpret the higher-genus objects and make them harmless – and equally importantly, you need to figure out the details of the dynamics that actually allow you to calculate the quantative predictions similar to the cross sections. At the end, a theory of everything must be a theory of... everything. If your theory ignores and fails to explain or predict (almost) everything, it's a theory of (almost) nothing instead!

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