Why do elementary particles have such strange looking mass ratios?

Why do elementary particles have such strange looking mass ratios?

Elementary fermions of four different values of electric charge are observed in nature. In units of the charge of the positron, these values are 0, 1/3, 2/3, 1. The positron has charge 1, the up quark has charge 2/3, the anti-down quark has charge 1/3, and the anti-neutrino has charge 0. Their respective anti-particles have same absolute value of the electric charge, but of the opposite sign [electron, anti-up, down, neutrino]. We hence say that charge is quantised in these discrete units? But why these and only these, and why is it quantised in the first place?

Each of these four particles has a corresponding second generation particle, and a third generation particle. The second and third generation copies have the same electric charge as its first generation relative. Thus the counterparts of the electron are the muon and the tau-lepton, each of them having charge minus one. The down quark has as its counterparts the strange quark and bottom quark, all having charge 1/3. The up quark's copies are called charm and top, and they all have charge 2/3. We see that the value of electric charge does not change across generations.

The only known difference between the three copies of  a particle is their mass. The electron has a mass of 0.5 MeV. The muon at about 105 MeV is some 200 times heavier than the electron, The tau lepton at 1777 MeV is about 3500 times heavier than the electron. 

The up quark, charm and top have respective masses of 2.3 MeV, 1275 MeV and 173210 MeV. The down, strange and bottom quark have respective masses of 4.7 MeV, 95 MeV and 4180 MeV.

Neutrinos are known to have a non-zero mass, but much smaller than the mass of the charged fermions, and the actual value of their masses is unknown. Let us leave them out of the discussion for now.

It is obvious that unlike electric charge, mass ratios appear strange and random, and show no apparent pattern. If we decide say to compare the various masses with respect to the up quark, and for simplicity take the square root of the ratio, we get the numbers 1, 1.4, 0.47, 6.4, 6.8, 23.5, 42, 274.3, 27.8 The elegant simplicity of quantised values of electric charge is lost. Is there a simple pattern to these mass ratios, or not, and how are we to find the pattern, in case there is one? This profound question has remained unanswered for decades after all these particles were found and their masses measured experimentally.

An answer may now have been found, and it comes from a very surprising and unexpected quarter. We started in a very different realm: addressing a foundational problem in quantum theory. Quantum mechanics is formulated on an external classical space-time but such classical elements should strictly not be a part of quantum theory. We should be able to describe quantum phenomena without referring to classical time. In one specific approach to finding such a description, it has been found that the theory must be  formulated in eight dimensions, which are labelled not by real numbers, but by eight dimensional numbers known as the octonions.

When we try to place fermions in such an octonionic space-time, we are in for a surprise. We are not allowed to assign arbitrary properties and quantum numbers to these particles. The space-time dictates that the electric charge must be quantised, precisely in the units 0, 1/3, 2/3 and 1, as observed. And the space-time also dictates that particles have anti-particles of opposite charge, and come in three generations. 

If the space-time dictates there are three generations, and if the only difference between the three generations is mass, the octonionic space-time must also determine mass ratios, just as it determines ratios of electric charge. Happily, it does. Just as there is a charge value associated with every particle, there is a mass number associated with every particle, called its Jordan eigenvalue. These Jordan mass numbers are shown in the table below (Ignore the numerical entry in the first column). The entries in the next three columns are the respective mass numbers.

These mass numbers are very simple and pretty. For the three generational copies of a particle, the middle value is its electric charge, and the other two values are symmetrically placed about the middle value, always departing from the middle by a factor of square root of 3/8. 

The theory dictates that mass ratios will be determined by these Jordan values, and these mass ratios are shown in the table below, scaled with respect to the down quark mass which is set as one. It can be easily verified that these simple fractions reproduce the strange pattern of mass ratios observed in nature! Mass is quantised, just as electric charge is, and the ratios are quite simply given, though not as simple as the charge ratios 1/3, 2/3 and 1. 

We believe that the mystery of the strange mass ratios has finally been solved. At the heart of the resolution lies the realisation that elementary particles are described by the octonions, as long suspected by several physicists.

Also:

Mass ratios and Majorana neutrinos:

Getting the correct mass ratios from the octonion algebra requires us to assume that the neutrino is a Majorana particle [i.e. its own anti-particle]. Assuming the neutrino to be a Dirac particle gives wrong mass ratios. We hence predict that Neutrinoless Double Beta Decay does occur in nature and will indeed be observed once adequate sensitivity is achieved in experiments.

Reference: https://www.preprints.org/manuscript/202101.0474/v4

What do the interpretational problems of quantum mechanics have to do with the failed unification programme of string theory?

What do the interpretational problems  of quantum mechanics  have to do with the failed unification programme of string theory?

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The context of my present post is this beautiful video chat:

Steven Weinberg and Andrew Strominger in conversation [April, 2021] YouTube video https://youtu.be/PFJ46G8BflQ

Towards the end of this very watchable video, a member of the audience put a question to both of them:

In your opinion, is there some problem in our understanding of quantum mechanics [i.e. interpretational issues, measurement problem]. And if so, could this unsolved problem be holding up progress in theoretical high energy physics etc. ?

Weinberg: Yes there is a problem. Quantum mechanics gives a great importance to observers. It pre-assumes a quantum-classical divide so as to be able to make sense of the theory [classical apparatus, measurement]. A reductionist theory must not have to depend on its own limit for us to understand the theory. Rather, working from bottom up, the theory should be able to explain the classical properties of the measuring apparatus as a consequence of the theory itself, instead of having to assume them a priori without proof. Essentially, Weinberg is dissatisfied with Bohr's Copenhagen interpretation. Then he correctly points out that Everett had the same dissatisfaction and therefore came up with what became known as the Everett interpretation. Wave functions never collapse during measurements, and the universe is forever in a state of quantum superpositions of everything. Weinberg says in the conversation that he does not agree with / like the Everett interpretation either. Hence, according to him there is something missing in our understanding of quantum theory.

Strominger: No. There is no problem. We can calculate marvellously with quantum theory. The Lamb shift has been calculated to an unprecedented accuracy. No experiment has ever disagreed with quantum mechanics. As for the interpretational issues, these are just words. It is not physics. You could side with Bohr, or you could side with Everett. It does not make a difference. You can still do your excellent calculations with quantum field theory and predict the world. In other words, Strominger is saying: Shut up and calculate.

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These contrasting responses by Prof. Weinberg and by Prof. Strominger are noteworthy, and have a deep connection with the current status of string theory.

Fast forward to the present: "Strominger: It does not make a difference'. ?? Interestingly, it does!! And I try to say this as clearly as possible: The reason string theory has failed in its unification programme, and fails to predict the standard model despite being almost there, is because string theory adheres to the Everett interpretation of quantum mechanics. If string theory is modified a little bit so as to allow for [a dynamical implementation of] Bohr's Copenhagen interpretation and wave function collapse, it can predict the standard model, uniquely. So Bohr vs. Everett makes a huge difference. As big as the difference between success and failure. As I now try to explain.

It is well-known that string theory can be consistently formulated as a unified theory in a higher dimensional space-time [not four]. Ten space-time dimensions, to be precise. (Eleven, for M-theory). So far so good. However the universe we live in is four dimensional, not ten. Why do we not see the remaining six spatial dimensions? The answer proposed in string theory is that the extra dimensions are curled up, compactified, too small to be seen, say as small as the Planck length scale. This proposed solution ruins the theory. For it turns out there are a very large number of inequivalent ways of compactifying the extra dimensions, all of which produce different particle physics theories in four dimensions. String theory loses predictive power. Which compactification to use? In fact it is not clear whether the standard model is even there as one of the compactifications. As a consequence, as Strominger notes, the ambitious unification programme of string theory was over in the 1980s itself, in a couple of years after the excitement set in.

There is a different mechanism, other than compactification, for recovering a four dimensional space-time from a ten dimensional space-time. It requires us to preferentially and deliberately pick Bohr over Everett, and modify quantum mechanics a little bit [while still remaining consistent with all lab tests of quantum theory] and allow for a dynamically induced rapid collapse of the wave function in macroscopic systems. This is known as the Ghirardi-Rimini-Weber (GRW) mechanism of spontaneous localisation, and would happen very naturally in string theory too, provided we remove the restriction that at the Planck scale as well, the Hamiltonian of the theory must be self-adjoint. Instead, allow for the possibility that under suitable circumstances, evolution at the Planck scale can be non-unitary. Such a possibility is certainly not ruled out by current experiments.

How does this help with the compactification problem in string theory? When we say that the universe is four dimensional, what we mean is that classical objects in the universe live and evolve in four spacetime dimensions. Nobody can claim that quantum systems live in a four dimensional space-time!! A quantum system can well be thought of as living in ten space-time dimensions [as string theory does] even in today's universe, provided the support of its wave-function is non-vanishing only over microscopic distances. Here, microscopic does not mean Planck length. Microscopic can be as large as a micron, roughly before the classical-to-quantum transition takes place around an Angstrom, into the world of atoms, which are of course quantum.

Consider then a string theory type quantum field theoretic system living in a ten dimensional spacetime. Except that the dynamics is now given by the GRW modified quantum theory. and the Hamiltonian possesses an anti-self-adjoint part. When sufficiently many degrees of freedom living in 10D get entangled, the GRW mechanism of spontaneous localisation sets in, and the entangled system becomes classical. And now is the key point, in becoming classical, the entangled system descends from ten to four spacetime dimensions. The support of its wave-function over the extra six spatial dimensions is vanishingly small, smaller than Planck length - this has actually been proved. While the size of their extent in the 4D spacetime remains large. This way we have achieved effective dynamical compactification, or so to say, compactification without compactification. Quantum systems, including those in today's universe, continue to live in ten dimensions. The forces that curve the extra six spatial dimensions are precisely the internal symmetries of the standard model.

We have developed a unification theory in ten spacetime dimensions, very similar to string theory. Except that the dynamics is modified quantum dynamics. The theory has a very promising potential to unify gravity and the standard model, and to predict the values of the free parameters of the standard model (work in progress).

So dear Prof. Strominger , it matters: Bohr or Everett. These are not mere words; foundational questions of quantum mechanics are important. And now they are important in your own backyard Prof. Weinberg is absolutely right on this count; sadly he is no longer with us to witness the unfolding of this story.

We can hence have a failed string theory and an unmodified quantum mechanics. Or we can have a successful string theory and a modified quantum mechanics. It confounds me that string theorists, extremely smart physicists though they are, do not get this. Why do they not consider that the problem is not with strings, but with quantum theory? I sincerely hope they change their mind.