Subversive Epiphany

I have just gotten back from an extended business trip to the United States.

This was a lot of fun. I went to the SIAM Boston meeting on Computers in Science & Engineering. Later in the trip I went to PyCon2013 and PyData2013 to catch up with where things are at in the Pythonic universe.

It is probably close to fifteen years since I have been to a scientific conference. I very much enjoyed the developments in computational science since they involved many practical problems.

Regular readers of this blog will appreciate my love-hate relationship with mainstream physics. I tend to get very annoyed when I read physics journals, but I do enjoy the computer and applied mathematics literature.

However, I may yet come to some rapprochement with physics-at-large.

The epiphany for me was the sudden realization that most physicists today do not seem to believe in the Copenhagen interpretation but they do believe in point-like particles.

I don’t know exactly when that dawned on me, but it was somewhere in the middle of listening to some talk on numerical solutions of the Schroedinger equation in the semi-classical regime. None of the correspondents in that session seemed to know anything about my work in this area so I kept quiet.

I did not want to spoil the fun of searching for the elusive classical limit.

Reflecting upon what I already knew to be a grand folly I realized that physicists in general seem very sure that they know what rests within the Schroedinger equation. Look at it this way. They know three things:

1) the Schroedinger equation is right
2) the Classical world seems real enough and sensible
3) therefore, it must fall out of the mathematics somehow

All very sensible, but sadly untrue. The relevant mathematics does exist but is not what they are looking for!

Now to the epiphany. The physics community, in general, believe that we know particles are real. However, they are confused about what a wavefunction might be or mean since a wave is clearly not a particle!

What the community has yet to appreciate is that in a certain limit, that of the Classical Schroedinger Equation, the wavefunctions do bounce around, scatter and behave exactly like particles. However, that is a limit where the wave aspect of the physics is frozen out. You get to the idealised particle from the wave description.

However, that regime of behavior is very special and only ever approximate.

Let us now turn things around. Suppose there are no particles at all. Suppose that is merely an illusion and matter is pure wave. Even further, suppose that the phase of that wave is the gauge field (e.g. the photon). Then there is no light separate from its sources. They are part and parcel of the same phenomenon.

In that case, we have things perfectly upside down. We are using a micro-level mental picture of particles and then wondering why the classical level continuum physics is not easily recovered. Turn that around and employ a micro-level picture of pure waves. How then do you recover familiar billiard ball behavior?

That is easy, it is the decorrelated approximation of mean-field theory for which the Classical Schroedinger Equation is just the simplest example in a family (the next one up is the Hartree-Fock approximation).

What then is the reality? Well, in the alternative picture it is a matter wave in configuration space.

What about measurement theory, you ask? How come we only see fields in 3+1 dimensions not (3+1)N dimensions? How can you possibly shrink a beast in configuration space to a manageable quasi-classical field?

Easy. The very same rule invented by Max Born still works!

If you calculate the one-body density of the matter wave you get the classical level of experience. The mapping from (3+1)N dimensions to (3+1) is trivial and we already know the empirically supported rule.

Once we abandon thinking about particles, then there is no measurement theory at all. There is nothing separate, just a whole. There is no particle being measured by something, and no observer either. You can just junk the lot.

There is only one single wave and a continuum foundation to everything. Since the wave equation does admit eigenfunctions, that wave is quantized. Think of it as Universal Jelly with Natural Modes of Vibration.

Furthermore, the classical limit is merely an idealization. The wave never breaks up into independent particles in the sense that quantum field theory describes. Entanglement is ubiquitous and permanent (eat your qubit socks quantum computing zealots).

Wilder still, if you analyze the causality structure of such a theory it is not determinable.

While the underlying wave evolution may well be deterministic the one-body quantities are not sufficient as initial data. You could know them exactly and still not be able to predict what happens.

There is no need for God to Play Dice. You can have a non-local fully deterministic hidden wave theory. This you cannot do for particles, since local hidden variable theories are excluded!

The epiphany which struck me in Boston was the realization that hidden variable theories are alive, but only when constructed in the wave formulation.

If you insist that the wave describes a point-like particle then you cannot conceive of a hidden variable theory. This is because particles are local entities. Waves, on the other hand, are non-local entities. If you only think of particles you will miss this possibility.

The totality of the wave in configuration space is a non-local hidden variable.

I think it is possible to build a new theory now. However, this journey is not for the faint hearted. Quantum Field Theory simply cannot survive such a revision of physical interpretation in its present form.

QFT is necessarily a theory of particles not waves.

If we do get new physics it will be New Physics. Interpretation changes everything.

Getting the particle back as an idealized concept is easy. That is the Classical Schroedinger Equation.

Sionara QED I. Enter QED II, the sequel with added Gravitation.

The question is what to call this hidden layer of reality we are positing. Since the idea of junking QFT in its entirety is so utterly subversive I favor the term subverse.

To be really perverse, let us call the perceivable layer the PERVERSE and the imperceivable hidden layer the SUBVERSE. As Confucius himself might opine:

Contemplation of perverse perceivables guides us to subversive imperceivables.

We are now on the road to SUBVERSIVE QUANTUM FIELD THEORY (SQFT).

SIAM meetings are a lot of fun.

I’ll be back.