’t Hooft on the Foundations of Superstring Theory

atyy

Thanks for your answers. I'm still learning about BM so just have a bunch of stupid questions to ask, and will probably take a long time to understand the details. It is definitely helpful to have expert opinion like yours to guide my "homework".

Anyway, if you are right, then 't Hooft if wrong, ie. there is no foundations problem in QM, QFT, string theory?

Demystifier

I think the main property of the Bohmian approach which 't Hooft does not like is non-locality. There are very general theorems which say that non-locality is unavoidable, but 't Hooft tries to avoid some assumptions of these theorems. See also
http://www.physicsforums.com/blog.php?b=3622

RUTA

There are two things one can abandon to avoid the conclusion of the Bell inequality -- locality and statistical independence. So, if he doesn't like non-locality, then he must abandon statistical independence, e.g., as is done with time-symmetric interpretations.

atyy

Is cosmology a problem for Bohmian mechanics, since if there is only one universe, there is no distribution of initial conditions?

The Valentini essays that Ilya mentioned in the other thread seem to provide a way out, ie. non-equilibrium Bohmian mechanics, so that equilibrium BM = standard QM emerges from the dynamics. But I don't think there's any concrete proposal for this at the moment.

Demystifier

This is like asking is cosmology a problem for classical mechanics, because in classical statistical mechanics applied to one universe there is no distribution of initial conditions. The answer, of course, is that it is not a problem. Even though statistical reasoning plays a role in both classical and Bohmian mechanics, both theories are fundamentally deterministic, not statistical.

atyy

But just as we still don't know how statistical mechanics arises from classical mechanics, then we still don't know how quantum mechanics arises from Bohmian mechanics?

In trying to get stat mech from classical mechanics, there's usually some coarse graining, and there have been proposals for chaos to be involved, or involving canonical typicality or eigenstate thermalization (but I think those assume the Born rule). What are the corresponding ideas for getting QM from Bohmian mechanics?

mitchell porter

This is a peculiar statement. It becomes even more peculiar when I look at the links you provided to back it up, because two of them are about quantum mechanics. (And the third one, after the part devoted to study of Boltzmann's words, is about technicalities to do with chaos and defining entropy away from equilibrium.)

If we have a classical equation of motion, then we can also figure out how a probability distribution over classical states will evolve. So where is the foundational problem? Consulting Wikipedia, it seems the basic challenge is to physically motivate the probability distributions that one might use. On what grounds do I say that a uniform distribution over a certain set of microstates is an appropriate description for a system at equilibrium? Well, that's a bit like the general problem in probability theory, of where you get your prior from.

Anyway, I would like you to explain the difference between "statistical mechanics of classical systems" and "mathematics of probability distributions over classical systems". I hope we can agree that there's no deep mystery about the latter, if you already have the classical equation of motion. So any foundational problem of "classical statistical mechanics" must arise somewhere else. But where, exactly?

In the case of what I call "cosmological Bohmian mechanics", what one would need (in my opinion) is a hypothesis about cosmic initial conditions (both for the pilot wave and for the classical system it guides), such that, if you looked at the "reduced pilot waves" associated with small sets of "classical" degrees of freedom, in the subsequent history of the Bohmian universe, the "demographics" of this association would resemble the Born rule. E.g. if you picked out a random electron, from somewhere in the space-time history, and looked at the reduced density matrix associated with that degree of freedom (derived from the universal pilot wave at that time), you should expect a Born-like probability relation between its position and its reduced density matrix. I have no idea how far people like Valentini have gone towards such a goal. But the need to gauge-fix in Bohmian gravity (the shift and lapse functions) seems a far more important difficulty, anyway.

atyy

Sure, I did note the latter two links were about QM. The general question is how does stat mech arise? And yes, the question is how does one justify the initial distribution. Valentini's approach is indeed in the same spirit of my question - have any concrete examples been worked out?

Demystifier

While there are some uncertainties regarding how statistical mechanics arises from classical mechanics, I think those uncertainties are not very serious. Anyway, the situation is very similar with Bohmian mechanics.

Demystifier

Yes, I definitely agree with that.

atyy

Why? If the initial condition problem is solved, then just apply Bohmian mechanics to QFT and get quantum gravity by AdS/CFT.

Demystifier

You cannot get gravity by AdS/CFT if QFT of interest is not conformal, and if the gravitational background is not AdS. Which, in the world in which we live, is not.

atyy

Yes, no realistic cosmologies yet. But I think it's been extended to non-CFTs, eg. section 1.3.3 of http://arxiv.org/abs/gr-qc/0602037 .

Demystifier

The evidence for general gauge/gravity duality is still rather poor. Most evidence on it (e.g., in QCD) suggests that, at best, it is only an approximation.

atyy

According to http://particle.physics.ucdavis.edu/blog/?p=240 , that case is weak coupling and small N. So it doesn't contradict that one can have the duality for non-CFTs that are strongly coupled with large N.

atyy

Do you agree with a sentiment such as "in the context of inflationary cosmology, that corrections to the Born rule in the early universe would in general have potentially observable consequences for the cosmic microwave background (CMB). This is because, according to inflationary theory, the primordial perturbations that are currently imprinted on the CMB were generated at early times by quantum vacuum fluctuations whose spectrum is conventionally determined by the Born rule." http://arxiv.org/abs/1103.1589

Is the proof of deviations from QM part of what you consider almost certainly part of Bohmian mechanics applied to cosmology?

Demystifier

I think it is a possibility, but not an almost certain one.