The Quantum-Classical Debate:

reply to Andrei

Today I will reply to the arguments Andrei made last week in his guest post. But let me first start by giving out the answer to the questions from two posts ago. First, on why there is no uncertainty relationship for spin, from any two non-commuting observables A and B one obtains:

\(\sigma_A \sigma_B \geq \frac{1}{2} |\langle [A,B] \rangle|\)

The key point of Heisenberg uncertainty relationship for position and momenta is to be pedantic and observe that the commutator is proportional with the identity operator \(I\):

\([x,p] = i \hbar I\)

which is not true in the case of spin. Because of this, in the spin case there exists states for which the right hand side value \(|\langle [A,B] \rangle|\) is zero. The position-momenta uncertainty remains bounded from below for any state.

For the other question on the apparent violation of the uncertainty principle. here is what Heisenberg stated:

"If the velocity of the electron is at first known, and the position then exactly measured, the position of the electron for times previous to the position measurement may be calculated. For these past times, δpδq is smaller than the usual bound." and "the uncertainty relation does not hold for the past." I think this is not a well known or appreciated fact by the majority of physics community.

Then Heisenberg pointed out that these values can never be used as initial conditions in a prediction about the future behavior of the electron.

Now back to answering Andrei's challenge to quantum mechanics, Andrei discussed 3 points:

Objection 1: Classical, local theories have been ruled out by Bell’s theorem.
Objection 2: Classical theories cannot explain single-particle interference (double slit experiment), quantum tunneling, the stability of atoms or energy quantification in atoms or molecules.
Objection 3: Even if one could elude the previous points, there is no reason to pursue classical theories because quantum mechanics perfectly predicts all observed phenomena.

Let's analyze them in turn.

On Objection 1, I agree that classical, local theories have been ruled out by Bell’s theorem with only one loophole left: super-deterministic theories pursued by 't Hooft. Any statistical theory obeying Kolmogorov's axioms respects Bell's inequalities. It is interesting to see how different realistic quantum mechanics interpretations escape Kolmogorov's axioms: Bohmian interpretation is contextual while quantum mechanics in phase space uses negative probabilities.

On superdeterminism, one needs to deny free will and this is a very tall order. While I (and anyone else) cannot give a rigorous definition of free will, I know that I have it. Andrei contends that classical theory is deterministic. While true, this is both an insufficient and an irrelevant argument. Superdeterminism is only a pre-requisite step: you need to obtain from it quantum correlations, and so far I am not aware of any successful model. Second, determinism does not imply superdeterminism because the existence of chaotic evolution equations. Predicting weather is a classical example. I do not think superdeterminism has any chance of success.  

On Objection 2, I again agree with its statement. Quantum mechanics arose out of the inability of classical mechanics to explain atomic phenomena. But instead of expanding on this let's reply to the concrete arguments Andrei raised. Let's start with:

" This is all nice, but classical physics is not the same thing as Newtonian physics of the rigid body. Let’s consider a better classical approximation of the electron, a charged bullet. The slits are made of some material that will necessarily contain a large number of charged “bullets”. As the test bullet travels, its trajectory will be determined by the field generated by the slitted barrier. The field will be a function of position/momenta of the “bullets” in the barrier. But the field produced by a barrier with two slits will be different than the field produced by a barrier with only one slit, so the effect with both holes open is NOT the sum of the effects with each hole open alone."

This argument is wrong on two counts. First, one can make an interference experiment with neutrons where the neutrons not passing through the slits will be simply absorbed. Using electrically neutral particles renders irrelevant Andrei's objection. Second, "the field produced by a barrier with two slits will be different than the field produced by a barrier with only one slit" is incorrect as shown by a simple order of magnitude analysis. The electric fields near the slit are relevant on an atomic distance scale, while the distance between slits is macroscopic. You are looking at about seven order of magnitude difference in the ratio of relevant distances which translates in terms of force into a ten to minus fourteen order of magnitude effect. But the interference pattern is macroscopic and the difference between two Gaussian distributions vs. interference pattern cannot be explained away by a force fourteen of orders of magnitude smaller than what it is needed.

The next objection is appealing to Yves Couder's results. Those are interesting experiments, but they are not a confirmation of quantum mechanics emergence from classical physics and I know no one who claims it so. As such the argument is irrelevant to the current debate.

On the free fall atomic model, I did not read those papers so do not know if the claims are correct or not. The author may simply have proposed a model and analyzed the consequences and never claimed that his model describes nature.  Based on the general information available it is immediately clear that that model has nothing to do with reality. Also peer review is no magic bullet for avoiding publishing incorrect results. In my area of expertise in the last 12 months I read 2 published papers which were pure unadulterated garbage: the errors were not subtle, but blatant and packaged in a dishonest way to bamboozle the reader. Moreover I have concrete proof that the authors were aware of their mistakes when they published it. Physics is not immune to charlatans, crooks, and incompetent reviewers.

On the ionic crystals argument, without quantum mechanics the collection of electrons and nuclei will behave like a plasma and not like a crystal. This is moderately easy to test: create a computer simulation of say 1000 atoms and use Maxwell's and Newtonian equations of motion only to model the interaction. Then try to find an initial configuration which will be stable. I think there is none. Prove me wrong with such a model and I'll concede this point.

On quantum tunneling, the argument is pure handwaiving. Let me make an analogy. I know how my microwave works. But an alternative explanation might be that little Oompa-Loompas inside it are heating the food and I cannot see them because they move really fast.  The point is that the argument needs to have more predictive power than a fuzzy non-committal: "A new theory could predict a much stronger force." Show me the money. Propose such a theory and then we can discuss its merits. I am not asking something impossible. Regarding tunneling, quantum mechanics provides testable predictions which were confirmed experimentally. I only hold any alternative theory to the same level of experimental confirmation.

On Objection 3, I somewhat disagree with it. It is worthwhile to pursue non-quantum toy theories to better understand quantum mechanics, but not to search for an alternative to quantum mechanics.

Let me answer the four sub-points raised by Andrei:

a.       If nature is not probabilistic after all, there is much to be discovered. Detailed mechanism behind quantum phenomena should be revealed, bringing out a deeper understanding of our universe, and maybe new physical effects.

There is no "sub-quantum" or "hidden variable" explanation to quantum effects. Quantum mechanics is at the core of Nature, and my work is about proving this rigorously and not as a result of personal beliefs.


b.      Quantum theories are not well equipped to describe the universe as a whole. There is no observer outside the universe, no measurement can be performed on it, not even in principle.

This is a sterile objection to quantum mechanics and this cannot be used to justified a realistic alternative theory. First, even in quantum mechanics there are realistic interpretations. Second, epistemic interpretation like Qbism avoids this because they only talk about Bayesian probabilities. This objection only applies to naively using quantum mechanics in cosmology. Loop quantum gravity is unaffected by this objection.


c.       Due to its inability to provide an objective description of reality, quantum mechanics may not be able to solve the cosmological constant problem. A theory that states clearly “what’s there” could provide a much better estimate of the vacuum energy. After all we are not interested in what energy someone could find by performing a measurement on the vacuum, but what the vacuum consists of, when no one is there to pump energy into it.

The statement underscores a deep misunderstanding of the vacuum. Vacuum is actually a very violent place filled with virtual particles due to interplay of relativity and quantum mechanics. See this poor quality but brilliant video of a Sidney Coleman lecture to understand why merging them is not a trivial thing as one may naively expect that adding symmetries to quantum mechanics always results in simplifications. See also the QCD "Lava Lamp" which was shown at the 2004 Nobel Physics lecture. The cosmological constant problem is not a problem of quantum mechanics. I am not an expert in string theory but I know it has at least a solution to this problem (I don't know if it got rid of Susskind's "Rube Goldberg" label).

d.      Quantum mechanics requires an infinitely large instrument to measure a variable with infinite precision. When gravity is taken into account, it follows that local, perfectly defined properties cannot exist, because, beyond a certain mass, the instrument would collapse into a black hole.

The same argument can be used in the case of classical deterministic physics.

As you can see I disagree with the points Andrei was making, but nevertheless I want to thank him for participating in this debate and I look forward to discuss his replies in the commenting section of this post. I think such debates are useful, and I feel that the professional community of physicists is not doing a good job in engaging the public or explaining what it is doing. Physicists are very busy people trying to get ahead in a very competitive field. However the outside world usually experiences an arrogant wall of silence.