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5/13/2016 3:41 pm  #1

PSR, quantum randomness and QM interpretations

I'd like to focus on the issue of whether the explanation of quantum events by (ontic) random causation is acceptable for the purposes of the Principle of Sufficient Reason (PSR), or if the PSR requires deterministic natural causation for all physical events not directly caused by the free action of rational or intellectual beings.

Let there be a lab system described by QM such that an observation may obtain results A, B, C or D with different probabilities, which when added amount to 1. If a particular observation obtains A, in the Cophenhaguen Interpretation (CI) of QM there is no reason why the result of that observation was A instead of B, C, or D. On the other hand, there is a reason why the observation should yield one of A, B, C, or D, namely that those are the possible values of the observed property of the system. Thus, while the explanation of why there was an observed value within the possible set is deterministic (the system remained in being with the same nature), the explanation of why the observed value was A instead of B, C or D is "because the system randomly caused A", which would be analogous to the case of a human person freely choosing X instead of Y or Z.

Now, as a theist holds also divine concurrence, he may describe divine causality in this case as God throwing the dice to see which way the system will go. When another theist raised the issue of divine eternity, he would say that God actually threw the dice for all random events in eternity. And when yet another theist objects that the very notion of a process not involving free wills whose outcome is not predetermined by God, such as the hypothetical throwing of virtual dice, is incompatible with classical theism, he will admit that "God throws the dice" really means "God determines the specific outcome of a quantum event which in itself is not relevant to his design (such as an event in a lab experiment) on the basis of fulfilling the probability pattern intrinsic to the event, and not on the basis of the specific outcome itself."

On the one hand, Prof. Alexander Pruss in his book on PSR [1] finds explanation by random causation wholly compatible with PSR:

Alexander Pruss in his book "The Principle of Sufficient Reason: A Reassessment", p. 168, wrote:

However, probably, the defender of the PSR should not be very afraid of indeterminism. After all, if we insisted that all explanations be of a deterministic sort, then the PSR would indeed become incompatible with contingency by the van Inwagen argument as well as with libertarian free will. One way to explain contingent events nondeterministically is provided by the reasonless-choice models of free will. We could understand the phrase randomly caused to be analogous to freely chose and say that the system's initial state and its randomly causing A explains why A occurred. Here, we can infoke the principle that when we have given the causes of an event, we have explained why the event occurred.

On the other hand, I know at least a couple of Thomists who find it completely unacceptable and will not settle for anything less than God determining outcome A instead of B for a specific reason (even if that reason is known only to Him) and not just because it is one of the possible outcomes. In other words, they do not accept "explanation by random causation" as good enough for the PSR, and insist that randomness is present only at our epistemic level, but in reality the course of physical events is completely deterministic at the ontic level, with that natural determinism overriden only by divine miracles and the free operation of the human soul on the human brain (plus angelic direct operation on matter when it is allowed by God).

Thus my question to users of this site: Is the explanation of events by (ontic) random causation a "sufficient reason" for the purposes of the PSR? Or does the PSR requires explanation by deterministic causation?

Whatever the answer to this question, it is interesting to know that a fully deterministic description of quantum events can be achieved by an alternative interpretation of QM, namely de Broglie–Bohm theory, aka the pilot-wave theory or Bohmian mechanics (BM). Summarizing the situation in view of Bell's Theorem or Bell's Inequality, which shows that a theory based on local realism cannot reproduce the successful predictions of QM, where, quoting Wikipedia, "local realism is the combination of the principle of locality with the "realistic" assumption that all objects must objectively have a pre-existing value for any possible measurement before the measurement is made" [2], it is necessary to give up either locality or realism (the latter understood as just said, not in the broad sense that the entity really exists), being the main resulting options:

Copenhaguen Interpretation, o its newer smarter version Relational Interpretation:

- preserves locality;
- abandons realism: the coordinates of a system do not have defined objective values between observations;
- epistemic wave function: just a mathematical tool for predicting observations;
- physical indeterminism.

Bohmian Mechanics:

- abandons locality: the universe works as a whole, as reflected by the title of Bohm's posthumous book: "The Undivided Universe: An Ontological Interpretation of Quantum Theory" (Bohm & Hiley 1993).
- preserves realism: the coordinates of a system have defined objective values, computable but not observable, between observations;
- ontic wave function, with exact nature dependent on philosophical position: Aristotelianism, real Platonism, or "direct guidance" theism.
- physical determinism.

There is a very good description of the deterministic feature of BM by quantum computing scholar Scott Aaronson:

"Again, the amazing thing about this theory is that it's deterministic: specify the "actual" positions (I add: and velocities) of all the particles in the universe at any one time, and you've specified their "actual" positions at all earlier and later times. So if you like, you can imagine that at the moment of the Big Bang, God sprinkled particles across the universe according to the usual |ψ|2 distribution; but after that He smashed His dice, and let the particles evolve deterministically forever after. And that assumption will lead you to exactly the same experimental predictions as the usual picture of quantum mechanics, the one where God's throwing dice up the wazoo." [3]

By the way, an issue with BM (which provided the occasion for further discussing this subject with user "Erich" in a combox at Prof. Feser's blog [4],) is the enormous additional computational work required for simulating the operation of a quantum system according to BM in comparison with simulating its operation according to CI. Quoting Scott Aaronson again:

"My conclusion is that, if you believe in the reality of Bohmian trajectories, you believe that Nature does even more computational work than a quantum computer could efficiently simulate—but then it hides the fruits of its labor where no one can ever observe it." [5]

It was precisely this observation which served to me as a hint that BM could be the description of the behaviour of quantum systems from God's viewpoint, a notion which I hereby present as the following hypothesis:

Hypothesis: The Bohmian and Copenhaguen interpretations of QM (with the latter being exchangeable by its newer smarter version: Carlo Rovelli's Relational QM) are formally correct descriptions of the behaviour of quantum systems from different viewpoints, with the first describing that behaviour as it really is, i.e. as perceived by an Observer with unlimited observational and computational capabilities, and the second describing that behaviour as is perceived by embodied observers with inherent observational and computational limitations.

Corollary 1: The only practical consequence of a hypothetical future development of Bohmian Mechanics that provides it with capabilities of description of phenomena that are on par with the current capabilities of orthodox QM will be just to confirm the hypothesis above, as the result of that development will be equations that allow exactly the same predictions of observations that the existent equations of QFT, QED, QCD and SM, while probably being much more complex.

Corollary 2: The development of Bohmian Mechanics is an endeavour of philosophical nature, done for the purposes of ontological satisfaction and, possibly, indirect theistic apologetics.

This notion was expressed in a rather ironical way by Prof. Reinhard F. Werner of Hannover University in a discussion thread with Bohmian physicists which he started with the title "God knows where all the particles are!" in the "Bohm's theory" online forum of the online Quantum Foundations Workshop 2015 hosted by the International Journal of Quantum Foundations (IJQF) from 9th July 2015 to 19th July 2015 [6]:

"For in the end it achieves precisely the explanatory power of the exclamation “God knows where all the particles are!”."

"Do the trajectories actually give you an insight? Or is their only role, on honest inspection, to just be there and soothe your ontological pains?"


[1] Alexander Pruss, "The Principle of Sufficient Reason: A Reassessment", Cambridge University Press, 2006, p. 168.






Last edited by Johannes (4/02/2018 9:57 am)


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