Beyond Einstein and Schrodinger? The Quantum Mechanics of Closed Quantum Systems

We live in the “information age,” begat by Shannon, Kolmorov Information theory which has no semantics and does not tell us what information is, and the famous Turing Machine, the basis of universal computers. It is almost fundamental to our view of our own deepest humanity that we largely see ourselves in the legacy of Newton, and the mechanistic world view of Descartes’ Res Extensa, as Machines.  This is nowhere more evident than in our view of our “minds”  among many in computer science, strong Artifical Intelligence, and even in neurscience, as “emergent properties” of sufficiently complex classical physics Turing machines. We are, in short, machines, body and soul.

A massive computer built of bowls of water pouring into one another, 1 or 0 if above or below bowl threshold levels, will somehow “emerge” into consciousness.

I believe ever more firmly that this view is badly wrong, that we are not “just machines”, and that a wonderfully new view of ourselves can be glimpsed. To escape the trap we are in requires, I think, going beyond classical physics to quantum physics and the mind. Roger Penrose trod these pathways first in the Emperor’s New Mind and Shadows of the Mind, which I recommend strongly.

I hope to lay this glimpsed new view of our humanity out in the coming blogs. I will discuss standard quantum mechanics in this blog, and in later blogs open system quantum mechanics, the Poised Realm, Trans-Turing Systems, offer a new and hopefully useful interpretation of quantum mechanics which, to my astonishment, leads to a view of what consciousness is, and even what “qualia”, the “experience of the color blue” are.  And to my astonishment, this latter hypothesis seems testable in principle. We have never even had an hypothesis about what qualia are.  That does not, of course, make what I suggest true, but I’m astonished that it fell into place in, well, a sudden human insight, whether true or false.

We’ll see what you think. Remember: I am not a physicist, and less a quantum physicist.

My midterm aim is to go beyond Turing to the Trans-Turing System which has both embodied information, hence a semantics, and is NOT algorithmic as is a Turing Machine. The “algorithmic” character of the Turing machine is precisely the basis of our view of our minds as machines, and the trap of classical physics. The Trans-Turing System is based on open quantum systems, hence escapes the trap of classicity for our view of ourselves. Open quantum systems can lose phase information into their environment and both decohere to classicity (for all practical purposes, FAPP) and, it begins to appear, can recohere from classicity FAPP to open quantum system behavior.  To reach this, I must first review the physics of closed quantum systems that cannot lose phase information.

Consider the famous two slit experiment.  There is the photon gun, a screen with two slits allowing photons to pass, and a photodetector surface on the far side of that screen from the photon gun. If either slit is covered, and photons fly from the photon gun toward the screen with the remaining open slit a bright spot is found behind that slit on the photodetector.

But if both slits are open, the famous “interference” pattern of light and dark bands is found on the photodetector behind the two slits. As R. Feynman points out, most of the mysteries of Quantum Mechanics, QM, are found in this two slit experiment. It is critical that if one photon an hour flies towards the open two slits, it makes the same size spot on the photodetector as any subsequent photon. More, the same interference pattern is found to build up as many photons, hour by hour, one by one, fly toward the photodetector.

For readers not familiar with quantum mechanics and the Schrodinger equation, the next helpful step is an analogy with plane water waves propagating towards a sea wall with two gaps, and a beach beyond the sea wall.  The plane wave, upon hitting the sea wall, passes through the two gaps and yields from each semicircular waves propagating toward the beach. If the two semicircular wave fronts overlap when they hit the beach, then the following processes happen: 1) where two wave peaks from the two gaps hit the same spot on the beach, their amplitudes sum to a higher amplitude. 2) Where two wave troughs hit the same spot on the beach, a deeper trough is found. 3) But where the peak of one wave from one gap meets the trough of a wave from the other gap, the two cancel out entirely.

With this, we gain an intuitive understanding of the Schrodinger linear wave equation.  This Schrodinger law has an “action” which oscillates with an “amplitude” as the Schrodinger wave propagates towards the two slits and the photodetector. The action keeps track of the “phase” of the wave at each point in space and time. At the photodetector, where peaks and peaks from the two slits meet, they sum in constructive interference and a bright bar arises. Similarly where two troughs from the two slits meet, they sum in constructive interference and again a bright bar arises. But where the peak from one slit meets the trough from the other slit, the two entirely cancel in destructive interference and a dark bar arises on the photodetector.

I note here R. Feynman’s formulation of Quantum Mechanics and return to it below. In this formulation, Feynman states mathematically that even a single photon propagating from the photon gun towards the two slits and to the photodetector, must be thought of as simultaneously taking all possible pathways in space and time from the photon gun through the slits to the photodetector.

This formulation is fully accepted as one of the equivalent formulations of quantum mechanics.

Pierce and the Law of the Excluded Middle

The 19th Century American philosopher, C.S. Pierce, noted that Actuals and Probables obey Aristotle’s law of the Excluded Middle. Possibles, he noted, do not.  With Actuals, Aristotle said either the statement A is true or A is false, there is nothing in the middle. But the same is true for statements of probability, say on the frequency interpretation of probabilities. Say we calculate the probability of 4764 heads in 10,000 flips of a fair coin and use the binomial distribution to calculate the probability. Let that probability be 0.2364. We then flip coins 10,000 times in a million repetitions and the average centers on 0.2364 as predicted. The statement that the probability is .2364 is true or false, there is nothing in the middle. Probabilities obey the law of the excluded middle.

Now try, A is true, A is Possible, A is False.  “A is Possible” is precisely in the middle between A is true and A is false.  As Pierce noted, Possibles do not obey the law of the excluded middle.

Feyman’s description of a single photon simultaneously taking all possible pathways through the two slits to the photodetector also avoids the lay of the excluded middle.  I will expand on this in later blogs.

I will use this feature of “Possiblies” in later blogs to offer a new, fourth, interpretation of quantum mechanics.  To foreshadow, I think we are invited to consider tentatively, with Aristotle and the 20th Century British philosopher Alfred North Whitehead, that Possibles may be ontologically real. With them, I will explore with you the beginning implications of the postulate that Reality consists in both ontologically real Possibles and ontologically real Actuals, which I will call Res Potentia and Res Extensa.

We have not known for 70 years what quantum mechanics is “about”. I will offer the hypothesis that quantum mechanics is about Res Potentia.



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