Classical Theory, Quantum Theory, or somewhere in between?
Classical Theory, Quantum Theory, or somewhere in between? APCortizasJr/istockphoto.com
In this blog I am going to take us beyond known physics, or at least the physics that I, a non-physicist, know is known. We are all more or less familiar with the weird world of Quantum Mechanics, and of course, the classical world of Newton and Einstein. I have begun to suspect, on grounds I discuss below, that there is an entire realm that I will call the "Poised Realm" between the two. If there is this realm, its importance may be twofold, first perhaps very novel physics. Second, in a later blog I will advance the working hypothesis that this "Poised Realm" in the human and probably other brains, IS consciousness. Since we have had no idea what consciousness "is", a new working hypothesis may, one day, be testable and become real science.
In past blogs I have introduced in outline the famous two slit experiment in which photons from a "photon gun, directed toward a barrier with two slits cut in it, and beyond to a photodetector screen, give rise to the astonishing interference patterns of light and dark bands on the screen. As Feynman taught in his famous lectures on physics, no classical view of reality can account for this phenomenon. Now the interference bands look something like the patterns on the bottom of a swimming pool were two pebbles dropped into the still water of the pool. This image helps understand the famous Schrodinger time dependent wave equation. This wave equation "propagates" a quantity, which, like ordinary waves, undulates in time and space. Therefore, there is a "phase" associated with each point on this wave. The light and dark bands of the interference pattern arise because when the wave passes through the two slits, then, like a plane water wave hitting a similar wall with two holes, the Schrodinger waves passing through the two slits give rise to roughly semicircular spreading waves from both slits that advance and hit the photodetector. Where two peaks or two troughs meet at the same point on the photo detector, the "amplitudes" of the two waves add together to create a higher amplitude. Where a peak of one wave meets a trough of the second wave, the two cancel out entirely, leaving zero amplitude. This adding of in phase and out of phase wave amplitudes is called, respectively, "constructive interference" and "destructive interference".
In the mathematics of quantum mechanics, the next step is to square the absolute value of the amplitude. By the so called "Born rule", this squared value is the PROBABILITY that a photon will be measured at that time and space location. Three points are essential here.
First, the "probability" is ontological, not epistemological. A photon may or equally well may not be detected at that spot, with an acausal probability. Note that Aristotle's Boolean law of the excluded middle, (A and Not A) cannot both be true simultaneously, is not valid here. In this quantum situation, A as well as Not A may happen. Both are true.
Second, all the phase information, ie where the peaks and valleys are in time and space, must be available when the waves hit the photodetector screen, for the interference patterns to arise.
Third, and critically, if we distinguish between a quantum system and its enviroment, quantum or quantum + classical, phase information may be lost from the quantum system to the quantum envornonment and not be recoverable. This process, as described in earlier blobs, in called "Decoherence".
Now, if phase information is lost from the system to its environment, at some point so much phase information has been lost from the system that the system alone can no longer exhibit the light band interference patterns that are the hallmark of quantum behavior. For this reason, many if not most physicists now say that decoherence is the best current account of how the classical world of Actual things emerges from the quantum world. The famous Copenhagen interpretation of the Schrodinger wave is that it is a wave of "possibilities". These possibilities are ontologically real. So, in decoherence, ontologically real possibilities yield the classical world. More, this transformation is acausally, for there is no causal account of the loss of phase information. Phase information is just lost into the environment.
But something radically new has emerged in recent physics: The transformation from quantum to classical is now thought by a number of physicists to be reversible. That is, the quantum possibilities can decohere to the classical world of actual events or entitities, then recohere to quantum possibilities! Assume for the moment this is correct, I'll give the grounds for it below.
If quantum can convert to classical and classical can convert to quantum via decoherence and recoherence, then there may be an entire new "Poised Realm" between quantum and classical worlds. Why? Well, it takes time for a quantum system to decohere, often on the order of a femtosecond, or 10 to the -15 seconds. That sounds short, but the shortest time scale in the universe is the Planck time scale of 10 to the - 43 seconds, so 10 to the 28th Planck moments pass while decohrence happens. Conversely, presumably, but not surely, it takes time for recoherence to happen. No data are available, but lets say a femtosecond. During these intervals, the quantum system is losing coherence in some or all of its "quantum degrees of freedom", or recohering with respect to some or all of its quantum degrees of freedom. Thus, there must be time periods where the system is in my "Poised Realm.
Then IF the quantum to classical conversion is reversible, it is logically possible that a physical system can remain in the Poised Realm for a long time. I explore next what this might mean, for it is an entirely unexplored area of physics, with possible implications for consciousness.
Is decoherence experimentally verified? Absolutely. Decoherence is the bane of quantum computers, for the quantum degrees of freedom that are carrying out the computation are known to gradually decohere. Many lines of evidence demonstrate decoherence and it is familiar to many physicists.
Can the rate of decohrence be slowed down? Astonishing new evidence says that the answer is almost surely "Yes". Chlorophyll is the molecule in plants that carries out photosynthesis. Photons hit a receptor site and migrate to a reaction center. Recent experimental work has demonstrated that the quantum coherent state of chlorophyll during this process lasts 1000 femtoseconds, or a nanosecond, or even longer! So decohrence can be slowed down, and the coherent state is thought to sharply increase the efficiency of energy extraction by the plant from the photon. More, the chlorophyll molecule is surrounded by an "antenna" protein which is thought to suppress decohrence, or possible enable recoherence. This hypothesis can be tested using mutant antenna proteins.
The long time scale coherence at ambient temperature of a quantum coherent state is important because until recently, most physicists would have believed that at room temperature, decoherence would rapidly destroy all quantum coherence. This suggests that long lived coherence may be biologically useful, selected for, and tuned for sundry functions.
What about the converse? What is now known about conversion from a decohered, classical (for all practical purposes) state to regain the quantum coherent state? There are, at present, two bodies of work.
First, mathematician Shor proved a quantum error correction theorem for quantum computers. This work has been expanded upon. Briefly, if quantum degrees of freedom in a quantum computer are decohring due to loss of phase information from the computer (the system), to its environment, then Shor showed that if information is added to the system from the outside, the decohering degrees of freedom could be made to recohere again. This clearly says that recoherence is possible.
Second, physicist Hans Briegel, University of Innsbruck, Austria, has published two papers showing that a quantum coherent "entangled" system can decohere to classicity than recohere to quantum entangled coherence.
I am not a physicist or mathematician. But based on the above, I will assume that the quantum coherent to classical conversion can happen acausally by decoherence, and recoherence can also be attained.
This immediately raises four huge sets of questions. First, what determines the ratio of quantum to classical processes in the universe? Second, can a sustained, partially decohrent "Poised Realm" be attained and maintained? Third, and critically, what laws, if any laws exist, describe the behavior of a system in the "Poised Realm"? I return to this in a moment, for we really know almost nothing. But we do know one critical thing. Fourth, how can one expermentally achieve and study a possible sustained partially decohrent "poised realm" physically?
I will jump to the third question: If a Poised Realm exists and persists between quantum and classical, partially decoherent, in a system in its environment, what laws if any apply to its behavior? At this stage the only thing that seems certain is this: The quantum system is losing phase information to its environment, therefore the Schrodinger equation for the system cannot be propagated "unitarily. "Unitarily" means that the Schrodinger wave propagates in such a way that the square of the amplitudes of all the possibilities, interpreted as probabilities, sum to 1.0. This is the only way physicists know how to compute the forward time (or reversed time) behavior of the Schrodinger equation describing the behavior of a quantum system. But this cannot be done for the system alone if phase information is being lost from the system to the environment. Thus, at present, we have no idea if the behavior of a system in the Poised Realm is lawful or not, or what that or those laws may be. Thus, if a maintained Poised Realm can be created, it seems to be a realm of very new physics.
One possibility to bear in mind is a contrast. We are used, since Newton, to ordinary differential equations and partial differential equations in physics. In areas of computer science we grow used to "agent based models", which interact to exhibit behavior, but so far we typically cannot write down differential equations for their detailed behavior. With respect to the Poised Realm, if a sustained Poised Realm can exist, we don't have any idea what happens except at the quantum and classical limits of this Realm.
The second question asks: Can a Poised Realm state be maintained? It would seem possible. If the quantum system is losing phase information to its environment, Shor's theorem assures us that addition from the outside of information can cause decohering quantum "degrees of freedom" to recohere. Thus it is conceivable that a balance can be struck between decoherence and recoherence, leading to a sustained state in the Poised Realm. Obviously, at this point, how to do this "in principle" possibility is unknown.
If the quantum to classical transition via decoherence is reversible, then the first question looms large: What is the balance between quantum and classical processes in the universe and its "parts", via what means, laws, or otherwise. One radical possibility is a kind of abiotic natural selection in which bits of classical matter which are good at avoiding return to a quantum state persist. If they have variants by accretion of different added bits of classical matter there are even more resistant to return to a quantum state, they will be abiotically "selected" ie they will persist better.
I turn to the third and fourth questions with some initial thoughts. Anton Zeilinger, an Austrian physicist, is carrying out experiments with objects of increasing mass, in the famous two slit experiment, looking, as mass increases, for the failure of interference bands. To date, Zeilinger has used a beam of Buckmeisterfullerenes molecules, 60 atom carbon molecules, and shown that they exhibit interference. Now one expects that a beam of dead rabbits flung at a two slit apparatus would result in two distinct piles of dead rabbits, one behind each slit, with no interference pattern of band of rabbits, no rabbits, rabbits across the "rabbit detector". Thus, at some point, as the mass of entities in the the beam increases, and presumably as their density increases, decoherence will set in and interference bands will start to disappear.
If the above can be found, two things follow. First at such densities where decoherence sets in, a sustained, partially decoherent state in the Poised Realm would seem to have been attained. Second, as I have noted in an early post, in a Special Relativity setting, no law would seem to describe the decohrence process, based on Popper's argument about past and future light cones. Lawlessness in the Poised Realm with or without a special relativity setting might be testable. For example, the way interference bands "fade" as decoherence sets in might not be precisely repeatable or stable over time, and could be shown not to be due to experimental noise.
In a future blog, after laying a foundation in some of contemporary philosophy of mind issues, and seeking answers to 350 year old questions about how mind can "act" on matter, how we might have a responsible free will, and why consciousness might have been of selective advantage, I will offer, as noted, the obviously improbable working hypothesis that consciousness is associated with the Poised Realm and sensors and effectors to couple to the world. Perhaps one day this could be demonstrated for the mammalian brain.