Law Or Not At The Quantum-Classical Boundary? : 13.7: Cosmos And Culture Since Newton, physicists have believed that all that occurs in the universe is entailed by the fundamental laws of physics. This view sets much of our shared world view. In the present post I argue that even at the quantum-classical boundary no a...
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Law Or Not At The Quantum-Classical Boundary?

Since Newton we scientists, particularly physicists, have believed that all that unfolds in the universe is entailed by the fundamental laws of physics. I believe this view is false and its implications deeply alter our world view, heal the breech between science and the humanities, much of it discussed in my book "Reinventing the Sacred". I have already discussed "Breaking the Galilean Spell based on our incapacity to finitely prestate Darwinian "exaptations." I have discussed whether we can talk of ever novel opportunities for adaptation being generated in evolution, and suggesting that opportunities, as future possibilities, are not "Actual" efficient causes. If they are not efficient causes, they nevertheless change the course of evolution. This stance depends upon taking "Possibilities" as "real" along with "Actualities" in the universe. We may not wish to do so. In this post I am going to discuss whether "law" prevails at the quantum-classical boundary. I think not. The implications may be large. But I may be wrong.

To discuss this, I have to give an outline of quantum mechanics. To do so, I describe the famous "two slit experiment". A source of light, a "photon gun", shines light on a barrier with two slits cut in it. The light that passes through and hits a photodetector screen. Nobel physicist Richard Feynman famously shows the problem: Think of photons as little bullets. If they were real bullets, what would we expect? Well, let's cover one of the two slits, say the "second" slit. Then the bullets can pass through the open "first" slit, and will leave a humped mound of lead bullets on the "bullet detector", say a sand surface, behind that slit in line with the shots. If the second slit is opened and the first one covered, again we expect a mound of bullets in the sand behind the second, open slit.

Now if both slits are open, and our shots are a bit random, we expect two mounds of bullets behind the two slits, in the sand. That is exactly what we find. Bullets are fine "classical" physical objects.

Now watch.

Let's try it with photons from the photon "gun". With either slit covered, and the other slit open, one finds a bright spot behind the open slit on the photo-detector, the analogue of the mound of bullets. But, if both slits are open, one sees light and dark "bands" on the photodetector! These are a bit like the light and dark pattern on the bottom of a swimming pool if, in daylight, two pebbles are dropped at the same time at two points not too far apart in a still pool.

This light and dark banded pattern is called an "interference pattern". As Feynman succinctly says, the entire mystery of quantum mechanics is captured in this simple experiment, for no bullet-like particle behavior of the photons can give rise to this interference pattern! Photons do not behave like classical bullets!

Even worse! If the photon gun fires off a photon each hour, and one collects the pattern that accumulates on the photodetector, one gets the same interference pattern!

Like what?

To account for this pattern, that is similar to interference of wave patterns in the swimming pool, Erwin Schrodinger came up with an equation that bears his name. In this time dependent Schrodinger wave equation, a wave spreads out in space from the photon gun, with peaks and valleys like water waves. If a plane front water wave were to hit a barrier with two openings, semicircular waves would spread out on the side away from the incoming wave, and peaks of one wave arriving at a beach might coincide with peaks of another wave, to create a mark in the sand. Or peaks of one wave might meet the troughs of another wave, canceling one another out, leaving no mark on the sand.

Analogously, the Schrodinger peaks and valleys interact to create the interference band pattern when the light goes through both slits. Even for a photon an hour this happens!

Now the locations of the peaks and valleys is carried by what is called "phase information" in the Schrodinger wave.

Yes, weird.

So given the fundamental nature of quantum mechanics, how does the classical world of rocks happen?

In the favored Copenhagen interpretation due to Bohr, and the Born rule, the absolute value of the amplitude of the wave can be squared mathematically to yield the probability of a photon at that point. Where peaks or where troughs are in sync, the probability is high. Where peaks meet troughs the probability is low, creating the light and dark bands in the interference pattern.

On the Copenhagen interpretation, this "probability" is purely acausal. Einstein famously objected that "God does not play dice with the universe". But on Copenhagen, quantum events just "happen" acausallly, with a probability, upon measurement.

Fine, but what about the classical world that Newton talked about? Here is the magic step in the Copenhagen interpretation: When the Schrodinger wave is propagating toward the slits, through them and to the photodetector, that wave represents simultaneously all the possibilities of the photon positions at once, as a mathematical "superposition." But, when the photon hits the photodetector and is detected "the wave function of all the possibilities" "collapses" to a single possibility, the now classical "Actual" reality. The propagation of Schrodinger's wave is time reversible, but the collapse is irreversible.

That, in very brief outline, was where quantum mechanics was until about twenty years ago. But fewer and fewer people were happy with this "collapse of the wave function" as the magical step in the emergence of the classical world from the fog of the quantum world.

In its place a beautiful new approach, called "decoherence" has grown. Here is the idea. For the interference pattern to occur in the two slit experiment all the "phase information" about where the peaks and troughs of the waves are, must be present at the photodetector. Then peaks and troughs can cancel, peaks and peaks, or troughs and troughs, can add to higher amplitudes.

What if that phase information got lost somewhere? Then interference could not happen and instead "decoherence" would happen. So the hallmark of quantum weirdness would disappear and maybe the classical world could appear.

But in a "closed" quantum system, all the phase information is carefully preserved.

However in a quantum "system" in a quantum "environment", for example the rest of the universe, quantum phase information can get lost, never to be retrieved. That is the essence of "decohrence". In an open quantum system, phase information can get lost into the environment and cannot (typically) be reassembled, so interference goes away, and the classical world can be approached as closely as we want. In the jargon, the system approaches classicity for all practical purposes, FAPP.

This is now the leading idea now about how the quantum world gives rise, acausally, to the classical world. It is acausal because on Copenhagen, all quantum mechanics is acausal, and besides its just phase information being lost which is also acausal.

Here comes the crux question: Is there a law for how decohrence happens that tells us in detail how the phase information is lost?

I'm now going to show you that in a specific sense, and the context of Einstein's Special Relativity, the answer is NO.

So, on to Special Relativity. Einstein showed that if two objects are moving with respect to one another at a uniform velocity, that simultaneity as formerly conceived, did not make sense. He posited, and it has been confirmed, that the speed of light as viewed by you is constant whatever your velocity is, say with respect to any other object, or frame of reference as it is called.

This stunning fact implies that more than one pair of events can be seen as simultaneous, depending upon how we are moving with respect to one another. This is called a "region of possible simultaneity".

Now I need a simple diagram.

Picture a V pointing on a page with the point to the right, and in the middle of the page. Picture the tails of the V horizontally to the left of the point, above and below it on the page. Label the point of the V, "event A". This V shaped "cone" is called the "past light cone of event A", and depicts time flowing past to future from left to right on the page. The V is called the past light cone of A because it contains all the events and processes, traveling at the speed of light or slower, as seen from A, that can causally influence A. The past light cone contains all the events and processes that can causally affect A because, says Einstein, nothing can travel faster than the speed of light.

Now picture a similar V, with the point at event A, and the tails out to the right on the page, above and below A. Since "left to right" on the page represents past to future, this V represents the "future light cone" of event A. It contains all the space time regions in the future that event A can causally influence by processes at or slower than the speed of light as seen from A.

The regions above and below the two opposed Vs on the page are the regions of "possible simultaneity."

So far so good.

Now we need a second pair of Vs, to represent an event B. Place event B inside the future light cone of A. So A can affect B causally. Now picture the past and future V light cones of event B meeting at B, and use the same shaped Vs for both A and B.

The crucial insight, first noted by philosopher Sir Karl Popper in his "The Open Universe" is that the past light cone of event B both contains all of the past light cone of A, and also regions that are outside of the past light cone of A.

I hope you can easily picture this. The past light cone of B, because it is in the future light cone of A, must have parts of its own past light cone outside of A's past light cone.

Now here was Popper's correct point. At event A, no local observer can, in principle, know what is happening in the regions outside of A's past light cone but inside of B's past light cone that might impact event B. The observer at A is in principle precluded from knowing what is "in" the past light cone of B, but outside its own past light cone.

But, as Popper pointed out, this means that no observer at A can write down a law that describes that will happen at B! More precisely, because the observer at A is missing information that is in the past light cone of B, but outside the past light cone of A, in that specific sense of Missing Information, no observer at A can write down a law for what happens at B.

A bit more precisely, no observer at A can write down a deterministic function, F, at A covering the space time region within A's future light cone up until just before B, for what will happen at B.

Popper used this to argue for indeterminism in the classical world. But the same will apply to Schrodinger's determinsitic wave equation in the quantum world.

I want to extend his argument to decoherence in an open quantum "system" and its "environment." In quantum mechanics, the Special Relativity setting could be realized by two photodetectors moving away from one another, and from event A, at uniform velocity, or just one moving away from A at uniform velocity. Now decoherence happens because some quantum "degree of freedom" for example, a photon, is emitted from, say a protein, constituting event A, and propagates from that "system" out into the universe as "environment." Some time later the photon might be absorbed, for example by an electron, or hit a telescope mirror miles away, or across the universe. Those events, whichever happens, will affect the loss of phase information and how decoherence happens in the protein in this specific case.

But by Popper's argument, no observer at A can know, or write down a function F, that maps the space time region in the future light cone of A up to just before event B, the decohrence event. The needed information cannot in principle be had, it is partially outside the past and future light cones of A until just before B.

But this means no function, F, available at event A to a local observer maps A to the decohrence event B.

We can call this a failure of a useful law due to an in principle lack of information, or we can say, "There just is no law, F, that maps A to just before B."

But that means we don't and can't know how the local part of the universe around the system will behave. So we don't know how decoherence actually happens in this specific case, or any specific case.

This seems right. It implies that because of a lack of information about the relevant conditions outside of A's past light cone, but inside of B's past light cone, we cannot write down a law, or no law exists. In either interpretation, WE can have no law.

So what? Well, that is not what Laplace thought when he formulated the simplest version of reductionism: a Lapalacian demon, given the positions, and momenta of all the particles in the universe could, using Newton's laws, calculate the entire future and past of the universe.

Popper says "No" in the classical physics setting. I, borrowing from him, say "NO", in the quantum decoherence setting. No Law, or usable law, in the Special Relativity setting describes in detail how decoherence happens. More, the special relativity setting is very general, it only requires that the event A, and detector be moving relative to one another. The "lack of relevant information" effect, as noted next, will be small if relative velocities are small compared to the speed of light.

As it happens these ideas may have testable consequences, for they should be more marked a the relative velocities of the event A and one or two receding detectors increase toward the speed of light. And, since quantum decohrence is easier if the quantum processes in the "environment" are locally abundant, they should be more visible in that case. These are testable consequences of Popper's original idea and my use of it with credit.

I hope the experiments are done.

In summary, both the Breaking of the Galilean Spell post and this post make arguments that the becoming of the universe is beyond sufficient natural law. This is a major change in our world view, if true. My previous post also argued that future adaptation possibilities are opened up by evolution, whether acausally by quantum events causing mutations, or by classical events. In the former case, both the opportunity, and the event that creates the adaptation, another quantum event mutation, may both arise acausally by random quantum chance. But, to take this part of my argument seriously, we have to take a metaphysical step: We either think possibilities can be real, with Aristotle and Whitehead, or only Actuals can be real, with Empedocles and Einstein's General Relativity. The world is different on these alternative views, for future possible ways to adapt cannot be past efficient causes. Are possibilities real? The standard interpretation of Quantum Mechanics itself often treats what is waving in Schrodinger's wave equation as "possibilities". Equivalently, Feynman's famous sum over all possible histories approach to quantum mechanics speaks of "all possible histories". We cannot escape metaphysical commitments, we can only ignore or examine them and their usefulness to our world views.