The past is particles, the future is a wave
These are my current thoughts on the foundations of quantum mechanics, life, the universe and everything. They are stolen from many sources without any guarantee that their original owners would recognize let alone authorize this representation of them. They are also connected to my present thinking on matters religious/philosophical. Though I agree with the essential separation of science and religion, I am pleasantly surprised when my thoughts on these two sides seem to converge.
Several readers, especially from physics, are very bothered that I discuss consciousness in the same breath as quantum mechanics. Please will such readers simply delete all references to the topics which disturb them? At some point I may prepare two versions of the document to accomodate the two classes of readers. In the meantime, do read on, as I assure you that there is pure scientific content to what I have to say.
Credits: the slogan is borrowed from Slava Belavkin and my thoughts are inspired by his mathematics - "eventum mechanics" - and his "Quantum New Interpretation".
Discussions of the interpretation of quantum mechanics often start with the rhetorical question: "what is a photon?" No-one knows, or rather, there is much disagreement; but everyone agrees that detector clicks in the past are real. On the other hand, the future is a wave of possibilities, whose probabilities are determined by quantum mechanics. I like to take this picture very seriously, and add to it the following.
We and our consciousness reside on the boundary between the past (particles) and the future (a wave of potentialities). As the present moves relentlessly forward the "past" crystallizes out of it, randomly. There is now no measurement problem, no non-locality problem, no problem of interpretation. The probabilities are for real, the past is real, the wave function is objective and non-localized since computed from the whole past (cf. Belavkin). Consciousness resides on the interface and is localizable (cf. Pirsig [Zen and the art of motor cycle maintenance]).
Why is Nature like that? Reality (past reality, that is) is discrete, finite. The only way to simultaneously have it invariant under continuous rotations, shifts is to make it random - probabilities can be invariant, continuous, ... This leaves us with QM as the only possibility (cf. Helland, one of many arXiv papers and new book).
Mathematical details have been supplied by Slava Belavkin. There is a unitary but irreversible evolution on a product algebra consisting of a classical part (the past) and a quantum part (the future). Everything is arranged to ensure locality/causality (compatibility with relativity theory). The classical part can also be thought of as a coarse-graining. Contrary to the currently salonfähig many worlds theory, there is only one "objective reality" (the past), and the multitude of possible worlds of the future do not "exist" except as a figure of speech. Contrary to the currently popular Bayesian interpretations of quantum physics, there is an objective reality (again: the past) [Chris Fuchs does not agree that I represent "the Bayesian view" here. Perhaps I only represent some Bayesians' view]. Quantum randomness is ontological, not epistemological. Naturally the past may not be fully known and naturally one could use the Bayesian apparatus to combine subjective and objective probabilities if one is inclined... [Of course one can combine true quantum randomness with subjective randomness due to ignorance - that is the power given by Bayes' theorem - but to my mind this is throwing the baby away with the bathwater, or more precisely, dissolving the baby in the bathwater! Not a pretty thought].
Belavkin's theory is a mathematical formalism which shows that Bohr's Copenhagen interpretation can be given mathematical substance and precision. Bell's theorem makes it clear that the randomness in quantum mechanics is completely different from all other familiar kinds of randomness in physics: it has no antecedents. There is no tracing back to initial conditions. The very fact that quantum probability is for real, unlike classical probability, underlines the importance of splitting the epistemological and the ontological. The theory can be applied just as well to small parts of the world (laboratory experiments) as to the whole universe (cosmology). Though there is a separation in classical and quantum this does not correspond to some artificial observer. The separation is simply the separation between past and future (both of which are scientific constructions built on our experience of the present).
It is nice though that just like Laplace's probability and all classical physics probability, invariance (symmetry) determines ultimately in an objective way what the probabilities must be.
The theory has nice (at least, for me, nice) philosophical connotations. The past is a brutally physicalistic cold pattern of unchangeable objective events, inferred by the present, which is a vibrant interface before the waves of possibility of the future. Only the present is fundamentally real, and it is shimmering and sparkling with light and creativity and being.
Coming to consciousness, I would like to see the argument developed that I can and should believe in my own free will and simultaneously know that every one else's free will is an illusion; while simultaneously I know that everyone else can justly have the same beliefs! Well, perhaps that is just too crazy, but then again it reminds me of Gödel's theorems and their applications in model theory.
There is a problem in how to define the past. We can't take it as the macroscopic positions of macroscopic objects defined as means of quantum position operators of constitutent particles; such means only approximately commute with one another and are only approximately classical. A further coarse-graining is required - and makes sense. The position of Ayer's rock (measured in centimeters from some even larger object) is quantum when we look at its twentieth decimal. So it should be rounded off and expressed eg in millimeters. In fact I would posit that delimiting the classical world (how many decimals) is a matter for experimental research.
Of course, you should be worried about whether or not one can construct a relativistically invariant and second quantized (field) version of the theory. I understand that Slava Belavkin is acutely aware of this / is worrying about it / does not see an essential problem ... ? (Maybe he already did it?). I hope he is right.
Chris Fuchs has complained that I am inconsistently above claiming reality and disclaiming reality and/or objectivity for past and future. Here is my response which also claims the solution to yet another grand problem (alongside the problem of "NOW" and the problem of interpretation of QM and the problem of consciousness and freewill): quantum gravity. My new insight is that quantum gravity has not been successfully incorporated into quantum physics because it does not exist! Gravity exists only in the past. After all, it is nothing else than the curvature of space-time. But the curvature of spacetime only exists in the past because space-time is only fixed in the past. Future space-time is not determined because of the ontological randomness of the future. Thus: gravity is classical because gravity is in the past. We will never observe quantum gravity waves. This links a bit to Penrose's claim that the solution lies in gravity, but it is a bit different from how he thinks about it!
Chris Fuchs' objections (Mon, September 18, 2006 5:44 pm):
"Taking a look at your Gdansk talk, I noticed isn't there a contradiction in these two sentences in your closing transparency:
1) "I think that only detector clicks in the past are real."
2) "The probabilities are for real, the past is real, the wave function is objective ..."
Specifically, if "ONLY detector clicks in the past are real" how can there be room for the probabilities to be real TOO? I'll say (tongue in cheek): Make up your mind!"
My answer to Chris Fuchs' objections (Mon, September 18, 2006 6:41 pm):
"Well, there are different degrees of reality and objectivity.
To my mind actually only NOW is truly real. However in a mathematical physical model of the universe, I also attribute reality to detector clicks in the past, more accurately, to gravitational space-time in the past; from knowledge of the past we can compute the wavefunction for the future.
I think the reason that gravity has not been succesfully incorporated into quantum physics is because it only exists in the past, ie as a classical object.
Life and consciousness and freewill exist in the NOW. The NOW is the only thing that counts, really. The NOW evolves stochastically from the past, the past I think of as being fixed (that is - once it has happened). It isn't around any more - does this make it real or not? I think it exists objectively, even if we don't know it.
The future doesn't exist yet, obviously. But given a surface separating past from future in space-time and knowing everything in the backwards lightcones of the surface, one can compute probabilities of everything in the forward lightcones (by QM).
More complaints and a reference (Wed. Sep. 20, 09:25)
Chris Fuchs objects strongly to my blatant misrepresentation of the Bayesian point of view. QBayesians do accept the reality of detector clicks... OK, I have to reread his works and modify my remarks. This web page was "fired" by a brilliant talk of Rüdiger Schacks at Gdansk (and other things which seemed to come together there), and conversations with Rüdiger afterwards. I agreed with everything he said except the conclusions and the terminology. Coming from statistics I hate to see sensible physicists associate themselves with the crazy (though often original and important thinkers) Bayesian statisticians with whom I have to coexist in my statistician's world.
Chris also points out a link with the ideas about "the present" of the philosopher George Herbert Mead.
David Mermin has made some telling remarks which I need more time to digest but in the meantime please read his splendid "what is QM trying to tell us", quant-ph/9801057; American Journal of Physics 66, 753-767 (1998). As an arm-chair physicist I agree that certain problems are too big to solve yet, but as an arm-chair philosopher I would still like to point out that when one faces simultaneously several seemingly insurmountable and not obviously related problems, a solution could lie exactly in their intersection.
Seen on a poster in Aarhus
The past is history
The future is a mystery
Today is a gift