OK, last post I was a bit hasty saying Simon Saunders undermined Max Tegmark. Saunders eventually finds his way to recover a theory of probability from his favoured Many Worlds Interpretation. But I do think he over-analyses the theory of probability. Maybe he is under-analysing it too in some ways.
What the head-scratchers seem to want is a Unified Theory of Probability. Something that gives what we intuitively know is a probability but cannot mathematically formalise in a way that deals with all reality. Well, I think this is a bit of a chimera. Sure, I’d like a unified theory too. But sometimes you have to admit reality, even abstract mathematical Platonic reality, does not always present us with a unified framework for everything we can intuit.
What’s more, I think probability theorists have come pretty close to a unified framework for probability. It might seem patchwork, it might merge frequentist ideas with Bayesian ideas, but if you require consistency across domains then apply the patchwork so that on overlaps you have agreement, then I suspect (I cannot be sure) that probability theory as experts understand it today, if fairly comprehensive. Arguing that frequentism should always work is a bit like arguing that Archimedean calculus should always work. Pointing out deficiencies in Bayesian probability does not mean there is no overarching framework for probability, since where Bayesianism does not work probably frequentism, or some other combinatorics, will.
Suppose you even have to deal with a space of transfinite cardinality and there is ignorance about where you are, then I think in the future someone will come up with measures on infinite spaces of various cardinality. They might end up with something that is a bit trivial (all probabilities become 0 or 1 for transfinite measures, perhaps?), but I think someone will do it. All I’m saying is that it is way too early in the history of mathematics to say we need to throw up our hands and appeal to physics and Many Worlds.
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That was along intro. I really meant to kick off this post with a few remarks about Max Tegmark’s second lecture at the Oxford conference series on Cosmology and Quantum Foundations. He claims to be a physicist, but puts on a philosophers hat when he claims, “I am only my atoms”. Meaning he believes consciousness arises or emerges merely from some “super-complex processes” in brains.
I like Max Tegmark, he seems like a genuinely nice guy, and is super smart. But here he is plain stupid. (I’m hyperbolising naturally, but I still think it’s dopey what he believes.)
It is one thing to say your totality is your atoms, but quite another to take consciousness as a phenomenon seriously and claim it is just physics. Especially, I think, if your interpretation of quantum reality is the MWI. Why is that? Because MWI has no subjectivity. But, if you are honest, or if you have thought seriously about consciousness at all, and what the human mind is capable of, then without being arrogant or anthropocentric, you have to admit that whatever consciousness is, (and I do not know what it is just let me say, but whatever it is) it is an intrinsically subjective phenomenon.
You can find philosophers who deny this, but most of them are just denying the subjectiveness of consciousness in order to support their pet theory of consciousness (which is often grounded in physics). So those folks have very little credibility. I am not saying consciousness cannot be explained by physics. All I am saying is that if consciousness is explained by physics then our notion of physics needs to expand to include subjective phenomena. No known theories of physics have such ingredients.
It is not like you need a Secret Sauce to explain consciousness. But whatever it is that explains consciousness, it will have subjective sauce in it.
OK, I know I can come up with a MWI rebuff. In a MWI ontology all consistent realities exist due to Everettian branching. So I get behaviour that is arbitrarily complex in some universes. In those universes am I not bound to feel conscious? In other branches of the Everett multiverse I (not me actually, but my doppelgänger really, one who branched from a former “me”) do too many dumb things to be considered consciously sentient in the end, even though up to a point they seemed pretty intelligent.
The problem with this sort of “anything goes” so that in some universe consciousness will arise, is that it is naïve or ignorant. It commits the category error of assuming behaviour equates to inner subjective states. Well, that’s wrong. Maybe in some universes behaviour maps perfectly onto subjective states, and so there is no way to prove the independent reality of subjective phenomenon. But even that is no argument against the irreducibility of consciousness. Because any conscious agent who knows of (at least) their own subjective reality, they will know their universes branch is either not all explained by physics, or physics must admit some sort of subjective phenomenon into it’s ontology.
Future philosophers might describe it as merely a matter of taste, one of definitions. But for me, I like to keep my physics objective. Ergo, for me, consciousness (at least the sort I know I have, I cannot speak for you or Max Tegmark) is subjective, at least in some aspects. It sure manifests in objective physics thanks to my brain and senses, but there is something irreducibly subjective about my sort of consciousness. And that is something objectively real physics cannot fully explain.
What irks me most though, are folks like Tegmark who claim folks like me are arrogant in thinking we have some kind of secret sauce (by this presumably he means a “soul” or “spirit” that guides conscious thought). I think quite the converse. It is arrogant to think you can get consciousness explained by conventional physics and objective processes in brains. Height of physicalist arrogance really.
For sure, there are people who take the view human beings are special in some way, and a lot of such sentiments arise from religiosity.
But people like me come to the view that consciousness is not special, but it is irreducibly subjective. We come to this believing in science. But we also come without prejudices. So, in my humble view, if consciousness involves only physics you can say it must be some kind of special physics. That’s not human arrogance. Rather, it is an honest assessment of our personal knowledge about consciousness and more importantly about what consciousness allows us to do.
To be even more stark. When folks like Tegmark wave their hands and claim consciousness is probably just some “super complex brain process”, then I think it is fair to say that they are the ones using implicit secret sauce. Their secret sauce is of the garden variety atoms and molecules variety of course. You can say, “well, we are ignorant and so we cannot know how consciousness can be explained using just physics”. And that’s true. But (a) it does not avoid the problem of subjectivity, and (b) you can be just as ignorant about whether physics is all their is to reality. Over the years I have developed sense that it is far more arrogant to think physical reality is the only reality. I’ve tried to figure out how sentient subjective consciousness, and mathematical insight, and ideal Platonic forms in my mind can be explained by pure physics. I am still ignorant. But I do strongly postulate that there has to be some element of subjective reality involved in at least my form of consciousness. I say that in all sincerity and humility. And I claim it is a lot more humble than the position of philosophers who echo Tegmark’s view on human arrogance.
Thing is, you can argue no one understands consciousness, so no one can be certain what it is, but we can be fairly certain about what it isn’t. What it is not is a purely objectively specifiable process.
A philosophical materialist can then argue that consciousness is an illusion, it is a story the brain replays to itself. I’ve heard such ideas a lot, and they seem to be very popular at preset even though Daniel Dennett and others wrote about them more than 20 years ago. And the roots of the meme “consciousness is an illusion” is probably even centuries older than that, which you can confirm if you scour the literature.
The problem is you can then clearly discern a difference in definitions. The consciousness is an illusion folks use quite a different definition of consciousness compared to more onologically open-minded philosophers.
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On to other topics …
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Is Decoherence Faster than Light? (… yep, probably)
There is a great sequence in Max Tegmark’s talk where he explains why decoherence of superpositions and entanglement is just about, “the fastest process in nature!” He presents an illustration with a sugar cube dissolving in a cup of coffee. The characteristic times for relevant physical processes go as follows,
- Fluctuations — changes in correlations between clusters of molecules.
- Dissipation — time for about half the energy added by the sugar to be turned into heat. Scales by roughly the number of molecules in the sugar, so it takes on the order of N collisions on average.
- Dynamics — changes in energy.
- Information — changes in entropy.
- Decoherence — takes only one collision. So about 1025 times faster than dissipation.
(I’m just repeating this with no independent checks, but this seems about right.)
This also gives a nice characterisation of classical versus quantum regimes:
- Mostly Classical — when τdeco≪τdyn≤τdyn.
- Mostly Quantum — when τdyn≪τdeco, τdiss.
See if you can figure out why this is a good characterisation of regimes?
Here’s a screenshot of Tegmark’s characterisations:
The explanation is that in a quantum regime you have entanglement and superposition, uncertainty is high, dynamics evolves without any change in information, and hence also with essentially no dissipation. Classically you get a disturbance in the quantum and all coherence is lost almost instantaneously, and yeah, it goes faster than light because with decoherence nothing physical is “going” it is a not a process, rather decoherence refers to a state of possible knowledge, and that can change instantaneously without any signal transfer, at least according to some theories like MWI or Copenhagen.
I should say that in some models decoherence is a physically mediated process, and in such theories it would take a finite time, but it is still fast. Such environmental decoherence is a feature of gravitational collapse theories for example. Also, the ER=EPR mechanism of entanglement would have decoherence mediated by wormhole destruction, which is probably something that can appear to happen instantaneously from the point of view of certain observers. But the actual snapping of a wormhole bridge is not a faster than light process.
I also liked Tegmark’s remark that,
“We realise the reason that big things tend to look classical isn’t because they are big, it’s just because big things tend to be harder to isolate.”
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And in case you got the wrong impression earlier, I really do like Tegmark. In his sugar cube in coffee example his faint Swedish accent gives way for a second to a Feynmanesque “cawffee”. It’s funny. Until you here it you don’t realise that very few physicists actually have a Feynman accent. It’s cool Tegmark has a little bit of it, and maybe not surprising as he often cites Feynman as one of his heroes (ah, yeah, what physicist wouldn’t? Well, actually I do know a couple who think Feynman was a terrible influence on physics teaching, believe it or not! They mean well, but are misguided of course! ☻).
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The Mind’s Role Play
Next up: Tegmark’s take on explaining the low entropy of our early universe. This is good stuff.
Background: Penrose and Carroll have critiqued Inflationary Big Bang cosmology for not providing an account for why there is an arrow of time, i.e., why did the universe start in an extremely low entropy state.
(I have not seen Carroll’s talk, but I think it is on my playlist. So maybe I’ll write about it later.) But I am familiar with Penrose’s ideas. Penrose takes a fairly conservative position. He takes the Second Law of Thermodynamics seriously. He cannot see how even the Weyl Curvature Hypothesis explains the low entropy Big Bang. (I think WCH is just a description, not an explanation.)
Penrose does have a few ideas abut how to explain things with his Conformal Cyclic Cosmology ideas. I find them hugely appealing. But I will not discuss them here. Just go read his book.
What I want to write about here is Tegmark and his Subject-Object-Environment troika. In particular, why does he need to bring the mind and observation into the picture? I think he could give his talk and get across all the essentials without mentioning the mind.
But here is my problem. I just do not quite understand how Tegmark goes from the correct position on entropy, which is that is is a coarse graining concept, to his observer-measurement dependence. I must be missing something in his chain of reasoning.
So first: entropy is classically a measure of the multiplicity of a system, i.e., how many microstates in an ensemble are compatible with a given macroscopic state. And there is a suitable generalisation to quantum physics given by von Neumann.
If you fine grain enough then most possible states of the universe are unique and so entropy measured on such scales is extremely low. Basically, you only pick up contributions from degenerate states. Classically this entropy never really changes, because classically an observer is irrelevant. Now, substitute for “Observer” the more general “any process that results in decoherence”. Then you get a reason why quantum mechanically entropy can decrease. To whit: in a superposition there are many states compatible with prior history. When a measurement is made (for “measurement” read, “any process resulting in decoherence”) then entropy naturally will decrease on average (except for perhaps some unusual highly atypical cases).
Here’s what I am missing. All that I just said previously is local. Whereas, for the universe as a whole, globally, what is decoherence? It is not defined. and so what is global entropy then? There is no “observer” (read: “measurement process”) that collapses or decohere’s our whole universe. At least none we know of. So it all seems nonsense to talk about entropy on a cosmological scale.
To me, perhaps terribly naïvely, there is a meaning for entropy within a universe in localised sub-systems where observations can in principle be made on the system. “Counting states” to put it crudely. But for the universe (or Multiverse if you prefer) taken as a whole, what meaning is there to the concept of entropy? I would submit there is no meaning to entropy globally. The Second Law triumphs right? I mean, for a closed isolated system you cannot collapse states and get decoherence, at least not from without, so it just evolves unitarily with constant entropy as far as external observers can tell, or if you coarse grain into ensembles then the Second Law emerges, on average, even for unitary time evolution.
Perhaps what Tegmark was on about was that if you have external observer disruptions then entropy reduces (you get information about the state). But does this not globally just increase entropy since globally now the observer’s system is entangled with the previously closed and isolated system. But who ever bothers to compute this global entropy? My guess is it would obey the Second Law. I have no proof, just my guess.
Of course, with such thoughts in my head it was hard to focus on what Tegmark was really saying, but in the end his lecture seems fairly simple. Inflation introduces decoherence and hences lowers quantum mechanical entropy. So if you do not worry about classical entropy, just focus on the quantum states, then apparently inflationary cosmology can “explain” the low entropy Big Bang.
Only, if you ask me, this is no explanation. It is just “yet another” push-back. Because Inflationary cosmology is incomplete, it does not deal with the pre-inflationary universe. In other words, the pre-inflationary universe has to also have some entropy if you are going to be consistent with taking Tegmarks’ side. So however much inflation reduces entropy, you still have the initial pre-inflationary entropy to account for, which now becomes the new “ultimate source” of or arrow of time. Maybe it has helped to push the unexplained entropy a lot higher? But then you get into the realm of, “what is ‘low’ entropy in cosmological terms?” What does it mean to say the unexplained pre-inflationary entropy is high enough to not worry about? I dunno’. Maybe Tegmark is right? Maybe pre-inflation entropy (disorder) is so high by some sort of objectively observer independent measure (is that possible?) that you literally no longer have to fret about the origin of the arrow of time? Maybe inflation just wipes out all disorder and gives us a proverbial blank slate?
But then I do fret about it. Doesn’t Penrose come in at this point and give baby Tegmark a lesson in what inflation can and cannot do to entropy? Good gosh! It’s just about enough confusion to drive one towards the cosmological anthropic principle out of desperation for closure.
So despite Tegmark’s entertaining and informative lecture, I still don’t think anyone other than Penrose has ever given a no-push-back argument for the arrow of time. I guess I’ll have to watch Tegmark’s talk again, or read a paper on it for greater clarity and brevity.
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One Over Epsilon 