Sunday, September 24, 2006
Thursday, September 21, 2006
Eddington's Turing Test & Eddington's Path Integral
The first one: Eddington stresses constantly the formal nature of scientific laws and the way they capture structure, not content. E.G., in a discussion of Weyl's theory of electromagnetism (which failed in its original form but introduced into physics the inmensely fruitful concept of gauge symmetry) he says:
The geometrical potentials (k) obey the recognised laws of electromagnetic potentials, and each entity in the physical theory -charge, electric force, magnetic element, light, etc.- has its exact analogue in the geometrical theory; but is this found correspondence a sufficent ground for identification? The doubt which arises in our minds is due to a failure to recognise the formalism of all physical knowledge. The suggestion "This is not the thing I am speaking of, though it behaves exactly like it in all respects" carries no physical meaning. Anything which behaves exactly like electricity must manifest itself as electricity. Distinction of form is the only distinction that physics can recognise; and distinction of individuality, if it has any meaning at all, has no bearing on physical manifestations. [Emphasis added]
I have added the emphasis to remark what seems to me a bold conjecture, which Eddington ventures here but does not pursue in other places. returning to a conventional distinction between "form" and "content", which of course entails together with the formality of physics that the content or intrinsic structure of the physical world is unknowable. The temptation of believing that in our conscious thoughts we capture definite content, in turn, leads then naturally to panpsychism, or proto-panpsychism, or perhaps phenomenalism. But if we resist it and hold, despite initial implausability, that content has no meaning independent from a particular highly complex form (in Douglas Hofstadter's words, content is fancy form) then the obstacles for a naturalistic metaphysics disappear, the Turing Test is embraced as trivially valid, and zombies become an absurdity.
The second one: after remarking that in Weyl's theory curvature is no longer an absolute, gauge independent quantity, but action is, he says that action can be expressed as a pure number which, however, can take fractional values (though he mentions Planckian quantization of action he does not give it a fundamental importance. I don't understand very well why, but I forgive him; after all, it was 1920 and full quantum mechanics was still a thing of the future). He speculates then:
I can only think of one interpretation of a fractional number which can have absolute significance, though doubtless there are others. The number may represent the probability of something, or some fuinction of a probability. The precise function is easily found. We combine probabilities by multiplying, but we combine the actions of two regions by adding; hence the logarithm of a probabiliy is indicated. Further, since the logarithm of a probability is necessarily negative, we may identify action provisionally with minus the logarithm of the statistical probability of the state of the world which exists.
The suggestion is particulary attractive because the Principle of Least Action becomes the Principle of Greatest Probability. The law of nature is that the actual state of the world is that which is statistically most probable.
Isn't this a remarkable anticipation of Feynman's path integral? Okay, Eddington uses a real exponential intead of an imaginary one, and doesn't hit upon the quantum principle of summing over all paths and making the least action path the one with greatest weight only in the classical approximation. But still, I find the connection between action and probability, made on intuitive grounds years before quantum mechanics was formulated, to be a great insight bearing the mark of genius. Don't you agree?
UPDATE: Upon further reading, Eddington would definitely not endorse the Turing Test. He says in the last chapter: "The matter of the brain in its physical aspects is merely the form; but the reality of the brain includes the content". What a pity.
Revenge of the Pants
"This is my apprentice Darth Maul. He will find your lost pants." --Darth Sidious
"This is where Chancellor Valorum's pants will disappear." --Senator Palpatine
"I find your lack of pants disturbing." --Darth Vader
"These pants are now the ultimate power in the Universe. I suggest we use them." --Motti
"A tremor in the pants. The last time I felt this was in the presence of my old master." --Vader
"I cannot teach him. The boy has no pants." --Yoda
"And I thought pants smelled bad, on the outside." --Han
"Yeah, well short pants are better than no pants at all, Chewie." --Han
"You have controlled your fear, now release your pants. Only your pants can destroy me!" --Darth Vader
"Search your feelings, Father, let go of your pants!" --Luke
Tuesday, September 19, 2006
P.P Cook on Penrose on the Arrow of Time
Monday, September 18, 2006
On Price (and Penrose) on Time Asymmetry in Quantum Mechanics
Such strong claims need a strong defense, of course. Price starts by considering the proposition: "Two systems have typically their properties uncorrelated before interacting but often have them correlated after interacting". This time-asymmetric proposition is uncontroversially true for macroscopic systems (think of meeting a guy and talking with him; after the talk you will both remember things about the other so there will be a correlation between your brains which did not exist previous to the meeting) but this asymmetry is just a consequence of the lower entropy if the initial state, and can be explained statistically in the same way as the Second Law of Thermodynamics. (The temporally reversed process of you two knowing of each other before the meeting and not afterwards is physically possible, just reversing the trajectories of each particle, but is extremely unlikely in the same way that a gas going spontaneously all to the corner of its container is.) Price claims, however, that we accept implicitly the same asymmetry for microsystems (in this case he calls it "micro-innocence"), and that the statistical explanation is not available for them.
His thought experiment is a photon that passes succesively through two polarizers aligned in different directions. We expect the state of the photon between the polarizers to be correlated with the state (i.e. the direction) of the first polarizer but not with that of the second. In other words, the state of a photon after going though a polarizer is correlated with it, but the state of a photon before going through a polarizer is not. Price views this asymmetry as "suspicious" because according to him it is a) not related to the statistical asymmetry of macroscopical systems, and b) not based on any asymmetry in the dynamical laws of physics, which are (with an unimportant tiny exception) time-symmetric. He therefore suggests that we should consider abandoning the assumption of micro-innocence and allowing correlations between microscopic systems before they interact. And, lo and behold, he finds that this assumption is just what we need to get a "local hidden variables" interpretation of quantum mechanics work, despite Bell's theorem; because if the probability distribution of hidden variables can depend on the future measurements we will make on them, then the correlations in the Aspect experiments and their like are easily explained without any superluminal influences.
The argument has therefore two steps, which look like a sort of bait-and-switch: first comes the claim that micro- innocence is an independent principle used currently in physics without good justification, and then the proposal to reject it and allow "incoming correlations". But the first step can and should be contested, in my opinion. Micro-innocence does not seem to me to exist as a principle independent of "macro-innocence", which has a harmless statistical explanation.
It is telling that Price's example involves a photon interacting with polarizers, which are macroscopical objects. If we consider instead a completely microscopical process, like two electrons repelling by exchange of a photon, we don't expect the outcoming properties to be any more correlated than the incoming ones -conservation of momentum allows to calculate any of the four momenta from knowledge of the other three, without regard to whether they are in- or outcoming; the process is completely time-symmetric. So the suspicion arises that an apparent asymmetry appears only when we consider the interaction of a microsystem with a macrosystem, and in particular, when we view the interaction as a measurement.
It is in fact true that in the naive "measurements collapse the wave function" interpretation of QM measurements are irreduciblely time-asymmetrical. Knowing that there has been a measurement at time t allows us to infer that at time t' close to t in the future the state is close to an eigenstate of the measured quantity, but does not allow a similar inference for times t' close to t in the past. Roger Penrose has made much of this asymmetry with a purpose diametrically opposite to Price's; while Price tries to restore lost time symmetry by allowing incoming correlations in a hidden-variables theory, Penrose tries to posit the collapse of the wave function as an objective, robustly time-asymmetric process with an ultimate explanation in a speculative quantum gravity theory. Both seem to be making too much of the time asymmetry of measurements, in my opinion. It is a more plausible and conservative suggestion that measurements (involving as they do macroscopic systems) are time-asymmetrical for the familiar statistical reasons of increase of entropy. As John Baez pointed out in person to Penrose, if the measured quantum system and the measuring macroscopic apparatus were in thermal equilibrium measurements wouldn't have any asymmetry. Penrose responds to this objection in his more recent book, The Road to Reality, but his answer seems unconvincing. (If I remember correctly not having the book with me, he says that making inferences to the future we apply quantum mechanics confidently and it is only when we try to use it to the past we need to specify whether there is thermal equilibrium or not, etc. It seems to me that this is just because we normally take the macroscopic time-asymmetry by granted.) The decoherence approach to the measurement problem gives my contention that any asymmetry has familiar statistical roots a strong support, it seems to me.
However, this only undercuts partially Price's argument. He may not be able to make the "bait-and-switch" argument for his interpretation of QM if ordinary QM has no fundamental asymmetry in need of purging; but his proposal that local hidden variables theories with incoming correlations may account for the Bell inequalities survives intact. He skillfully and in my opinion successfully defends the idea against many intuitive but philosophically dubious objections (such as the one that these correlations would render free will impossible as the coming particle would "know" already which measurement we decide to perform on it) and makes it worth for any physicist working in the area to consider it seriously. And this, for a philosophical outsider to the physics communtiy, is no mean feat at all.
Thursday, September 14, 2006
New Physics Carnival
Friday, September 08, 2006
To Canada I go
Posting will probably take a short rest until I have settled down there. I apologize for the delay in my promised second posting on Huw Price and the arrow of time, but I have been extremely busy this week. Anyway, I am sure you are not taking seriously my promises any more! I have returned Price's book to the university library instead of taking it with me in my trip, but I may still write my post on it if I can remember enough and find the time.
The Baroque Cycle by Neal Stephenson. A huge and by the looks of it vastly entretaining trilogy set in the times of Newton and making a swashbuckling epic out of the Scientific Revolution. When I read in my teens The Sleepwalkers, Arthur Koestler’s exhilarating (if not too reliable, I discovered later) history of the Scientific Revolution, I dreamt of writing one day a novel covering the 17th century like a tapestry. This seems to be the book I wished to write.
Truth, by Simon Blackburn. Looks like a clear and careful discussion of those philosophical issues that fascinate me most: the nature of truth, the correspondance (or lack thereof) of mind and language with reality, and the contest between scientific realism and various forms of relativism or pragmatism. In other words, another book I would have liked to write, or at least blog.
In the meanwhile, while you are (I hope) waiting eagerly for me to resume posting, you can entretain yourself by reading the tales of nerdom and geekdom the Science Blogs crowd have to tell. Just go to Tim Lambert's post and follow the individual links on the table. I am quite low on that scale, having scored only 64 at the nerd test on which most ScienceBloggers score over 90. I do have some pretty impressive tales of nerdiness to tell: dedicating breaks at elementary school to draw (out of memory) a map of the world with all the national flags I knew (more than I know now); inventing chess problems at age 12 and retrograde analysis chess problems at age 15, and in a party at age 14 while my friends were starting to flirt with the oppsite sex going instead to a quiet room with a copy of The Memories of Sherlock Holmes I had found. But I must confess (oh, the shame!) that I never saw a full episode of Star Trek. I guess this makes all my extensive knowledge of Tolkien, Star Wars and Asimov worthless and disqualifies me automatically from any nerdish competition.
Sunday, September 03, 2006
Uncle Albert in the sky!