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I have hidden yesterday's posting. Here is why.

27 aprilo 2012, 08.07

 I have a constant obsession that I will drop dead while working on a problem and not finish it. This leads to a compulsion to post whatever half-baked level of thought I have at the moment, so at least that won’t be lost. It used to be much worse.

That this is due to my fear of leaving an unfinished problem, due to death, is a clarifying insight after many years of self-observation. By that I mean this explanation for the compulsion may actually be correct.

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Non-loco scribbles

25 aprilo 2012, 17.53

See https://bytebucket.org/chemoelectric/pure-geomalg/wiki/nonloco_scribbles.xml

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Misfortune

24 aprilo 2012, 22.13

Unfortunately, if I get this right, I still won’t write a paper, due to my disability. I’ll just make a summary available to people who can write papers. We could use more laypeople writing scientific papers, though.

The difficult part, which I have not seen done by anyone, is how to make correlation due to phase more intuitive without forcing the reader to revert to the mind-picture of a classical field. Little known may be that it is insufficient to produce the right numbers; you must convince with geometry. This goes against the romantic picture of ‘self-correcting’ science; the force of your argument depends on how you speak.

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My brain pain, and my back pain

24 aprilo 2012, 21.55

Hofer’s argument in geometric algebra can be more intuitively given in the conformal model of space and by using coordinate systems less. Also his presentation uses questionable (though probably not uncommon) GA terminology and has at least two ‘shortcuts’ given without explanation. I plan to reformulate, as soon as I figure out one or two things. Well, really, it’s how best to fill in one of those shortcuts.

Meanwhile I have back spasm. Not fun.

On the other hand, the burn on my arm seems to be healing.

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Feynman

24 aprilo 2012, 03.29

BTW I imagine the late Dr. Feynman as one of the majority of physicists who don’t understand QM but also don’t care enough to worry about it. I saw some of his lecture statements today and they were of the ‘I don’t understand this and don’t think anyone does’ variety, without any ideology laden upon that. Also his own contributions to physics are renowned for their contrived character and desire mainly to get the answer as easily as possible, from what I have read.

As so often is the case, it’s the philosophers we really have to worry about. (For this dispute, their main technique is Special Pleading. I think d’Espagnat was illustrating the method at its finest, though for some reason he wrote in florid free verse.)

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Hypothesis confirmed

23 aprilo 2012, 22.51

I was curious to verify my prediction that the author of the postmodern poetry at http://arxiv.org/pdf/quant-ph/0302167 would be a kook, and was not disappointed: http://en.wikipedia.org/wiki/Bernard_d%27Espagnat

What I did not predict was that he would be a kook of a little stature, who has even been published in Supersticious American.

( :) I unsubbed from Scientific American many years ago, having tired of its ‘balanced journalism’, ‘he said, she said’. Have they reformed, or by now are they publishing ‘Intelligent Design’ articles to balance out the paleontology reports?)

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Surprise, surprise!

23 aprilo 2012, 19.47

I had been trying to remember who it was, and when I found him again (http://www.liv.ac.uk/~whofer/) it turned out he too recently used geometric algebra to make an argument against ‘non-locality’.

This actually shouldn’t surprise me, even though it does; geometric algebra is increasingly popular in physics as a substitute for the vector algebra we used when I was in school. (Whether GA has made inroads in the electromagnetic engineering field [pun intended] I do not know.)

Looking over Joy Christian’s paper, I see she seems to give Bell’s ambiguous notations a different reading that IMO does not apply to his Lyons-Lille example, so IMO probably she is reading them incorrectly, or alternatively the Lyons-Lille example was a poorly devised analog for his argument about EPR. (Bell wrote several papers, sometimes using very poor notation.) But that would merely change where the math error manifests, given that no matter how you read Bell he arrives at the wrong result. She’s going to argue (I peeked ahead) that he assumed the products of functions of the ‘hidden variables’ in the ‘local’ theory had to be commutative.

Hofer’s article looks more interesting, because it seems he’s actually claiming something like a new interpretation for the quantum mechanics; he seems to be blaming Bell’s error on discounting a phase component (in the ‘local realistic’ case) because in QM it was represented by imaginary numbers. In geometric algebra it can be represented by real numbers and given a visualizable geometric interpretation.

Wish me luck.

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A disproof of Bell's conclusion by (counter)example that I ought to read

23 aprilo 2012, 18.17

See http://arxiv.org/abs/quant-ph/0703179.  The math in it is geometric algebra, which I happen to be working with at the moment anyway, so it is fresh in my mind. Therefore, it is a good time for me to read this paper, especially as I am in a programming rut (partly due to migraine).

One type of response to this kind of argument is that it doesn’t strive to provide a model for that actual experiment. This response is entirely irrelevant, though it is understandable how it would appeal to physicists. If you write a simulation, for instance, it is necessary not only that the simulation disprove the argument, but that it look as much like the published experiments as possible. Thus we have papers like this one: http://arxiv.org/abs/quant-ph/0105034

(An error in application of Bayes’ rule is just one of the ways the problem can be characterized, and happens to be the first on record and probably the one most accessible to non-specialists. Lots of people know probability theory, and some of them actually trust it to give the right answers if you strictly follow its rules.)

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Watching Mister Ed

23 aprilo 2012, 16.59

I am not the biggest advocate of television, but watching Mister Ed is a far superior use of one’s time than speculating on the philosophy of a brain in a vat. That horse hasn’t seen a mitzvah he can’t violate and try to make up for later.

(It is an obvious fact that every healthy, living brain already is in exactly the type of vat that would be necessary! Just do scientific research, and refer the philosophers to a psychiatrist.)

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As I said, catalogued at Nizkor

22 aprilo 2012, 21.20

Bell’s error in writing P(AB) = P(A)P(B): http://www.nizkor.org/features/fallacies/ignoring-a-common-cause.html

Actually his error is the contrapositive of this (‘A cannot cause B, therefore A and B are not connected’).

When someone commits one of these catalogued errors, in a way it is not a big deal; they are catalogued because they are so common. Many of them are a challenge to avoid. More interesting, I think, is the psychology behind the whole scandal. To quote ET Jaynes in ‘Clearing up mysteries::

[S]omehow, many physicists became persuaded that the success of the QM mathematical formalism proved the correctness of Bohr's private philosophy, even though hardly any { even among his disciples { understood what that philosophy was. All the attempts of Einstein, Schrödinger, and others to point out the patent illogic of this were rejected and sneered at; it is a worthy project for future psychologists to explain why.

In part it may be that Bohr was some kind of modernist:

Since today some think that merely to verify the correlations experimentally is to refute the
EPR argument, let us stress that EPR did not question the existence of the correlations, which are
to be expected in a classical theory. Indeed, were the correlations absent, their argument against the
QM formalism would have failed. Their complaint was that, with physical causation unavailable,
only instantaneous psychokinesis (the experimenter's free{will decision which experiment to do) is
left to control distant events, the forcing of S2 into an eigenstate of either q2 or p2. Einstein called
this ‘a spooky kind of action at a distance’.

To understand this, we must keep in mind that Einstein's thinking is always on the ontological
level; the purpose of the EPR argument was to show that the QM state vector cannot be a
representation of the ‘real physical situation’ of a system. Bohr had never claimed that it was,
although his strange way of expressing himself often led others to think that he was claiming this.
From his reply to EPR, we nd that Bohr’s position was like this: ‘You may decide, of your
own free will, which experiment to do. If you do experiment E1 you will get result R1. If you
do E2 you will get R2. Since it is fundamentally impossible to do both on the same system, and
the present theory correctly predicts the results of either, how can you say that the theory is
incomplete? What more can one ask of a theory?’

While it is easy to understand and agree with this on the epistemological level, the answer that
I and many others would give is that we expect a physical theory to do more than merely predict
experimental results in the manner of an empirical equation; we want to come down to Einstein's
ontological level and understand what is happening when an atom emits light, when a spin enters a
Stern-Gerlach magnet, etc. The Copenhagen theory, having no answer to any question of the form:
‘What is really happening when - - - ?’, forbids us to ask such questions and tries to persuade
us that it is philosophically naïve to want to know what is happening. But I do want to know,
and I do not think this is naïve; and so for me QM is not a physical theory at all, only an empty
mathematical shell in which a future theory may, perhaps, be built.

My own attitude is indeed that a scientific ‘theory’ is not actually a theory unless it has the ontological character. A purely epistemological ‘theory’ is not a theory; it is a phenomenological law, a kind of pre-Newtonian regression. It is Kepler’s elliptical orbits, without comprehension of why and how planets move in elliptical orbits around the sun. A theory, on the other hand, gives you a kind of metaphorical picture of how the world works; if for no other reason, it is necessary for science to do this to satisfy the same deeply human urges that used to explain day, night, rain, and drought as the activities of divine beings. But we could always let religions continue to fill that gap, even if they do a halfass job of it. Perhaps more important is that a purely epistemological theory is a dead end for future scientific development; the human brain simply cannot function most efficiently unless it can picture what it is thinking about.

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Fun with reading

22 aprilo 2012, 16.19

I’m re-reading Kracklauer Elder and Younger’s paper on the Twin Paradox at http://nonloco-physics.0catch.com/ and came across this lovely sentence:

A moment’s reflection convinces one that as a result of this alternate
Ansatz, ‘simultaneous’ events in any frame must be those on a worldline parallel to the pure space-like axis.

I had to draw a picture in my head, in that non-euclidean Minkowski geometry, to realize this was saying simply that time and simultaneity work exactly the way we commonly imagine them to work. :) (Actually the non-euclideanness is irrelevant in this case.)

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Motivation for the argument that quantum mechanics _does_ involve "spooky action at a distance"

22 aprilo 2012, 14.31

Why are scientists so desperate, in the first place, to show that quantum mechanics involves what I think Einstein-Podolsky-Rosen called ‘spooky action at a distance’? A hint comes from one of my college physics professors, the best damn teacher I ever had, but despite being a good teacher he had a fondness for using QM to say ‘Nyeah! Nyeah!’ to Albert Einstein. The mythical Einstein is an Olympian figure, whom I imagine a lot of people would like to defeat in mental battle. (The actual Einstein was an above average theoretical physicist who had gone to a public engineering school. You’d probably never hear of him, if he tried to break into the field now.)

Another possible factor is that quantum mechanics historically developed in a suck-up atmosphere of leader and bootlicking minions, and the suck-up cultural aspect remained, except, as with the Church, the great leader became replaced by an institutional orthodoxy.

Another factor may be that Einstein himself primed people into believing ‘anything goes’ in physics. This is a complex subject, for which I refer to (the difficult and also pop-up ad laden site) http://nonloco-physics.0catch.com/

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The point of all this

22 aprilo 2012, 03.15

Before I attempt to sleep I want to get some clarifications of http://chemoelectric.livejournal.com/1026770.html out there. It is hard to follow the arguments Bell is making in part because, in a way, they are too stupid to believe someone would make them.

Physicists stipulate that the electrons or photons in the EPR experiment have correlated properties due to being produced at the same time and place in the same particle source, and so the interactions of these particles with physically separated detectors also are correlated. This is not in dispute. What is in dispute is whether it is possible, at least in principle, to come up with a more fundamental theory than quantum mechanics, in which all the effects are propagated in the normal, intuitive way, at speeds less than or equal to the speed of light. (This is, after all, a problem about the propagation of light!)

Bell’s argument proceeds more or less as follows: (1) The correlated particles reach the detectors, where they proceed to cause correlated detector results. (2) In classical physics, Detector A is distant from Detector B and therefore has no effect on it; likewise Detector B is distant from Detector A and can have no effect on it. (3) Therefore the readings at Detector A and Detector B are ‘independent’ and we can write P(AB|background conditions) = P(A|background conditions)P(B|background conditions). (4) From this we can deduce certain mathematical expressions that are violated by actual experiments, which instead show exactly the correlations stipulated in step (1). (5) Therefore (2) is wrong, and indeed Detector A does affect Detector B, in an exact instant, across any distance whatsoever; and vice versa, in a special, quantum mechanical way. This is ‘quantum non-locality’. Furthermore it is impossible to explain the correlations as effects propagated at or below light speed, and you shouldn’t even try to do so; to do so would be like trying to make a perpetual motion machine or square the circle.

What is actually wrong, however, is step (3), which is nothing but a formal expression of one of those logical fallacies you can find catalogued on websites such as Wikipedia and Nizkor.

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Why not PRNG?

21 aprilo 2012, 17.08

All of the preceding shows why I prefer ‘random number generator’ to ‘pseudo-random number generator’. The only essential difference between ‘pseudo-random numbers’ and ‘true random numbers’ is that we have a good idea of the process by which the first kind come about; we simply choose to ignore that process; whereas for the second kind it is impossible or intractable to know how the numbers came about. They may still be fully determined in ways we do not know and/or cannot reproduce. This is what makes them essential to good cryptography, where the goal is explicitly nothing more than to make decryption intractable.

Better distinguishing terms might be something like ‘algorithmically generated random numbers’ versus ‘random numbers from real-world sampling’, etc.

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How come you get bell-shaped curves in generalized logic

21 aprilo 2012, 16.59

When I learned a little probability theory in school, we arrived at bell-shaped ‘gaussian’ curves as the result of mixing a bunch of ‘random variables’ together. Theorems showed they tended to spread out into that well known bell shape. At least, that’s how I remember the theory going.

But probability theory as logic has no ‘random variables’, so how come it ends up with the same ‘gaussian’ functions? It turns up as a way of saying that some facts are unknown. If you think about it, this is exactly what the idea of a ‘random variable’ is trying to capture -- facts that are there but which for some reason we don’t know exactly, but can only make an educated guess. it is not the rolling of the dice that makes them a ‘random variable’, but the fact that we don’t know what sides will end up on top until after we have rolled the dice. This is what makes an abstract view necessary. Suppose, for instance, that we know there are 5d6 lying somewhere, and someone has arranged them purposely rather than rolled them, but hasn’t told us the arrangement. Then the same exact ‘random variable’ applies here as in the case of rolled dice; it is the not-knowing that makes a probability problem what it is, not the fact that rolling was involved. (Rolling of dice is probably about as deterministic a process as one can imagine, anyway, akin to shooting pool. Few would doubt that it is simply an intractable problem in Newtonian dynamics.)