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Eliezer Yudkowsky wrote an introduction to quantum physics from a strictly realist standpoint. However, he has no qualifications in the subject and it is not his specialty. Does it paint an accurate picture overall? What mistaken ideas about QM might someone who read only this introduction come away with?

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It's just quantum mechanics with Everett built in. If you learn from Dirac's book or Landau's, it is no more difficult to tack on the Everett at the end, so long as you don't spend so much time worrying about philosophy while learning the calculations. –  Ron Maimon Apr 16 '12 at 4:19
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I realize I'm late to this discussion. For whatever it's worth, I disagree in the strongest terms with Ron Maimon and Dmytry, when they criticize Yudkowsky for being "too conceptual." As I see it, that's exactly what you should and must do if your goal is to explain QM to an audience of non-physicists! Indeed, most popularizations of QM go off the rails precisely because they try to describe a huge array of weird phenomena that people were trying to make sense of in the years between 1900 and 1926, while burying or downplaying the single conceptual point that was eventually found to underlie all of those phenomena.

That point, of course, is that we have to replace probabilities (which are nonnegative real numbers) by amplitudes (which are complex numbers)---and that unlike probabilities, amplitudes can "interfere" and cancel each other out. As demonstrated by any modern quantum information textbook, it's possible to explain almost all of what the typical non-physicist wants to know about QM -- e.g., what's entanglement? what's the Bell inequality? what are the arguments for and against Many-Worlds? -- while just talking about qubits, unitary transformations, and vectors of amplitudes, and never saying anything about the energy levels of hydrogen (or even particles and fields at all!). Of course, once someone understands the mathematical framework of QM, they're then in a much better position to learn some of the physics built on top of that framework, should they want to. But if you try to tell a layperson about tunneling, energy levels, wave/particle duality, etc. etc., before he or she even understands the concept of an amplitude vector, then the take-home message is simply going to be "anything is possible in the weird and wonderful world of QM!"

So I commend Yudkowsky for writing an entertaining series of posts (well, at least, I enjoyed them :) ) that explain QM from his personal, non-physicist perspective, and that actually get most of the technical stuff right. I would criticize Yudkowsky, not for focusing on "dinner-party" topics, but for two other things:

(1) I think Yudkowsky's central argument---basically, that anyone who rejects Everett needs to have their head examined---is to put it mildly, a bit overstated. :) I'll resist the temptation to elaborate, since this is really a discussion for another thread.

(2) In several posts, Yudkowsky gives indications that he doesn't really understand the concept of mixed states. (For example, he writes about the No-Communication Theorem as something complicated and mysterious, which it's not from a density-matrix perspective.) As I see it, this might be part of the reason why Yudkowsky sees anything besides Many-Worlds as insanity, and can't understand what (besides sheep-like conformity) would drive any knowledgeable physicist to any other point of view. If I didn't know that in real life, people pretty much never encounter pure states, but only more general objects that (to paraphrase Jaynes) scramble together "subjective" probabilities and "objective" amplitudes into a single omelette, the view that quantum states are "states of knowledge" that "live in the mind, not in the world" would probably also strike me as meaningless nonsense.

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I wasn't criticizing them for being too conceptual. I was criticizing them for being too long. The point of view that quantum states are "states of knowledge" is difficult, because you need to ask "knowledge of what?" There is no further information to specify once you have the pure state. Further, the only consistent ignorance calculus is probability (diagonal density matrices), and this is a limit that is only asymptotically approached in QM. –  Ron Maimon Apr 30 '12 at 4:43
    
I should also point out that there is no reason in today's media environment for there to be a nonphysicist--- anyone has the available information to learn this quantum stuff properly. –  Ron Maimon May 1 '12 at 22:54
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I skimmed a majority of the articles, and there are no glaring errors that I could find, but there is an unnecessary verbosity which is best eliminated by reading a terser introduction to the Everett interpretation. The amount of text that is presented is not commensurate with the amount of insight.

The philosophical issues are discussed at great length, with references to Chalmers, but these issues are essentially ignorable, because Philosophers had it right originally 50 years ago when they were positivists. In positivism, you don't admit questions which do not have an impact on observation. So "is does my friend a soul, or is he a zombie?" is exactly the kind of question which is completely meaningless. The notion of zombie is fundamentally inconsistent, it is an abuse of language in the sense of Carnap. The only reason philosophers use zombies is to make sure that their students do not discover positivism, since just by considering that a zombie makes sense, you are automatically engaging in positivistically meaningless discourse.

If you absorb the logical positivist's insights, as all physicists have done for at least a century, you don't have to bother with the first few posts at all. The sections on splitting and decoherence are basically correct, but again too verbose--- the basic idea is presented on Wikipedia in a few paragraphs, and in Everett's 1957 paper in a few pages. The verbosity is a problem, as the main problem is the "thin worlds stop existing" which is explained with a mysterious and not completely satisfactory gloss in the blog posts.

The problem with non-physicist sources is that they generally waste too much time on "profound" ideas, and spend too little time on actual calculations. A person should at least know how to solve the H-atom, and calculate the photon emission transition probabilities between a few levels. You should know how the entanglement in molecules or in He look like, at least qualitatively. You should learn Feynman's methods that work so well to organize condensed matter and high energy physics calculations.

Once you learn how to do the calculations, the profound ideas will take only a miniscule effort by comparison. To internalize the ideas required for the calculations require you to construct a mental lever to multiply your conceptual powers, as these ideas are like a heavy boat weighing thousands of tons. Once you construct the lever with enough power to lift the boat, and you drag the boat ashore over a period of months and years, the philosophical problems are like a dinky boulder, too heavy to lift with the bare hands, but trivially light compared to the ship. You use the same lever and lift the boulder with your pinky. It is trivial in comparison.

But it is not completely trivial to those who didn't spend enough time making a good lever. Instead of making longer and longer explanations to make the task achievable for the lever-less, one should explain how to build the lever.

I think that the presentation is essentially accurate, but too long to be useful.

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"The amount of text that is presented is not commensurate with the amount of insight." Pretty much universally true of Yudkowski. –  user1631 Apr 16 '12 at 16:32
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Starting with his page 'Configurations and Amplitude' he describes a Mach-Zender interferometer (link, http://en.wikipedia.org/wiki/Mach%E2%80%93Zehnder_interferometer).

His formulation is,

starting phase = -1 + 0i

on hitting a mirror we multiply by i

For the straight path both photons hit two mirrors so we sum (-1 + 0i) * i * i, and (-1 + 0i) * i * i = 2(1 + 0i)

take the modulus, we get a number hence signal.

For the path that turns pi/2, we're hit reflected by either three mirrors or one mirror, sum (-1 + 0i) * i + (-1 + 0i) * i * i * i = 0

take the modulus hence no signal.

Unfortunately the traditional maths goes more like this,

We see a phase inversion, when we reflect at a surface with a higher refractive index.

The straight path, gives one reflection each by a normal mirror, therefore both paths have inverted phase, therefore no cancellation.

The pi/2 path gives either one reflection by a normal mirror, or three reflections, one from a normal mirror (phase shift), one from half silvered mirror at the front of the mirror (phase shift), one from a half silvered mirror at the back (no phase shift). Therefore one signal has the phase inverted once, one has it inverted twice. They interfere and no signal is produced.

Coincidentally this is the same answer as above.

To turn this into testable predictions, if you turn the first half silvered mirror around, under Eliezer Yudkowskys formation nothing would change, under the classical formulation the signal would move to the other detector.

Carrying out this experiment involves a fair number of practical difficulties (in particular this is an idealised experiment that currently is missing all the bits of glass required to compensate for refractive indices which would have to be moved appropriately, plus it's very important for the half silvered mirror surface to remain in exactly the same place). In the absence of an easy experimental verification I think it's reasonable to assume that the theory of optics as taught by every university physics course is probably right, and Eliezer is not.

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+1: Nice catch--- I didn't check any of the phase stuff... sorry for missing it. You don't need either experiment or authority to see the phase is -1 not i --- the experiments are already done. He did not give a reason for the "i" factor, it is incorrect, and the reason for the "-1" factor is the fixed boundary conditions at the mirror, requiring vanishing field near the mirror. If you have a vanishing field, you need a reflection phase of -1, so the reflected and incident waves sum to zero at the mirror. –  Ron Maimon Apr 17 '12 at 0:25
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@Alex1167623: The mirror does not have to be a perfect plane to make a reflection with phase factor -1, just make reflection in a region significantly smaller than the wavelength (and this is true of commercial mirrors). –  Ron Maimon Apr 17 '12 at 6:43
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@Alex1167623: your objections are not correct, so I hope it wasn't edited. Dude should edit his blog--- it's not a major error, but it is annoying. –  Ron Maimon Apr 17 '12 at 7:52
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@Alex1167623: Even if so, if the device has a quarter-wavelength turn, why not just put that after the reflection? It's a weird choice, and definitely pedagogically suboptimal. The way it is phrased on the blog should be changed. If he wants an i phase, just put in an extra phase--- it's easy, stick a dielectric in the path of the light. –  Ron Maimon Apr 17 '12 at 8:27
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Experiment doesn't matter - if what Eliezer presents makes different predictions than standard theory in an in-principle measurable way, that counts as an error for my (and his) purposes. –  Paul Crowley Apr 17 '12 at 8:31
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I recommend to actually study physics if you want to learn physics. This kind of stuff is for dinner table talk, and still you are much better off reading popularizations written by physicists than by professional bloggers. I stopped at

The early scientists—you're going to laugh at this—thought that the silver mirror deflected the photon half the time, and let it through half the time.

Ha, ha! As if the half-silvered mirror did different things on different occasions! I want you to let go of this idea, because if you cling to what early scientists thought, you will become extremely confused. The half-silvered mirror obeys the same rule every time.

The 'half silvered mirror' is a messy layer of metallic silver (think some crystalline structures) attached to a glass substrate, a couple wavelengths thick [actually I'm not sure how thick it has to be for silver], of varying thickness, with oxide stuck on it. It also absorbs some of the light, it has different delay for reflecting and transmitting [namely, half the wavelength for reflection, but that may just be the ideal case]. Followed by extra delay by the glass plane. The light of different polarization directions reflects to different extent. The interferometer set up in question has all the light going into one eye, or into other eye, if one of the paths warms up because you stand next to it, and increases in length by a half wavelength. Likewise if the pieces of glass are not of exactly equal thickness. What you actually see if you build this back in the day, is interference fringes, because the light that is going at an angle, does encounter different path length.

This is to give a little backgrounder on what this set up does do, which is very worthwhile to learn first before getting into quantum mechanics. What it does not do, is behave like a neat abstract system, where it is clear what is going on if only you are a rationalist and don't have biases.

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To my ears, this seems a little like you're pointing out that there are no perfectly spherical masses or inelastic massless rods; you're saying that real-world objects have more complex behaviour than the simplified objects used to teach physics. This is true, but it's true of most physics teaching isn't it? –  Paul Crowley Apr 15 '12 at 21:14
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I was responding to "The early scientists—you're going to laugh at this—thought that the silver mirror deflected the photon half the time, and let it through half the time. Ha, ha! As if the half-silvered mirror did different things on different occasions!" . See, when you read physics texts by a physicist, it's not some inside loyalty, that they aren't making such passages. It's that when your 'half silvered mirror' is god knows what at micro scale, it is perfectly reasonable to imagine that it may be letting photons through half of the time. Is he trying to teach arrogance? –  Dmytry Apr 15 '12 at 22:57
    
I think I see his purpose, but in any case it looks like you're complaining about something other than an inaccuracy in the physics, so I'll leave this here. –  Paul Crowley Apr 16 '12 at 6:06
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Well, as far as I can see he isn't actually teaching any physics - I don't see how you would be better able to make any predictions after reading this. So you wouldn't learn any non-errors. One would probably generate some misconceptions from jumping straight at the ideal cases; he speaks of interferometer as if the phase did not depend to distance. –  Dmytry Apr 16 '12 at 8:52
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@Ron Maimon: Ya. Well the issue is that we know physics so we read sense into stuff. I'm not entirely sure author realized that phase depends to distance, and I don't think reader would realize that. I think naive reader would believe that the photon is somehow multiplied with a fancy quantum mechanical imaginary multiplier, not thinking in terms of wave phase. And also would believe that it is obvious the half silvered mirror can't do different things to different photons. –  Dmytry Apr 17 '12 at 8:41
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