How accurate is the quantum physics sequence?

17th Apr 2012

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68 comments, sorted by Click to highlight new comments since: Today at 3:13 AM

If you think you've learned quantum mechanics from it, you're a fool. If you think you've learned enough about quantum mechanics to be justified as a physical realist, you're correct. Oodles of things are left out, and many others simplified, but there are few things that are actually wrong, and they have little impact.

in Configurations and Amplitude, a multiplication factor of i is used for the mirrors where -1 is correct.

The main question is *relative* phase, and the transmitted portion can have an arbitrary phase shift, by selecting the thickness of the mirror. Therefore, the error is even more minor than it seems.

Edited to add: I have a PhD in physics.

Also edited to add: it is possible to build a device that actually has the exact phases listed, not even just relative. It's not an off-the-shelf half-silvered mirror, to be sure.

I have a PhD in physics.

Got one of those, too, and my opinion is basically the same, except for the MWI advocacy, which takes away from the QM sequence's usefulness (advocacy always does).

In a nutshell:

There are no particles, only fields (described by amplitudes evolving in space, time and other coordinates). Particles/waves show up as pattern matching to classical concepts, depending on the experiments.

The measurement step (the Born rule) is still mysterious (i.e. an open problem in Physics), despite what anyone, including EY, says. Hence the dozens of "interpretations".

Well, that and demonstrating that Identity Isn't in Specific Atoms because there is no such thing as specific atoms, and being a good example of weirdness being a reaction of the mind, not a property of the physics.

Well, that and demonstrating that Identity Isn't in Specific Atoms because there is no such thing as specific atoms, and being a good example of weirdness being a reaction of the mind, not a property of the physics.

And, subordinate to those three, the point that Occam's Razor applies to code not RAM (so to speak). Worth mentioning since I think that's the part that went over shminux's head.

And, subordinate to those three, the point that Occam's Razor applies to code not RAM (so to speak). Worth mentioning since I think that's the part that went over shminux's head.

You are right, it did the first time I tried to honestly estimate the complexity of QM (I wish someone else bother to do it numerically, as well). However, even when removing the necessary boundary conditions and grid storage (they take up lots of RAM), one still ends up with the code that evolves the Schroediger equation (complicated) and applies the Born postulate (trivial) for any interpretation.

But collapse interpretations require additional non-local algorithms

Not for computations, they do not. If you try to write a code simulating a QM system, end up writing unitary evolution on top of the elliptic time-independent SE (H psi = E psi) to describe the initial state. If you want to calculate probabilities, such as the pattern on the screen from the double-slit experiment, you apply the Born rule. And computational complexity is the only thing thing that matters for Occam's razor.

And, subordinate to those three, the point that Occam's Razor applies to code not RAM (so to speak). Worth mentioning since I think that's the part that went over shminux's head.

I think the supposed Occamian benefit is overstated. E.g., the transactional interpretation has an Occamian benefit in that you don't asymmetrically reject advanced wave solutions to Maxwell's equations, and yet I don't see anyone telling me that therefore the T.I. is obviously correct. Mirror matter: predicted by fundamental-ness of supersymmetry, Occamian benefit, still highly speculative. (Don't have a PhD in physics (dropped out of high school physics), only felt justified in replying to wedrifid because AFAIK he doesn't have a PhD in physics either. Someone with domain knowledge, please correct/refine/embarrass my point.)

Mirror matter comes from "N=2" supersymmetry, where along with the usual particle and its superpartner, you have a mirror partner for both of those. Ordinary "N=1" supersymmetry doesn't have the mirrors. N=2 supersymmetry is of major interest mathematically, but it's difficult to get the standard model from an N=2 theory. But if you did, the mirror matter might be the dark matter. It's in my top ten of cool possibilities, but I can't say it's favored by Occam.

I think the supposed Occamian benefit is overstated.

To clarify, do you mean that Eliezer overstated the degree to which the RAM vs code simplicity point applies to this specific physics example, or that Eliezer overstated the principle itself? I'm more inclined to accept the former than the latter.

Maybe he didn't overstate the significance of the principle even when it comes to interpreting QM, but I think using it to pick out a particular interpretation (whether MWI or TI) leads to overconfidence, and isn't very good evidence in itself, compared to relatively naive considerations like "using straightforward physical intuition, this idea that other worlds are somehow in a metaphysical sense as 'real' as our world doesn't seem likely to hold water". In retrospect I might be attributing connotations to Eliezer's original argument that weren't in that specific argument and only implicit in the overall tone of the sequence. It's been two years since I read the QM sequence.

Maybe he didn't overstate the significance of the principle even when it comes to interpreting QM, but I think using it to pick out a particular interpretation (whether MWI or TI) leads to overconfidence, and isn't very good evidence in itself, compared to relatively naive considerations like "using straightforward physical intuition, this idea that other worlds are somehow in a metaphysical sense as 'real' as our world doesn't seem likely to hold water".

I place less value on metaphisical intuitions about what 'real' means. I do not particularly like the baggage that comes with MWI, I do like the principle of asserting that we can consider reality as we understand it to be more or less just like the core math - with any additional mechanisms required to make our intuitions fit rejected out of hand.

The undesirable baggage of "MWI" extends to the titular concept. The whole idea of "Many Worlds" seems to be a description that would be made by those stuck in the mindset of someone stuck with trying to force reality to be like our metaphisical intuitions of a simple classical world. As far as I am aware experiments have not identified any level at which the worlds are discrete like that (except for the sense in which you could allocate each possible configuration of a universe down to the level of plank distances and suchforth as a 'World'.) So the question "are the other Worlds 'real'" doesn't seem to qualify for a yes or no answer so much as a "huh? There's just a 'reality' of the stuff in this wave equation. Call some specific subset of that a 'world' if you really want to."

It's been two years since I read the QM sequence.

It's been at least that for me too (it isn't a sequence that works in audio format, which is my preferred media). I place very low confidence on what I remember of QM from there and research elsewhere and only placed slightly higher confidence on my understanding even back when I remembered it.

There are certain assertions that I am comfortable *rejecting* but the specific positive assertions I have little confidence. For example I have no qualms with dismissing "but they are all just 'interpretations' and all interpretations are equal" sentiments. If additional mechanisms are introduced that isn't just *interpretation*. Interpretation is a question of which words are used to describe the math.

This might be a good time for me to respond to one of your earlier comments.

I was under the impression that it's a big mystery what complex numbers are *doing* (i.e., what is their *physical function*, what do they *mean*) in QM. I was under the impression that this is a matter of much speculative debate. Yet when I said that, I was downvoted a lot, and you implicitly alleged that I was obviously ignorant or misinformed in some way, and that we have a perfectly good understanding of what complex numbers are doing in the Dirac equation. Could you or someone please give me some background info, so that I can better understand the current state of understanding of the role of complex numbers in QM?

Note that complex numbers can be replaced with 2x2 real matrices, such as i=(0,-1;1,0), since multiplication by i is basically rotation by 90 degrees in the complex plane. Given that the Dirac equation is already full of matrices, does it make you feel better about it?

A momentary note on why the conversation went the way it did:

what the hell are complex numbers doing in the Dirac equation?

Hopefully you can see why this looked like a rhetorical objection rather than a serious inquiry.

~~~~

So, what IS the i doing in Dirac's equation? Well, first let's look into what the i is doing in Schrödinger's equation, which is

with H the 'Hamiltonian' operator: the operator that scales each component of psi by its energy (so, H has only real eigenvalues. Important!)

The time-propagation operator which gives the solutions to this equation is

To see how you can take e to the power of an operator, think of the Taylor expansion of the exponential. The upshot is that each eigenvector is multiplied by e to the eigenvalue.

In this case, that eigenvalue is the eigenvector's energy, times time, times a constant that contains i. *That i turns an exponential growth or decay into an oscillation*. This means that he universe isn't simply picking out the lowest energy state and promoting it more and more over time - it's conserving overall state amplitude, conserving energy, and letting things slosh around based on energy differences.

The i in the Dirac equation serves essentially the same purpose - it's a reformulation of Schrödinger's equation in a way that's consistent with relativity. You've got a field over spacetime, and the relation between space and time is that in every constant-velocity reference frame, it looks a lot like what was described in the previous paragraph.

IF on the other hand you aren't bothered by that i, and you mean 'what are the various i doing in the alpha or gamma matrices', well, that's just part of making a set of matrices with the required relationships between the dimensions - i in that case is being used to indicate physical rotations, not complex phase. You can tell because each of those matrices is Hermitian - transposing it and taking the complex conjugate leaves it the same - so all of the eigenvalues are real. If it had anything to do with states' complex phase as a thing in itself instead of just any other element of the state it's operating on, it would let some of the imaginary part of the matrix get out. Instead, it keeps it on the inside as an 'implementation detail'.

From the profile of the person whose answer is currently the most upvoted one:

I have no PhD, I am almost entirely self taught. I like physics, but I think the professionals are, for the most part, completely incompetent. I have a lot of my own personal theories about physics which I like to spread online. I am unemployed and not by choice. Despite this, I consider myself to be the next Isaac Newton.

I wonder if and how the answer of a professional physicist would differ.

I'm pretty familiar with Ron Maimon, since I use Physics.Stackexchange heavily.

He seems to have other things going on in his life that prevent him from being accepted by the physics community at large, but in terms of pure knowledge of physics he's really, really good. Every time I've read an answer from him that I'm competent to judge, it's been right, or else if it has a mistake (which is rare) and someone points it out, he thanks them for noticing and corrects his answer.

When crackpots answer physics questions, they consistently steer away from the topic towards whatever their crackpot ideas are. Ron doesn't do that. Crackpots tend to claim things that are pretty much known to be impossible, and display little depth of understanding or willingness to talk about anything other than their theories. Ron doesn't do that. He also doesn't claim that he's being repressed by the physics establishment. He'll call professional physicists idiots, but he doesn't say that they're trying to hide the truth or suppress his ideas. And when he sees a professional physicist who comes on the site and writes good answers, he generally treats them with respect. He leaves positive feedback on good answers of all sorts. None of this fits in with being a crackpot.

He does get into fights with people about more advanced theoretical stuff that's over my head. But when he talks about physics that I know, he does it extremely well, and I've learned a lot from him. He's more knowledgeable and insightful than most professional physicists.

The stuff other users mentioned about his bible interests and his profile description is ad hominem.

Anyway, if you are interested in what a professional physicist would say, I'm quasi-professional in that I'm a graduate student. My opinion is that the sequence, so far as I read it, is fine. I haven't finished reading it, so I didn't offer a comment before, but so far I haven't found any significant mistakes (beyond those real but relatively minor ones pointed out on the thread on Phys.SE) The fact that many LessWrongers have read and enjoyed it indicates it's not too verbose for the target audience.

**Edit** several people gave feedback indicating that the sequence isn't as well-received as I indicated. I should have read more of it before commenting.

The fact that many LessWrongers have read and enjoyed it indicates it's not too verbose for the target audience.

It appears to be one of the *least*-read of the original Sequences - I say this based on the low, zero or even negative karma scores and the few comments. This is evidence for the precise opposite of your claim.

It's simpler than you think: you just treat *i* as an unknown variable where all you know is that *i*^2 = -1. Then if you want to, say, multiply together two complex numbers, it's all the algebra you're already familiar with: (*a* + *bi*)(*c* + *di*) = *ac* + *adi* + *bci* + *bdi*^2 = *ac* - *bd* + (*ad* + *bc*)*i*. That's it - that's all the complex maths you need to follow the QM sequence.

Yep, he says so explicitly here: http://physics.stackexchange.com/questions/22578/can-black-holes-be-created-on-a-miniature-scale#comment52219_22601

Um... I am not exactly knighted, so I don't know why you would call me "sir" (except perhaps the jokey Isaac Newton business in my bio--- that's a nod to John Baez "crackpot index", where comparison of yourself to Newton gets you 100 points).

I think the professionals are, for the most part, completely incompetent

I consider myself to be the next Isaac Newton

That's a few points on the crackpot index.

Although, looking at a few of his other answers he doesn't seem to get many more, and in his description of one of his theories he lists both predictions and limitations.

To me it seemed like he was only complaining that the Quantum sequence is *too easy*. Something like -- the first part was so obvious, that it's a waste of time; and the second part should be shorter and full of heavy math, because those able to solve all that math would get a better understanding.

I guess the point of the sequence was to explain some confusion and mystery related to quantum physics, without having to do all the heavy math. For me, it worked. Some parts could be shorter, but I am thankful that the other parts were not shorter.

An extremely intelligent friend of mine who is studying physics as an undergraduate read the quantum physics sequence for me. He said that it's an alright explanation of the physics, in an extremely qualitative way. He said that he would personally prefer to learn QM properly via a textbook with more math.

He says that the argument given for many-worlds is valid iff you're a scientific realist, which not all scientists are.

in Configurations and Amplitude, a multiplication factor of i is used for the mirrors where -1 is correct.

So, it's a bit more subtle. The -1 refers to a phase shift of pi, which is what you happen when reflecting off of e.g. a silver mirror. And interestingly, you only get this if you reflect off of the silvered side, rather than the glass side (I only found this out when googling for this :D ). But for a dielectric mirror (which happens to be symmetric), I think you get a phase shift of pi/2, which corresponds to multiplying by i.

Anywho, I guess it's... fine. If you are familiar with the basic math of QM already, there are certainly better places to go. If you're not, reading the first couple of posts is a good introduction. Ignore all the parts about "mangled worlds," which actually contradicts the rest of the stuff and is highly unlikely to be experimentally confirmed (see "nonlinear schrodinger equation"). Oh, and almost all of the timeless physics stuff (except "thou art physics") should be replaced by watching Richard Feynman explaining the principle of least action (video here, I think it's in there somewhere after minute 30 :P Of course explaining the principle of least action takes 10 seconds, the point is to get you to watch Richard Feynman).

And of course, the ra-ra-many-worlds stuff is a bit silly, but you may indulge in silly stuff if you wish.

Thanks, that's a good explanation. What do you think is silly about "ra-ra-many-worlds"? The Everett interpretation itself, or just the amount of time EY spends making fun of other interpretations?

Also, my memory may be failing me, but I thought the "mangled worlds" stuff was Nick Bostrom, and not in the QM sequence. Am I thinking of something else?

Most of the silliness is just the making fun of other teams / boosting your team stuff. But some of the silliness is in overconfidence (under-caution?) with a dash of ignorance. We still have a whole theory of everything to figure out still, after all. And until there's a derivation of the Born probabilities, many worlds isn't necessarily simpler than a model with physical collapse. Many worlds and discontinuous faster than light collapse aren't the only two options, despite the dichotomous presentation. And cetera.

The "mangled worlds" stuff is Robin Hanson's idea originally, echoed by Eliezer occasionally in the QM sequence (for example, in the most recent sequence rerun).

And until there's a derivation of the Born probabilities, many worlds isn't necessarily simpler than a model with physical collapse.

I find that difficult to believe. Born probabilities are comparable to a law that causes particles to become disentangled, if you ignore the violations of the Tao of physics. In order to get a complete theory, you also have to have a law that causes particles to become entangled, and a law that causes particles to interact without ever becoming entangled.

Am I missing something?

(for example, in the most recent sequence rerun)

Please link when you do that. It's not going to stay the most recent sequence rerun.

And until there's a derivation of the Born probabilities, many worlds isn't necessarily simpler than a model with physical collapse.

How's this?

So it's not hard to get a Born rule - Everett did it nicely in his original paper. But in order to do so, he had to introduce the requirement that the probability measure of different observations should be defined for vectors in the Hilbert space of solutions to the Schroedinger equation. An extra law of physics, basically. Which is fine. But it means that many worlds isn't necessarily simpler than other stuff.

To meet my challenge, you'd need to require the Born probabilities instead the naive probabilities using only the Schroedinger equation and a Hamiltonian, basically. By "the naive probabilities," I mean assigning each eigenstate equal probability. Which isn't what we observe. But if the Schroedinger equation alone isn't enough, it would make sense that just using it gives us probabilities that aren't what we would observe.

But in order to do so, he had to introduce the requirement that the probability measure of different observations should be defined for vectors in the Hilbert space of solutions to the Schroedinger equation. An extra law of physics, basically. Which is fine. But it means that many worlds isn't necessarily simpler than other stuff.

What? No, seriously... what? The extra law of physics you just listed was, 'The Schrodinger Equation determines physical reality'

Which is to say, it's entirely redundant with the rest of quantum mechanics. This is not new information, here.

To meet my challenge, you'd need to require the Born probabilities instead the naive probabilities using only the Schroedinger equation and a Hamiltonian, basically. By "the naive probabilities," I mean assigning each eigenstate equal probability. Which isn't what we observe.

Did you even read the derivation? How much do you actually know about quantum mechanics anyway? Are you a physicist?

So, let me see if I can restate what you're saying, building up a bit of the background:

1) Suppose you've got a Hamiltonian. Then the SE constrains the world to a specific set of vectors (forming some oddly-shaped manifold) in a Hilbert space on spacetime.

2) Any one of these vectors can be given an equal weight of probability.

There's more to it, but... I'd like to stop here for a moment anyway. See, these vectors are not instantaneous state vectors. Each vector is the history of a whole many-worlds universe, with all of the quantum branching included. Each vector includes ALL of the branches, all of the weights, everything.

The different vectors, here, are just the cases where different initial conditions (or boundary or other conditions, if you want to really seriously demote time) are taken.

If I'm right about this interpretation, then this isn't what the Born Probabilities are talking about. Maybe they all are real, with equal weights. No observation we could make would contradict that. Meanwhile, the Born Probabilities are, as you indicated above, highly experimentally testable.

Two days ago Scott Aaronson have commented on this topic. At this moment, his answer has as many upvotes as the Ron Mainmon's one (former most upvoted one).

Scott enjoyed the sequence and thinks that it is "exactly what you should and must do if your goal is to explain QM to an audience of non-physicists". However, he gives two criticisms of Yudkowsky, both connected to the Eliezer's claim that MWI vs CI debate is completely one-sided.

Since what Scott Aaronson is saying in point 2 sounds very interesting to me, would someone be so nice and elaborate on the following sentence (so that I don't have to wait until I am able to reduce the inferential distance :-):

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.

Prompted by Mitchell Porter, I asked on Physics StackExchange about the accuracy of the physics in the Quantum Physics sequence:

What errors would one learn from Eliezer Yudkowsky's introduction to quantum physics?

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?

I've had some interesting answers so far, including one from a friend that seems to point up a definite error, though AFAICT not a very consequential one: in Configurations and Amplitude, a multiplication factor of

iis used for the mirrors where -1 is correct.Physics StackExchange: What errors would one learn from Eliezer Yudkowsky's introduction to quantum physics?