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Quantum Explanations

29 Post author: Eliezer_Yudkowsky 09 April 2008 08:15AM

I think I must now temporarily digress from the sequence on zombies (which was a digression from the discussion of reductionism, which was a digression from the Mind Projection Fallacy) in order to discuss quantum mechanics.  The reasons why this belongs in the middle of a discussion on zombies in the middle of a discussion of reductionism in the middle of a discussion of the Mind Projection Fallacy, will become apparent eventually.

It's a sequence that has been weighing on my mind, demanding to be written, for a quite a long time.  Years.  This seems like a good time to insert it.

I wrote the "Intuitive Explanation of Bayesian Reasoning" because people were complaining that Bayes's Theorem was "counterintuitive"—in fact it was famously counterintuitive—and this did not seem right.  The equation just did not seem complicated enough to deserve the fearsome reputation it had.  So I tried explaining it my way, and I did not manage to reach my original target of elementary school students, but I get frequent grateful emails from formerly confused folks ranging from reporters to outside academic college professors.

I am not a physicist, and physicists famously hate it when non-professional-physicists talk about QM.  But I do have some experience with explaining mathy things that are allegedly "hard to understand".

Besides, as a Bayesian, I don't believe in phenomena that are inherently confusing.  Confusion exists in our models of the world, not in the world itself.  If a subject is widely known as confusing, not just difficult... you shouldn't leave it at that.  It doesn't satisfice; it is not an okay place to be.  Maybe you can fix the problem, maybe you can't; but you shouldn't be happy to leave students confused.

The first way in which my introduction is going to depart from the traditional, standard introduction to QM, is that I am not going to tell you that quantum mechanics is supposed to be confusing.

I am not going to tell you that it's okay for you to not understand quantum mechanics, because no one understands quantum mechanics, as Richard Feynman once claimed.  There was a historical time when this was true, but we no longer live in that era.

I am not going to tell you:  "You don't understand quantum mechanics, you just get used to it."  (As von Neumann is reputed to have said; back in the dark decades when, in fact, no one did understand quantum mechanics.)

Explanations are supposed to make you less confused.  If you feel like you don't understand something, this indicates a problem—either with you, or your teacher—but at any rate a problem; and you should move to resolve the problem. 

I am not going to tell you that quantum mechanics is weird, bizarre, confusing, or alien.  QM is counterintuitive, but that is a problem with your intuitions, not a problem with quantum mechanics.  Quantum mechanics has been around for billions of years before the Sun coalesced from interstellar hydrogen.  Quantum mechanics was here before you were, and if you have a problem with that, you are the one who needs to change.  QM sure won't.  There are no surprising facts, only models that are surprised by facts; and if a model is surprised by the facts, it is no credit to that model.

It is always best to think of reality as perfectly normal.  Since the beginning, not one unusual thing has ever happened.

The goal is to become completely at home in a quantum universe.  Like a native.  Because, in fact, that is where you live.

In the coming sequence on quantum mechanics, I am going to consistently speak as if quantum mechanics is perfectly normal; and when human intuitions depart from quantum mechanics, I am going to make fun of the intuitions for being weird and unusual.  This may seem odd, but the point is to swing your mind around to a native quantum point of view.

Another thing:  The traditional introduction to quantum mechanics closely follows the order in which quantum mechanics was discovered.

The traditional introduction starts by saying that matter sometimes behaves like little billiard balls bopping around, and sometimes behaves like crests and troughs moving through a pool of water.  Then the traditional introduction gives some examples of matter acting like a little billiard ball, and some examples of it acting like an ocean wave.

Now, it happens to be a historical fact that, back when students of matter were working all this stuff out and had no clue about the true underlying math, those early scientists first thought that matter was like little billiard balls.  And then that it was like waves in the ocean.  And then that it was like billiard balls again.  And then the early scientists got really confused, and stayed that way for several decades, until it was finally sorted out in the second half of the twentieth century.

Dragging a modern-day student through all this may be a historically realistic approach to the subject matter, but it also ensures the historically realistic outcome of total bewilderment.  Talking to aspiring young physicists about "wave/particle duality" is like starting chemistry students on the Four Elements.

An electron is not a billiard ball, and it's not a crest and trough moving through a pool of water.  An electron is a mathematically different sort of entity, all the time and under all circumstances, and it has to be accepted on its own terms.

The universe is not wavering between using particles and waves, unable to make up its mind.  It's only human intuitions about QM that swap back and forth.  The intuitions we have for billiard balls, and the intuitions we have for crests and troughs in a pool of water, both look sort of like they're applicable to electrons, at different times and under different circumstances.  But the truth is that both intuitions simply aren't applicable.

If you try to think of an electron as being like a billiard ball on some days, and like an ocean wave on other days, you will confuse the living daylights out of yourself.

Yet it's your eyes that are wobbling and unstable, not the world.

Furthermore:

The order in which humanity discovered things is not necessarily the best order in which to teach them.  First, humanity noticed that there were other animals running around.  Then we cut them open and found that they were full of organs.  Then we examined the organs carefully and found they were made of tissues.  Then we looked at the tissues under a microscope and discovered cells, which are made of proteins and some other chemically synthesized stuff.  Which are made of molecules, which are made of atoms, which are made of protons and neutrons and electrons which are way simpler than entire animals but were discovered tens of thousands of years later.

Physics doesn't start by talking about biology.  So why should it start by talking about very high-level complicated phenomena, like, say, the observed results of experiments?

The ordinary way of teaching QM keeps stressing the experimental results.  Now I do understand why that sounds nice from a rationalist perspective.  Believe me, I understand.

But it seems to me that the upshot is dragging in big complicated mathematical tools that you need to analyze real-world situations, before the student understands what fundamentally goes on the simplest cases.

It's like trying to teach programmers how to write concurrent multithreaded programs before they know how to add two variables together, because concurrent multithreaded programs are closer to everyday life.  Being close to everyday life is not always a strong recommendation for what to teach first.

Maybe the monomaniacal focus on experimental observations made sense in the dark decades when no one understood what was fundamentally going on, and you couldn't start there, and all your models were just mysterious maths that gave good experimental predictions... you can still find this view of quantum physics presented in many books... but maybe today it's worth trying a different angle?  The result of the standard approach is standard confusion.

The classical world is strictly implicit in the quantum world, but seeing from a classical perspective makes everything bigger and more complicated.  Everyday life is a higher level of organization, like molecules versus quarks—huge catalogue of molecules, six quarks.  I think it is worth trying to teach from the perspective of the quantum world first, and talking about classical experimental results afterward.

I am not going to start with the normal classical world and then talk about a bizarre quantum backdrop hidden behind the scenes.  The quantum world is the scene and it defines normality.

I am not going to talk as if the classical world is real life, and occasionally the classical world transmits a request for an experimental result to a quantum-physics server, and the quantum-physics server does some peculiar calculations and transmits back a classical experimental result.  I am going to talk as if the quantum world is the really real and the classical world something far away.  Not just because that makes it easier to be a native of a quantum universe, but because, at a core level, it's the truth.

Finally, I am going to take a strictly realist perspective on quantum mechanics—the quantum world is really out there, our equations describe the territory and not our maps of it, and the classical world only exists implicitly within the quantum one.  I am not going to discuss non-realist views in the early stages of my introduction, except to say why you should not be confused by certain intuitions that non-realists draw upon for support.  I am not going to apologize for this, and I would like to ask any non-realists on the subject of quantum mechanics to wait and hold their comments until called for in a later post.  Do me this favor, please.  I think non-realism is one of the main things that confuses prospective students, and prevents them from being able to concretely visualize quantum phenomena.  I will discuss the issues explicitly in a future post.

But everyone should be aware that, even though I'm not going to discuss the issue at first, there is a sizable community of scientists who dispute the realist perspective on QM.  Myself, I don't think it's worth figuring both ways; I'm a pure realist, for reasons that will become apparent.  But if you read my introduction, you are getting my view.  It is not only my view.  It is probably the majority view among theoretical physicists, if that counts for anything (though I will argue the matter separately from opinion polls).  Still, it is not the only view that exists in the modern physics community.  I do not feel obliged to present the other views right away, but I feel obliged to warn my readers that there are other views, which I will not be presenting during the initial stages of the introduction.

To sum up, my goal will be to teach you to think like a native of a quantum universe, not a reluctant tourist.

Embrace reality.  Hug it tight.

 

Part of The Quantum Physics Sequence

Next post: "Configurations and Amplitude"

(start of sequence)

Comments (56)

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Comment author: Hopefully_Anonymous 09 April 2008 09:49:11AM -2 points [-]

This should be a fun project. As usual, I wonder what your writing would be like without some of your "I need an opponent/"I need something to evangelize" baggage. I'm often tempted to make a parallel blog, which reproduces your and Robin's posts from Overcoming Bias, with what I consider to be the weaker elements removed from them. For example I would extract sentences like "I'm a pure realist" and "Embrace reality. Hug it tight." or at least modify them with sentences like "as far as I can tell, the pure realist approach models reality best".

Comment author: Lake 09 April 2008 11:07:34AM 14 points [-]

You could call it "Overcoming Fun".

Eliezer's polemical tone is one of the great strengths of his pedagogical approach, IMO.

Comment author: John_Seiffer_The_Small_Business_Coach 09 April 2008 11:14:25AM 3 points [-]

When I was in college back in the dark ages (1972-76) I had a wonderful professor, Herb Bernstein who taught theoretical physics. I took a 3 semester series with him that started with quantum mechanics the first semester. Next we went on to electricity and magnetism and finally dealt with Newtonian laws. He even enlisted a math prof to teach a sister course in math just so we could keep up with the physics. Net result - I have done nothing in that field for a career but I have always loved following QM as an amateur. I'm looking forward to your discussion.

Comment author: Will_Pearson 09 April 2008 11:58:01AM 5 points [-]

His polemical style reminds me too much of political rhetoric for my liking. It hooks too much into the us vs them psychology e.g. rationalists vs irrationalists.

"Finally, I am going to take a strictly realist perspective on quantum mechanics - the quantum world is really out there, our equations describe the territory and not our maps of it,"

Why isn't this an example of the mind projection fallacy? I know you said to give you a break, but I really don't like it when people contradict themselves.

Comment author: Constant2 09 April 2008 12:24:00PM 1 point [-]

Why isn't this an example of the mind projection fallacy?

Surely it is not fallacious to subscribe to the Many-worlds interpretation (which is surely what Eliezer is talking about). If this is the sort of use to which the "mind projection fallacy" is put, then it turns out merely to be a cheap way to put down competing interpretations of the math.

Comment author: Nick_Nolan 09 April 2008 01:01:22PM 6 points [-]

I wish you luck with your quantum effort.

There is few things that previous explanations miss or explain badly, I hope you could dive into them more deeply:

1) quantum decoherence, 2) the fact that QM is symmetrical in time.

QM and its time indifference time is really fascinating subject. For example, many-worlds interpretation fails to mention that it works equally well into the past. If you entertain the many-worlds interpretation, you must acknowledge that it works as well backwards in time. From any "current", moment there are multiple histories backward (with thermodynamic constraints, of course)

Comment author: Rolf_Nelson2 09 April 2008 01:16:17PM 1 point [-]

In many of your prior posts where you bring up MWI, your interpretation doesn't fundamentally matter to the overall point you're trying to make in that post; that is, your overall conclusion for that post held or failed regardless of which interpretation is correct, possibly to a greater degree than you tend to realize.

For example: "We used a true randomness source - a quantum device." The philosophers' point could equally have been made by choosing the first 2^N digits of pi and finding they correspond by chance to someone's GLUT.

Comment author: Ben_Jones 09 April 2008 03:13:18PM 2 points [-]

Will, remember that we're talking about perspectives here. There are ways of talking about the world that are useful and ways that aren't. It's not mind projection to talk about QM in a way that agrees with experiment. In fact, talking about billiard balls and waves is horribly classical-centric.

QM is so far removed from what we think the world is like that it's only ever really described in two ways - metaphor and algebra (metaphor with symbols). As soon as you start saying 'there are these tiny particles that zip around' you're already picturing those billiard balls. Macroscopic Bias! So I'm looking forward to the next few posts. Long, detailed and mathsy please!

Comment author: DaveInNYC 09 April 2008 04:47:09PM 1 point [-]

Cool! I am REALLY looking forward to this. Even if I don't end up grasping QM after this series, at least you are taking an honest shot at it. I can't stand it when I try to ask someone (that allegedly knows this stuff) about QM and they come back with, "it is so strange you can't even try to understand it, but here are the results of various QM experiments".

Comment author: Will_Pearson 09 April 2008 05:27:57PM 0 points [-]

Ben Jones: Do you mean that realist view of QM is that QM is a map of the territory, rather than a map of a different map? I wouldn't say that the first entailed what Eliezer said, "the quantum world is really out there".

It is the best map we have at the moment, but we should always strive to make better maps that make QM as illusory as classical mechanics.

I'd also question whether any attempted interpretation is consistent with occams razor, unless you are trying to explain something new of course. Not that I would mind myself, interpretations might leads us to the places where we can perform experiments to determine whether they are useful or not.

Comment author: Zubon 09 April 2008 05:55:11PM 2 points [-]

I would like to ask any non-realists on the subject of quantum mechanics to wait and hold their comments until called for in a later post. Do me this favor, please. ... Still, it is not the only view that exists in the modern physics community. I do not feel obliged to present the other views right away, but I feel obliged to warn my readers that there are other views, which I will not be presenting during the initial stages of the introduction.

I believe we have an incoming inferential distance issue here. By Hofstadter's Law, this series on quantum mechanics will take longer than you expect. If dealing with objections or rival theories is scheduled for a place far along the trail, it could be weeks or months away. What is to be done about comments during that time? Not just from non-realists, but from other disputants. I have never seen a quantum mechanics discussion that was not plagued with fundamental disagreements and differing interpretations.

"Please hold your questions until the end" means that the comments will be less useful than average while waiting. Moderation could enforce that request, but you might stifle quite a bit, and how many people hold comments in abeyance for weeks rather than just wandering off? Alternately, the comment threads could repeatedly derail on issues you plan to address somewhere down the line.

I mean to say that there will be objections at many points, some of which you will want to discuss at a later date. Failure to address or channel those objections productively will remove much of the value of approaching the topic through the blog format. I presume that you have at times been surprised by objections to ideas that you considered fairly obvious, or the vehemence and persistence of objections after you have explained your views. I suggest that this will be one of those times. Even if you have already taken that into account, I suggest that you have likely underestimated what is coming. Re-pad any estimates.

Comment author: Ryan_Glinski 09 April 2008 06:14:42PM 0 points [-]

Interesting. I think students could use a better explanation of QM than the one I got in college which was "Light is not a wave. Light is not a particle. No one knows what light it. Light is a quantum mechanical beast." In all fairness, it's pretty accurate to say no one knows what light is. That doesn't mean anyone needs to be taught that light behaves sort of like a wave and sort of like a particle.

I've always thought the universe is best understood as consisting of two substances, gravitational ether and electromagnetic field. Gravitational ether can wrap itself into vortexes of different energies and densities. The vortexes stretch and pile the ether. So a high energy vortex will contain much more dense ether, and the surrounding ether will become much less dense. The force of gravity then becomes a simple function of a density gradient.

The other substance, electromagnetic field, somehow (this is the big hole in my theory) latches on or interacts with vortexex ether and the interaction gives rise to what we call particles. But the particle is not real, we perceive teh interation between the two substances as a particle/wave dualtiy. This flows from the model I've described. Vortexes of ether with proper internal forces would be very well described as billiard balls. Electric and magnetic fields on their own almost perfectly obey wave equation predictions. However, the electron or photon or whatever, is not actually gravitational ether, nor is it eletromagnetic (or electro-strong-weak) field. What we see as the particle is actually the interaction, and we can prod the interaction to emphasize the particle or wave qualities, but since this is an interaction we're talking about and not some real object, we can never force experimental results that would have the interaction actually be a particle or a wave. In that sense the Heisenberg uncertainty principle could even be used to deduce some of the basic ratios and quantums of interaction between ether and field.

Comment author: Nick_Tarleton 09 April 2008 06:34:24PM 0 points [-]

The posts could be cross-posted to another (single-purpose) blog, and all objections or questions required to go on that blog, perhaps to be aggregated later and addressed on OB.

Comment author: anonymous28 09 April 2008 06:37:58PM -1 points [-]

A problem about teaching QM is the very fact of linear persepctive and absolute reality , when discussing there are no is , only appears to be , e prime

Comment author: ryan3 09 April 2008 06:42:09PM 1 point [-]

My gosh I can't spell or even edit. I apologize for my subpar grammer. in my defense, my mom is a child psychologist and she thinks I have a learning disability that prevented me from picking up how to spell when I was in elementry school. I like to think that's the case. Along with that, I've always felt that if the words would just be spelled the way they sound life would be a lot easier. Words used to be spelled the way they sound, then the "great vowel shift" happened and english language pronunciation lost all connection to spelling. I don't see why we don't redo the spelling of all our words to make them actually reflect the sounds. I mean, that's the idea of a phoneticl alphabet as I understand it. If the words aren't going to be spelled like they sound, aren't we really just using chinese/japanese symbol-based written languages?

Comment author: Silas 09 April 2008 07:16:14PM 5 points [-]

Anyone drawn a tree (specifically, an acyclic directed graph) showing all of Eliezer's posts with all the dependencies (and perhaps other information) indicated? That would be pretty neat. Does typepad offer that functionality?

Would anyone be interested in such a thing if I made it?

Comment author: Z._M._Davis 09 April 2008 07:34:30PM 0 points [-]

Silas, that would be really interesting.

Comment author: Eliezer_Yudkowsky 09 April 2008 07:37:37PM 5 points [-]

William Pearson said:

"Finally, I am going to take a strictly realist perspective on quantum mechanics - the quantum world is really out there, our equations describe the territory and not our maps of it,"

Why isn't this an example of the mind projection fallacy? I know you said to give you a break, but I really don't like it when people contradict themselves.

A Bayesian calculation describes your state of knowledge. When a physicist talks about nonprobabilistic laws that govern water flowing downhill, he is talking about the water, not describing how to update your probabilistic beliefs about water.

Beliefs, by default, are part of our map and about the territory.

If you want to talk explicitly about beliefs - or probabilities! - then you have to employ beliefs about beliefs, which are then part of your metamap and about your map.

If you want to talk about beliefs about beliefs, you have to use beliefs about beliefs about beliefs, which are then about beliefs about beliefs, etc.

When I talk about quantum mechanics, I am of course using words and stating my beliefs; but those words and beliefs refer directly to the territory, they are not about my or anyone else's knowledge.

There is nothing mind-projection-fallacious about saying, "This coin has landed heads", because the interpretation of your beliefs is as a statement directly about the coin and it talks only about the coin's state, even though what you have just said is your belief about the coin.

If you say "I believe the coin has landed heads," that is not your belief, it is your belief about your belief, which is about your belief in the same way that your order-1 belief is about the coin.

Saying, "This coin has a 50% probability of landing heads", rather than "I assign 50% probability to the coin landing heads", is technically (though rather nitpickingly) a mind projection fallacy; you are talking about your beliefs as if they were directly in the coin.

Comment author: mtraven 09 April 2008 07:53:09PM 4 points [-]

Not to steal Elezer's thunder, but people here would be interested in Gary Drescher's book Good and Real: Demystifying Paradoxes from Physics to Ethics, which treats quantum physics, the free-will illusion, Newcomb's Problem, and a number of other relevant areas, from a strictly materialist viewpoint (which I've tried to label, unsucessfully so far, as ultramaterialism).

Comment author: cyd 09 April 2008 08:16:19PM 0 points [-]

The problem is that no well-understood route exists from the classical world to the quantum world. No one has ever come up with a realistic quantum mechanical model of measurement (several toy models exist, and are actively studied). In the absence of such understanding, it's just a matter of splitting hairs to say either that we don't understand how quantum mechanics works, or that we don't understand how classical mechanics emerges.

This can be contrasted with the theory of relativity. Relativity violates our everyday picture of reality, but we pretty much completely understand how to recover (or derive) the classical limit. The theory doesn't give the impression of lurking secrets that quantum mechanics does.

Feynman's quote is still pretty much accurate.

Comment author: Eliezer_Yudkowsky 09 April 2008 08:42:50PM 4 points [-]

Just ordered Good and Real on Amazon.

Gary Drescher sounds like a major fellow traveler. Everett, timelessness, all the way down to Newcomb's Problem!

Comment author: Will_Pearson 09 April 2008 09:34:15PM 0 points [-]

Eliezer: It is not, "I believe the coin has landed heads," that I think, "the coin has landed heads," implicitly embodies. It is the belief that such things as coins, landing and heads, are meaningful concepts (clusters in thingspace if you have to).

If you want to continue the map analogy, parts of the key of the map.

""coin" is a meaningful concept," carries no information above, "the coin has landed heads," because you would hope that all statements are meaningful and so all their constituent concepts.

Comment author: The_Uncredible_Hallq 09 April 2008 09:54:05PM 0 points [-]

Cool, I've always wanted something like this on QM. Question on supplementary reading: any books that you think do an okay, if not great, job explaining it, out there already?

Comment author: Frank_Hirsch 09 April 2008 11:11:43PM 1 point [-]

Wow, good teaser for sure! /me is quivering with anticipation ^_^

Comment author: Davud_Tardif 10 April 2008 01:37:21AM -2 points [-]

I don't really like the author's attitude to be honest. He talks about QM like it is absolute truth, that we should accept it for realism and reject our preconceived perceptions. Then, at the end, he claims to be a "strict realist". It's almost like he's trying to make me feel like I am biased and boorish for trying to equate everything into simple and analagous terms, whereas I don't feel like that is a poor metric to work by.

Particle-wave duality is taught to try and convince students that not everything works in a classically sterile manner, and I believe that it is a good stepping stone toward the counterintuitive (yes, I said it, and I believe it) results that QM foretells. It is a simple case of explaining that things don't work out the way you think they do. The lesson of the particle-wave duality lesson, from a competent professor, is never "think of it as a particle and a wave," it is "we model it as a particle that acts like a wave," which should convey to the students that it is neither uniquely, and not to think in classical terms. I think this lesson is not only fine, but appropriate.

Comment author: Marcello 10 April 2008 01:48:53AM 1 point [-]

Silas, Z.M. Davis: As far as I know typepad doesn't do that. This particular use of typepad probably wasn't anticipated. That said, I can never resist a programming challenge, so here it is: http://stanford.edu/~marce110/elidex/

Comment author: Silas 10 April 2008 02:40:18AM 0 points [-]

Marcello: Nice job, but I was hoping for an overall visual view. Plus, don't forget, Eliezer would consider the "technical explanation" Bayes stuff to be general dependencies.

Comment author: Scott_Aaronson2 10 April 2008 03:13:23AM 1 point [-]

When I talk about quantum mechanics, I am of course using words and stating my beliefs; but those words and beliefs refer directly to the territory, they are not about my or anyone else's knowledge ... Saying, "This coin has a 50% probability of landing heads", rather than "I assign 50% probability to the coin landing heads", is technically (though rather nitpickingly) a mind projection fallacy; you are talking about your beliefs as if they were directly in the coin.

The fun part, of course, will be to see how you handle mixed states, where the "map" and the "territory" get scrambled together into a non-uniquely-decomposable linear-algebraic soup...

Comment author: Tom_McCabe2 10 April 2008 03:57:31AM 1 point [-]

"The fun part, of course, will be to see how you handle mixed states, where the "map" and the "territory" get scrambled together into a non-uniquely-decomposable linear-algebraic soup..."

I am not a professional quantum physicist, but the suggestion that our thoughts about a quantum process somehow influence the outcome of that process seems to me to be patently absurd. Our thoughts are not somehow separated from the rest of reality; they are made up of the same quarks and leptons that we study in QM experiments. At no point are these quarks and leptons aware of the higher levels of organization within the brain. If there *is* an interaction between you and the QM experiment, it will be on the level of -> , not -> .

Comment author: Tom_McCabe2 10 April 2008 04:02:43AM 1 point [-]

My apologies for the earlier formatting error. Basically, objects on one level of organization (fundamental particles) should only interact in any significant sense with objects on the same level, not with mental representations of fundamental particles or macroscopic blocks of matter. There *are* exceptions to this (eg, an errant lepton causes quantum physicists to jump for joy), but they require some sort of complex mechanism (in the Kolmogorov sense) to carry information into a different organizational level.

Comment author: Scott_Aaronson2 10 April 2008 04:50:53AM 1 point [-]

Tom: Yes, for as long as QM has been around people have tried to hitch doofus ideas about "mind influencing reality" to it -- and for those of us who spend a significant part of our lives fighting such idiocy, it'll be great to see Eliezer bring his considerable didactic skills to the fight.

I was talking about something completely different: namely, the philosophical debate about whether we should regard a quantum state as what's really out there (like a coin), or as our description of what's out there (like a probability distribution over coin flips). Neither view implies any ability to change the world just by wishing it, any more than you can bias a coin flip by just changing your probability estimate. But (unless I misread him) Eliezer was promising come down hard in favor of the former view, and I was pointing to mixed states as the battlefield where the two views really meet in an interesting way.

Comment author: Z._M._Davis 10 April 2008 05:21:47AM 0 points [-]

Neat, Marcello!

Comment author: Eliezer_Yudkowsky 10 April 2008 06:35:47AM 1 point [-]

Density matrices were specifically what I had in mind when I talked about dragging in great big complicated math tools before people understand what's going on at a fundamental level.

I didn't know mixed states were a battleground, but it's pretty easy to imagine. Confusion about the subjective Bayesian character of statistical mechanics + confusion about the objective character of quantum states = extreme confusion about mixed states, right?

Comment author: Ben_Toner 10 April 2008 07:25:37AM 1 point [-]

Hi Scott,

Are mixed states really the main battlefield? It seems to me that the subjective vs. objective debate for mixed states is not much different from the classical case, except it's much messier mathematically, just as Eliezer writes.

Rather, the interesting question for me (and, as I understand, the quantum Bayesian crowd) is whether pure quantum states should also be interpreted as states of knowledge.

Comment author: Jeremy 10 April 2008 07:42:26AM 0 points [-]

Having read very little about quantum mechanics I am unfamiliar with the non-realist view that you're contrasting yourself with, so please make sure to explain as you go along. I think this is a great idea!

Comment author: Scott_Aaronson2 10 April 2008 12:44:44PM 1 point [-]

Ben and Eliezer: Any reply puts me in great danger of violating the spirit of Eliezer's rule that non-realists hold their fire! (I say the spirit and not the letter, since I'm not actually a non-realist myself, just an equal-opportunity kibitzer.)

OK, quickly. Sure, an interesting question for subjectivists is how to deal with pure states, but an interesting question for realists is how to deal with mixed states! The issue is that you can't just say a density matrix ρ represents a statistical ensemble over "true states of the world" and be done with it, since then you have to make a completely arbitrary, physically-unmotivated choice for whether those true states lie in the {0,1} basis, the {+,-} basis, etc. In an interpretations of QM seminar at Berkeley, we spent pretty much the entire semester arguing about this and nothing else! Yes, it got tiresome, and no, I wasn't even suggesting that Eliezer bring in mixed states before people understood the fundamentals. I was just alluding to it as a key thing to get to eventually, that's all.

Comment author: Ben_Jones 10 April 2008 12:45:19PM 0 points [-]

Silas - seconded, that would be a very useful page indeed.

mtraven - sounds good. What's the rough level of maths required to get much out of Good and Real?

Comment author: RobinHanson 10 April 2008 01:00:21PM 0 points [-]

Scott, is there a paper somewhere that elaborates this argument from mixed-state ambiguity? To my mind, the fact that two different situations of uncertainty over true states lead to the same physical predictions isn't obviously a reason to reject that type of view regarding what is real.

Comment author: Scott_Aaronson2 10 April 2008 01:38:54PM 1 point [-]

Robin, a good place to start would be pretty much any paper Chris Fuchs has ever written. See for example this one (p. 9-12). As Chris points out, the argument from the non-uniqueness of mixed state decompositions basically goes back to Einstein (in a version involving two-particle entanglement). From a modern perspective, where Einstein went wrong was in his further inference that QM therefore has to be incomplete.

Comment author: Rolf_Nelson2 10 April 2008 01:42:41PM 2 points [-]

Robin: is there a paper somewhere that elaborates this argument from mixed-state ambiguity?

Scott should add his own recommendations, but I would say here is a good starting introduction.

To my mind, the fact that two different situations of uncertainty over true states lead to the same physical predictions isn't obviously a reason to reject that type of view regarding what is real.

The anti-MWI position here is that MWI produces different predictions depending on what basis is arbitrarily picked by the predictor; and that the various MWI efforts to "patch" this problem without postulating a new law of physics, are like squaring the circle. I think the anti-MWI'ers math is correct, but I'm not an expert enough to be 100% sure; what *really* makes me think MWI is wrong is the inability of the MWI'ers, after many decades, to produce an *algorithm* that you can "turn the crank" on to get the correct probabilities that we see in experiments; they have the tendency of trying to patch this "basis problem" by producing a new framework, which itself contains an arbitrary choice that's just as bad as the arbitrary choice of basis.

More succinctly, in vanilla MWI you have to pick the correct basis to get the correct experimental results, and you have to peek at the results to get the correct basis.

Comment author: Scott_Aaronson2 10 April 2008 01:57:51PM 0 points [-]

the fact that two different situations of uncertainty over true states lead to the same physical predictions isn't obviously a reason to reject that type of view regarding what is real.

Sorry, I meant to add: in Einstein's version, the problem is that which of the two "situations of uncertainty" is the right one to talk about could depend on what someone does to another quantum system light-years away. And therefore, nature is going to have to propagate updates about what's "really real" faster than the speed of light.

Comment author: RobinHanson 10 April 2008 02:50:45PM 0 points [-]

Scott, I can accept that reality talks to itself faster than light, though it is moderately troubling if we haven't found a covariant way to describe such a situation of real things we are uncertain about. Maybe reality isn't covariant?

Comment author: mtraven 10 April 2008 03:04:20PM 0 points [-]

Ben - Good and Real requires very little mathematics as I recall, maybe just the ability to do basic probability calculations.

Comment author: Scott_Aaronson2 10 April 2008 03:11:09PM 0 points [-]

though it is moderately troubling if we haven't found a covariant way to describe such a situation of real things we are uncertain about.

What's worse, Bell's Theorem implies that in some sense such a description can't exist.

Comment author: Ben_Toner 10 April 2008 04:00:28PM 0 points [-]

I can accept that reality talks to itself faster than light, though it is moderately troubling if we haven't found a covariant way to describe such a situation of real things we are uncertain about.

Robin, can you clarify the second half of this sentence? Are you troubled that there is no local realistic model for the predictions of quantum theory, or by something more subtle?

Comment author: Ben_Jones 11 April 2008 09:22:23AM 0 points [-]

mtraven, many thanks.

Comment author: [deleted] 10 September 2011 10:05:33AM *  0 points [-]

our equations describe the territory and not our maps of it

I would disagree on similar statements about pretty much any physical theory (or even, any theory at all). Our equations describe a model which approximates the real world to a good-enough degree in their scope of applicability, but is not the real world. (For example, standard QFT describes a world with a fixed background flat spacetime, and the real world isn't like that.)

Comment author: Konkvistador 06 February 2012 09:54:58AM 2 points [-]

I am not going to tell you: "You don't understand quantum mechanics, you just get used to it." (As von Neumann is reputed to have said; back in the dark decades when, in fact, no one did understand quantum mechanics.)

In 2009 I still heard professors say this at the start of such classes. :/

Comment author: lukeprog 08 April 2013 01:27:05AM 5 points [-]

Aaronson takes a similar approach to explaining quantum mechanics in chapter 9 of Quantum Computing Since Democritus (2013):

As a direct result of [the way quantum mechanics is usually taught in textbooks], the subject acquired an unnecessary reputation for being complicated and hard. Educated people memorized the slogans — "light is both a wave and a particle," "the cat is neither dead nor alive until you look," "you can ask about the position or the momentum, but not both," "one particular instantly learns the spin of the other through spooky action-at-a-distance," etc. But they also learned that they shouldn't even try to understand such things without years of painstaking work.

The second way to teach quantum mechanics eschews a blow-by-blow account of its discovery, and instead starts directly from the conceptual core...

Just for the heck of it, here's another passage from that chapter:

So what is quantum mechanics? ...In the usual "heirarchy of sciences" — with biology at the top, then chemistry, then physics, then math — quantum mechanics sits at a level between math and physics that I don't know a good name for. Basically, quantum mechanics is the operating system that other physical theories run on as application software (with the exception of general relativity, which hasn't yet been successfully ported to this particular OS). There's even a word for taking a physical theory and porting it to this OS: "to quantize."

But if quantum mechanics isn't physics in the usual sense — if it's not about matter, or energy, or waves, or particles — then what is it about? From my perspective, it's about information and probabilities and observables, and how they relate to each other.

My contention in this chapter is the following: Quantum mechanics is what you would inevitably come up with if you started from probability theory, and then said, let's try to generalize it so that the numbers we used to call "probabilities" can be negative numbers. As such, the theory could have been invented by mathematicians in the nineteenth century without any input from experiment. It wasn't, but it could have been.

And yet, with all the structures mathematicians studied, none of them came up with quantum mechanics until experiment forced it on them. And that's a perfect illustration of why experiments are relevant in the first place! More often than not, the only reason we need experiments is that we're not smart enough.

Comment author: paper-machine 08 April 2013 01:59:44AM 0 points [-]

Wow! Is the rest of the book that good? I've read some of Aaronson's lecture notes and blog (and largely approve of his interpretation of QM as probability with a 2-norm), but I didn't know he could write like this.

Comment author: jbay 08 April 2013 02:07:20AM 1 point [-]

I think it's been up for a long time on his website as a lecture series. http://www.scottaaronson.com/democritus/

I think he might be simplifying it a little bit. As I understand QM, it's more like probability with complex numbers, rather than with negative numbers.

Comment author: paper-machine 08 April 2013 02:11:34AM *  0 points [-]

I think he might be simplifying it a little bit. As I understand QM, it's more like probability with complex numbers, rather than with negative numbers.

Yes, he is. Must be for rhetorical purposes, because elsewhere he says exactly that.

Comment author: jbay 08 April 2013 02:56:11AM 0 points [-]

Ah, okay. It's been a while since I read it. I remember it being excellent though.

Comment author: lukeprog 08 April 2013 02:40:15AM 1 point [-]

The book is cleaned up and updated. There's a section at the beginning explaining all the new results that have come out since 2006, requiring updates to the lecture notes when he was turning them into a book.

Comment author: lukeprog 08 April 2013 02:38:13AM 0 points [-]

Yeah, I think the book will be a pretty great read for the most mathematically capable LWers. (Most of it is, alas, over my head.)

Comment author: Mollie 16 November 2014 02:09:03AM 0 points [-]

The link to an "Intuitive Explanation of Bayesian Reasoning" is broken. The new URL is here: http://yudkowsky.net/rational/bayes