# How accurate is the quantum physics sequence?

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 i is used for the mir­rors where −1 is cor­rect.

Physics Stack­Ex­change: What er­rors would one learn from Eliezer Yud­kowsky’s in­tro­duc­tion to quan­tum physics?

• 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”.

• de­spite what any­one, in­clud­ing EY, says.

I’m pretty sure I re­call that EY says (re­peat­edly) that the Born rule is not yet un­der­stood.

• the MWI ad­vo­cacy, which takes away from the QM se­quence’s usefulness

Well, ex­cept for the fact that the MWI ad­vo­cacy was pretty much the whole point of the se­quence!

• 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, which to me seem to be, by ne­ces­sity, in­cred­ibly complicated

• 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.

• Where can I get the se­quences in au­dio for­mat?

• Where can I get the se­quences in au­dio for­mat?

I recom­mend Tex­tAloud.

• the point that Oc­cam’s Ra­zor ap­plies to code not RAM (so to speak).

This is true only if you are us­ing some var­i­ant of a Kol­mogorov prior. Many ways of deal­ing with Pas­cal’s mug­ging try to use other pri­ors. More­over, this will be not true in gen­eral for any com­putable prior.

• Eliezer de­scribes the Born prob­a­bil­ities as a “se­ri­ous mys­tery” and an “open prob­lem”.

• 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

$i\\hbar \\; \\partial\_\{t\}|\\psi> = H|\\psi>$

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

$U = e^\{\-iHt/\\hbar\}$

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’.

• 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

I did (on the phys­i­cal use­ful­ness and non-mys­te­ri­ous­ness of com­plex num­bers, not quan­tum me­chan­ics speci­fi­cally).

• And thanks for that, but I’m in­ter­ested in their role in QM speci­fi­cally. I don’t have an ob­jec­tion to com­plex num­bers, I just want to know what they’re do­ing, if you see what I mean.

• 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.

• Data point: I only read part of the QM se­quence, but that wasn’t due to the ver­bosity as such, but rather be­cause I wasn’t fa­mil­iar with com­plex num­bers and it felt like too much work to learn to use a new math con­cept and then work my way through the calcu­la­tions.

• 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 = acbd + (ad + bc)i. That’s it—that’s all the com­plex maths you need to fol­low the QM se­quence.

• Alright, thanks.

• To bet­ter un­der­stand why it is used imag­ine a map, go­ing right is +, go­ing left is -, go­ing up is i, go­ing down is -i. Turn­ing left is mul­ti­ply­ing by i, turn­ing right is mul­ti­ply­ing by -i. So i is used to calcu­late things where you need 2 di­men­sions.

• Okay, thanks. I have only read the first few posts. On those, the karma score was higher and there was pos­i­tive feed­back from read­ers say­ing it was helpful to them. I should have read fur­ther in the se­ries be­fore char­ac­ter­iz­ing it as a whole.

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

Or else the au­di­ence is self-se­lect­ing so that the peo­ple who read it don’t find it too ver­bose...

• Good point, thanks. Konkvis­ta­dor in­di­cates it was too ver­bose for him/​her.

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

I’ve found them too ver­bose.

• Thanks for let­ting me know—John’s point about se­lec­tion effects is well taken.

It would have been bet­ter for me to say that be­cause many LessWrongers en­joyed the se­quence, it wasn’t too ver­bose for ev­ery­one, though clearly it was for some read­ers.

• He is prob­a­bly more like Isaac New­ton than you think. For in­stance, he seems to spend a lot of time “cor­rect­ing” mod­ern trans­la­tions of the Bible.

• Good­ness, that’s quite a few of Baez’s check­boxes ticked. Is there any chance he’s mak­ing fun?

• 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.

• Ron doesn’t seem to ap­pre­ci­ate that the au­di­ence of these posts isn’t in­ter­ested in what Ron wants them to learn (which is, the math­e­mat­ics of quan­tum me­chan­ics), and for this au­di­ence, tak­ing your time is not a prob­lem.

It seems like he has un­re­al­is­ti­cally high ex­pec­ta­tions of peo­ple...

• Yeah, Ron’s main com­plaint is that it pre­sents Eliezer’s philo­soph­i­cal view­point, not Ron’s. Of course Ron’s philo­soph­i­cal view­point is so right that, un­like Eliezer’s, it isn’t a philo­soph­i­cal view­point at all!

• 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.

• I think that he ba­si­cally nailed it.

EDIT: I sus­pect that what he means by pos­i­tivism is ac­tu­ally post­pos­i­tivism.

• 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.

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

Even then it’s not ob­vi­ous that it’s the best ex­pla­na­tion. Also de­pends on what you mean by ‘re­al­ist’.

• Ap­par­ently Solvent’s friend thinks oth­er­wise. My own physics-grad-stu­dent friend said MWI looks like the best ex­pla­na­tion, though he stressed our ig­no­rance more.

• Well, an­other ap­proach is to de­cide that prob­a­bil­ity dis­tri­bu­tions are merely a clas­si­cal ap­prox­i­ma­tion to den­sity ma­tri­ces.

• 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.

• It would be great if you could find a cite for the di­elec­tric mir­ror ob­ser­va­tion and com­ment in the Stack­Ex­change thread—thanks!

• Googling di­elec­tric mir­ror phase shows up sev­eral cita­tions for a pi phase shift (though I think those were all 100% re­flec­tance mir­rors). A good cita­tion for a pi/​2 phase shift seems to be here, though I haven’t ac­tu­ally dou­ble-checked it.

• 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?

http://​​less­wrong.com/​​lw/​​8p4/​​2011_sur­vey_re­sults/​​5e7e

• 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?

• Well, if you could say that in a way that isn’t also true for the naive prob­a­bil­ities that would be a good av­enue to pur­sue. Yes. A fair bit. Yes.

• 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.

• I sup­pose the main ig­no­rance I men­tioned would be about point 3 - dis­con­tin­u­ous, faster than light col­lapse is some­what of a straw hy­poth­e­sis when there’s gen­uine (though not su­per promis­ing) re­search be­ing done on con­tin­u­ous, light-speed col­lapse.

• Thanks!

• 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.

• Two days ago Scott Aaron­son have com­mented on this topic.

And, as usual for Scott, he nailed it, too

• Where is Scott’s com­ment?

• 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.

• I’ve been look­ing ev­ery­where to an an­swer to this ques­tion. Can some­one, any­one with deep knowl­edge of QM and who ac­cepts MWI please try to an­swer it?