Have We Been Interpreting Quantum Mechanics Wrong This Whole Time?

Link post

• Is it wrong that I’m hop­ing that I click on this link and it just goes to a web site with word ‘No’, in huge let­ters?

• As a good heuris­tic, any time the head­line ends with the ques­tion mark, in 90+% of the cases the an­swer is “No”.

• Sup­pose there’s some idea, X, which you think might help to solve a prob­lem, Y. And there’s also a dumb ver­sion of X, X’, which you know doesn’t work, but which still has en­thu­si­asts.

And then one day there’s a head­line: CAN IDEA X SOLVE PROBLEM Y? Only you find out that it’s ac­tu­ally X’, the dumb ver­sion of X, that is be­ing pre­sented to the world as X… and noth­ing is done to con­vey the differ­ence be­tween X’ and the ver­sion of X that ac­tu­ally war­rants at­ten­tion.

That is, more or less, the situ­a­tion I find my­self in, with re­spect to this ar­ti­cle. I wish there were some snap­pier way to con­vey the situ­a­tion, with­out talk­ing about X and X’ and so on, but I haven’t found a way to do it.

Prob­lem Y is: ex­plain why quan­tum me­chan­ics works, with­out say­ing that things don’t have prop­er­ties un­til they are mea­sured, and so on.

Idea X is, these days, usu­ally called Bohmian me­chan­ics. To the Schrod­inger equa­tion, which de­scribes the time evolu­tion of the wave­func­tion of quan­tum me­chan­ics, it adds a clas­si­cal equa­tion of mo­tion for the par­ti­cles, fields, etc. The par­ti­cles, fields, etc., evolve on a tra­jec­tory in state space which fol­lows the prob­a­bil­ity cur­rent in state space, as defined by the Schrod­inger equa­tion.

The origi­nal ver­sion of this idea is due to de Broglie, who pro­posed that par­ti­cles are guided by waves. This was called pi­lot-wave the­ory, be­cause the wave “pi­lots” the par­ti­cle.

Pilot-wave the­ory was pro­posed in the very early days of quan­tum the­ory, be­fore the sig­nifi­cance of en­tan­gle­ment was prop­erly ap­pre­ci­ated. The sig­nifi­cance of en­tan­gle­ment is that you don’t have one wave­func­tion per par­ti­cle, you just have one big wave­func­tion which pro­vides prob­a­bil­ities for joint con­figu­ra­tions of par­ti­cles.

A pi­lot-wave the­ory for many par­ti­cles, in the form that de Broglie origi­nally pro­posed—one wave per par­ti­cle—con­tains no en­tan­gle­ment, and can’t re­pro­duce the multi-par­ti­cle pre­dic­tions of quan­tum me­chan­ics, as Bell’s the­o­rem and many other the­o­rems show. Bohmian me­chan­ics can re­pro­duce those pre­dic­tions, be­cause in Bohmian me­chan­ics, the wave­func­tion that does the pi­lot­ing is the sin­gle, en­tan­gled, multi-par­ti­cle wave used in ac­tual quan­tum me­chan­ics.

All this is ut­terly ba­sic knowl­edge for the peo­ple who work on Bohmian me­chan­ics to­day. But mean­while, ap­par­ently a group of peo­ple who work on fluid dy­nam­ics, have re­dis­cov­ered de Broglie’s origi­nal idea—“wave guid­ing a par­ti­cle”—and are now pro­mot­ing it as a pos­si­ble ex­pla­na­tion of quan­tum me­chan­ics. They don’t seem to care about the the­o­rems prov­ing that you can’t get Bell-type cor­re­la­tions with­out us­ing en­tan­gled waves.

So ba­si­cally, this ar­ti­cle de­scribes the sec­ond-rate re­searchers in this field—in this case, peo­ple who are do­ing the equiv­a­lent of try­ing to force the square peg into the round hole—as if they are the in­tel­lec­tual lead­ers who define it!

• “The ex­per­i­ments in­volve an oil droplet that bounces along the sur­face of a liquid. The droplet gen­tly sloshes the liquid with ev­ery bounce. At the same time, rip­ples from past bounces af­fect its course. The droplet’s in­ter­ac­tion with its own rip­ples, which form what’s known as a pi­lot wave, causes it to ex­hibit be­hav­iors pre­vi­ously thought to be pe­cu­liar to el­e­men­tary par­ti­cles — in­clud­ing be­hav­iors seen as ev­i­dence that these par­ti­cles are spread through space like waves, with­out any spe­cific lo­ca­tion, un­til they are mea­sured.

Par­ti­cles at the quan­tum scale seem to do things that hu­man-scale ob­jects do not do. They can tun­nel through bar­ri­ers, spon­ta­neously arise or an­nihilate, and oc­cupy dis­crete en­ergy lev­els. This new body of re­search re­veals that oil droplets, when guided by pi­lot waves, also ex­hibit these quan­tum-like fea­tures.”

• So, does the bounc­ing oil droplet also tun­nel through bar­ri­ers, spon­ta­neously arise or an­nihilate, and oc­cupy dis­crete en­ergy lev­els?

Be­cause to me this seems like merely an anal­ogy that works in some as­pects, but fails in other as­pects.

• Per the ar­ti­cle:

Dro­plets can also seem to “tun­nel” through bar­ri­ers, or­bit each other in sta­ble “bound states,” and ex­hibit prop­er­ties analo­gous to quan­tum spin and elec­tro­mag­netic at­trac­tion. When con­fined to cir­cu­lar ar­eas called cor­rals, they form con­cen­tric rings analo­gous to the stand­ing waves gen­er­ated by elec­trons in quan­tum cor­rals.

and

Like an elec­tron oc­cu­py­ing fixed en­ergy lev­els around a nu­cleus, the bounc­ing droplet adopted a dis­crete set of sta­ble or­bits around the mag­net, each char­ac­ter­ized by a set en­ergy level and an­gu­lar mo­men­tum.

• Yes and yes and yes (those are all ex­am­ples men­tioned in the ar­ti­cle). If you have a spe­cific ex­am­ple of a quan­tum phe­nomenon that pi­lot wave the­ory doesn’t ex­hibit, I’d like to know. Pilot wave ad­vo­cates claim that pi­lot wave the­ory re­sults in the same pre­dic­tions, al­though I haven’t had time to chase down sources or work this out for my­self.

• My knowl­edge of it is pretty su­perfi­cial, but I’m pretty con­fused about how it rep­re­sents states with a su­per­po­si­tion of par­ti­cle num­bers. For fixed num­ber of (non rel­a­tivis­tic) par­ti­cles you can always just put the in­ter­est­ing me­chan­ics (in­clud­ing spin, elec­tro­mag­netic charge, etc!) in the wave­func­tion and then add an epiphe­nom­e­nal on­tolog­i­cally-fun­da­men­tal-par­ti­cle like a cherry on top. We’ll, epiphe­nom­e­nal in the Von Neu­mann mea­sure­ment paradigm, pre­sum­ably ad­vo­cates think it plays some role in mea­sure­ment, but I’m still a bit vague on that.

Any­how, for mix­tures of par­ti­cle num­bers, I gen­uinely don’t know how a Bohmian is sup­posed to get any­thing in­tu­itive or pseudo-clas­si­cal.

• Note that the the­ory seems to have been around since the 1930′s, but these ex­per­i­ments are new (2016).

• Isn’t this a fun­da­men­tal log­i­cal er­ror? They’re try­ing to show that the Bohmian in­ter­pre­ta­tion is cor­rect by con­struct­ing a clas­si­cal model that ex­hibit quan­tum be­hav­ior, but we already know that Bohmian in­ter­pre­ta­tion, since it’s an in­ter­pre­ta­tion, already has all the fea­ture of quan­tum me­chan­ics.

• Ah, pi­lot wave the­ory. It gets around the “no lo­cal re­al­ism” the­o­rem by us­ing non-lo­cal hid­den vari­ables...

• Does it use any­thing non-lo­cal? The ex­per­i­ments in the ar­ti­cle use macro­scopic fluids, which pre­sum­ably don’t have non-lo­cal effects.

• Bah! Who needs lo­cal­ity?
What I need are elec­trons. Bohm doesn’t be­lieve in elec­trons.