Why Many-Worlds Is Not The Rationally Favored Interpretation

Eliezer re­cently posted an es­say on “the fal­lacy of priv­ileg­ing the hy­poth­e­sis”. What it’s re­ally about is the fal­lacy of priv­ileg­ing an ar­bi­trary hy­poth­e­sis. In the fic­tional ex­am­ple, a de­tec­tive pro­poses that the in­ves­ti­ga­tion of an un­solved mur­der should be­gin by in­ves­ti­gat­ing whether a par­tic­u­lar, ran­domly cho­sen cit­i­zen was in fact the mur­derer. Towards the end, this is likened to the pre­sump­tion that one par­tic­u­lar re­li­gion, rather than any of the other ex­ist­ing or even merely pos­si­ble re­li­gions, is es­pe­cially worth in­ves­ti­gat­ing.

How­ever, in be­tween the fic­tional and the su­per­nat­u­ral illus­tra­tions of the fal­lacy, we have some­thing more em­piri­cal: quan­tum me­chan­ics. Eliezer writes, as he has pre­vi­ously, that the many-wor­lds in­ter­pre­ta­tion is the one—the ra­tio­nally fa­vored in­ter­pre­ta­tion, the pic­ture of re­al­ity which ra­tio­nally should be adopted given the em­piri­cal suc­cess of quan­tum the­ory. Eliezer has said this be­fore, and I have ar­gued against it be­fore, back when this site was just part of a blog. This site is about ra­tio­nal­ity, not physics; and the quan­tum case is not es­sen­tial to the ex­po­si­tion of this fal­lacy. But given the reg­u­lar­ity with which many-wor­lds meta­physics shows up in dis­cus­sion here, per­haps it is worth pre­sent­ing a case for the op­po­si­tion.

We can do this the easy way, or the hard way. The easy way is to ar­gue that many-wor­lds is merely not fa­vored, be­cause we are nowhere near be­ing able to lo­cate our hy­pothe­ses in a way which per­mits a clean-cut judg­ment about their rel­a­tive mer­its. The available hy­pothe­ses about the re­al­ity be­neath quan­tum ap­pear­ances are one and all un­finished mud­dles, and we should let their ad­vo­cates get on with turn­ing them into ex­act hy­pothe­ses with­out pick­ing fa­vorites first. (That is, if their ad­vo­cates can be both­ered turn­ing them into ex­act hy­pothe­ses.)

The hard way is to ar­gue that many-wor­lds is ac­tu­ally dis­fa­vored—that we can already say it is un­likely to be true. But let’s take the easy path first, and see how things stand at the end.

The two ex­am­ples of fa­vor­ing an ar­bi­trary hy­poth­e­sis with which we have been pro­vided—the mur­der in­ves­ti­ga­tion, the ri­valry of re­li­gions—both pre­sent a situ­a­tion in which the ob­vi­ous hy­pothe­ses are ho­mo­ge­neous. They all have the form “Ci­ti­zen X did it” or “De­ity Y did it”. It is easy to see that for par­tic­u­lar val­ues of X and Y, one is mak­ing an ar­bi­trary se­lec­tion from a large set of pos­si­bil­ities. This is not the case in quan­tum foun­da­tions. The well-known in­ter­pre­ta­tions are ex­tremely het­ero­ge­neous. There has not been much of an effort made to ex­press them in a com­mon frame­work—some­thing nec­es­sary if we want to ap­ply Oc­cam’s ra­zor in the form of the­o­ret­i­cal com­plex­ity—nor has there been much of an at­tempt to dis­cern the full “space” of pos­si­ble the­o­ries from which they have been drawn—some­thing nec­es­sary if we re­ally do wish to avoid priv­ileg­ing the hy­pothe­ses we hap­pen to have. Part of the rea­son is, again, that many of the known op­tions are some­what un­der­de­vel­oped as ex­act the­o­ries. They sub­sist partly on rhetoric and hand­wav­ing; they are math­e­mat­i­cal va­por­ware. And it’s hard to bench­mark va­por­ware.

In his lat­est ar­ti­cle, Eliezer pre­sents the fol­low­ing ar­gu­ment:

″… there [is] no con­crete ev­i­dence what­so­ever that fa­vors a col­lapse pos­tu­late or sin­gle-world quan­tum me­chan­ics. But, said Scott, we might en­counter fu­ture ev­i­dence in fa­vor of sin­gle-world quan­tum me­chan­ics, and many-wor­lds still has the open ques­tion of the Born prob­a­bil­ities… There must be a trillion bet­ter ways to an­swer the Born ques­tion with­out adding a col­lapse pos­tu­late...”

The ba­sic wrong as­sump­tion be­ing made is that quan­tum su­per­po­si­tion by de­fault equals mul­ti­plic­ity—that be­cause the wave­func­tion in the dou­ble-slit ex­per­i­ment has two branches, one for each slit, there must be two of some­thing there—and that a sin­gle-world in­ter­pre­ta­tion has to add an ex­tra pos­tu­late to this pic­ture, such as a col­lapse pro­cess which re­moves one branch. But su­per­po­si­tion-as-mul­ti­plic­ity re­ally is just an­other hy­poth­e­sis. When you use or­di­nary prob­a­bil­ities, you are not ra­tio­nally obli­gated to be­lieve that ev­ery out­come ex­ists some­where; and an elec­tron wave­func­tion re­ally may be de­scribing a sin­gle ob­ject in a sin­gle state, rather than a mul­ti­plic­ity of them.

A quan­tum am­pli­tude, be­ing a com­plex num­ber, is not an or­di­nary prob­a­bil­ity; it is, in­stead, a mys­te­ri­ous quan­tity from which us­able prob­a­bil­ities are de­rived. Many-wor­lds says, “Let’s view these am­pli­tudes as re­al­ities, and try to de­rive the prob­a­bil­ities from them.” But you can go the other way, and say, “Let’s view these am­pli­tudes as de­rived from the prob­a­bil­ities of a more fun­da­men­tal the­ory.” Math­e­mat­i­cal re­sults like Bell’s the­o­rem show that this will re­quire a lit­tle imag­i­na­tion—you won’t be able to de­rive quan­tum me­chan­ics as an ap­prox­i­ma­tion to a 19th-cen­tury type of physics. But we have the imag­i­na­tion; we just need to use it in a dis­ci­plined way.

So that’s the ker­nel of the ar­gu­ment that many wor­lds is not fa­vored: the hy­pothe­ses un­der con­sid­er­a­tion are still too much of a mess to even be com­men­su­rable, and the in­for­mal ar­gu­ment for many wor­lds, quoted above, sim­ply pre­sup­poses a mul­ti­plic­ity in­ter­pre­ta­tion of quan­tum su­per­po­si­tion. How about the ar­gu­ment that many wor­lds is ac­tu­ally dis­fa­vored? That would be­come a gen­uinely tech­ni­cal dis­cus­sion, and when pressed, I would ul­ti­mately not in­sist upon it. We don’t know enough about the the­ory-space yet. Sin­gle-world think­ing looks more fruit­ful to me, when it comes to sub-quan­tum the­ory-build­ing, but there are ver­sions of many-wor­lds which I do oc­ca­sion­ally like to think about. So the ver­dict for now has to be: not proven; and mean­while, let a hun­dred schools of thought con­tend.