MWI, copies and probability

Fol­lowup to: Poll: What value ex­tra copies?

For those of you who didn’t fol­low Eliezer’s Quan­tum Physics Se­quence, let me re­it­er­ate that there is some­thing very messed up about the uni­verse we live in. Speci­fi­cally, the Many Wor­lds In­ter­pre­ta­tion (MWI) of quan­tum me­chan­ics states that our en­tire clas­si­cal world gets copied some­thing like 1040±20 times per sec­ond1. You are not a line through time, but a branch­ing tree.

If you think care­fully about Descartes’ “I think there­fore I am” type skep­ti­cism, and ap­proach your stream of sen­sory ob­ser­va­tions from such a skep­ti­cal point of view, you should note that if you re­ally were just one branch-line in a per­son-tree, it would feel ex­actly the same as if you were a unique per­son-line through time, be­cause look­ing back­wards, a tree looks like a line, and your mem­ory can only look back­wards.

How­ever, the rules of quan­tum me­chan­ics mean that the in­te­gral of the mod­u­lus squared of the am­pli­tude den­sity, ∫|Ψ|2, is con­served in the copy­ing pro­cess. There­fore, the tree that is you has branches that get thin­ner (where thick­ness is ∫|Ψ|2 over the lo­cal­ized den­sity “blob” that rep­re­sents that branch) as they branch off. In fact they get thin­ner in such a way that if you gath­ered them to­gether into a bun­dle, the bun­dle would be as thick as the trunk it came from.

Now, since each copy­ing event cre­ates a slightly differ­ent clas­si­cal uni­verse, the copies in each of the sub-branches will each ex­pe­rience ran­dom events go­ing differ­ently. This means that over a timescale of decades, they will be to­tally “differ­ent” peo­ple, with differ­ent jobs, prob­a­bly differ­ent part­ners and will live in differ­ent places though they will (of course) have your DNA, ap­prox­i­mate phys­i­cal ap­pear­ance, and an iden­ti­cal his­tory up un­til the time they branched off. For timescales on the or­der of a day, I sus­pect that al­most all of the copies will be vir­tu­ally iden­ti­cal to you, even down to go­ing to bed at the same time, hav­ing ex­actly the same sched­ule that day, think­ing al­most all of the same thoughts etc.

MWI mixes copies and probability

When a “ran­dom” event hap­pens, ei­ther the event was pseu­do­ran­dom (like a large digit of pi) or it was a copy event, mean­ing that both (or all) out­comes were re­al­ized el­se­where in the wave­func­tion. This means that in many situ­a­tions, when you say “there is a prob­a­bil­ity p of event X hap­pen­ing”, what this re­ally means is “pro­por­tion p of my copy-chil­dren will ex­pe­rience X”.

LW doesn’t care about copies

In Poll: What value ex­tra copies?, I asked what value peo­ple placed upon non-in­ter­act­ing ex­tra copies of them­selves, ask­ing both about lock-step iden­ti­cal and statis­ti­cally iden­ti­cal copies. The over­whelming opinion was that nei­ther were of much value. For ex­am­ple, Sly com­ments:2

“I would place 0 value on a copy that does not in­ter­act with me. This might be odd, but a copy of me that is non-in­ter­act­ing is in­dis­t­in­guish­able from a copy of some­one else that is non-in­ter­act­ing. Why does it mat­ter that it is a copy of me?”

How to get away with at­tempted mur­der

Sup­pose you throw a grenade with a quan­tum deto­na­tor at Sly. The deto­na­tor will sam­ple a qbit in an even su­per­po­si­tion of states 1 and 0. On a 0 it ex­plodes, in­stantly va­por­iz­ing sly (it’s a very pow­er­ful grenade). On a 1, it de­fuses the grenade and dis­penses a $100 dol­lar note. Sup­pose that you throw it and ob­serve that it doesn’t ex­plode:

(A) does Sly charge you with at­tempted mur­der, or does he thank you for giv­ing him $100 in ex­change for some­thing that had no value to him any­way?

(B) if he thanks you for the free $100, does he ask for an­other one of those nice free hun­dred dol­lar note dis­pensers? (This is the “quan­tum suicide” option

(C) if he says “the one you’ve already given me was great, but no more please”, then pre­sum­ably if you throw an­other one against his will, he will thank you for the free $100 again. And so on ad in­fini­tum. Sly is tem­po­rally in­con­sis­tent if this op­tion is cho­sen.

The punch line is that the physics we run on gives us a very strong rea­son to care about the welfare of copies of our­selves, which is (ac­cord­ing to my sur­vey) a counter-in­tu­itive re­sult.

EDIT: Quite a few peo­ple are bit­ing the quan­tum suicide bul­let. I think I’ll have to talk about that next. Also, Wei Dai sum­ma­rizes:

Another way to think about this is that many of us seem to share the fol­low three in­tu­itions about non-in­ter­act­ing ex­tra copies, out of which we have to give up at least one to re­tain log­i­cal con­sis­tency:

  1. We value ex­tra copies in other quan­tum branches.

  2. We don’t value ex­tra copies that are just spa­tially sep­a­rated from us (and are not too far away).

  3. We ought to value both kinds of copies the same way.

  • Giv­ing up 1 is the po­si­tion of “quan­tum im­mor­tal­ity”.

  • Giv­ing up 2 seems to be Roko’s po­si­tion in this post.

  • Giv­ing up 3 would im­ply that our val­ues are rather ar­bi­trary: there seems to be no morally rele­vant differ­ences be­tween these two kinds of copies, so why should we value one and not the other? But ac­cord­ing to the “com­plex­ity of value” po­si­tion, per­haps this isn’t re­ally a big prob­lem.

I might add a fourth op­tion that many peo­ple in the com­ments seem to be go­ing af­ter: (4) We don’t in­trin­si­cally value copies in other branches, we just have a sub­jec­tive an­ti­ci­pa­tion of be­com­ing them.

1: The copy­ing events are not dis­crete, rather they con­sist of a con­tin­u­ous de­for­ma­tion of prob­a­bil­ity am­pli­tude in state space, but the shape of that de­for­ma­tion looks a lot like a con­tin­u­ous ap­prox­i­ma­tion to a dis­crete copy­ing event, and the clas­si­cal rules of physics ap­prox­i­mately gov­ern the time evolu­tion of the “copies” as if they were com­pletely in­de­pen­dent. This last state­ment is the phe­nomenon of de­co­her­ence. The un­cer­tainty in the copy­ing rate is due to my ig­no­rance, and I would wel­come a physi­cist cor­rect­ing me.

2: There were many oth­ers who ex­pressed roughly similar views, and I don’t hold it as a “black mark” to pick the op­tion that I am ad­vis­ing against, rather I en­courage peo­ple to hon­estly put for­ward their opinions in a spirit of com­mu­nal learn­ing.