Ontological uncertainty and diversifying our quantum portfolio

The word “on­tol­ogy” in the ti­tle refers to our con­cep­tion of the ba­sic build­ing block of re­al­ity. In quan­tum me­chan­ics the on­tol­ogy is the wave func­tion, in gen­eral rel­a­tivity it is space­time.

This idea in this post as­sumes the many-wor­lds in­ter­pre­ta­tion of quan­tum me­chan­ics is the cor­rect one. In this in­ter­pre­ta­tion there is an in­finity of uni­verses which be­gin as the same. When an event hap­pens it can go one way in some uni­verses (Schröd­inger’s cat dead) and an­other way in an­other (Schröd­inger’s cat al­ive). The num­ber of uni­verses stays con­stant, they just get di­ver­sified.

True ran­dom num­ber gen­er­a­tors are of­ten based on phys­i­cal phe­nom­ena which can be traced to quan­tum me­chan­ics, as op­posed to the more com­monly used pseu­do­ran­dom num­ber gen­er­a­tors. We can call such quan­tum-me­chan­i­cal ran­dom num­ber gen­er­a­tors QMRNGs for short. This kind of ran­dom gen­er­a­tor gen­er­ates differ­ent num­bers in differ­ent uni­verses while the agent us­ing the gen­er­a­tor is un­cer­tain about in which uni­verse he will end up.

Although it is not widely known, the laws of gen­eral rel­a­tivity ac­tu­ally al­low for time travel un­der some spe­cial cir­cum­stances. Time travel is widely con­sid­ered im­pos­si­ble since it leads to cer­tain para­doxes, such as the grand­father para­dox and is hence deemed log­i­cally in­con­sis­tent. Those para­doxes are re­solved if the time trav­eler trav­els not only in time, but also to an­other uni­verse, as David Deutsch ex­plains. In this setup a time ma­chine is built and the trav­eler en­ters it, some time passes, and when he opens the door and ex­its the ma­chine, he is in the past. Not only is he in the past, he is also in a par­allel uni­verse. When he kills “his own” grand­father in that par­allel uni­verse he is not re­ally kil­ling his own grand­father, but a par­allel-grand­father, a grand­father of par­allel-him.

The fun­da­men­tal laws of physics are not yet known since there is yet no phys­i­cal the­ory of ev­ery­thing. Hence, it is not known what are the ba­sic build­ing blocks of re­al­ity (we can call them sim­ply “on­tol­ogy”). In quan­tum me­chan­ics the on­tol­ogy it is the wave func­tion, in gen­eral rel­a­tivity the on­tol­ogy is space­time. What­ever the true laws of the uni­verse are, the Earth will still be round and sin­gle pho­tons will still in­terfere in the dou­ble-slit ex­per­i­ment. What­ever the true laws of physics are, they will prob­a­bly in­clude par­allel uni­verses. It is not so clear if they will al­low for travel be­tween those uni­verses. Even if they al­low, it is not clear will such travel be prac­ti­cally fea­si­ble as a mat­ter of en­g­ineer­ing the ac­tual ma­chines which al­low for such travel.

There are three ba­sic pos­si­bil­ities with re­gards to our on­tol­ogy and in­ter-uni­verse travel:

  1. There are no par­allel universes

  2. There are par­allel uni­verses but we can’t travel be­tween them

  3. There are par­allel uni­verses and we can travel be­tween them

  4. There are par­allel uni­verses and we can travel be­tween them but such travel is too expensive

Since we are in a state of on­tolog­i­cal un­cer­tainty, we can only as­sign prob­a­bil­ities to each sce­nario. A util­i­tar­ian who as­signs a non-zero prob­a­bil­ity to the pos­si­bil­ity num­ber 3 should think about the con­se­quences of us­ing QMRNGs since the use of them causes quan­tum di­ver­sifi­ca­tion.

Let’s say we have 10 uni­verses which are all iden­ti­cal, they all have you in them, you are tied to the tracks and a trol­ley is ap­proach­ing. You have two but­tons to press. But­ton A in all uni­verses has the same effect but you are not sure which the effect is, there is a 90% of it not do­ing any­thing and 10% of it stop­ping the trol­ley. But­ton B uses a QMRNG and it is cer­tain to stop the trol­ley in 1 uni­verse while let­ting it run you over in 9 uni­verses. The ran­dom­ness comes from the fact that you don’t know in which uni­verse you are go­ing to end up. From a mul­ti­verse-wide-per­spec­tive it op­er­ates de­ter­minis­ti­cally. To a util­i­tar­ian the to­tal ex­pected util­ity from press­ing any but­ton is the same. In case A, the ex­pected util­ity for each uni­verse is 0.1 lives saved, so for to­tal we get 10 * 0.1 = 1 life saved. In case B, the to­tal ex­pected util­ity is 1 * 1 + 0 * 9 = 1 life saved.

The ex­pected util­ity is the same, ex­cept… if in­ter-uni­verse travel is pos­si­ble and you are an ex­pert sur­geon which can save your copy’s life af­ter it has been run over. In that case you sur­vive in one uni­verse, en­ter a in­ter-uni­verse travel ma­chine, travel to a par­allel uni­verse, step out of the ma­chine and save the copy’s life. You do that one by one, for all 10 uni­verses, sav­ing ev­ery­one in the end. Tak­ing the sum of util­ity of all uni­verses for all times, the situ­a­tion when a QMRNG is used looks a lot differ­ent than when not used. When not used the ex­pected util­ity is 1 life saved. In the worst case, at one point in the fu­ture the util­ity be­comes zero and stays zero. On the other hand, when QMRNG is used, you can re­cover, so the long-term ex­pected util­ity of us­ing a QMRNG is ac­tu­ally 10 lives saved. This ap­plies to ex­is­ten­tial risk if we just sub­sti­tute “our copy” with “our en­tire species” and “re­vival” with “re­pop­u­la­tion”.

Let’s say that in the mo­ment you are push­ing the but­ton you don’t know if in­ter-uni­verse travel is pos­si­ble. There is a non-zero prob­a­bil­ity p of it be­ing pos­si­ble. As long as it does not cost you any­thing, the ex­pected util­ity of press­ing the but­ton B (which we can write as EU(B)) is always higher, since you always save at least one life and there is a prob­a­bil­ity p you save 9 more lives. The util­ity of ev­ery­one be­ing al­ive (writ­ten U(all), which is equal to 10) is higher than EU(A) which is equal to 1. EU(B) = (1 - p) * EU(A) + p * (U(all)) = (1 - p) + 10p = 1 + 9p. If there is a cost C, we just sub­tract it from the re­sult. In case C > 9p, it is bet­ter to press the but­ton A.

The mul­ti­verse nat­u­rally has a cer­tain de­gree of di­ver­sifi­ca­tion be­tween uni­verses. Events in some uni­verses go one way, in oth­ers go an­other way. It is not clear what is the ex­tent of this di­ver­sifi­ca­tion. When walk­ing through the city I may be un­sure should I go left or right. It could be the case that I go left in 1% of the uni­verses and right in 99% of them, or I go left in 5%, or any other per­cent, the closer the per­cent be­ing to 50% the higher the di­ver­sifi­ca­tion. It could also be the case that in 100% of situ­a­tions I go right, and only rarely is there a de­ci­sion I make differ­ently in differ­ent uni­verse, with most my de­ci­sions be­ing the same in all uni­verses. As we know from chaos the­ory there are sys­tems which are highly sen­si­tive to ini­tial con­di­tions, such as the weather, and they could in­tro­duce di­ver­sifi­ca­tion. In those cases, ini­tially the changes be­tween some uni­verses are small but they get am­plified with time. The effect of us­ing QMRNG could still be neg­ligible if:

  1. The chance of cheap tech­nolog­i­cally fea­si­ble in­ter-uni­verse travel is very small

  2. There is a high amount di­ver­sifi­ca­tion already

We can as­sume that in­ter-uni­verse travel would con­sume some re­sources and take some time, per­haps there would also be a con­straint that uni­verses you travel to need to be similar enough to your own. This would limit the speed of our travel through the con­figu­ra­tion space (the lin­ear space in which each uni­verse is a point) and also limit the range of such travel. Imag­ine a situ­a­tion where there is an as­tro­nom­i­cally high pro­por­tion of uni­verses in which homo sapi­ens went ex­tinct and only a small pro­por­tion in which it didn’t. It would be bet­ter to in­crease the pro­por­tion of sur­vivors, since the travel to ex­tinct uni­verses in that case would be faster. Also, in­creas­ing the num­ber of sur­vivor uni­verses means that sur­vivors will be spread out in con­figu­ra­tion space and as such they will be able to re­vive a larger area of con­figu­ra­tion space. Diver­sify­ing our quan­tum port­fo­lio through the us­age of quan­tum me­chan­i­cal ran­dom num­ber gen­er­a­tors re­duces ex­is­ten­tial risk.

The im­pli­ca­tions of QMRNGs are even greater for nega­tive util­i­ta­ti­ans. Aiming to re­duce suffer­ing, they are already wor­ried that space coloniza­tion will pro­duce more suffer­ing, and spread­ing through the mul­ti­verse mul­ti­plies their con­cerns. The im­pli­ca­tions are great for those con­cerned with ex­treme suffer­ing. There is such a thing as a worst uni­verse and a best uni­verse. In­creas­ing di­ver­sifi­ca­tion could po­ten­tially put some uni­verses in a state which would pre­vi­ously not be achieved, so we could cre­ate a new even more ter­rible worst uni­verse. This is coun­ter­acted by cre­at­ing an even more awe­some best uni­verse, but may still on net be nega­tive since bad is stronger than good.

The use of quan­tum-me­chan­i­cal ran­dom num­ber gen­er­a­tors in­creases the di­ver­sifi­ca­tion of par­allel uni­verses. Our on­tolog­i­cal un­cer­tainty gives a non-zero prob­a­bil­ity to the pos­si­bil­ity of in­ter-uni­verse travel. From these two premises, as illus­trated by the trav­el­ling sur­geon thought ex­per­i­ment, we can con­clude that us­ing quan­tum-me­chan­i­cal ran­dom num­ber gen­er­a­tors re­duces the prob­a­bil­ity of our species’ ex­tinc­tion.