Utilitarianism and Relativity Realism


Most peo­ple on less wrong seem to be some kind of he­do­nic con­se­quen­tial­ist. They think states with less suffer­ing and more joy are bet­ter. More­over, it is in­tu­itive that if you can cause some im­prove­ment in hu­man well-be­ing to be achieved then (other things be­ing equal) it is bet­ter to re­al­ize that im­prove­ment as soon as pos­si­ble. Also, most peo­ple on this site seem to be re­al­ists about spe­cial rel­a­tivity. That is they as­sume that any in­er­tial refer­ence frame is an equally valid point from which to de­scribe re­al­ity rather than be­liev­ing there is one true refer­ence which offers a preferred de­scrip­tion of re­al­ity. I will point out that these be­liefs (plus some in­nocu­ous as­sump­tions) lead quickly to para­dox.

Rel­a­tivity Realism

Be­fore I con­tinue I want to point out that em­piri­cal ob­ser­va­tions re­ally are ag­nos­tic about the ex­is­tence of a preferred refer­ence frame. In­deed, it’s a con­se­quence of the the­ory of rel­a­tivity it­self that it’s pre­dic­tions are equally well ex­plained by pos­tu­lat­ing a sin­gle true in­er­tial refer­ence frame and sim­ply us­ing the Lorentz con­trac­tion and time di­la­tion equa­tions to com­pute be­hav­ior for all mov­ing ob­jects. To see that this must be true not that if we take rel­a­tivity se­ri­ously the laws of physics must work cor­rectly in any refer­ence frame. In par­tic­u­lar, if we imag­ine des­ig­nat­ing one refer­ence frame to be the true refer­ence frame then, rel­a­tivity it­self, tells us that ap­ply­ing the laws of physics in that refer­ence frame has to give us the cor­rect re­sults.

In other words once we ac­cept Ein­stein’s equa­tions for length con­trac­tion and time di­la­tion with ve­loc­ity we can in­ter­pret those equa­tions as ei­ther un­der­min­ing the idea of a fixed ether against which ob­jects move (any refer­ence frame is equally valid) or that there re­ally is a fixed ether but ob­jects in mo­tion be­have in such a man­ner that we can’t em­piri­cally dis­t­in­guish what is at rest.

At first blush this sec­ond re­sult seems so jury rigged that surely the sim­pler as­sump­tion is that there is no preferred refer­ence frame. This re­lies on a false de­scrip­tion of the situ­a­tion. The ques­tion isn’t, “do we as­sign a low prior prob­a­bil­ity to the laws of physics con­spiring to hide the true rest frame from us?” Pre­sum­ably we do. The ques­tion should be, “given that the laws of physics do con­spire to make a spe­cial rest frame em­piri­cally in­dis­t­in­guish­able from any other in­er­tial frames what prob­a­bil­ity do we as­sign to such a frame ex­ist­ing?” After all it is a math­e­mat­i­cal truth that the time di­la­tion and length con­trac­tion do perfectly con­spire to pre­vent us from mea­sur­ing mo­tion rel­a­tive to some true rest frame (if it ex­isted) so in de­cid­ing whether to be­lieve in a preferred rest frame we aren’t de­cid­ing be­tween laws that would and wouldn’t hide such a frame from us. We are only de­cid­ing whether, given we have such laws, whether we think such an un­de­tectable true rest frame ex­ists.

To make it even more plau­si­ble that there is some true rest frame I will re­mark (but not ar­gue) that rel­a­tivity is a pretty gen­eral phe­nom­ena that can be de­rived from any model that con­serves mo­men­tum, where the forces obey the in­verse square law and all prop­a­gate at a con­stant speed rel­a­tive to some fixed back­ground, mat­ter is held to­gether in equil­ibrium states of these forces and time is im­plic­itly mea­sured via the rate it takes these forces to prop­a­gate. In other words if you have atoms held to­gether by EM forces and the time it takes phys­i­cal pro­cesses to hap­pen is gov­erned by the time it takes ei­ther forces or mat­ter to cross cer­tain dis­tances then rel­a­tivity comes for free. So it isn’t amaz­ing that we might have a true prefered refer­ence frame and yet it be im­pos­si­ble to ex­per­i­men­tally de­ter­mine that frame.

(As an aside this in­ter­pre­ta­tion of rel­a­tivity, fully con­sis­tent with all ob­serv­ables so far, makes for much bet­ter scifi since FTL travel doesn’t al­low any­one to go back in time).

A Para­dox Re­sult­ing From Rel­a­tivity Realism

Sup­pose we have two differ­ent brain im­plants that will be im­planted in two differ­ent con­scious but coma bound in­di­vi­d­u­als. After a de­lay of 10 min­utes af­ter im­plan­ta­tion the first de­vice de­liv­ers an in­stan­ta­neous burst of eu­pho­ria ev­ery sec­ond. The other de­liv­ers an in­stan­ta­neous burst of dis­com­fort ev­ery sec­ond. I as­sume we would all agree that (with suffi­cient ad­di­tional as­sump­tions) the world is a bet­ter place if we im­plant just a de­vice of the eu­pho­ria in­duc­ing kind and a worse place if we just im­plant a de­vice of the sec­ond kind. So as­sume the de­vices are ap­pro­pri­ately cal­ibrated so that the effect of im­plant­ing both is neu­tral (or very very nearly so). So far so good.

I think we can all agree that the world would be bet­ter off if we de­layed im­plant­ing the dis­com­fort­ing de­vice by 10 min­utes (or equiv­a­lently im­planted the plea­surable de­vice 10 min­utes ear­lier). If you dis­pute this con­clu­sion then you get ab­surd re­sults if you even ad­mit the pos­si­bil­ity of a uni­verse that ex­ists for­ever as in such a uni­verse it is no bet­ter to per­ma­nently in­crease hu­man welfare now than to de­lay that in­crease by 10 min­utes or 10 cen­turies.

Now as­sume that the two in­di­vi­d­u­als re­ceiv­ing the trans­plants are ac­tu­ally on space­ships mov­ing in op­po­site di­rec­tions at high rates of speed and the im­plan­ta­tion is done at the in­stant they pass by each other. For sim­plic­ity we as­sume ev­ery­one else dies at this in­stant (or add an ir­rele­vance of iden­ti­cal out­comes as­sump­tion and note that the two ships are mov­ing at the same ve­loc­ity rel­a­tive to ev­ery­one else).

From the refer­ence frame of the in­di­vi­d­ual who re­ceived the benefi­cial im­plant we can an­a­lyze the situ­a­tion as fol­lows. Without loss of gen­er­al­ity we can as­sume the ships are trav­el­ing at an ap­pro­pri­ate speed so that for ev­ery sec­ond that pases in our refer­ence frame only 12 a sec­ond passes on the other ship. Thus in this refer­ence frame the first ex­pe­rience of dis­com­fort is de­layed by 10 min­utes and then only oc­curs ev­ery other sec­ond. Now surely the world is no worse off be­cause the dis­com­fort oc­curs less fre­quently. But ig­nor­ing the fact that the dis­com­fort­ing de­vice fires less fre­quently this is ex­actly equiv­a­lent to im­plant­ing the de­sir­able de­vice 10 min­utes be­fore the un­de­sir­able one. Thus, since im­plant­ing both in the same refer­ence frame was neu­tral, it is ac­tu­ally fa­vor­able (bet­ter than not im­plant­ing them) to do so when the re­cip­i­ents are in fast mov­ing refer­ence frames mov­ing in op­po­site di­rec­tions. Note the same re­sult holds if we as­sume the de­vice only cre­ates dis­com­fort or eu­pho­ria a sin­gle time with the minor as­sump­tion that if two wor­lds only differ in events be­fore time t then what hap­pens af­ter time t is ir­rele­vant to which one is prefer­able.

How­ever, the same anal­y­sis done in the refer­ence frame of the un­pleas­ant im­plant gives the ex­act op­po­site con­clu­sion.

Avoid­ing the Paradox

Per­haps one might try and avoid the para­dox by in­sist­ing that no ex­pe­rience truly oc­curs in­stan­ta­neously. How­ever, this is eas­ily seen to be fu­tile.

As­sume that each de­vice in­flicts plea­sure or dis­com­fort for du­ra­tion ep­silon << 1 sec­ond. If you as­sume that the to­tal bad­ness of the un­com­fortable ex­pe­rience is some­how me­di­ated by changes in neu­ro­chem­istry or other phys­i­cal prop­er­ties you are lead to the as­sump­tion that even de­scribed from the refer­ence frame of the de­sir­able im­plant the ex­pe­rience of 2*ep­silon sec­onds of dis­com­fort by the time di­lated in­di­vi­d­ual is re­ally no worse than the ex­pe­rience of ep­silon sec­onds of dis­com­fort would be for some­one with that im­plant in your refer­ence frame. In other words when time is di­lated the ex­pe­rience of pain per unit time is diluted. This leads to the ex­act same re­sult as above.

On the other hand if we re­ally do in­crease the weight we give to pain ex­pe­rienced by those un­der­go­ing time di­la­tion an even sim­pler set of im­plants leads to para­dox. Th­ese im­plants start work­ing im­me­di­ately, one gen­er­at­ing a pleas­ant ex­pe­rience for 5 min­utes the other an un­pleas­ant ex­pe­rience for 5 min­utes again cal­ibrated so that in­stal­ling both is over­all neu­tral. Now by as­sump­tion from the refer­ence frame of the benefi­cial im­plant things are over­all worse (the longer du­ra­tion of dis­com­fort ex­pe­rienced by the other in­di­vi­d­ual is over­all worse than some­one in the same refer­ence frame get­ting the un­de­sir­able im­plant) and vice versa from the other refer­ence frame.

The use of in­stan­ta­neous ex­pe­riences was merely a way to sim­plify the ex­am­ple but ir­rele­vant to the un­der­ly­ing in­equal­ities. Those in­equal­ities are a re­sult of the im­plicit time dis­count­ing forced by the as­sump­tion that other things be­ing equal it is bet­ter for im­prove­ments to oc­cur now rather than later com­bined with the fact that re­al­ism about rel­a­tivity ren­ders facts about si­mul­tane­ity in­co­her­ent.

Per­son­ally, I think the only de­cent way of avoid­ing this para­dox is to deny re­al­ism about rel­a­tivity. Sure, it’s a rad­i­cal move. How­ever, it’s also a rad­i­cal move to say it’s not true that it’s bet­ter to cure can­cer now than in 10 cen­turies even if the hu­man race will con­tinue to ex­ist for­ever. In­deed, even if you don’t as­sume liter­ally in­finite du­ra­tion of effects even an un­bounded po­ten­tial length of effect with prob­a­bil­ities that de­crease suffi­ciently slowly is equally prob­le­matic.


I’ve de­liber­ately avoided phras­ing this dilemma in terms of a for­mal para­dox and list­ing the as­sump­tions nec­es­sary to gen­er­ate the para­dox. Partly this is laz­i­ness but it’s also a de­sire to see how peo­ple are in­clined to re­spond be­fore I at­tempt to draw up for­mal con­di­tions. After all I ul­ti­mately want to cap­ture com­mon views in the as­sump­tions and if I don’t know what peo­ple’s re­ac­tions are I can’t pick the right as­sump­tions.