# Is backwards causation necessarily absurd?

In New­comb’s prob­lem an agent picks ei­ther one-box or two-box and finds that no mat­ter which op­tion they picked, a pre­dic­tor pre­dicted them in ad­vance. I’ve gone to a lot of effort to ex­plain how this can be with­out re­quiring back­wards cau­sa­tion (The Pre­dic­tion Prob­lem, De­con­fus­ing Log­i­cal Coun­ter­fac­tu­als), yet now I find my­self won­der­ing if back­wards cau­sa­tion is such a bad ex­pla­na­tion af­ter all.

Un­for­tu­nately I’m not a physi­cist, so take what I say with a grain of salt, but there seems to be a rea­son­able ar­gu­ment that ei­ther time or its di­rec­tion is an illu­sion. One promi­nent the­ory of time is Eter­nal­ism in which there is no ob­jec­tive flow of time and terms like “past”, “pre­sent” and “fu­ture” can only be used in a rel­a­tive sense. An ar­gu­ment in favour of this is that it is of­ten very con­ve­nient in physics to model space-time as a 4-di­men­sional space. If time is just an­other di­men­sion, why should the fu­ture be treated differ­ently than the past? Noth­ing in this model differ­en­ti­ates the two. If we have two blocks X and Y next to each other, we can view ei­ther X as the left one or Y as the left one de­pend­ing on the di­rec­tion we look at it from. Similarly, if A causes B in the tra­di­tional for­wards sense, why can’t we sym­met­ri­cally view B as back­wards caus­ing A, where again if we viewed it an­other way A to B would be back­wards cau­sa­tion and B to A would be for­wards cau­sa­tion.

Another rel­a­tivis­tic ar­gu­ment against time flow­ing is that si­mul­tane­ity is only defined rel­a­tive to a refer­ence frame. There­fore, there is no unified pre­sent which is sup­posed to be what is flow­ing.

Thirdly, en­tropy has of­ten been the ar­row of time with other phys­i­cal laws claimed to be re­versible. We are in a low-en­tropy world so en­tropy in­creases. How­ever, if we were in a high-en­tropy world, it would de­crease, so time and cau­sa­tion would seem to be go­ing back­wards (from our per­spec­tive). This would seem to sug­gest that back­wards cau­sa­tion is just as valid a phe­nomenon as back­ward cau­sa­tion.

I want to re­mind read­ers again that I am not a physi­cist. This post is more in­tended to spark dis­cus­sion that any­thing else.

(Another pos­si­bil­ity I haven’t dis­cussed is that cau­sa­tion might be in the map rather than the ter­ri­tory)

• cau­sa­tion might be in the map rather than the territory

Of course it is. There is no atom of cau­sa­tion any­where. It’s a tool for em­bed­ded agents to con­struct use­ful mod­els in an in­ter­nally par­tially pre­dictable uni­verse.

“Back­ward cau­sa­tion” may or may not be a use­ful model at times, but it is cer­tainly noth­ing but a model.

As a trained (though not prac­tic­ing) physi­cist, I can see that you are mak­ing a large cat­e­gory er­ror here. Rel­a­tivity nei­ther adds to not sub­tracts from the cau­sa­tion mod­els. In a de­ter­minis­tic New­to­nian uni­verse you can imag­ine back­ward cau­sa­tion as a use­ful tool. Sadly, its use­ful­ness it rather limited. For ex­am­ple, the diffu­sion/​heat equa­tion is not well posed when run back­wards, it blows up af­ter a finite in­te­gra­tion time. An in­tu­itive way to see that is that you can­not re­con­struct the shape of a glass of wa­ter from the pud­dle you see on the ground some time af­ter it was spilled. But in cases where the rele­vant PDEs are well posed in both time di­rec­tions, back­ward causal­ity is equiv­a­lent to for­ward causal­ity, if not com­pu­ta­tion­ally, then at least in prin­ci­ple.

All that spe­cial rel­a­tivity gives you is that the ab­solute tem­po­ral or­der of events is only defined when they are within a light­cone, not out­side of it. Gen­eral rel­a­tivity gives you both less and more. On the one hand, the Hilbert ac­tion is for­mu­lated with­out refer­ring to time evolu­tion at all and poses no re­stric­tion on the type of mat­ter sources, be they pos­i­tive or nega­tive den­sity, sub­lu­mi­nal or su­per­lu­mi­nal, finite or singlu­lar. On the other hand, to calcu­late most in­ter­est­ing things, one needs to solve the ini­tial value prob­lem, and that one poses var­i­ous re­stric­tions on what topolo­gies and mat­ter sources one can start with. On the third hand, there is a lot of free­dom to define what con­sti­tutes “now”, as many differ­ent space­time fo­li­a­tions are on equal foot­ing.

If you add quan­tum me­chan­ics to the mix, the Born rule, needed to calcu­late any­thing use­ful re­gard­less of one’s fa­vorite in­ter­pre­ta­tion, breaks lin­ear­ity and uni­tar­ity at the mo­ment of in­ter­ac­tion (loosely speak­ing) and is not time-re­ver­sal in­var­i­ant.

The en­tropic ar­gu­ment is also with­out merit: there is no rea­son to be­lieve that en­tropy would de­crease in a “high-en­tropy world”, what­ever that might mean. We do not even know how ob­server-in­de­pen­dent en­tropy is (Jaynes ar­gued that ap­par­ent en­tropy de­pends on the ob­server’s knowl­edge of the world).

Ba­si­cally, you are con­fus­ing map and ter­ri­tory. If back­ward causal­ity helps you make more ac­cu­rate maps, go wild, just don’t claim that you are do­ing any­thing other than con­struct­ing mod­els.

• I think we can go a bit farther in pre­dict­ing that back­wards cau­sa­tion will be a use­ful con­cept in some very spe­cific cases, which will break down far above the scale of the nor­mal sec­ond law.

We “see” back­wards cau­sa­tion when we know the out­come but not how the sys­tem will get there. What does this be­hav­ior sound like a hal­l­mark of? Op­ti­miza­tion pro­cesses! We can pre­dict in ad­vance that back­wards cau­sa­tion will be a use­ful idea to talk about the be­hav­ior of some op­ti­miza­tion pro­cesses, but that it will stop con­tribut­ing use­ful in­for­ma­tion when we want to zoom in past the “in­ten­tional stance” level of de­scrip­tion.

• Another rel­a­tivis­tic ar­gu­ment against time flow­ing is that si­mul­tane­ity is only defined rel­a­tive to a refer­ence frame. There­fore, there is no unified pre­sent which is sup­posed to be what is flow­ing.

Rel­a­tivity does not make the ar­row of time rel­a­tive to ob­server. Events in one’s fu­ture light cone re­main in their fu­ture light cone also from a per­spec­tive of some­one else.

• “Rel­a­tivity does not make the ar­row of time rel­a­tive to ob­server”—I didn’t say that. I said there was no unified no­tion of the present

• Yes, but the di­rec­tion of causal­ity is very much pre­served. The no­tion of pre­sent is not nec­es­sary in a di­rected acyclic graph.

• I don’t think back­wards cau­sa­tion is ab­surd, more or less for the rea­sons you sketch. Another minor rea­son: Some philoso­phers like “effec­tive strat­egy” ac­counts of cau­sa­tion, ac­cord­ing to which we define cau­sa­tion via its use­ful­ness for agents try­ing to achieve goals. On these ac­counts, back­wards cau­sa­tion is pretty triv­ial—just sup­pose you live in a de­ter­minis­tic uni­verse and your goal is to “make the state of the uni­verse at the Big Bang such that I eat break­fast to­mor­row.” The philoso­pher Gary Drescher ar­gues some­thing similar in Good and Real if I re­call cor­rectly.

That said, I don’t think we are re­ally ex­plain­ing or de-con­fus­ing any­thing if we ap­peal to back­wards cau­sa­tion to un­der­stand New­comb’s Prob­lem or ar­gue for a par­tic­u­lar solu­tion to it.

• “That said, I don’t think we are re­ally ex­plain­ing or de-con­fus­ing any­thing if we ap­peal to back­wards cau­sa­tion to un­der­stand New­comb’s Prob­lem or ar­gue for a par­tic­u­lar solu­tion to it.”—How come?

• Per­haps I was too hasty. What I had in mind was the effec­tive strat­egy strat­egy—if you define cau­sa­tion by refer­ence to what’s an effec­tive strat­egy for achiev­ing what, then that means you are as­sum­ing a cer­tain de­ci­sion the­ory in or­der to define cau­sa­tion. And so e.g. one-box­ing will cause you to get a mil­lion if EDT is true, but not if CDT is true.

If in­stead you have an­other way to define cau­sa­tion, then I don’t know. But for some ways, you are just fight­ing the hy­po­thet­i­cal—OK, so maybe in the origi­nal New­comb’s Prob­lem as stated, back­wards cau­sa­tion saves the day and makes CDT and EDT agree on what to do. But then what about a mod­ified ver­sion where the back­wards cau­sa­tion is not pre­sent?

• I feel that ques­tions like this have a hard time es­cap­ing con­fu­sion be­cause the no­tion of lin­ear time is so deeply as­so­ci­ated with causal­ity already.

Could you point me to the ar­gu­ments about a high-en­tropy uni­verse be­ing ex­pected to de­crease in en­tropy?