# johnswentworth comments on Time Travel, AI and Transparent Newcomb

• Does Gödel met­ric say any­thing about pro­hi­bi­tion of para­doxes?

The real ques­tion here is what me­chan­ics + GR “says” about para­doxes; there’s noth­ing spe­cial about the Gödel met­ric other than that it’s a spe­cific ex­am­ple of a sys­tem con­tain­ing closed time-like loops.

The an­swer is that me­chan­ics + GR can­not rep­re­sent a sys­tem con­tain­ing a para­dox, at all. We just have a bunch of par­ti­cles and/​or fields mov­ing around a space with a met­ric. The lo­cal laws of me­chan­ics + GR con­strain their be­hav­ior. A “para­dox” would, for in­stance, as­sert that there is a par­ti­cle at (x, t) with ve­loc­ity v, but also not a par­ti­cle at (x, t) with ve­loc­ity v—the un­der­ly­ing the­ory can’t even rep­re­sent that.

We don’t know how to in­te­grate QFT with GR, but con­cep­tu­ally a similar prob­lem should arise: we just have some quan­tum fields with com­plex am­pli­tudes at each point in space­time. A para­dox would as­sign two differ­ent am­pli­tudes to the field at the same point. Again, our phys­i­cal mod­els can’t even rep­re­sent that: the whole point of a field is that it as­signs an am­pli­tude at each point in space­time.

We could maybe imag­ine some sort of mul­ti­val­ued state of the uni­verse, but at that point our “time ma­chine” isn’t ac­tu­ally do­ing time travel at all—it’s just mov­ing around in a some­what-larger mul­ti­verse.

• As we lack the means to rep­re­sent the differ­ent op­tions we prob­a­bly do not have a law that para­doxes will be avoided (partly be­cause we do not have a tech­ni­cal analo­goue for “para­dox”)

In the ex­tended on­tol­ogy what cor­re­sponds to old time would be an open ques­tion. That is if you have a mul­ti­val­ued state in the past and some of the val­ues of that are effects of (par­tial) val­ues in the fu­ture it’s still pretty much “time travel”.

I also thought that quna­tum me­chan­ics is pretty chill with su­per­po­si­tion. Could not one ex­tend the model by hav­ing a differ­ent imag­i­nary unit and then have a su­per­po­si­tion of am­pli­tudes? And I thought get­ting a sure eigen­value is a spe­cial case. Isn’t the non-eigen­value case already cov­er­ing a si­mul­tanoues at­tri­bu­tion of mul­ti­ple real val­ues? I case there are two cases 1) we do not rep­re­sent that cur­rently in our mod­els or 2) Our rep­re­sen­ta­tions used in our mod­els can not rep­re­sent that.