Physics has laws, the Universe might not

In­spired by http://​​back­re­ac­​​2018/​​06/​​physi­cist-con­cludes-there-are-no-laws.html, which dissed this ar­ti­cle: https://​​www.quan­ta­m­agaz­​​there-are-no-laws-of-physics-theres-only-the-land­scape-20180604.

Epistemic sta­tus: very raw, likely dis­cussed el­se­where, though in differ­ent terms, but feels like has a ker­nel of use­ful­ness in it.

What does it mean for the uni­verse to be gov­erned by phys­i­cal laws? What does the term phys­i­cal law mean? It means that some­one know­ing that law can pre­dict with some ac­cu­racy the state of the uni­verse at some point in the fu­ture from its state at the time of ob­ser­va­tion. Ac­tu­ally, a qual­ifier is in or­der. Can pre­dict the ob­served state of the uni­verse at some point in the fu­ture from its ob­served state at the time of ob­ser­va­tion. So

laws ⇒ predictability

This is more than a one-di­rec­tional im­pli­ca­tion, how­ever. What does it mean for some­thing to be pre­dictable? Again, it means that, by ob­serv­ing the state of the uni­verse at some point in time the ob­server can make a rea­son­ably ac­cu­rate pre­dic­tion of the ob­served state of the uni­verse at some point in the fu­ture. No­tice the qual­ifier “ob­served” again. How can an ob­server make this pre­dic­tion? They must have a model of the ob­served uni­verse (“map of the ter­ri­tory”) in­side, and use this model (“trace the map”) to pre­dict the ob­served state of the uni­verse at some point in the fu­ture. This model can be very sim­ple, “Raarg hold rock. Raarg let go. Rock fall”, or more com­pli­cated, “In ab­sence of other forces all ob­jects ac­cel­er­ate down­ward at 9.81 me­ters per sec­ond squared”, or even more ab­stract, “The stress-en­ergy ten­sor is pro­por­tional to the space­time cur­va­ture.” But it is a model nonethe­less.

When is a model pro­moted to the sta­tus of a law? When it is use­ful for more than a sin­gle case. When the pre­dic­tion can be made re­peat­edly in similar but slightly differ­ent cir­cum­stances us­ing the same model. There is a lot of com­plex­ity hid­ing un­der the sur­face of this “sim­ple” state­ment, but at the end of the day, mod­els are only use­ful if they can be reused, and thus be­come pat­terns, tem­plates for the ob­servers to pre­dict the uni­verse. Thus we have the im­pli­ca­tion in the other di­rec­tion:

pre­dictabil­ity ⇒ laws

Thus the two terms are equiv­a­lent, at least in this frame­work:

pre­dictabil­ity ⇔ laws

Let’s restate the defi­ni­tions, which are ad­mit­tedly only the first ap­prox­i­ma­tion, and may not looks stan­dard:

Pre­dictabil­ity: an ob­server in­side the uni­verse can in­fer the state of the uni­verse at some fu­ture point in time, with the ac­cu­racy ac­cept­able to the ob­server.

Phys­i­cal (or other) laws: reusable mod­els of the uni­verse that are part of the ob­server and let the uni­verse ap­pear pre­dictable to the ob­server.

I have been try­ing re­ally hard to avoid, or at least to min­i­mize, the mind pro­jec­tion fal­lacy, such as stat­ing that the phys­i­cal laws are the ob­jec­tive laws of the uni­verse. They might well be, but that would be a next step in mod­el­ing the uni­verse, po­ten­tially use­ful, but not min­i­mal.

Re­turn­ing to the ti­tle of this post, “Physics has laws, the Uni­verse might not,” what I mean by it is that Physics is one of the sci­ences that we hu­mans, “ob­servers” call a col­lec­tion some of those reusable mod­els, and so is in it­self an ag­gre­gate model. The laws of Physics are the con­stituent mod­els. On the other hand, the Uni­verse, or “the ter­ri­tory” may or may not have some­thing that Stephen Hawk­ing once phrased as a ques­tion:

“What is it that breathes fire into the equa­tions and makes a uni­verse for them to de­scribe?”

The min­i­mal an­swer might be that the cause and effect are re­versed here: the uni­verse just ex­ists (as­sum­ing it does), and is some­what pre­dictable, and the equa­tions are those phys­i­cal laws in­side the ob­servers’ minds.

Now, the above is, of course, an­other (meta-)model. And mod­els are not very use­ful if they do not re­sult in bet­ter pre­dic­tions. Or, in the lan­guage of this site, the be­liefs must pay rent. So, what does this one pre­dict? Well, for ex­am­ple, if the uni­verse has no “in­ter­nal” laws, ac­cord­ing to this model, then one could po­ten­tially gen­er­ate a “toy uni­verse,” pos­si­bly with some form of pre­dictabil­ity but with­out any pre­set laws and see if any­thing that could be called (toy) laws would “emerge” in this toy uni­verse, and un­der what con­di­tions. It would be in­ter­est­ing to ex­plore this ap­proach fur­ther, but it re­quires a fair amount of de­com­po­si­tion and anal­y­sis to make sense in more than a hand­wavy way. Here are some ques­tions that come to mind:

  • Can one start with a se­quence of ran­dom num­bers as a toy uni­verse, i.e. no or­der and get some­where that way, just by find­ing spu­ri­ous pat­terns in the se­quence?

  • An ob­server is a part of the uni­verse, how would a sub-se­quence of num­bers rep­re­sent an ob­server?

  • A “phys­i­cal law” in this toy uni­verse would be a part of the ob­server, or maybe the even the whole ob­server, that can be con­sid­ered a reusable tem­plate, the way our phys­i­cal laws are. How might it be rep­re­sented in this case?

  • Can the above con­di­tions be re­laxed enough to ap­ply to a toy model, but still be offer use­ful in­sights?

Should an ex­per­i­ment like that worked out, it would lend some cre­dence to the above con­jec­ture, that the phys­i­cal laws are not some in­her­ent prop­erty of the Uni­verse, but a hu­man at­tempt to make sense of it by cre­at­ing reusable tem­plates in­side them­selves.