# Physics has laws, the Universe might not

In­spired by http://​​back­re­ac­tion.blogspot.com/​​2018/​​06/​​physi­cist-con­cludes-there-are-no-laws.html, which dissed this ar­ti­cle: https://​​www.quan­ta­m­agaz­ine.org/​​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.

• This post re­ally ex­pands my in­tu­ition from years ago; “what if no finite set of equa­tions can fully de­scribe the uni­verse” https://​​groups.google.com/​​d/​​msg/​​sci.physics.re­search/​​Pr­lzkXUPq2o/​​WBdj0ThbsyoJ

But see the re­main­der of that dis­cus­sion thread for links to opinions of oth­ers far more qual­ified than my­self on this topic.

• The idea of a uni­verse “with­out pre­set laws” seems strange to me. Say for ex­am­ple that you take your uni­verse to be a uniform dis­tri­bu­tion over strings of length n. This “uni­verse” might be highly chaotic, but it still has an or­derly short de­scrip­tion—namely, as the uniform dis­tri­bu­tion. More gen­er­ally, for us to even SPEAK about “a toy uni­verse” co­her­ently, we need to give some sort of de­scrip­tion of that uni­verse, which ba­si­cally func­tions as the laws of that uni­verse(prob­a­bil­is­tic laws are still laws). So even if such uni­verses “ex­ist”(what­ever that means), we couldn’t speak or rea­son about them in any way, let alone run com­puter simu­la­tions of them.

• if a short com­pu­ta­tion pro­duces a ran­dom uni­verse, then there is not go­ing to be any­thing like a law of na­ture in­side it. The ex­is­tence of laws from the out­side, and the ob­serv­abil­ity of laws from the in­side are differ­ent ques­tions.

• “ex­ist”(what­ever that means)

What are you im­ply­ing here? It’s clear that *we*, or at least *you* ex­ist, in the sense that the com­pu­ta­tion of our minds is be­ing performed and in­puts are be­ing given to it. We can also say, (with slightly less cer­tainty) that ob­serv­able ex­ter­nal phys­i­cal ob­jects such as atoms ex­ist be­cause the evolu­tion of their states from one Planck in­stant to the next is be­ing performed (even when we’re not ob­serv­ing it—if the eas­iest way to get from ob­ser­va­tion t1 to ob­ser­va­tion t2 is by com­put­ing all the in­ter­me­di­ate states be­tween t1 and t2, it’s likely that the ex­ter­nal ob­ject ex­ists on the en­tire in­ter­val [t1..t2]). This is my con­cep­tion of an ob­ject’s ex­is­tence, that the com­pu­ta­tion of an ob­ject’s state is be­ing done. What is yours?

• I largely agree with your con­cep­tion. That’s sort of why I put scare quotes around ex­ist—I was talk­ing about uni­verses for which there is NO finite com­pu­ta­tional de­scrip­tion, which (I think) is what the OP was talk­ing about. I think it would ba­si­cally be im­pos­si­ble for us to rea­son about such uni­verses, so to say that they ‘ex­ist’ is kind of strange.

• Some thoughts:

(1) “What does the term “Phys­i­cal law?” mean?” This is a long­stand­ing de­bate in philos­o­phy, see https://​​plato.stan­ford.edu/​​en­tries/​​laws-of-na­ture/​​ I think you’d benefit from read­ing up on the liter­a­ture.

(2) ” 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.” Nit­pick: The pre­sent vs. fu­ture stuff is a red her­ring. For ex­am­ple, we use the laws to pre­dict the past also.

(3) The ques­tion I’d ask about your pro­posal to iden­tify laws with pre­dictabil­ity is: What is pre­dictabil­ity? Do you mean, the ac­tual ra­tio of true to false pre­dic­tions made us­ing the law is high? Or do you mean some­thing more ro­bust—if the ob­server had made many pre­dic­tions us­ing the law, most of them would have been true? Or prob­a­bly would have been true? Or what? No­tice how it’s hard to say what the sec­ond and third for­mu­la­tions mean with­out in­vok­ing laws. (We can use laws to ground coun­ter­fac­tu­als, or coun­ter­fac­tu­als to ground laws, but the hope would be to ground both of them in some­thing less mys­te­ri­ous.)

• What sort of thing is the uni­verse? If it is a math­e­mat­i­cal ob­ject, then at least we have an an­swer to the ques­tion, and it is not clear how to an­swer it oth­er­wise. This seems to me to be strong ev­i­dence that the uni­verse is a math­e­mat­i­cal ob­ject.

• What does the phrase “math­e­mat­i­cal ob­ject” mean?

• Peo­ple not be­ing able to come up with any idea but that dis­eases are a curse of the gods is strong ev­i­dence not for dis­eases be­ing a curse of gods but for the ig­no­rance of those peo­ple. The most likely an­swer to that ques­tion is ei­ther some­thing no one will think of for cen­turies to come or sim­ply that the model of sep­a­rat­ing ob­jects into “sorts of things” is not use­ful for de­ci­pher­ing the mis­ter­ies of the uni­verse de­spite be­ing an evolu­tion­ary ad­van­tage on the an­ces­tral sa­vanna.

• So, I don’t think that I would have the same kind of in­tu­ition about dis­eases and curses as I do about math­e­mat­i­cal ob­jects and ex­is­tence, even if I didn’t know any pos­si­ble cause of dis­ease ex­cept for curse. But of course my in­tro­spec­tion about that could be wrong.

I don’t think that I am sep­a­rat­ing ob­jects into “sorts of things”. It is more like I am ask­ing the ques­tion “what does it mean to be a thing?” and an­swer­ing it “to be a thing is to be a math­e­mat­i­cal ob­ject”.

• “What kind of a thing is that ex­ist­ing thing” and “what is ex­is­tence any­way” are rather or­thog­o­nal ques­tions. If you re­ject MUH, you need to ex­plain what breathes fire into the equa­tions.

• I am not sure why you seem to think I re­ject MUH?

• That be­gan with an ‘if’. If you ac­cept the MUH, the prob­lem you have is lack of ev­i­dence for it, or even ev­i­dence against it.

• Ah I see. How could fire be breathed into equa­tions? That con­cept doesn’t make sense to me.

• Can you con­ceive of one thing ex­ist­ing and an­other thing not ex­isitng?

• “Ex­ists” is one of the words I tend to taboo. Peo­ple usu­ally just use it to mean “is part of the Everett branch that I am cur­rently in” but there are also some us­ages that seem to de­rive their mean­ing by anal­ogy, like the ex­is­tence of math­e­mat­i­cal ob­jects. I’m not sure if there is a prin­ci­pled dis­tinc­tion be­ing drawn by those kinds of us­ages.

In­stead I would talk about whether we can sen­si­bly talk about some­thing. And I can imag­ine peo­ple try­ing to talk about some­thing, and not mak­ing any sense, but it doesn’t seem to mean that there is a “thing” they are talk­ing about that “doesn’t ex­ist”.

• Peo­ple usu­ally just use it to mean “is part of the Everett branch that I am cur­rently in”

Not when they are as­sert­ing the ex­is­tence of other branches. And most peo­ple have never heard of Everett branches.

“Ex­ists” is one of the words I tend to taboo.

Con­si­tently taboo­ing it and all its syn­onyms is pretty difficult, and you are not suc­ceed­ing, since your said ““to be a thing is to be a math­e­mat­i­cal ob­ject”.

You are com­ing to a pretty con­tentious con­clu­sion, and do­ing so based on in­con­sis­tent taboo­ing—al­low­ing your­self to use words like “be” when ex­press­ing what you be­lieve, but in­sist­ing on taboo­ing when challenged or asked to ex­plain your­self.

• There I was us­ing “to be” in the sense of equal­ity, which is differ­ent from the sense of ex­is­tence. So I don’t think I was taboo­ing in­con­sis­tently.

• Con­sciously taboo­ing a term like “ex­ist” is what I have been do­ing, as well. Makes a lot of things less con­fus­ing.

• or sim­ply that the model of sep­a­rat­ing ob­jects into “sorts of things” is not use­ful for de­ci­pher­ing the mis­ter­ies of the universe

It’s prob­le­matic when ap­plied to the uni­verse , be­cause “uni­verse” is a very broad cat­e­gory. If you are go­ing to say it is some spe­cific thing cho­sen from an even broader cat­e­gory, then you have to ex­plain why that thing and not some­thing else—the more spe­cific your model of the uni­verse, the more bits of in­for­ma­tion are un­ac­counted for.

• All finite length se­quences ex­ist in any in­finite ran­dom se­quence. So, in the same way that all the works of shake­speare ex­ist in­side an in­finite ran­dom se­quence, so too does a com­plete rep­re­sen­ta­tion of any finite uni­verse.

I sup­pose one could ar­gue by the an­thropic prin­ci­ple that we hap­pen to ex­ist in a well or­dered finite sub­se­quence of an in­finite ran­dom se­quence. But it is sort of like mul­ti­verse the­o­ries where it lacks the ex­plana­tory power or ver­ifi­a­bil­ity of sim­pler the­o­ries.

• All finite length se­quences ex­ist in any in­finite ran­dom se­quence

Yep. For­tu­nately, the se­quences I played with are quite finite, 1024 sam­ples, see the fol­lowup post. And I agree that mus­ing about mul­ti­verses, while fun, has not been sci­en­tifi­cally fruit­ful so far.