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Background and Question

Here's something I was wondering: The (known) laws of physics can be formulated in such a way that one say: "initial condition" + "laws of physics" gives us a "final solution." I am thinking of something along the lines of an initial value problem (if the law is a partial differential equation) or Born rule (where the "final solution" is not unique).

My question is this is there any line of argument in philosophy which argues for the removal of the distinction between the "initial condition" and the "laws of physics."

An argument effectively doing this by saying the space (Venn diagram) of initial values is a point. If any other other values are inserted then the law breaks down (we get an unacceptable solution for example: divergent solutions)

P.S: I have a degree in physics not in philosophy. I hope this is an acceptable question?

More Anonymous
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    Hi, welcome to Philosophy SE. Yes, this is the kind of well articulated, motivated and specific question that we are looking for. See Laws and Initial Conditions by Frisch:"I discuss two case studies from classical electrodynamics challenging the distinction between laws that delineate physically possible words and initial conditions". – Conifold Sep 20 '19 at 05:25
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    @Conifold Your link gave a 404 error.I googled the quoted words and found the paper. Yes, this is what I was looking for. Here's the link I used: https://pdfs.semanticscholar.org/bf43/591d38aaa5f2a28e0c44779fcda2e17d961e.pdf – More Anonymous Sep 20 '19 at 06:10
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    Lee Smolin in his musing about temporality argues that in cosmology the distinction does not make sense, e.g.the absolute separation of laws and initial conditions, and thus of laws and states, is tied to the empirical context of studying small subsystems of the universe. He is certainly not the first but a quick look at his views might be of interest; the book or at least https://www.bu.edu/cphs/files/2013/01/Lee-Smolin-Time-and-Law-in-Cosmology-10.18.13.pdf – sand1 Sep 20 '19 at 10:33
  • General relativity is a theory that in its most general form isn't really about taking initial conditions and evolving them forward, as seen for example by the fact that you can have spacetimes that respect the field equations but involve closed timelike curves. If you think of the mathematical space of all possible Lorentzian manifolds with matter/energy fields defined on them, the equations just pick out a subset which respect the field equations at all points. – Hypnosifl Sep 20 '19 at 14:02
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    @Hypnosifl I don't think that is true. See https://en.wikipedia.org/wiki/Initial_value_formulation_(general_relativity) . It is simply a very difficult initial value problem. – More Anonymous Sep 20 '19 at 14:07
  • @MoreAnonymous — that’s why I said “in its most general form”, that page is about how it’s possible to mathematically reformulate general relativity in terms of initial conditions and deterministic dynamical laws, but this can only be done for a certain subset of the spacetimes permitted by the more general form. In particular my understanding is that the initial value formulation is usually restricted to “globally hyperbolic” spacetimes, though a footnote on p. 3 of this paper says it can work for some other types. – Hypnosifl Sep 20 '19 at 14:45
  • Are you asking about determinism vs. indeterminism? – Geremia Sep 22 '19 at 03:03
  • @Geremia I was asking: Given there exists the law(s) that govern the time evolution of a system (say the universe). Are there any adherents who argue such law of this system can only handle effectively one initial condition (an observable universe of being of point size). I'm not sure what - the doctrine of "tychism, anancism, and agapism" - would have to say about this? – More Anonymous Sep 22 '19 at 03:20
  • @Conifold would you like to answer this post so I can accept your answer? – More Anonymous Sep 23 '19 at 02:32
  • "the set of initial values is a point" reminds me of the Big Bang. physics basically asserts that the big bang was a "uniform point" of spacetime. my other answer is, fractals which can seem to yield arbitrary complexity even from "primitive" or "nearly nonexistent" initial conditions. an example/ mini case study/ toy problem is (reverse) "trajectories" arising in the collatz problem all originating from a single value, 1. the collatz problem has many properties evocative of physics eg density, "trajectories" etc... – vzn Nov 26 '19 at 03:30
  • This seems the right course of action, si! Remove the distinction between an apple and an apple. – Agent Smith Mar 15 '23 at 07:46
  • Frisch's paper can be found here https://faculty.philosophy.umd.edu/mfrisch/papers/laws_and_ic.pdf. Also of interest https://link.springer.com/article/10.1007/s11229-016-1203-0, https://dergipark.org.tr/tr/download/article-file/694714 – Nikos M. Mar 15 '23 at 13:57

2 Answers2

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There is indeed a line of argument in philosophy that aims to blur the distinction between initial conditions and the laws of physics. This view is called the "best system analysis" (BSA) of laws of nature, and it is associated with philosophers such as David Lewis and Bas van Fraassen.

The BSA is rooted in the Humean approach to laws of nature, which claims that laws are just regularities or patterns in the world, rather than entities that govern or cause events. According to the BSA, the laws of physics are those that comprise the best system – that is, the system that best balances simplicity, strength, and fit to the actual world.

In this view, the initial conditions are part of the description of the world, and the laws are derived from the best systematization of these descriptions. In other words, there's no fundamental distinction between initial conditions and laws, since the laws are an emergent product of the overall pattern of the world's initial conditions and subsequent events.

By integrating initial conditions into the best system, the BSA approach to some extent eliminates the need for a sharp distinction between initial conditions and laws of physics. However, this view does not go as far as to say that the space of initial values is a single point or that any other values would necessarily lead to a breakdown of the laws.

TN157
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This is largely an argument at cross purposes. Take Newton's laws of motion. Clearly there is a sense in which a clear distinction can be drawn between the laws applying to a system and the initial conditions uniquely associated with the system. I can take ten different physical systems, each with their own unique initial conditions- they will all evolve into different states, but all do so in accordance with Newton's laws. There I am using the term 'initial conditions' specifically to refer to the dispositions of the individual elements of a system at some time t which I take to be the start of a period of particular interest. Now, if you want to lump into that definition of 'initial conditions' the fact that the objects obey Newton's laws then you are simply using the term 'initial conditions' in a different way, and moreover a way that blurs a useful distinction.

Marco Ocram
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  • The laws of physics are clearly not a part of the initial conditions. The laws only describe the relation between the initial state and the subsequent states. – Pertti Ruismäki Mar 15 '23 at 11:36
  • @PerttiRuismäki Hear hear- you make the point more succinctly than I did! – Marco Ocram Mar 15 '23 at 12:00
  • One can equally say that for each initial condition (ie each distnct system) a different law applies (boundary conditions+Newton's law) which has only some similarities to the laws applicable to other systems (ie abstracting Newton' laws for example). – Nikos M. Mar 15 '23 at 13:47
  • @NikosM. You could, but you would be obscuring rather than illuminating the underlying commonality. – Marco Ocram Mar 15 '23 at 13:55
  • @MarcoOcram the issue here is how much commonality should we accept or expect. So personally I don't take this as a serious objection. – Nikos M. Mar 15 '23 at 13:58
  • @NikosM. whatever floats your boat. And therein lies one of the joys of philosophy- the fact that through idiosyncratic usage the meaning of terms becomes so broadened that the scope for arguments at cross purposes becomes virtually endless. – Marco Ocram Mar 15 '23 at 14:02
  • @MarcoOcram I would not call this view peculiar or idiosyncratic. First of all the boundary conditions play a major role in defining a system and its dynamics, which can indeed result in qualitatively different systems and outcomes. Chaotic systems being prime examples. So taking into account boundary conditons in this sense, prevents us from making simplistic assumptions of similarity. – Nikos M. Mar 15 '23 at 15:01
  • @NikosM. You said that one could equally argue that a different 'law' applies to every system, if you define 'law' to mean the combination of the boundary conditions plus the laws that are independent of those boundary conditions. I am simply saying that defining 'law' in that way is confusing the terminology with the usual definition. – Marco Ocram Mar 15 '23 at 15:29
  • @MarcoOcram of course, we are re-defining the term "law" in this case. I am simply arguing that it might be better if we do re-define it that way. – Nikos M. Mar 15 '23 at 15:39
  • @NikosM. IVery well. Perhaps you might post a question about the suggestion, as it would be interesting to see a range of views about it – Marco Ocram Mar 15 '23 at 16:24
  • @marcoocram this question is exactly that. And it is nice to see different points of view on this. – Nikos M. Mar 15 '23 at 17:49