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The laws of physics observably change, that is their expression in terms of mathematics can, both through internal coherance & through physical insight.

One supposes that there are actually laws of nature - that these laws of physics approximate in some way.

It seems that they must be distinguished. For one thing, for simplicity I'm going to assume we have a fully coherent axiomatic description; its easy to imagine that there will be many theories and (most likely infinitely many) with either the same physical content, and inter-interpretable with each other (This could be concieved as a structuralist contexualisation of physical law).

This means there is no single distinguished description of the laws of physics.

So what do we mean, if we can mean anything, by the laws of nature?

And what exactly is the relationship between the laws of physics and the laws of nature.

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  • There are "laws of" many things: physics, chemistry, biology, economics, etc. All these laws are (human) constructs based on our perception of events and/or experiments. I'm sure you know this already. So, I don't get what you're asking exactly.
    – prash
    Dec 17, 2013 at 20:18
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    @Prash: Well it is a subtle point - I'm asking about the laws of physics and laws of nature - not the laws of chemistry or of the state. Now, when you drop a stone it falls in a regular motion. Although this is a law, its a small segment of a much larger one. Its a plausible hypothesis, and one that is taken by modern physics that the laws of nature are a unity. Now we describe these laws mathematically, sure they're a social construction but they also have a contact with reality - that is whats known their physical context - that is its measurable effects.
    – Mozibur Ullah
    Dec 17, 2013 at 20:33
  • But one cannot reduce the idea of a law to its measurable effects. And given there maybe many different but equivalent descriptions what do we then actually meaan by a law of nature? Does it actually have a meaning? This is a philosophical question, and not a physical one. A physicist will saw that the law of gravity is obviously a law of nature - whichis the right way to do that science.
    – Mozibur Ullah
    Dec 17, 2013 at 20:37
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    @Prash: sure - you can use analytical techniques to magick the problem away; but I don't think its helpful. Feynman, in his book - the character of physical law - said we didn't understand matter, he didn't say it wasn't there though. He goes on to explain that we do understand physical laws. I'm saying there is a distinction between that and a law of nature - and not that either aren't there.
    – Mozibur Ullah
    Dec 17, 2013 at 21:18
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    @Kaznatcheev: The idea of a physical law goes back to Francis Bacon, and much earlier to ideas of logos - that is the universe is rationally ordered; its part of the history of science & philosophy, as I'm sure you're aware. I'm being vague because the question is meant to be thought-provoking rather than admitting some specific answer. As the SEP entry that Nicolas kindly provided shows that there are philosophical problems as what is meant or understood by physical laws.
    – Mozibur Ullah
    Dec 18, 2013 at 0:36

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Your question leads directly to 2 important considerations.

First, whether the physical laws we discover through science are merely 'resemblances' - that they reflect but are not actual natural realities; and Second, that the laws of physics do reflect physical content or constituents themselves as it is like in nature. This in turn depends on your own metaphysical view of what is possible to be known by the human senses.

The problem with the term 'Laws of Nature' that is often used in science today (or in textbooks) is that it is a misleading way of putting what in actuality are our best theories. These theories are what, after multiple tests and confirmations, verified as they are separately in experiments, are considered to be true because they give us the best results. They are not considered final.

In this sense, 'Laws' as they are used, are actually tentative theories, they are not the final say in any descriptions of reality. This is because even the most well tested and described laws, such as Newton's Laws of Motion and gravitation, have limits. For instance, after Einstein, the laws do not give predictable results at high speeds or small quantities.

Thus, Laws can never be Laws in our modern sense of certainty because they are incomplete. They raise further questions about physical phenomena that require further experimentation and testing. These questions are raised when we synthesize it with other laws that we know from other experiments, or from before.

For example the recent discovery of the Hiigs Boson can be considered a result that has been built upon not just our knowledge of quantum mechanics, but also our understanding of electromagnetism and classical mechanics.

The lack of a unifying theory does not mean that we do not understand nature. Often, we are dependent on these theories to built upon our understanding of reality and nature. It is fundamentally important then to distinguish between the metaphysical question of whether nature can really be discovered as it is by our senses, and whether there are laws of nature that are scientific theories to be discovered through experimentation, that are dependent on our senses.

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  • Newton himself was well aware of the limitations of his own law - for example relying on 'action at a distance' - but as you point out it their empirical efficiency that is important.
    – Mozibur Ullah
    Dec 23, 2013 at 0:35
  • I'm distinguishing between nature as it is, or noumena in Kants terminology with laws of nature. Where that lies in his epistemology I'm not sure; their primitive manifestations are immediate & intuitive, but their intellectual form is synthetic.
    – Mozibur Ullah
    Dec 23, 2013 at 0:38
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There is no such thing as law or connection in this world, but we are thinking that there is a great deal of connection.When we see things happen a number of times in a certain sequence, we call it cause and effect, and say that the thing will happen again. James Gleick say in Chaos: Making a New Science - "There as a story about the quantum theorist Werner Heisenberg, on his deathbed, declaring that he will have two questions for God: why relativity, and why turbulence. Heisenberg says 'I really think He may have an answer to the first question'" in the footnote to this story he adds "Orszag cites four substitutes for Heisenberg--von Neumann, Lamb, Sommerfeld, and von Karman-- and adds,'I imagine if God actually gave an answer to these four people it would be different in each case.'" I also heard another variation to this in which God says to Einstein he'll answer the first question about relativity, but just winks about the second.

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  • Interesting thoughts! "Why turbulence?" is a great question...
    – Joseph Weissman ♦
    Dec 25, 2013 at 14:32
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You just answered your own question.

  1. The laws are physics are models of laws of nature
  2. The laws of nature are self-evident truths which dictate reality

Say the laws of physics are reducible or chemistry is reduced to physics. Why would that create any implications that laws of physics are not distinguishable? Wouldn't it mean they are all theorems from the same axioms?

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