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Physics = ghost of of mathematics?

  1. May 29, 2003 #1
    How often studying some "sure physical" phenomenon you were disappointed to find no physical object behind it, but a mathematical relationship causing illusion of "physicality" of the phenomenon? I found it so often (when analysing origin of phenomena in depth, not just staring at it's "physical surface") - that it is like chasing a ghost.

    "Physics" is just a label we use for what we (personally) don't know the mathematical origin of yet.

    Example. Yesterday (well, a couple hundred years ago) a "force" was a "solidly physical" phenomenon. Starting with Einstein's general relativity and especially developing quantum mechanics it became obvious that force does not physically exist. Say, in GR a "force" does not exist at all. In quantum mechanics all we have is conservation of momentum during interactions - and this conservation is perceived as "force". Averaging over many interactions we then define macroscopic "force" as the average of rate of change of momentum F=dp/dt.

    So, there are no "forces" in nature. All there is a mathematical result (say, of of bent space in GR, or of conservation of momentum during interactions in QM) which we perceive as s "physical force".

    Same with, say, many known "physical" properties (say, rigidness of solid bodies) - at close look they begin losing "physicality" but instead become more and more a mathematical consequence of rules of interaction of their "parts". Rules of interaction are, by the way, strictly mathematical: symmetries, idistinguishability of "parts" or states the parts can occupy, quantization (=indivisibility without radical change of properties), etc.

    "Parts" themselves (say, atoms) at close look happen to be NOT ultimate "physical" blocks but rather "intermediate mathematical results" of more fundamental "blocks" (and of mathematical rules of play). Today no one can claim anymore that there is anything "surely physical" in our universe.

    So, when we DON'T know the origin of some object (say, of electron), we call the object "physical".

    But when we DO know (say, of origin of rigidness of fermions versus softness of bosons) then we no longer call object/phenomenon as "physical" but call it "mathematical consequence" instead (statistics resulting in Pauli exclusion and Bose condensation in this case being the origin of this "repulsion" of fermions and "attraction" of bosons).
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  3. May 29, 2003 #2


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    I've often heard physics labelled as "applied mathematics". :smile:

    Anyways, back to seriousness. It appears you're just arguing semantics, but because that's not an interesting discussion, I'll assume otherwise! (forgive the rest of this post if you are just arguing semantics)

    From studying the logical structure of mathematics, physical sciences, and the methods of computer science, I'm convinced that abstraction is the way to go for higher levels of pursuit of knowledge.

    From a practical point of view, a scientist only needs to study the aspects of his field. An mechanical engineer doesn't need to know that the pauli exclusion principle is the root cause of the force that moves the pistons of the engine he's designing. Even worse, accounting for quantum field theory instead of just taking force as a fundamental concept would probably hurt his productivity!

    From a robustness point of view, this abstraction acts as an insulating layer. If some GUT was proven tomorrow and QFT was defenestrated, ZFC was found to be inconsistent and a new set theory was proposed, or the law of the excluded middle was soundly debunked, the mechanical engineer doesn't care. As long as the new theory provides him with the same abstract tools like force, his work continues as usual.
  4. May 29, 2003 #3
    I do not propose to replace textbooks for engineers. I propose to analyse origin of things and phenomena in universe in depth.

    And definition of physics as "applied math" is indeed very accurate. The question is if universe itself is just "applied math" or there are "really physical" objects in it? My experience shows that known objects (with known origin) are ALL just "applied math". Objects of unknown origin (say, quark, or electron) can not qualify to be called "physical" simply because we dont't know their origin yet.

    History shows that all "claimed physical" objects were later found to be just another mathematical floor of reality. Say, all macroscopical objects were found to be "applied math" of interaction of molecules, then later molecules were found to be not "physical" but results of interaction of atoms, then atoms -of electrons and nucleons, then nucleons - "applied math" of quarks, etc).
  5. May 30, 2003 #4
    Very interesting, Alexander.

    But mathematics is only able to describe interactions between physical objects. It is not able to stand by itself. You can't add 2+2 without saying 2 of something, like 2 of a certain paricle.

    I just realized that my statement above sounds an aweful lot like the question in QM, when presented with the idea that a photon is a wave, one tends to ask "A wave of what?" So maybe your idea of physics being the ghost of mathematics isn't that far off after all.
  6. May 30, 2003 #5


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    It depends what you mean by physical. It seems that while solid objects have disappeared from view, geometry has remained. We no longer have billiard ball like particles floating around, but we do have fields. While GR explains a mysterious force in terms of curved spacetime (sorry Euclid), many physicists are likewise attempting to construct a theory to explain all the different fields (and the zoo of particles) in terms of pure geometry. String theory, Supergravity and Loop Quantum Gravity are some examples.

    So the question is, do you consider geometry to be physical? Would a unified field of pure geometry constitue physical existence?? It seems to be just a problem with intuition again. We see all kinds of objects in life that we call substances, but the reality is that we only percieve the geometry of said objects. What justification then, do we have for claiming different substances exist at all?

    Anyway, while math has been called the language of the universe, surely geometry is the physical form of nature itself.
  7. May 30, 2003 #6
    Both fields and geometry at close look begin to lose "physicality". Say, fields are a bunch of virtual states (particles?), geometry depends on state of motion and on amount of energy nearby, space-time lose its "physical" sense (if it had any) on a small (=Plank) scale.
  8. May 30, 2003 #7
    Alexander, I don't think that your arriving at this conclusion is some strange chance, as your mind is already biased toward that opinion.

    My problem with saying that that which we percieve as physical phenomena is just mathematics is stated clearly in "The Hurdles to the Causal Mathematics" thread.

    One that I feel I should mention is the definition of mathematics. You see, mathematics is defined (by the dictionary, and by those who are professionals in the field) as a system for describing physical phenomena. It is nearly perfect (I only say "nearly" because of Godel's Incompleteness theorem, which shows that mathematics cannot describe itself), but it is still a description, by it's very definition.

    Also, to assume that percieved physical phenomena are just the result of mathematical logic, is to assume that there is no objective reality (as mathematical relationships are formulated in sentient minds).
  9. May 30, 2003 #8
    Isn't that the same as saying that Ben Franklin "invented" electicity. Mathematical relationships exist in the world around us regardless of whether or not they are observed by a sentient being.
  10. May 30, 2003 #9


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    That's a question of what spacetime really is like on a quantum level. And this is a fundemental question, because it's basically asking the nature of the physical world itself. So far we don't know have a quantum theory of gravity, but the candidates (LQG string theory, etc.) do seem to propose that the physical universe is nothing but geometry in motion. So if any of those theories turn out to be on the right track, it seems there still is a physical universe, and it is geometry.
  11. May 30, 2003 #10
    I didn't say that humans "invented" the way the universe works, I said that they conceptualized the already-existing relationships, and invented a way of describing them: math.
  12. May 30, 2003 #11
    I disagree on this point. These theories don't dictate that the physical universe is just geometry, but rather that all of it's interactions can be described by geometry. It's only a subtle difference, but an important one nonetheless.
  13. May 30, 2003 #12


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    There isn't really a difference, I don't think. Geometric relations are what define the universe, whatever way you chose to say it. But in the case of say, string theory, the individual strings are not made up of any substance. They are just geometry in motion, and the overall geometric relations of strings gives us spacetime.
  14. May 30, 2003 #13
    That's like saying that having one banana, and buying another one, is just arithmetic in action. It is not exactly so, even though the behavior of strings is entirely describable by geometry.

    The only reason I insist on there being a difference is because geometry, in the strictest sense, is just a branch of mathematics, and strings are not just mathematical abstracts, but physical wavicles.
  15. May 30, 2003 #14


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    No, there is a difference. As I said, mathematics in general is just a language to describe the universe. Geometry, while a branch of math, describes the actual physical form of the universe. In actual fact, geometry deals with space, which is the only structure you're going to find in this world.

    The geometric extent (length) of strings is exactly that - geometric extent. It's not made of anything. Now you can say geometry is just an abstract math that describes the spatial reality, but this is really semantics. The important thing to stress is that space=geometry, and that the spatial aspect of things is where our conception of "physical" likely comes from. This spatial (geometric) reality should hold even in modern physics.
  16. May 30, 2003 #15
    Mentat, do you know that, for instance, "mass" is NOT a physical quantity? I can show you mathematically how to derive what "appears" for us as a "mass" (ineria) out of completely massless object - relativistic wave. Inertia (inerial mass) can be considered as a by-product of Lorents transformations alone then.

    Also, Mentat, if you (probably) think that a magnetic field is something fundamental and "physical", then for your information: magnetic "field" is nothing than relativistic part of moving electric field.

    And again, so far ALL objects we KNOW the origin of, happen to be just a mathematical consequences of their "parts" behaving according to given mathematical circumstances around them (like symmetries, boundary conditions, etc).

    So, assigning "physicality" to something WITHOUT knowing its origin first (as you frequently do) is very risky business.
  17. May 30, 2003 #16
    Incorrect. What you fail to understand is that math also is NOT a human invention, it is human DISCOVERY of how universe works.

    Another serious mistake you still is making is equating math and language (by parroting that math just DESCRIBES things). There is a serious distinction between a language and a math: language (description) lacks predictive power, but math has it.

    Math (logic) is native language of nature, so to speak.
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  18. May 30, 2003 #17


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    So you are just debating semantics then.

    I don't expect you to be able to define it, but what are some of the properties of something that is "physical"?

    The next question is what do you think a person means when they say "physical"? (Note: this is a different question than that above).
  19. May 30, 2003 #18
    "So, assigning "physicality" to something WITHOUT knowing its origin first (as you frequently do) is very risky business."-Alexander
    That's a good point(not the finger of blame I mean), often I hear people say that this thing x causes w, well what causes x? It is a mix of t and r we call that one q , well what causes q? I just said t and r constitutes q what don't you understand? I want to know what causes q? There's no cause for q because it just exists, like a dog just exists.
    Kind of like what is mass? Mass is a product of gravity. What is gravity? A force that exists and causes mass. So what is mass again?
    The physicist and the engineer ought to seek whatever they are curious about, which is probably physics and engineering respectively.
    Einstein was an armchair authority.
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  20. May 30, 2003 #19
    thats the point I was trying to make before
    thanks, Alexander
  21. May 31, 2003 #20
    This is (almost exactly) my view, as you can see from the very first post of "The Language of Mathematics".
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