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Axiomatic approaches to physics

  1. Apr 14, 2008 #1
    Recently it has been really bothering me that physics is so unaxiomatic. See https://www.physicsforums.com/archive/index.php/t-223771.html. Do you think it is possible to construct a completely axiomatic approach to physics and by physics I really mean the heart of physics i.e. quantum field theory and quantum mechanics?
     
  2. jcsd
  3. Apr 14, 2008 #2
    You can derive much of the laws of physics a priori, if you start with point-of-view invariance.
     
  4. Apr 14, 2008 #3

    robphy

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    "complete" might be asking for too much [at least right now, when there are lots of loose threads]. There are formulations of many physical theories that try to start axiomatically. Can you be more specific about what you want?
     
  5. Apr 14, 2008 #4
    I want to put the theory of general relativity and quantum field theory into a computer, like http://en.wikipedia.org/wiki/Mizar_system. You're right though that they need to be unified first.
     
  6. Apr 14, 2008 #5

    tgt

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    Any physical theory dosen't give exact experimental results so there is no point in making them more axiomatic - in the name of physics. Maybe important in the name of mathematics, but not physics.
     
  7. Apr 14, 2008 #6
    *sigh* what does "axiomatic" mean?
     
  8. Apr 15, 2008 #7

    robphy

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  9. Apr 15, 2008 #8
    In my opinion, the point of physics is to construct theories that are consistent in two meanings: self-consistent and consistent with experiment. You're right the that making theories more self-consistent will not make them more consistent with experiment but still the first type of consistency is just as important as the second. Improving self-consistency will improve the "total" consistency and thus make our theories better. So, I strongly disagree that physics has nothing to gain by being more axiomatic.
     
  10. Apr 16, 2008 #9

    tgt

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    Mathematical physcists share your concerns. But for the genuine physicsts like Einstein and Feynman, not so. Not to mention any experimentalists.
     
  11. Apr 16, 2008 #10

    Astronuc

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    of or pertaining to the use of axioms.

    Axiom (from Merriam-Webster)
    Well, Newtons Laws of Motion are axioms.

    1. An object will remain at rest or in uniform motion in a straight line unless acted upon by an external force.
    http://hyperphysics.phy-astr.gsu.edu/hbase/newt.html#nt1

    2. External force is proportional the product of mass and acceleration.
    http://hyperphysics.phy-astr.gsu.edu/hbase/newt.html#fma

    3. Newton's third law: All forces in the universe occur in equal but oppositely directed pairs. There are no isolated forces; for every external force that acts on an object there is a force of equal magnitude but opposite direction which acts back on the object which exerted that external force.
    http://hyperphysics.phy-astr.gsu.edu/hbase/newt.html#nt3

    http://www.grc.nasa.gov/WWW/K-12/airplane/newton.html

    http://www-istp.gsfc.nasa.gov/stargaze/Snewton.htm


    See conservation laws - http://hyperphysics.phy-astr.gsu.edu/hbase/conser.html
     
  12. Apr 18, 2008 #11
    Feynmann and Einstein developed the groundwork of modern physics. When they were alive, the state of physics was not really advanced enough to admit an axiomatic approach. I think that now or in the near future, we will have enough experimental knowledge and mathematical tools to make an axiomatic approach possible. If they were still alive, I think they would work things out more rigorously.
     
  13. Apr 18, 2008 #12
    Do you think it is possible to construct a completely axiomatic approach to mathematics?
     
  14. Apr 18, 2008 #13
    Yes.
     
  15. Apr 18, 2008 #14
  16. Apr 18, 2008 #15
    Um--there is a difference between completely axiomatic and being complete if you read that carefully. Mathematics is almost by definition completely axiomatic. The existence of undecidable propositions is not even related to what this thread is about.
     
  17. Apr 18, 2008 #16

    ZapperZ

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    But you don't know that for sure. So it seems that your deduction here isn't based on any "axiomatic approach" either.

    This thread is rather puzzling. If you buy Popper's assertion that experiments cannot prove a theory, but rather can only falsify it, then there is no way that you can come up with any "axiom" to physics. While we accept conservation laws to be valid, we have no derivation to show that they are always true, which is why we continue to do experiments to look for when such-and-such conservation laws are falsified. Have you ever considered such a thing?

    Zz.
     
  18. Apr 18, 2008 #17

    tgt

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    In Feynman's Lectures, Feynman was always distinguishing or separating mathematicians from physicsts. I think he had a very good reason to do that. If he was still alive, he would be furthering physics. And there is actually more physics now then there was during his time so even less time for rigorous mathematics.
     
  19. Apr 18, 2008 #18
    Mathematics is not completely axiomatic. There are insurmountable problems related to set theory. You can find information about this here: Foundations of Mathematics. in the section entitled "Foundational crisis".

    I quote a small excerpt:
    Take your choice, don't work from axiomatic systems, or bury your doubts. Mathematicians call it proof by intimidation.
     
  20. Apr 18, 2008 #19
    You're right that experiments cannot prove theories, but it does not follow you cannot come up with any axioms. In fact the conservation laws would make good axioms since they form the logical basis for a lot of other theory. I am not saying that we should use some abstract mathematical principle like set theory to "prove" physics! I am saying physics should be based on a strict set of ground rules for itself. I think we should take concepts in physics that are most consistent with experiment and most important and call them axioms and formally derive the rest of physics on top of them. There is probably even some axiom that could precede the conservation laws.

    You may think physics has already done this but in that case I challenge you to give me a set of axioms that works. It is harder than you might think because you really should not assume anything in an axiomatic approach. You would have to define things such as mass and spacetime that you normally take for granted. Obviously we would borrow a lot from mathematics but there would still be a lot left.

    I will try to make this argument more coherent when school ends in two weeks.
     
    Last edited: Apr 18, 2008
  21. Apr 18, 2008 #20

    ZapperZ

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    There's nothing to indicate that what you said here is true.

    I do? Where did I indicate that? In fact, if you read my response carefully, I would say that the tone of that response was to contradict that there are sets of axioms in physics, or that there are obvious starting points where everything can be derived. So you are challenging me to producing something that I don't think is valid in the first place.

    Furthermore, even IF there are some axioms, or let's call them as "starting point", it doesn't mean that you can do physics that way. Read up on emergent phenomena. Tell me how you can derive superconductivity by starting from the Hamiltonian of every individual electrons in a metal.

    Zz.
     
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