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Re: complex numbers in QM

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  • brannenworks
    Dear David Strayhorn; ... The ether is supposed to be the medium which allows light to propagate. GR doesn t have much to say about light. For example,
    Message 1 of 23 , Mar 5, 2004
      Dear David Strayhorn;

      > What is the justification for the
      > statement: since there are waves,
      > there must be an ether? GR has waves but no ether.

      The "ether" is supposed to be the medium which allows light to
      propagate. GR doesn't have much to say about light. For example,
      even something as basic as the polaroid filters in sunglasses cannot
      be described in GR alone. The waves that do occur in GR are gravity
      waves, but they've not yet been observed (as far as I know). I'm
      not a GR type, and I don't have any guesses as to whether or not
      those gravity waves will be seen or not.

      > ie, what experiment could tell us
      > that there had to be an ether?

      QM uses a "momentum cutoff" (among other things) to make QED
      calculations work right. If nature has a momentum cutoff, then
      there is a maximum momentum. That says that any object (an
      electron, for example) has a maximum possible momentum. A test for
      this is to accelerate an object to very high momenta. If the
      momentum cutoff is there, then you will eventually reach a limit
      where it is impossible to accelerate any further. Note that this
      would be a violation of Newton's (or Galileo's, I forget which) as
      well as Einstein's relativity.

      To find the ether, repeat the experiment twice, once in the +x
      direction, and once in the -x direction. You are rest with respect
      to the ether when the results from those two experiments match.

      > What makes you say momentum is not "real"
      > in relativity? In general, for X to
      > be a "real" thing (according to the way
      > you define real), does X have to be
      > invariant? In your mind, is GR tainted
      > /tarnished because things that
      > classically seem "real" are viewed in
      > GR as not "real"?

      Momentum in GR is not "real" because it cannot be defined except
      with respect to a particular rest frame. That means that it cannot
      be a fundamental part of a universe made up of "real" things. By
      contrast, if one considers the universe to be a mathematical
      construct, rather than a "real" thing, then there is no problem with
      defining momentum that way.

      I am in no way saying that GR is inconsistent with itself, or
      incompatible with observations. What I'm saying is that its
      consistency is limited to that of a mathematical construct. It does
      not possess the consistency that a description of an object in the
      world possesses. It's an "as if" theory.

      Rather than "tainted or tarnished", I would use the
      word "incomplete". It's somewhat ironic that this is the same
      complaint that Einstein had of quantum mechanics.

      > It seems like what you are doing is to
      > describe what sort of things guide your
      > intuition on your search for something new.
      > ie, certain things are not strictly
      > forbidden, but they are "not beautiful" (?)
      > to you, and thus an indication that
      > some sort of new ideas are needed. IOW, the
      > aspects of a theory that cause
      > you "ontological angst" are the aspects
      > that you seek to replace. These are
      > the rocks that you turn over. Would that
      > be fair?

      It's not beauty that distinguishes between a phenomenological and an
      ontological theory. My movement in this direction is not due to an
      appreciation of beauty. There is nothing more beautiful than SR and
      GR. In fact, I think it is this beauty that has bedazzled the eyes
      of physicists for so many years. We'd all like nature to be a
      beautiful thing, and we all have a strong tendency to believe
      theories that are more beautiful than not. For example, for
      centuries astronomers believed that planets moved on circles, rather
      than ellipses, because circles are more beautiful (or symmetric).
      This is human nature. And it is this human nature that has misled
      us. Instead of more beautiful mathematical constructs, I believe
      that what we need in physics now is more realistic descriptions.

      About a century ago, there was an influential physicist named Ernst
      Mach. He believed in "empiriocentrism", which is pretty much the
      opposite of my point of view. Let me quote from the book "Nature
      Loves to Hide":

      Science, according to Mach, is nothing more than a description of
      facts. And "facts" involve nothing more than sensations and the
      relations among them. Sensations are the only real elements. All
      the other concepts are extra; they are merely imputed on the real,
      i.e., on the sensations, by us. Concepts like "matter" and "atom"
      are merely shorthand for collections of sensations; they do not
      denote anything that exists.

      What it all boils down to is this: "A good theory is no more than a
      condensation of observations in accordance with the principle of
      thought economy." If you believe this, then there is no reason to
      suppose that relativity is explained by a hidden dimension. But
      here it is 2004 and the strong and weak forces are still not unified.

      Physics has followed Mach's philosophy for 100 years, and now we're
      stuck. What I'm saying is that we may need to ditch the philosophy,
      and go back and rederive physics without it. And that implies that
      we need to have a physics that is more than just logically or
      mathematically consistent.

      For example, QED is obviously a mathematical construction, not a
      real description of what goes on with electrons and photons. This
      is clear from the way that infinities have to be cancelled out of
      the theory. The great physicists like Feynmann recognize this, as
      he notes in his book on QED. Here's what Landau and Lifshitz says
      about QED:

      There is as yet no logically consistent and complete relativistic
      quantum theory. We shall see that the existing theory introduces
      new physical features into the nature of the description of particle
      states, which acquires some of the features of field theory (see
      chapter 10). The theory is, however, largely constructed on the
      pattern of ordinary quantum mechanics. This structure of the theory
      has yielded good results in quantum electrodynamics. The lack of
      complete logical consistency in this theory is shown by the
      occurrence of divergent expressions when the mathematical formalism
      is directly applied, although there are quite well-defined ways of
      eliminating these divergences. Nevertheless, such methods remain,
      to a considerable extent, semiempirical rules, and our confidence in
      the correctness of the results is ultimately based only on their
      excellent agreement with experiment, not on the internal consistency
      or logical ordering of the fundamental principles of the theory.

      The original reason I started delving into these matters was to
      repair the above inconsistency. I felt that it had something to do
      with the appearance of complex numbers in the theory. But as I
      continued to work on it, I was unable to make progress until I gave
      up perfect Lorentz symmetry. And by "gave up", I mean exactly
      that. Relativity was torn from me only by years of failing efforts
      to make QM logically consistent under the assumptions of perfect
      relativity. I couldn't do it. Neither could the rest of the
      physics community.

      The most recent response to these consistency problems in QM are
      called "string theories", and these were what got me interested in
      physics once again. But when I picked up a few books, it rapidly
      became obvious that they had more infinities getting cancelled than
      anything dreamed of in QED. So I began working on physics.

      > Given a mathematical
      > formalism of a theory, do you think that
      > it is necessary (or required, or perhaps
      > merely preferred) that every term of
      > every equation correspond to something
      > that we can "point our finger to"? (ie,
      > to be ontologically palatable).

      To be ontologically correct, a theory need only have its most basic
      units be "real", not every term of every equation. Also, I suppose
      I should mention that if someone did have a unified field theory,
      even one that was only a mathematical construct, I wouldn't be
      searching for an ontologically correct unified field theory.

      Carl Brannen
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