Re: definition of science

DFS: I have noted that there are an infinite number of theories/models. To expand, some of them will be exact matches (QM alternates).

My thesis chairman used to say, "Theorists can explain anything in a variety of ways. It's up to experimenters to say who's right." He was an experimenter (as I also became). To be relevant, theorists need to be able to make predictions that distinguish their theories from others. I suspect theories that are exact matches in that all their predictions are identical to those of another theory are in fact identical theories even though expressed differently. In other words, it should be possible to show how two theories that predict the same things are alternate ways of saying the same thing.

You say, "Philosophers insist that equivalence is not identity." I'd need proof. In classical mechanics we have various formulations such as those by D'Alembert, Lagrange and Hamilton, but I've never heard anyone call these different theories; and in fact I'm sure it's possible to show they're all different ways of saying the same thing.

Going back to your comments on string theory: No doubt the math is very complicated (but I haven't looked at it, so I can't speak from experience). Greater complications are to be expected when the scope of the theory is greater. General Relativity is more complicated than Newton's law of gravitation, but it explains more. String theory tries to explain a lot more. But complicated as these theories are, in terms of Einstein's previously cited essay they would be simple in Einstein's usage.

(But string theory at this stage is still a branch of math. Not until it makes testable predictions can it be considered physics. Science requires a hard connection between the idea and the real world.)

QM as I understand it, however, would not be simple in that sense. Robert Dicke (with James Wittke) was the author of my undergraduate QM text, which lists seven "postulates of quantum mechanics." These are essentially assumptions that relate the math to the physics. To give the flavor, his postulate 1: "It is assumed for a system consisting of a particle moving in a conservative field of force (produced by an external potential) that there is an associated wave function, that this wave function determines everything that can be known about the system, and that it is a single-valued function of the coordinates of the particle and of the time." So QM is not derived from basic principles but simply assumes a lot of stuff at the outset. This is not significantly different (I think) from the "piecemeal curve fitting" I mentioned earlier (and possibly gave Einstein fits).

DFS: My impression from outside is that the "particle" theory and the "wave" theory give identical results for all computations.

DFW: OK, I have to say I don't know where you're coming from here. I've had several graduate-level courses in QM but have never heard of this.

Don

----- Original Message -----
  From: D. F. Siemens, Jr.<mailto:dfsiemensjr@juno.com>
  To: dfwinterstein@msn.com<mailto:dfwinterstein@msn.com>
  Cc: asa@calvin.edu<mailto:asa@calvin.edu>
  Sent: Saturday, April 30, 2005 12:34 PM
  Subject: Re: definition of science

  As I recall, I have noted that there are an infinite number of theories/models. To expand, some of them will be exact matches (QM alternates). Others will match up to a point (Whitehead and Einstein). The impression I got is that some of the theories mentioned in the SciAm article belonged in each of these categories--Dicke's in the latter.

  Call it what you will, a particle is not a wave, and neither are wavicles. A hole can be punched with a bullet or with a laser. But they are not the same. My impression from outside is that the "particle" theory and the "wave" theory give identical results for all computations. However, some computations that are devilishly difficult in the one are relatively simple in the other, but there are two theories for the same results. The pair, because equivalent, are used as one by scientists. Philosophers insist that equivalence is not identity. Scientists round off and substitute linear approximations for nonlinear equations. Mathematicians say it's wrong. This depends partly on the fact that scientists have to measure, necessarily with limited accuracy, while mathematicians submit to a perfect ideal. After measuring with limited accuracy, scientists idealize their results. Empiricism has its requirements, as do formalisms.
  Dave

  On Sat, 30 Apr 2005 01:41:02 -0700 "Don Winterstein" <dfwinterstein@msn.com<mailto:dfwinterstein@msn.com>> writes:
    DFS: Are you suggesting that only one mathematical model fits? ...

    DFW: Einstein believed, as do I, that one is superior to all others. Only experiment can decide. (Although, if you're Einstein, you can apparently decide also on the basis of which theory has the simpler math. : ) ) RH Dicke also presented an alternative to Einstein's General Relativity, as I recall. I think he wrote the SciAm article. But none of the other versions have earned widespread acceptance.

    DFS: Quanta may be approached either as particles or as waves, equivalent theories. ....

    DFW: There are different representations of the QM formalism (e.g., Dirac's bra & ket notation), but it's the same theory. Lots of people would like a more "reasonable" theory, and I've heard of attempts, but no one has yet improved on QM as we know it. As for waves and particles, it's not that we're invoking different but equivalent theories but that we're doing different kinds of experiments. Particles are also waves; but when measuring them, some experiments detect particle-like behavior and others wave-like behavior. It's called complementarity. Or don't I understand what you're saying?

    Don

      ----- Original Message -----
      From: D. F. Siemens, Jr.<mailto:dfsiemensjr@juno.com>
      To: dfwinterstein@msn.com<mailto:dfwinterstein@msn.com>
      Cc: asa@calvin.edu<mailto:asa@calvin.edu>
      Sent: Thursday, April 28, 2005 11:02 AM
      Subject: Re: definition of science

      Are you suggesting that only one mathematical model fits? After Einstein presented his work, Whitehead came up with a different version. Not liking Riemannian geometry, his was based on Euclidean. Eddington proved that the two were equivalent on the four matters then recognized as relevant. Later work disproved Whitehead's version of relativity because of other matters. I recall an article in /Scientific American/ that presented additional relativity theories, though it did not discuss the calculus underlying them. Some apparently were equivalent to Einstein's theories, while others were designed to be slightly different.

      Quanta may be approached either as particles or as waves, equivalent theories. I understand that two approaches to string theory were demonstrated equivalent. In other words, the fit is multiple. Beyond that, are four dimensions simple? What about 10 or 11? Is seeing a matching pattern simple? Once seen, it's "obvious," of course. Then why does it take brilliant people so long to see it? How many have an /annus mirabilis/?
      Dave
Received on Sun May 1 09:52:38 2005