Wednesday, November 9, 2016

Leaning new tricks from an old book

In my previous post, I referenced a book review [pdf] of a Bergmann's Theory of Relativity I bought as a teenager not because I understood it, but because I aspired to understand it. I thought I'd call out a couple of quotes. First, one that is partially a response to Blackford's claim that classical mechanics didn't have logical contradictions:
Someone may look for a book on Relativity Theory which states clearly and axiomatically the assumptions of this theory and develops deductively the conclusions from these assumptions. This is not what Bergmann's book tries to do. What it tries to do, and does excellently, is to show how we were compelled to adopt these assumptions, how the structure of Relativity grew from logical contradictions in the classical theory, how their removal leads naturally and simply to the Theory of Relativity. The author presents not the painful historical process, not how Relativity was discovered, but how it should have been discovered if we had known the simple and straight road of logic leading to its formulation. Even in Relativity Theory, created almost by the genius of one man, this difference between the historically and logically reconstructed process is remarkable; it is the difference between the broad highway and the pioneer's narrow pathway.
This also is an example of noting the difference between what I call "Wikipedia science" (where everything is worked out) and "real science" (which is messier). It's that difference between the broad highway and the narrow pathway.

Also, I remembered that it was the first place I'd heard about Kaluza-Klein theory:
The third part (pp. 245-279) is of much more special character and deals with the unification of the gravitational and electromagnetic field. Here we find an exposition of Weyl's and Kaluza's theories and of their generalizations on which the author collaborated with Einstein. This part will rather interest specialists than students.
The review is from July of 1943. When it came up in string theory and the discussion of extra dimensions in the late 1990s, I thought back to the book and its strange (at the time) final chapters.

You never know where theory will lead, or end up becoming useful or relevant again.

6 comments:

  1. "... how the structure of Relativity grew from logical contradictions in the classical theory, how their removal leads naturally and simply to the Theory of Relativity...."

    This entirely contradicts the Friedman/curve fitting/scientific methodology approach and supports Blackford's argument.

    ReplyDelete
    Replies
    1. Nope.

      Here's Blackford:

      "As far as I can tell, the basic paradigms of physics are not, for the most part at least, based on demonstrably false assumptions"

      Classical mechanics (still used today) is based on demonstrably false assumptions (logical contradictions in the classical theory).

      And since classical mechanics is still used today, it is an example of Friedman's "as if" methodology.

      Delete
    2. I don't know if it's that cut and dried.

      Why isn't it possible to argue that Classical mechanics works in the data scale that it works in because of its assumptions and logic?

      Delete
    3. I am going to rephrase your question as I understand it; let me know if I got it wrong:

      "Why isn't it possible to argue that Classical mechanics works for the data collected at the scales within its scope because of its assumptions and logic?"

      It is true that classical mechanics works for the scales within its scope because of its assumptions (which basically define that scope). It ends up being a bit circular that way (assumptions → scope → valid scales → assumptions).

      However, there are logical inconsistencies resulting from the assumptions (e.g. answers that give you infinity using classical mechanics), so the assumptions themselves are demonstrably false, yet we use them anyway (exactly "as if" methodology).

      Delete
    4. "It ends up being a bit circular that way (assumptions → scope → valid scales → assumptions)."

      Shouldn't this be this way?:

      assumptions -> scope -> scales validated by data -> therefore assumptions valid for scope/scale.

      Nothing circular there - just the logic.

      Delete
  2. "there are logical inconsistencies resulting from the assumptions (e.g. answers that give you infinity using classical mechanics), "

    You say there are logical inconsistencies. What do you mean by this? How can you say the mathematics is inconsistent just because they yield infinity as a result? Perhaps we just don't know what the result of infinity means?

    I understand Maxwell's equations yield terms containing negative frequency. Another case in point. What does negative frequency mean? Is it OK to discard and ignore it? These are separate issues. Maxwell equations work otherwise.

    However, the point is that the assumptions yield solutions which are useable within certain limits. Change those assumptions and the theory will not work. So the theory only works where it does because of the assumptions. You cannot ignore the assumptions and theory built upon them.

    ReplyDelete