Axiomatic postulates vs. experimental derivation.

[TRB8985]

In the book, 'Scale Relativity and Fractal Space-Time: A New Approach to Unifying Relativity and Quantum Mechanics', the author, Laurent Nottale, makes a few interesting comments in the introduction of his book which seems a bit unclear to me.

In the general introduction of the book, Nottale reveals to the reader that the present foundation of relativistic quantum mechanics and quantum field theories are founded on axiomatic postulates and rules, as compared to experimental derivation.

I brought this to the attention of one of my undergraduate physics professors, and he shook his head vigorously and commented on how stupid it is that only one of those ways is preferred, rather than utilizing both. Unfortunately, our conversation was cut short. In addition, I feel he may be a bit biased in that question, considering his background in fractional calculus.

My question is this: Is there a preference in the academic community towards one of those ways of founding knowledge compared to the other? If so, why?

Thank you for your time.

 

[Dale]

In the book, 'Scale Relativity and Fractal Space-Time: A New Approach to Unifying Relativity and Quantum Mechanics', the author, Laurent Nottale, makes a few interesting comments in the introduction of his book which seems a bit unclear to me.

In the general introduction of the book, Nottale reveals to the reader that the present foundation of relativistic quantum mechanics and quantum field theories are founded on axiomatic postulates and rules, as compared to experimental derivation.

So, first and most importantly, this book is a pop-sci book, not a professional scientific reference. The pop-sci literature, even when authored by well-respected professional physicists, is full of problems. Generally, things are presented in the most provocative way possible with the least rigor possible, which serves to confuse rather than inform while simultaneously giving the feeling of great insight.

Second, special relativity and quantum mechanics have already been unified for the last 40 years or so. I am not sure what the author thinks is the problem.

Third, the comment is completely bogus. Both axioms/postulates and experiments are essential for the progress of science. They work together very closely. For instance, around the turn of the 20th century it was noticed experimentally that the speed of light was invariant. This was an experimental observation. Einstein said, "ok, let's take that as a fact and see where it leads". A decade later he came up with general relativity from theoretical considerations and said "ok, let's propose spacetime is curved and see what experimental results this predicts". So even a single physicist will go between experiment driving theory and theory driving experiment. It is simply false to claim that one or the other is given broad preference in the community at large.

 

[TRB8985]

I had a nagging suspicion of the same thing. Thanks for clarifying, Dale.

I'm a bit worried that this book is considered a pop-sci book, however. When it was given to me by my professor, he told me several times over that this is graduate-level material (I'm only in my 3rd year of undergrad, so most of it is gibberish to me) and that the author is very well-renowned internationally.

Is that statement really true? I would hate to waste my time trying to understand his concepts of scale transformations with respect to fractional calculus.

 

[PeterDonis]

I'm a bit worried that this book is considered a pop-sci book, however.

The book itself might be considered a textbook (I can't be sure because I have not read it and am only going on what I see on the book's page on Amazon, and the published papers linked to on the author's web page). However, even if it is, the author's comments in the introduction that you refer to seem more typical of a pop science article than a textbook, so DaleSpam's comments still seem warranted to me. Even in textbooks authors often take liberties in the introduction since it isn't technically part of the textbook itself.

 

[TRB8985]

Hmm.. although a bit disappointing, I think the two of you may be correct. Here I was under the misapprehension that this was a professional-level publication on the introduction to fractals to spacetime just printed in a book format.

I appreciate the insight. Enjoy your weekends.

 

[Dale]

I have to say that I have not read the book. My characterization of it as pop sci is primarily based on your characterization of the comments in the book. That type of grandiose and sensational generalization is characteristic of pop sci literature, as is the conflict identified in the title.

I could certainly be mistaken about the rest of the book, but all of the characteristics described in the opening post scream "pop sci" to me.