Gravity - The weakest force?

[George Jones]

George, this is no time to get coy.

At work, I can procrastinate and make shorter posts while drinking tea, but for an adequate post here, it will take me some time to collect and organize my thoughts, and to compose a post. Can't do it tomorrow or Thursday; maybe Friday.

I can quote from the preface of a book that I have not read in depth, Quantum Field Theory: A Tourist Guide for Mathematicians by Gerald Folland.

"Sixty years after the growth of quantum electrodynamics (QED) and forty years after the discovery of the other gauge field theories on which the current understanding of the fundamental interactions of physics is based, putting these theories on a sound mathematical foundation remains an outstanding open problem ..."

I hope to say more.

[themos]

That would be great, thanks!

[brianb]

putting these theories on a sound mathematical foundation remains an outstanding open problem ...

So is the Extended Riemann Hypothesis. Nevertheless there are a lot of research papers by eminent & well-respected mathematicians which depend on ERH for proof.

QED depends on a mathematical shortcut for formal proof but nevertheless "works" as a physical model.

Just remember that Godel proved (rigidly) that no self-contained axiomatic system can be completely consistent in the sense that all true theorems can be proved ... as mathematics is a self-contained axiomatic system, it follows that there are theorems which are true (no counterexample can ever be found) but which are nonetheless unprovable. If you don't like the mathematics behind QED, it's your responsibility to find a example of specific inputs which yield an output which is at variance with observations, after allowing for experimental error. Disproof by counterexample is a very strong technique for demolishing incorrect deductions.

[George Jones]

Sorry for rearranging your post. If you think this distorts what you have written, I apologise.

QED depends on a mathematical shortcut for formal proof

I don't know what this statement means. What is the "mathematical shortcut"? What is the "formal proof"?

My point is not that QED is not proved (mathematically), my point is that QED is not mathematically well-defined as honest mathematics. Even if QED were well-defined, it would not be proved. I agree with the mathematical physicist Robert Geroch, who does care about such matters, and who wrote 'I wouldn't recognize a "proof of a physical theory" if I saw one.'

but nevertheless "works" as a physical model.

With great success! As physics, one couldn't ask for anything more from a physical theory.

So is the Extended Riemann Hypothesis. Nevertheless there are a lot of research papers by eminent & well-respected mathematicians which depend on ERH for proof.

Although unproved, the Extended Riemann Hypothesis is mathematically well-defined.

Just remember that Godel proved (rigidly) that no self-contained axiomatic system can be completely consistent in the sense that all true theorems can be proved ... as mathematics is a self-contained axiomatic system, it follows that there are theorems which are true (no counterexample can ever be found) but which are nonetheless unprovable.

QED will never be proved. The issue I have brought up is not one of proof, it is one of well-definedness, and hence Godel's theorems have no relevance whatsoever. I can't emphasize this strongly enough.

If you don't like the mathematics behind QED,

Where did I write that I "don't like the mathematics behind QED"? This is not a matter of subjective personal taste, it is a much more starightforward mathematical issue.

it's your responsibility to find a example of specific inputs which yield an output which is at variance with observations, after allowing for experimental error. Disproof by counterexample is a very strong technique for demolishing incorrect deductions.

Phys. Rev. 85, 631 (1952): Divergence of Perturbation Theory in Quantum Electrodynamics

is the seminal paper.

[themos]

Dyson's argument is interesting but it's basically hand-waving. We already know we can't expect spacetime to be "nice" at short distances and QED will need modification in terms of the concepts used but its calculations for phenomena in the accessible energy regime are stable.