Question

In Feynman's famous Physics book, The Feynman Lectures on Physics, in a discussion of the generality of Maxwell's equations in the static case, in which he addresses the problem of whether they are an approximation of a deeper mechanism that follows other equations or not, he says [Vol. II, Sec. 12-7 (The "underlying unity" of nature), Par. 7]:

Strangely enough, it turns out (for reasons that we do not at all understand) that the combination of relativity and quantum mechanics as we know them seems to forbid the invention of an equation that is fundamentally different from ∇⋅(κ∇ϕ)=−rhofreeϵ0.
, and which does not at the same time lead to some kind of contradiction. Not simply a disagreement with experiment, but an internal contradiction.

I was wondering first of all if this was a personal observation of Feynman's, or if it was a known thing that I will find in the future while studying and will somehow be pointed out to me in some Physics course. Then I was wondering: could we understand qualitatively what are we talking about? I.e.: how does one theory ensure that there cannot be another different and more precise theory for the phenomena it describes?

Combining Quantum Mechanics and Relativity (especially General Relativity) I think we get to very, very, very complicated things. At this point, could Feynman's point be understood like this: people have tried for a long time to build theories that combine them and in all cases Poisson-style equations popped up somewhere, so there's no theory on the horizon that seems to work but doesn't have that kind of structure?

Answer 1

Feynman's observation about the generality of Maxwell's equations and the combination of relativity and quantum mechanics is a personal observation. No known fact addresses this in physics courses. The complexity of combining quantum mechanics and relativity may be the reason why no fundamentally different equation has been found.

Step-by-step explanation:

Feynman's observation in his book, The Feynman Lectures on Physics, about the generality of Maxwell's equations and the combination of relativity and quantum mechanics is a personal observation. He stated that there seems to be no equation that is fundamentally different from ∇⋅(κ∇ϕ)=−rhofreeϵ0, which leads to contradictions. This observation is not a known fact taught in physics courses.

The inability to find a fundamentally different equation may be due to the complexity of combining quantum mechanics and relativity. It seems that all attempts so far have resulted in equations similar to Poisson-style equations, which are unable to avoid contradictions.