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Question
SRT unified mechanics and electrodynamics. The principle of equivalence equates relative motion with gravity. Why is the pursuit of a unified field theory so difficult?

Answer
First thing to know: field theory (ie, explaining fundamental forces and other physical phenomena though the use of fields) has, over the decades, been unbelievably successful in making predictions that match experiment. Quantum electrodynamics (QED), for example, has been able to predict experimental values to an accuracy of ten significant digits -- the equivalent of being able to state the EXACT NUMBER of stocks that will be sold tomorrow on the NYSE. Similarly, general relativity (GR) has been unchallenged in describing gravity.

QED met a major obstacle during its development: specifically, its mathematics led to a number of infinities. What happened in the 1940s was that mathematicians and physicists were able to make the infinities go away through a mathematical process called "renormalization."

In a (HIGHLY SIMPLIFIED) nutshell, they disappeared when scientists arbitrarily assumed that there was a minimum distance that could exist between two points in space, did calculations based on this assumption, found a finite number, made that distance go to zero, and then found that finite numbers still remained. They basically found that subtracting ∞ from ∞ gave a specific value!
If you find renormalization an ad hoc solution that was accepted only because it "worked," you're not alone. Even Richard Feynman, one of the founders of QED, criticized it in basically those terms. It was not until the 1980s that physicists developed a theory that was internally consistent.

A "unified field theory" is a mathematical description that will encompass both QED and GR. Any attempt to do so, however, runs immediately into this problem: you can NOT do renormalization with GR. If you assume there are any minimum distances in space-time, all the math becomes nonsensical. So you have one theory that REQUIRES renormalization with another theory that FORBIDS it! Despite decades of attempts by some of the most brilliant minds in the history of science, nobody has been able to resolve this conundrum.

The only theories that unify QED and GR are ones that explicitly reject the entire concept of fields as fundamental to our Universe. In that sense, ideas that might eventually be found to be the "theory of everything" are not unified field theories.

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I can help with understanding physics that does not involve eggs. I will NOT help with academic or professional questions, which are NOT limited only to homework. Please do not waste your time by asking a question that comes out of ANY kind of academic, professional, or business matters.

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Have been fascinated by physical laws ever since I learned, at age seven, that magnets work under water. My study continued through college and has not ceased even after I retired.

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B.A. in Physics (with honors) from University of California at Berkeley.M.A. in Physics (with honors) from University of Texas Austin.

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