Einstein's field equations are true, and have been tested. But the question why they are true has been attempted to be answered by string theory, etc.
Maxwell's equations are also true, but does string theory have anything to say about why?
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9$\begingroup$ Physics can describe nature by finding equations that match experimental observations. 'Why' questions of such a nature are indeed metaphysics - which isn't to say that someone on this forum might not have something interesting to say in response to your question. $\endgroup$– Martin C.Commented Apr 3 at 6:46
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2$\begingroup$ D.H. Sattinger arxiv.org/abs/1305.6874 derives the Maxwell equations from Hodge theory together with the laws of Gauss and Ampere taken as axioms. The MEs are therefore geometric in nature. $\endgroup$– Kurt G.Commented Apr 3 at 9:00
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3$\begingroup$ Science laymen and beginners always bring up the matter of "why" nature is describable as we find it to be. I suspect that, besides being the dominant mode of inquiry in the human world of intentioned social actors, it connects with a desire for sense of wonder and great vistas of really understanding the universe. And I suspect that desire may be behind your being somewhat satisfied upon hearing about string theory, and now about QED -- they give you hope. Yet consider that any eventual underpinning accounts from those directions will leave you with the same want all over again. $\endgroup$– ariolaCommented Apr 3 at 18:11
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1$\begingroup$ Your definition is at best that of 'relatively true' or 'often but not always true'. Not of 'True'. 'True' is a mathematical concept. $\endgroup$– my2ctsCommented May 4 at 14:10
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1$\begingroup$ @DanielFBest Do note that deleting questions/answers does not lift the block. It only makes it worse. $\endgroup$– Vincent ThackerCommented May 4 at 15:44
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I think this question is one of metaphysics and should be directed to philosophers of physics.
When asking a physicist "why are Maxwell's equations true?", one would be met with "because it agrees with observations, experiments and has predictive power".
This would be true with almost all physical theories. No one can satisfactorily explain why, but we seem to know a good deal about how.
And to be a little more accurate, Maxwell's equations are "true" as long as we are talking about macroscopic EM phenomena. The equations break down at the quantum level and so a new construct, namely QED, is sought. As for your example about general relativity, it is also a more accurate replacement for the classical Newtonian gravitation.
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2$\begingroup$ Thank you - that answers my question, especially your reference to QED. $\endgroup$ Commented Apr 3 at 6:49
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2$\begingroup$ No worries and good luck with your studies. $\endgroup$– joseph hCommented Apr 3 at 6:50
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1$\begingroup$ Even QED breaks down sufficiently microscopically (ie the Landau pole problem), so our current best understanding is still "true up to a point" $\endgroup$ Commented Apr 3 at 8:23
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$\begingroup$ @DanielFBest Definitely metaphysical. All pursuit of "why" can continue ad infinity. For scientist the job is to record the facts and construct the simplest possible theories with predictive power and correct description of phenomenology. $\endgroup$ Commented Apr 3 at 21:07