Maxwell’s equations look very nice when expressed in terms of the four-potential. Does that mean we should believe in its “physical reality” over the “reality” of the electric and magnetic vector fields?
If you consider which concepts are used in Quantum Mechanics, it seems right to favor a formulation of Classical Electromagnetism that focuses on potentials rather than fields.
One reason I’m wary of such questions is on John Baez’s crackpot index:
17. 10 points for arguing that while a current well-established theory predicts phenomena correctly, it doesn’t explain “why” they occur, or fails to provide a “mechanism”.
I understand being wary of the question, but imagine a Bayesian rationalist learning physics. First he learns about Classical Electromagnetism using fields, and he assigns this theory a prior probability based on the length of a program implementing this, and updates to a posterior probability based on the experimental evidence available. He then learns about the formulation based on potentials, which he finds makes all the same predictions, but has a shorter program length, so he adds some number of bits to his log-odds for the equivalence class, and he thinks that it is meaningless to ask whether reality uses potentials or fields, because no experiment could distinguish between them. Then he learns about Quantum Mechanics, which indicates that his classical understanding of potentials is an approximation of how they really work, that works on large scale, and that on the small scale where the approximation does not hold, fields are not a useful concept.
Should he be surprised to learn, having thought that experiment could not distinguish the two formulations, that there is an observable underlying reality in which uses potentials and not fields, and it is only in the domains he has previously encountered that fields make sense?
Note that while it is on the Crackpot index it is one of the weaker parts there. Many actually good scientists try to search for explanatory mechanisms and get annoyed when theories lack explanatory mechanisms.
I don’t know about potentials vs fields, but this seems backwards if you mean it to apply to MWI. That interpretation tries to say that the quantum math describes reality and we need assume no further mechanism.
Beyond that, it seems to me that we don’t care about Occam’s Razor due to William of Occam’s philosophical fapping, nor due to someone proposing the ideal of Solomonoff Induction. We care because Isaac Newton claimed to use a version of the Razor (applied to causes) in making his practical discoveries. Unlike those other formulations, Newton’s four Rules for Natural Philosophy inspired the rest of modern science. And it looks to me like Einstein made his most famous discoveries by interpreting Rule 2 more strictly than Newton himself did.
I mention this because Newton wrote these rules specifically to reduce the appeal of taking his mathematical theory of gravity and adding Cartesian or Aristotelian “mechanisms”, without adding predictions. The analogy with MWI seems inexact (if MWI still has a mathematical hole) but precise enough to encompass your objection. Newton made one possibly-new physical observation that I can recall, and it related to one of his laws of motion rather than his actual law of gravitation. He justified the latter part of his theory solely on the grounds of simplicity, since it allowed the derivation of pre-existing rules drawn from pre-existing observations. (I think the ‘good’ kind of mechanism, the kind JoshuaZ mentions, also brings together previously separate postulates or allows us to make novel predictions.) You’ll notice that Rule 4, the one that says we need new evidence to justify “contrary hypotheses”, technically doesn’t say the preferred theory has to come first (at least not in this English version). The author was no fool. He just said we should take “propositions inferred by general induction from phenomena as accurately or very nearly true,” which means that either induction includes Newtonian simplicity, or effective science has to judge theories by some criteria beyond truth, or this method contradicts itself.
If Solomonoff Induction doesn’t at least give us Newton’s Rules in Newton’s case, then Solomonoff Induction fails at its job.
If you consider which concepts are used in Quantum Mechanics, it seems right to favor a formulation of Classical Electromagnetism that focuses on potentials rather than fields.
One reason I’m wary of such questions is on John Baez’s crackpot index:
I understand being wary of the question, but imagine a Bayesian rationalist learning physics. First he learns about Classical Electromagnetism using fields, and he assigns this theory a prior probability based on the length of a program implementing this, and updates to a posterior probability based on the experimental evidence available. He then learns about the formulation based on potentials, which he finds makes all the same predictions, but has a shorter program length, so he adds some number of bits to his log-odds for the equivalence class, and he thinks that it is meaningless to ask whether reality uses potentials or fields, because no experiment could distinguish between them. Then he learns about Quantum Mechanics, which indicates that his classical understanding of potentials is an approximation of how they really work, that works on large scale, and that on the small scale where the approximation does not hold, fields are not a useful concept.
Should he be surprised to learn, having thought that experiment could not distinguish the two formulations, that there is an observable underlying reality in which uses potentials and not fields, and it is only in the domains he has previously encountered that fields make sense?
And then he learns Quantum Field Theory, and the shit really hits the fan.
Note that while it is on the Crackpot index it is one of the weaker parts there. Many actually good scientists try to search for explanatory mechanisms and get annoyed when theories lack explanatory mechanisms.
I don’t know about potentials vs fields, but this seems backwards if you mean it to apply to MWI. That interpretation tries to say that the quantum math describes reality and we need assume no further mechanism.
Beyond that, it seems to me that we don’t care about Occam’s Razor due to William of Occam’s philosophical fapping, nor due to someone proposing the ideal of Solomonoff Induction. We care because Isaac Newton claimed to use a version of the Razor (applied to causes) in making his practical discoveries. Unlike those other formulations, Newton’s four Rules for Natural Philosophy inspired the rest of modern science. And it looks to me like Einstein made his most famous discoveries by interpreting Rule 2 more strictly than Newton himself did.
I mention this because Newton wrote these rules specifically to reduce the appeal of taking his mathematical theory of gravity and adding Cartesian or Aristotelian “mechanisms”, without adding predictions. The analogy with MWI seems inexact (if MWI still has a mathematical hole) but precise enough to encompass your objection. Newton made one possibly-new physical observation that I can recall, and it related to one of his laws of motion rather than his actual law of gravitation. He justified the latter part of his theory solely on the grounds of simplicity, since it allowed the derivation of pre-existing rules drawn from pre-existing observations. (I think the ‘good’ kind of mechanism, the kind JoshuaZ mentions, also brings together previously separate postulates or allows us to make novel predictions.) You’ll notice that Rule 4, the one that says we need new evidence to justify “contrary hypotheses”, technically doesn’t say the preferred theory has to come first (at least not in this English version). The author was no fool. He just said we should take “propositions inferred by general induction from phenomena as accurately or very nearly true,” which means that either induction includes Newtonian simplicity, or effective science has to judge theories by some criteria beyond truth, or this method contradicts itself.
If Solomonoff Induction doesn’t at least give us Newton’s Rules in Newton’s case, then Solomonoff Induction fails at its job.