I would comment further on this matter.
Einstein said and I quote "What are light quanta? Nowadays every Tom, Dick and Harry thinks he knows it, but is mistaken".
Feynman was oft quoted to say that QFT an object of his own creation tells us nothing about the real nature of the objects in question.
John Bell said and I quote "I am a Quantum Engineer during the week but a man of priniciple on Sundays". By this he meant that he used all of the mathematical accounting methods which are significant by their accuracy during his normal work, but on Sundays he considered the realism of what the mathematical accounting represented.
Much more recently Rabi described the problem thus "One actually creates a remarkable thing like an electron. Its a marvelous thing. I dont see how its made. It just appears. Its a king of materialization-- the ghost shows up in reality. You can calulate how many electrons will be produced, and with what probability. But how was it born? What is it made of? Its these kind of questions I would like to see answered."
To claim that you can know all that can be known with mathematical abstraction is a complete philosophical copout. Undoubtedly, as Steven says most physicists will resort to this in the first instance (I have done it myself many times), but when pressed most will actually energise the grey matter and devote at least some of it to consideration of the epistomological implications of the mathematical concepts they are spoon fed.
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