The theory claims that the physical object is in some important sense isomorphic to the mathematical object, and thus you call the mathematical object the theory. But the theory is still distinct from the wave itself, at least as I see it.
I think how you view this depends heavily on your views in philosophy of science and metaphysics. It depends both on how realist a view you take about mathematical structures, and on how realist a view you take towards physical "reality".
A Copenhagenist, representing the extreme antirealist position, might say that there is nothing the mathematical theory is isomorphic to, the mathematical structures are creations of the human mind intended for the purpose of predicting events/experiences. Not as a model of some transcendant "Reality". Perhaps I'm exaggerating that viewpoint a little bit, but I think that's pretty close to how a lot of people in physics view it.
At the other extreme, you have people like Max Tegmark who have proposed that there is no difference whatsoever between mathematical structures and reality. All mathematical structures exist, and we happen to find ourselves in one particularly complex one that supports life. Calling this one "physical" and the other mathematical is just an illusion. This is closer to my point of view, although I've begun to doubt whether this can really be satisfactory.
A third view might be that the only difference between a mathematical model and physical reality is some kind of substance, like Brahman, that instantiates the model.
I guess I should also point out that the reason these issues come up with a TOE but not with normal theories, is that any other theory is intended as an approximation to reality, while a TOE is intended to exactly represent (or perhaps be) reality, with no approximations used.
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timeasmymeasure
no subject
Date: 2010-09-15 06:00 pm (UTC)The theory claims that the physical object is in some important sense isomorphic to the mathematical object, and thus you call the mathematical object the theory. But the theory is still distinct from the wave itself, at least as I see it.
I think how you view this depends heavily on your views in philosophy of science and metaphysics. It depends both on how realist a view you take about mathematical structures, and on how realist a view you take towards physical "reality".
A Copenhagenist, representing the extreme antirealist position, might say that there is nothing the mathematical theory is isomorphic to, the mathematical structures are creations of the human mind intended for the purpose of predicting events/experiences. Not as a model of some transcendant "Reality". Perhaps I'm exaggerating that viewpoint a little bit, but I think that's pretty close to how a lot of people in physics view it.
At the other extreme, you have people like Max Tegmark who have proposed that there is no difference whatsoever between mathematical structures and reality. All mathematical structures exist, and we happen to find ourselves in one particularly complex one that supports life. Calling this one "physical" and the other mathematical is just an illusion. This is closer to my point of view, although I've begun to doubt whether this can really be satisfactory.
A third view might be that the only difference between a mathematical model and physical reality is some kind of substance, like Brahman, that instantiates the model.
I guess I should also point out that the reason these issues come up with a TOE but not with normal theories, is that any other theory is intended as an approximation to reality, while a TOE is intended to exactly represent (or perhaps be) reality, with no approximations used.