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6/19/2025, 12:19:45 AM
>>16699836
>In other words, what medium is the wave function describing the oscillations of? what is actually waving when we describe an electron as a wave?
This is mostly philosophy. What is "space" even? For a quantum field, we just use [math]\mathbb{R}^4[/math] as indices for operators that all act on a single universal wave function. The interpretation of the indices as being "close" or "far" from each other comes from how we define the algebraic relations of the operators.
>Also, when we perform the double slit experiment with light, is it the electromagnetic wave or the wave function that is causing the interference pattern? Is the wave function of the photon actually the same as its electromagnetic wave or are they two unrelated concepts?
First of all, I recommend Lamb's article on the term "photon" and why he thinks it's retarded (https://link.springer.com/article/10.1007/BF01135846). I tend to agree with him, usually it is better to think in terms of the fields instead.
The way I think of it is like this: In a double slit experiment, you excite an electromagnetic field mode with a (close to) definite wave number. But this mode is short-lived because of interactions with the atoms in the slits; very quickly, you end up in a superposition of states where the occupation of the modes can be described very similarly to the classical solution of the problem. You then have another transition where one of the atoms in the photo plate ends up in its excited state, and the probability of this transition to happen at each point also ends up proportional to the classical amplitude.
But at every moment, you only have [math]\textit{one}[/math] wave function, which simultaneously describes all of the electromagnetic field modes and all the atoms in the experiment.
>In other words, what medium is the wave function describing the oscillations of? what is actually waving when we describe an electron as a wave?
This is mostly philosophy. What is "space" even? For a quantum field, we just use [math]\mathbb{R}^4[/math] as indices for operators that all act on a single universal wave function. The interpretation of the indices as being "close" or "far" from each other comes from how we define the algebraic relations of the operators.
>Also, when we perform the double slit experiment with light, is it the electromagnetic wave or the wave function that is causing the interference pattern? Is the wave function of the photon actually the same as its electromagnetic wave or are they two unrelated concepts?
First of all, I recommend Lamb's article on the term "photon" and why he thinks it's retarded (https://link.springer.com/article/10.1007/BF01135846). I tend to agree with him, usually it is better to think in terms of the fields instead.
The way I think of it is like this: In a double slit experiment, you excite an electromagnetic field mode with a (close to) definite wave number. But this mode is short-lived because of interactions with the atoms in the slits; very quickly, you end up in a superposition of states where the occupation of the modes can be described very similarly to the classical solution of the problem. You then have another transition where one of the atoms in the photo plate ends up in its excited state, and the probability of this transition to happen at each point also ends up proportional to the classical amplitude.
But at every moment, you only have [math]\textit{one}[/math] wave function, which simultaneously describes all of the electromagnetic field modes and all the atoms in the experiment.
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