I'm wondering if quantum field theory re-interprets the meaning of the wave function of Schrodinger's equation. But more specifically, I'm trying to understand how to explain the double slit experiment using quantum field theory's interpretation that, in the universe, "there are only fields."
As background, in this post, Rodney Brooks states:
In QFT as I learned it from Julian Schwinger, there are no particles, so there is no duality. There are only fields - and “waves” are just oscillations in those fields. The particle-like behavior happens when a field quantum collapses into an absorbing atom, just as a particle would.
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And so Schrödinger’s famous equation came to be taken not as an equation for field intensity, as Schrödinger would have liked, but as an equation that gives the probability of finding a particle at a particular location. So there it was: wave-particle duality.
Sean Carroll makes similar statements, that the question "what is matter--a wave or a particle?" has a definite answer: waves in quantum fields. (This can be found in his lectures on the Higgs Boson.)
In the bolded passage above, Dr. Brooks seems to suggest that QFT provides a physical interpretation which removes superposition. And he says as much in another post here:
In QFT there are no superpositions. The state of a system is specified by giving the field strength at every point – or to be more precise, by the field strength of every quantum. This may be a complex picture, but it is a picture, not a superposition.
So taking up the double slit experiment, is the following description accurate? When the electron passes through the double slit, waves in the electron quantum field interfere. When the wave collapses into a particle, it takes on the position at one of the locations where the electron quantum field is elevated. So the electron particle can't "materialize" in any locations where the electron quantum field interferes destructively. This gives rise to the interference pattern on the back screen.
Is this a correct description of the double slit experiment from QFT's interpretation that, in the universe, "there are only fields"? If this is correct, then it seems like QFT says the wave function is more than just a probability wave: the wave function describes a physical entity (excitations in the underlying quantum field). There is still a probabilistic element: the position where the wave collapses into a particle has some random nature. Am I understanding correctly that QFT adds a new physical entity (quantum fields) which expands our physical interpretation of the wave function?
Answer
There is overlap with other questions linked in the comments. But, perhaps the focus of this question is different enough to merit a separate answer. There are at least two distinct but equivalent formalisms of QFT, the canonical approach and the path integral approach. Although, they are equivalent mathematically and in their experimental predictions, they do provide very different ways of thinking about QFT phenomena. The one most suited for your question is the path integral approach.
In the path integral approach, to describe an experiment we start with the field in one configuration and then we work out the amplitude for the field to evolve to another definite configuration that represents a possible measurement in the experiment. So in the two slit case we can start with a plane wave in front of the two slits representing the experiment starting with an electron of a particular momentum. Then our final configuration will be a delta function at the screen representing the electron measured at that point at some later specified time. We can work out the probability for this to occur by evaluating the amplitude for the field to evolve between the initial and final configuration in all possible ways. We then sum these amplitudes and take the norm in the usual QM way.
So in this approach there are no particles, just excitations in the field.
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