In section III.B of this paper, he said:gentzen said:No, the quantum field and the wave function are not related like this for Hobson. The non-relativistic wave function is not considered as "real" by Hobson.
The best places to start areSambuco said:- Consistent histories (@Morbert, Where should I start?).
I read this as a statement about the relation between to the non-QFT single particle Dirac equation, and the non-QFT single particle Schroedinger equation. And as a (true) statement about second quantization in the wider context of that paragraph.Sambuco said:"The Schroedinger field is the non-relativistic version of the Dirac equation's relativistic field. It follows that the Schroedinger matter field, the analogue of the classical EM field, is a physical, space-filling field. Just like the Dirac field, this field is the electron."
The problem with this is that the term "space-filling" can't possibly be right, except for the obviously unphysical case of a single spinless quantum system alone in the universe. The "Schrodinger field" for any system more complicated than that is not a function on ordinary 3-dimensional space; it's a function on the configuration space of the system. For 3N spinless "particles", for example, this is a function on a 3N-dimensional space. So whatever the "Schrodinger field" is, it can't be interpreted the way the classical EM field is interpreted.Sambuco said:It follows that the Schroedinger matter field, the analogue of the classical EM field, is a physical, space-filling field.
It seems he is trying to say something like that, but it is really confusing. Indeed, in the conclusions, he says:gentzen said:I read this as a statement about the relation between to the non-QFT single particle Dirac equation, and the non-QFT single particle Schroedinger equation. And as a (true) statement about second quantization in the wider context of that paragraph.
It is not a claim that the n-particle wave function occuring in non-relativistic QM would be "real".
Yes, that is how one has to use QM as an instrumentalist in practical computations. This is the trouble with the word "measurement". However, what PeterDonis dislikes about this "to interact at x" interpretation is that you have to consider superpositions of such "to interact at x" events at some point (just like in MWI).Sambuco said:Thus Schroedinger's Ψ(x,t) is a spatially extended field representing the amplitude for an electron (i.e. the electron-positron field) to interact at x rather than an amplitude for finding, upon measurement, a particle.
No, that's not what I was saying. What I was saying is that as soon as you have more than one spinless particle, the wave function is not a function of ##x##, if ##x## is interpreted as a position in ordinary space. It's a function on configuration space, which is a 3N-dimensional space--for two spinless particles, it's a 6 dimensional space, 3 dimensions for each particle. In terms of "particle positions", for two spinless particles it's a function of two positions--the position of each of the two particles. Even a single such function, not a "superposition" of anything, is still not a function of "position" in ordinary space.gentzen said:what PeterDonis dislikes about this "to interact at x" interpretation is that you have to consider superpositions of such "to interact at x" events at some point
Incidentally, I find this topic particularly interesting because part of my work involves developing models for total dose in MOSFETs, and the charge generation stage is always modeled using semi-empirical expressions.gentzen said:(Simple example: The electron interacts with the valence electrons in a crystal, and can cause ionization events. But the secondary electrons "created" during those ionization events can interfere with other secondary electrons that could have been "created". Not an overly important effect, but still a measurable effect.)
It's not clear what it means that the Dirac field is "physical", given that this field operator is not self-adjoint, so it is not even an observable.Sambuco said:In section III.B of this paper, he said:
"The Schroedinger field is the non-relativistic version of the Dirac equation's relativistic field. It follows that the Schroedinger matter field, the analogue of the classical EM field, is a physical, space-filling field. Just like the Dirac field, this field is the electron."
Lucas.
To me it is clear. It represents a physical object, the field. On the other hand an observble cannot be real in this sense, it only represents some property of something that is real.Demystifier said:It's not clear what it means that the Dirac field is "physical", given that this field operator is not self-adjoint, so it is not even an observable.