Consul wrote: ↑March 24th, 2023, 10:44 amRight, "any energy…cannot exist without something possessing it," but I don't regard fields as substantial
substrata, thinking that they are nothing but
nonsubstantial collections or distributions of determinate physical quantities belonging to some determinable physical quantity such as energy or mass…
Footnote: What I write above is true of
classical fields but not of
quantum fields, because these do not consist in attributions of
determinate physical quantities to spacetime-points—which raises the question as to whether quantum fields are real physical fields at all rather than mathematical constructs.
There is an essential difference between classical fields and quantum fields. Mathematically, both kinds of fields are well defined and understood. Ontologically and physically, classical fields are well understood too, but quantum fields are not. For in quantum-field theory the quantum-field values assigned to spacetime points are not
determinate,
definite values of physical quantities but only
expectation values for physical quantities that express the
probability of measuring some value somewhere. Now the ontological question is: Are such probability fields (probabilistic quantum fields) really out there in the physical world, or are they just physically useful mathematical fictions? Since physics is the science of physical reality and its nature, this question is of utmost importance.
QUOTE>
"The transition from a classical field theory to a quantum field theory is characterized by the occurrence of
operator-valued quantum fields
phi(x,t), and corresponding conjugate fields, for both of which certain canonical commutation relations hold. Thus there is an obvious formal analogy between classical and quantum fields: in both cases field values are attached to space-time points, where these values are specified by real numbers in the case of classical fields and operators in the case of quantum fields. That is, the mapping
x –> phi(x,t) in QFT is analogous to the classical mapping
x –> phi(x,t). Due to this formal analogy it appears to be beyond any doubt that QFT is a field theory.
But is a systematic association of certain mathematical terms with all points in space-time really enough to establish a field theory in a proper physical sense? Is it not essential for a physical field theory that some kind of real physical
properties are allocated to space-time points? This requirement seems not fulfilled in QFT, however. Teller (1995: ch. 5) argues that the expression
quantum field is only justified on a “perverse reading” of the notion of a field, since no definite physical values whatsoever are assigned to space-time points. Instead, quantum field operators represent the whole spectrum of possible values so that they rather have the status of observables (Teller: “determinables”) or general solutions. Only a specific
configuration, i.e. an ascription of definite values to the field observables at all points in space, can count as a proper physical field."
Quantum Field Theory:
https://plato.stanford.edu/entries/quan ... ld-theory/
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