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Collin237 said:Why do you have what you call a "Thermodynamic Interpretation"?

A. Neumaier said:My ''thermal interpretation'' is an interpretation of quantum mechanics in general, and the measurement problem in particular. I developed this since none of the present interpretations gives an interpretation fully compatible with the actual practice of using quantum mechanics - where many things - such as spectral lines, Z-boson masses, or electric fields) are measured that are impossible to capture with the Born interpretation underlying all previous interpretations.

1. Within the framework of a Hilbert space for an atom one cannot find an observable in the sense of ''self-adjoint Hermitian operator'' that would describe the measurement of the frequency of a spectral line of the atom. For the latter is given by the differences of two eigenvalues of the Hamiltonian, not by an eigenvalue itself, as Born's rule would require.vanhees71 said:Well, all these quantities are measured with the corresponding measurement devices like spectrometers, particle detectors (for the Z-boson mass and width you measure dilepton spectra in various ways), etc. you find in the physics labs around the world. In physics in fact quantities are defined by giving appropriate (equivalence classes of) measurement protocols to quantitatively observe them. That's why they are called observables after all. Also there is nothing more needed concerning the application of the quantum-theoretical formalism (e.g., formulated as the representation of an observable algebra on Hilbert space, based on various symmetry principles which themselves are discovered by observation of conservation laws) than Born's rule, i.e., the minimal interpretation.

2. The measurement of a Z-boson is not a simple, essentially instantaneous act as the Born rule would require but a complex inference from a host of measurements on decay products. That the Born rule is used implicitly to derive the rules for working with an S-matrix does not make it applicable to the measurement of a Z-boson itself.

3. Electric field operators ##E(x)## are not Hermitian operators to which eigenvalues could be associated but oerator-valued distributions. Thus Born's rule cannot even be applied in principle. The measurement of an electric field already involves an averaging process and really measures an expectation, not an eigenstate.

And this is already needed to explain why we can measure electric fields.vanhees71 said:Where you need something like a "thermal interpretation" is when it comes to understand the overwhelming success of classical physics (including classical relativistic and non-relativistic mechanics, electrodynamics, and thermodynamics) to describe macroscopic systems. Here you need some coarse graining to describe macroscopic effective (relevant) degrees of freedom as (spatio-temporal) averages over many microscopic degrees of freedom.