- #36
No offence, my views are an extremal version of a sort of evolutionary information algorithmic qbism version. The supposed advantage I see, has todo with the quest of unification of forces. My view is that, if we disregard unification problems, and just wants to understand QM - as it is - then I am close to some minimalist statistical interpretation. Beacuse this interpretation makes perfect sense! but only as a limiting case of my general view. For the general case, modifcation of QM is required (this is my take on this).I'm sorry, but I can't see the advantage of the views you propose. (If I understand them at all.) No offence!
This seems to me wishful thinking.It doesn't. Born's rule is needed only when you think of the wave function as the linchpin of quantum theory, as an additional step (to obtain numbers that you can compare with experiment). But with a path integral over a complete time-path you can write down expressions for all measurable quantities directly. One obtains probabilities (rather than probability amplitudes) automatically. Born's rule is built-in, and there's no need to introduce "measurement" as a separate process that somehow disrupts unitary evolution. In my view QM/QFT is just a machinery for calculating correlation functions, and the closed time-path formalism doesn't need a derivation from a set of historical axioms. It works nicely.
There's more than one version of Schwinger's action principle. I had in mind the variant that he used in the paper in which he invented the closed time path formalism (J.Math.Phys. 2, 407):For example, how does one obtain the probabilities that go into Bell experiments (i.e., the relation between the photon count statistics and the incident two_photon states) from the equations deduced from the Schwinger's action principle? Or those for a Stern-Gerlach experiment?
It has the Born rule sort of "built in", because probability amplitudes on the forward time branch are accompanied by their complex conjugates on the backward time branch.[...] a knowledge of the transformation function referring to a closed time path determines the expectation value of any desired physical quantity [...]
How in QFT do you get probabilities? I thought that the primary quantity that Feynman diagrams(for example) allow you to calculate is amplitudes.It doesn't. Born's rule is needed only when you think of the wave function as the linchpin of quantum theory, as an additional step (to obtain numbers that you can compare with experiment). But with a path integral over a complete time-path you can write down expressions for all measurable quantities directly. One obtains probabilities (rather than probability amplitudes) automatically. Born's rule is built-in, and there's no need to introduce "measurement" as a separate process that somehow disrupts unitary evolution. In my view QM/QFT is just a machinery for calculating correlation functions, and the closed time-path formalism doesn't need a derivation from a set of historical axioms. It works nicely.
Of course it's easiest just to take the squared modulus of a scattering amplitude. Schwinger's closed time-path method is more complicated, because what it amounts to is computation of the product of the S-matrix with its time-reverse. For such cases where a single process is dominant it leads to the same result. But the closed time-path method also produces interference terms when more than one process is involved. It is especially useful for non-equilibrium systems.How in QFT do you get probabilities? I thought that the primary quantity that Feynman diagrams(for example) allow you to calculate is amplitudes.
The probabilities that "go into Bell experiments" can of course be worked out using QED, as you surely are aware.
This only gives the recipes for calculating the probabilities, but not the statement that these are probabilities for detecting individual photons. Here Born's rule needs to be assumed. See, e.g., the discussion relating S-matrix entries to detection rates in Chapter 3 of Weinberg's QFT book, where he gives explicit details.Of course it's easiest just to take the squared modulus of a scattering amplitude.
Of course Born's rule has to enter in one way or another. That's what I've been saying all along. Unitary evolution is not the whole story.This only gives the recipes for calculating the probabilities, but not the statement that these are probabilities for detecting individual photons. Here Born's rule needs to be assumed.
It doesn't. Born's rule is needed only when you think of the wave function as the linchpin of quantum theory, as an additional step (to obtain numbers that you can compare with experiment). But with a path integral over a complete time-path you can write down expressions for all measurable quantities directly. One obtains probabilities (rather than probability amplitudes) automatically. Born's rule is built-in,
You had claimed that Born's rule is built-in in his approach. I was just responding that Schwinger's approach does not eliminate the need for Born's rule (or something implying it) in addition to the formal mathematics. Thus it is not built-in but assumed in addition.Of course Born's rule has to enter in one way or another. That's what I've been saying all along. Unitary evolution is not the whole story.
For me Schwinger's closed time-path "recipe" has more logical coherence than the usual prescription of (1) calculating the scattering amplitude (unitary dynamics), and then (2) taking the squared modulus (Born rule, "measurement"). You are not saying that Schwinger didn't know how to apply QED, are you?
That depends on what you accept as first principle(s). I'm inclined to accept the closed time-path formalism as "the" principle of quantum theory, and be happy about the marvelous agreement with experiments. Asking the question why that is so is like asking why the speed of light is the same in all reference frames.The measurement problem - the quest to derive from first principles why the statistical expectations computed from measurement results (read from a large quantum system called detector) agree with the quantum expectations calculated from Schwinger's machinery (or its modern version given e.g., in the book by Calzetta and Hu) - remains unsolved.
The closed-time-path formulation (aka Schwinger-Keldysh formalism; when Keldysh was present, it has been better to call it only Keldysh formalism though) is just a method to calculate directly expectation values, taken with respect to a given statistical operator rather than transition amplitudes/S-matrix elements. The definition of expectation values in terms of the quantum-mechanical formalism, however, uses Born's rule to interpret the states, represented by statistical operators. So also with the closed-time-path action functional(s) you can't derive Born's rule but you use it to define the expectation values you calculate.There's more than one version of Schwinger's action principle. I had in mind the variant that he used in the paper in which he invented the closed time path formalism (J.Math.Phys. 2, 407):
It has the Born rule sort of "built in", because probability amplitudes on the forward time branch are accompanied by their complex conjugates on the backward time branch.
The probabilities that "go into Bell experiments" can of course be worked out using QED, as you surely are aware. But perhaps you are viewing it from a wrong angle, if your focus is on how a photon wave function collapses to produce a definite measurement result.
Conincidently I ask this question as well, and I think a potential explanation is not unrelated to the probability question.Asking the question why that is so is like asking why the speed of light is the same in all reference frames.
The CTP formalism does not say anything about measurement, it talks only about computing N-point functions. Why these N-point functions give expectation values of measurement results is not touched at all by this formalism.That depends on what you accept as first principle(s). I'm inclined to accept the closed time-path formalism as "the" principle of quantum theory, and be happy about the marvelous agreement with experiments. Asking the question why that is so is like asking why the speed of light is the same in all reference frames.
What you see as a defect of the closed-time-path formalism I see as its biggest virtue. It avoids the discussion of "measurement" and its strange interplay with unitary evolution. It handles reversible (microscopic) and irreversible processes ("measurements", "detection events") on the same footing. One needs quantum theory to understand how the detectors in the Bell-type experiments work. I find it odd that you seek a secure foundation of a microscopic theory in a rigorous description of macroscopic devices. As John Bell has argued, there should be no place for the term "measurement" in the foundations of QM. It does sound silly to phrase the discussion of nuclear reactions in the interior of the sun (for example) in terms of "state preparation" and "measurement".The CTP formalism does not say anything about measurement, it talks only about computing N-point functions. Why these N-point functions give expectation values of measurement results is not touched at all by this formalism.
Maybe I misunderstood something, but my impression was that you claimed Schwinger's closed-time-path formalism would have the Born rule sort of "built in". A. Neumaier and others were just reacting to this unexpected and surprising assertion. Your assertion was surprising, because it seemed to violate "conservation of difficulty". Now you seemed to have somewhat scaled back what you assert, but at the same time try to criticize A. Neumaier for pointing out that the CPT-formalism by itself does not provide the link to experiment in the way the Born rule does for "most other formalisms".What you see as a defect of the closed-time-path formalism I see as its biggest virtue. It avoids the discussion of "measurement" and its strange interplay with unitary evolution. It handles reversible (microscopic) and irreversible processes ("measurements", "detection events") on the same footing.
It is fine if you want to interpret it in that way. But this interpretation seems to imply an ontological commitment to "microscopic events", and that commitment seems to be something in addition to the pure CPT-formalism.I don't find the N-point functions as mysterious as they appear to you. They can and should be seen as describing the correlations between microscopic events
As I see it, the THEORY of the microscopic world, literally LIVES(=informaiton implies in it is inferred and encoded) in the macroscopic world. I do not see this as a problem. I see it as as RELATION between scales (but there are some subtle issues in this which you can handle in different ways).I find it odd that you seek a secure foundation of a microscopic theory in a rigorous description of macroscopic devices.
The split between unitary evolution and measurement has much to do with the idea that the wave function is the linchpin of quantum theory. I think that the two cannot be separated. The Born rule has been added as an afterthought (certainly for Born!), whereas it clearly belongs to the central core of the formalism (in which form whatever). The ongoing discussions about how the wave function relates to the real world has given the Born rule a peculiar status that I find distracting (making QM harder to understand).Maybe I misunderstood something, but my impression was that you claimed Schwinger's closed-time-path formalism would have the Born rule sort of "built in".
That's right. If continuous fields evolve continuously, it remains a deep mystery how photons can be counted. But it is easy to visualize a medium as having graininess, as being composed of atoms. Likewise a quantum field can have structure that is not present in the macroscopic theory from which it has been derived by quantization. There are plenty examples in statistical field theory and condensed matter physics. It is possible to express a photon absorption coefficient (i.e. the expected number of absorptions minus the number of stimulated emissions) as a Fourier integral over the current density fluctuations in the medium (a kind of Kubo formula). That's why I said that QFT is just a machinery for calculating correlation functions.It is fine if you want to interpret it in that way. But this interpretation seems to imply an ontological commitment to "microscopic events", and that commitment seems to be something in addition to the pure CPT-formalism.
Even though I think we may have too separated views, it's still interesting to try to let ideas meet.That's right. If continuous fields evolve continuously, it remains a deep mystery how photons can be counted. But it is easy to visualize a medium as having graininess, as being composed of atoms.