A Born Rule in Many Worlds Derived?

[gentzen]

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.

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".

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

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.

 

[Fra]

I find it odd that you seek a secure foundation of a microscopic theory in a rigorous description of macroscopic devices.

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).

A theory of measurement without actual measurements, and without actual measurement devices is what is really odd to me.

/Fredrik

 

[WernerQH]

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".

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).

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.

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.

 

[vanhees71]

We should really get rid of the historical approach to QT, again and again stressing, what's so weird about quantum theory but present it as the most successful theoretical description of everything except the gravitational interaction.

It is true that Schrödinger first thought that the wave function describes "the electron" as a "smeared particle-like object" analogously as electromagnetic waves describe "photons" as a "particle-like object" in the sense of the then much discussed socalled "wave-particle dualism". It was almost immediately clear that this original interpretation is contradicting the observed facts, and that was solved already in 1926 by Born in a footnote to his important paper on scattering theory, by introducing the probabilistic interpretation of $|\psi(t,\vec{x})|^2$, which is still considered valid today and is in accordance with all observations for nearly 100 years, and one should be aware that what we can today really observe are single particles/quanta, entangled two-particle (and multi-particle) states, etc. Even the most strange predictions of inseparability, which was the one point Einstein could never accept, are verified with an amazing accuracy and statistical significance. Thanks to the important work by Bell it's also clear that Einstein's hope for a way out, i.e., a deterministic hidden-variable theory (called "realistic" in the (in)famous EPR paper), is definitely closed, but QT is confirmed.

There is still this obsession about the apparent "unsolved" metaphysical problems. From a physical point of view, however, there are none. To put it positive: This obsession has lead to all the above mentioned stringent tests of QT and the development of amazing experimental techniques, which are now becoming a subject of engineering and the hope for ever better new devices useful for practical purposes as "quantum cryptography" and "quantum computers".

 

[Fra]

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.

Even though I think we may have too separated views, it's still interesting to try to let ideas meet.

I can relate to what you write here in the following sense: I share an objection to the continuum. I think the continuum is an idealisation.

In my understanding, it corresponds to an infinitely massive, infinitely dominant observer that has unlimited information processing capacity. That "actual limit" IMO, has IMO no place in a real interation, and any deductions from a formalism relying on the ACTUAL continuum will likely not be right, just approximately exact.

Also the "approximate" continuum, from my perspective does is not encoded in the microscopic system, it's encoded in the environment, in a form of compressed statistics. This is how one can form a continuum out of a historical binary flip. We should also know from other QM effects the significance of the boundary. You can not even observer empty space without a boundary where to put detectors. So no meaningful void without a bondary.

In sense sense, if one asks for some ontological inside picture of what is going on inside the microscopic system, I share the view that it is will have some discreteness. But it's the incomplete description of the discrete phenomena from a different scale, that gives the illustion of a continuuum, or optionallly that it's easier to model with calculus. I share this view, even if we may diverge a lot on other perspectives.

It's the allowance of the ACTUAL limit, that I think has given rise to pathologies that forces us to somewhat ambigous renormalisation methods that gives me a bad stomach feeling that something just isn't right about it, not matter how far we get away with it. IMO this is related to the issue of counting, and when the counter is saturated, then what happens? (I see if from an agent picture, but the idea is that the agent actions is indistinguishable from the interactions of matter actions, it's just a angle to gain causal insight).

I can also connet to some hidden variable traits, which I mentioed before. The inseparability is a statistical fact, but the causal explanation is lacking.

/Fredrik