Could QM Arise From Wilson's Ideas

[A. Neumaier]

(2) The Keldysh closed time-path formalism. It eliminates the need for "measurements".

How does it achieve this claimed fact??

The CTP formalism only calculates q-expectations (n-point functions) but does not relate these to measurements. Thus it does not even touch the questions associated with measurements, let alone eliminate the need for them.

 

[WernerQH]

The CTP formalism only calculates q-expectations (n-point functions) but does not relate these to measurements. Thus it does not even touch the questions associated with measurements, let alone eliminate the need for them.

Indeed, it doesn´t mention measurements. Why should it?
Through the fleeting presence of a virtual W-boson, the collision between two protons in the interior of the sun occasionally produces a deuteron. We have a good theory for that. What´s the place of "measurement" in a theory of the interior of the sun?

I think John Bell has made a strong case "Against Measurement". Von Neumann may have hoped to make a vague term like "measurement" precise by embedding it in a rigid set of axioms. But the continuing debates on the measurement problem indicate that this hasn´t happened. Mathematicians delight in the formal structure of a theory, but physicists are more interested in what it is that is being measured.

 

[WernerQH]

What's the rest of the truth?

A stochastic element is obviously missing. If evolution is perfectly continuous, you would have to conclude that the click of a Geiger counter is only a trick played on us by our senses.

 

[EPR]

Indeed, it doesn´t mention measurements. Why should it?
Through the fleeting presence of a virtual W-boson, the collision between two protons in the interior of the sun occasionally produces a deuteron. We have a good theory for that. What´s the place of "measurement" in a theory of the interior of the sun?

You already assume the existence of a classical Sun made of classical particles that bumb into each other. The only issue with this is that these classical particles do not exist
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[Demystifier]

A stochastic element is obviously missing. If evolution is perfectly continuous, you would have to conclude that the click of a Geiger counter is only a trick played on us by our senses.

So you mean something like Nelson interpretation? (Particles have stochastic trajectories ##x(t)## which are continuous but non-smooth.)

 

[stevendaryl]

Indeed, it doesn´t mention measurements. Why should it?
Through the fleeting presence of a virtual W-boson, the collision between two protons in the interior of the sun occasionally produces a deuteron. We have a good theory for that. What´s the place of "measurement" in a theory of the interior of the sun?

I agree that quantum mechanics SHOULDN'T be about measurements. But the clearest statement about how probabilities come into play in QM does involve measurements. When you measure an observable, you get an eigenvalue of the corresponding operator, with probabilities given by the Born rule.

Decoherence seems like a replacement for measurement in the formalization of QM. You take the full density matrix and trace out the environmental degrees of freedom and what's left looks approximately diagonal. As if the system had "collapsed" to one configuration with probabilities given by the Born rule. But that's a little unsatisfying to me because it seems very subjective to choose which degrees of freedom are the environment.

 

[stevendaryl]

I agree that quantum mechanics SHOULDN'T be about measurements. But the clearest statement about how probabilities come into play in QM does involve measurements. When you measure an observable, you get an eigenvalue of the corresponding operator, with probabilities given by the Born rule.

That's one way to state the "measurement problem": formulate QM in a way that doesn't mention measurements at all, but which gives the same probabilities as the standard recipe. Bohmian mechanics does that.

 

[A. Neumaier]

it doesn´t mention measurements. Why should it?

Because the problems are at the point where an experiment records permanent data - where the talk about probabilities ends. So not in the sun, but when the light emitted from the sun enters our instruments and leaves permanent traces.

The CTP formalism does not help in the least to understand how this can happen.

 

[WernerQH]

Because the problems are at the point where an experiment records permanent data - where the talk about probabilities ends. So not in the sun, but when the light emitted from the sun enters our instruments and leaves permanent traces.

Can nuclear reactions be understood without quantum theory? And don't you think of the accumulation of helium in the sun as a "permanent trace"?

 

[WernerQH]

So you mean something like Nelson interpretation? (Particles have stochastic trajectories ##x(t)## which are continuous but non-smooth.)

No. There must be discontinuities. The number of photons, for example, cannot increase by 0.77.

 

[Sunil]

I don’t understand the claim that “we know you can start with just about anything, and at low energies, the effective theory will look renormalizable”. I thought that the whole reason that quantum gravity is so hard is because the most naive way to quantize GR leads to something that is non-renormalizable.

But for low energy, gravity is extremely weak, so weak that it safely can be ignored. What remains observable in all those particle colliders are only renormalizable theories.

So, the point remains correct. While the whole theory of physics, gravity + SM, is not renormalizable because of GR, it looks renormalizable in particle colliders.

It is only because gravity has no negative charges, that all masses add up, which makes gravity visible in comparison with the SM fields.

 

[A. Neumaier]

Can nuclear reactions be understood without quantum theory? And don't you think of the accumulation of helium in the sun as a "permanent trace"?

How do we know there is accumulated helium in the sun? Even to measure the amount of helium accumulated in the sun, measurements are required. The understanding of the latter in terms of the microscopic quantum description of the equipment is missing.

 

[PeterDonis]

The number of photons, for example, cannot increase by 0.77.

Sure it can. There are plenty of states which are not eigenstates of photon number, and it's easy to find two of them whose expectation values of photon number differ by 0.77.

 

[WernerQH]

Sure it can. There are plenty of states which are not eigenstates of photon number, and it's easy to find two of them whose expectation values of photon number differ by 0.77.

That's interpretation-dependent. You're assuming that the wave function represents an individual system.

 

[PeterDonis]

That's interpretation-dependent. You're assuming that the wave function represents an individual system.

No, I'm just pointing out that your "number of photons" is not the simple thing you appear to think it is. Nothing I said was interpretation dependent: states and expectation values are part of the basic math of QM.

 

[Sunil]

Sure it can. There are plenty of states which are not eigenstates of photon number, and it's easy to find two of them whose expectation values of photon number differ by 0.77.

Yes. Given the beautiful mathematics necessary for doing this, it is useful to learn it. The tool is the holomorphic representation of the canonical commutation relations. (Formulas out of bad memory, thus, modulo signs, p replaced with q, and factors ##2, \sqrt{2}, \sqrt{2\pi}##.) On the complex plane ##z=p+iq## states are holomorph functions ##f(z)## with the scalar product
$$ \langle f,g \rangle \sim \int \bar{f}(z) g(z) e^{-z\bar{z}}$$
The probability density ##\rho(z)\sim\bar{f}(z) f(z) e^{-z\bar{z}}## has a quite simple physical interpretation. Make an approximate common measurement of ##\hat{p}## and ##\hat{q}## by measuring instead the communting operators ##\hat{p}+\hat{p}_1## and ##\hat{q}-\hat{q}_1##, where ##\hat{p}_1## and ##\hat{q}_1## describe a second test particle prepared in its harmonic oscillator ground state. So, if you want to measure energy, you can measure that p, q and compute H(p,q) as defined by classical physics.
Then, for every point ##z_0## of the plane you have a corresponding state localized around it, named coherent states, ##f(z)\sim e^{z-z_0}##, which gives ##\rho(z)\sim e^{-(z-z_0)(\bar{z}-\bar{z}_0)}##. Remarkably, in the harmonic oscillator with ##H=\frac12 z\bar{z}## these coherent states follow exactly the classical trajectory. And the energy eigenstates are simply ##f_n(z)\sim z^n##.

 

[Demystifier]

No. There must be discontinuities. The number of photons, for example, cannot increase by 0.77.

Discontinuity in the number of photons is one thing, discontinuity in the trajectory ##x(t)## is another.

 

[Interested_observer]

Einstein was right. QM is useful, but it is not complete.

 

[WernerQH]

Discontinuity in the number of photons is one thing, discontinuity in the trajectory ##x(t)## is another.

Of course. I dislike Nelson's theory because I think the notion of a "trajectory" is basically flawed.

 

[Demystifier]

Of course. I dislike Nelson's theory because I think the notion of a "trajectory" is basically flawed.

Why is it flawed?

 

[WernerQH]

Why is it flawed?

Why should a classical concept retain its usefulness down to the smallest scales of space and time?

 

[Demystifier]

Why should a classical concept retain its usefulness down to the smallest scales of space and time?

Do you know some interpretation of QM that does not retain any classical concept at the smallest scales?

 

[stevendaryl]

But for low energy, gravity is extremely weak, so weak that it safely can be ignored. What remains observable in all those particle colliders are only renormalizable theories.

Okay. I interpreted Wilson's quote as saying that every theory has a low-energy limit that is renormalizable (or looks renormalizable). But in the case of gravity, that low-energy limit is: "no (dynamical) gravity at all". (By "not dynamical", I mean that within QFT, the metric is unaffected by particles.)

 

[vanhees71]

It’s not that you can’t have a background geometry, but that geometry cannot take into account quantum particles.

You can have electrons moving in a background geometry but by definition that background doesn’t include the effect of those electrons. The background geometry would (contrary to the spirit of Newton’s third law) act on the electrons but would not be acted on by them.

The problem indeed is that we don't have a complete theory yet, i.e., the gravitational interaction is not successfully "quantized". Quantum theory describes everything except gravity in a given "background spacetime", i.e., the gravitational interaction is treated classically in the sense that it is reinterpreted as a spacetime which is determined by the Einstein field equations with the classical energy-momentum tensor of the macroscopic matter.

It's a bit like in quantum mechanics, where you describe the electromagnetic field as a classical field. In contradistinction to gravity electromagnetism (and also the weak and strong interaction) have been successfully quantized.

 

[WernerQH]

Even Steven Carlip (post #6) admitted that he cannot prove that gravity needs to be quantized. It's quite a different animal. It differs from the other interactions in that it doesn't couple to a discrete charge. One could even argue that it doesn't interact with elementary particles at all. It just tells them to follow the "most natural" path. I for one can't make sense of a superposition of space-time geometries; only an average background geometry makes sense to me.

 

[stevendaryl]

Even Steven Carlip (post #6) admitted that he cannot prove that gravity needs to be quantized. It's quite a different animal. It differs from the other interactions in that it doesn't couple to a discrete charge. One could even argue that it doesn't interact with elementary particles at all. It just tells them to follow the "most natural" path. I for one can't make sense of a superposition of space-time geometries; only an average background geometry makes sense to me.

But then what is the source (the stress-energy tensor) for the field equations? If it is the energy and momenta of quantum particles, then I don't see how you can get away without needing to quantize gravity. One alternative, possibly, is that the source is the expectation values of the quantum energy/momenta. Expectation values being c-numbers.

 

[Sunil]

Why should a classical concept retain its usefulness down to the smallest scales of space and time?

Why should a useful and successful classical concept lose its usefulness simply because of scales becoming small?

One can reasonably doubt that a classical concept fails if no interpretation exists which supports this concept. Else, there is simply no base for doubt.

 

[WernerQH]

But then what is the source (the stress-energy tensor) for the field equations? If it is the energy and momenta of quantum particles, then I don't see how you can get away without needing to quantize gravity. One alternative, possibly, is that the source is the expectation values of the quantum energy/momenta. Expectation values being c-numbers.

Yes, it's the expectation values. Also pressure is just an average taken over many moving atoms. I see GR as a macroscopic theory, microscopic physics enters only in an averaged form. Today nobody views elastic forces as fundamental, they are reduced to electromagnetic interactions. Gravity may be some kind of residue of the other three interactions, and quantizing gravity similar to, but of course much harder than quantizing elasticity.

 

[WernerQH]

Why should a useful and successful classical concept lose its usefulness simply because of scales becoming small?

Why should classical mechanics and electrodynamics fail to describe atoms?

 

[Sunil]

Why should classical mechanics and electrodynamics fail to describe atoms?

Because the experiment tells us that they fail. Why they fail remains, of course, unknown until the better theory has been found.

If a theory fails, it should be replaced by one which does not fail. Such is life in science.

But the classical philosophical concepts don't fail in such a way. That the founding fathers were unable to find an interpretation in agreement with classical common sense concepts is an irrelevant historical accident, what should matter is only what we know today. And today we have interpretations which are realistic, causal, and have a quite classical ontology, with the wave function interpreted as incomplete knowledge. Why would one reject principles which are viable, compatible with the best theories we have?

 

[Demystifier]

Even Steven Carlip (post #6) admitted that he cannot prove that gravity needs to be quantized.

Perhaps it does not need to be quantized in a sense in which electromagnetism is quantized, but it certainly needs to be quantized in a sense in which Schrodinger cat is quantized.

 

[bhobba]

To me, that’s just mush.

Maybe it is along the lines of Gell-Mann and Hartle:
https://arxiv.org/pdf/1106.0767.pdf

I do not think all the details have been worked out, but it is how I look at the emergence of a classical world from QM. Otherwise, such is a BIG problem, most definitely pointing to QM being incomplete (as Einstein sits laughing on the sidelines).

For those new to the issue, it needs to be said Einstein went through several phases in his attitude towards QM. His final position, contrary to popular myth, was that QM was correct but incomplete. Einstein took Dirac's Principles book wherever he went, and when he could not find it, he would ask: “Where is my Dirac?” Believe it or not, some scholars believe (as I am inclined to) Dirac sided with Einstein.
https://direct.mit.edu/posc/article/16/1/103/15218/Paul-Dirac-and-the-Einstein-Bohr-Debate

Thanks
Bill

 

[Quantumental]

Maybe it is along the lines of Gell-Mann and Hartle:
https://arxiv.org/pdf/1106.0767.pdf

I do not think all the details have been worked out, but it is how I look at the emergence of a classical world from QM. Otherwise, such is a BIG problem, most definitely pointing to QM being incomplete (as Einstein sits laughing on the sidelines).

Isn't Gell-Mann and Hartle just Everett in chronic denial?

 

[bhobba]

Isn't Gell-Mann and Hartle just Everett in chronic denial?

One could equally say that MW is just DH with a confusing sematic waffle added:

In one, we have potentially real outcomes. In the other actually real outcomes. Some may be interested in debating the difference of such semantics - to each their own. I have mentioned it before, and it is just a personal thing; actually real is too weird for me. It's not scientific, just a personal opinion. These days whenever I read about MW, I think of the worlds as potentially real.

It is like solipsism. I can't prove it wrong. However, personally, like most people, I believe it wrong. It simply does not sit well with the world as having an independent objective existence. In probability theory, we think of the outcomes we assign probabilities to as potentially real, and one becomes actually real. We do not think of all possible outcomes as actually real. It is just a convention - but one most people hold to.

Thanks
Bill

 

[*now*]

(Another alternative could be considering just what is relevant…)

The results of this could be interesting- Frontiers | On the Possibility of Experimental Detection of the Discreteness of Time | Physics (frontiersin.org) . I think CH treats time differently, as I think other views can treat it in different ways.