A Could QM Arise From Wilson's Ideas

[WernerQH]

But what is a microscopic event?

Theorists can create an infinite number of events like "the particle arrives at location $x_ {2731}$ ...". This is not the kind of event I have in mind. I think of events as real and finite in number in a given spacetime region. As you decrease the volume and time interval you eventually find regions of spacetime that are empty.

Heisenberg rejected the idea of trajectories of electrons. Unfortunately he offered no alternative. Looking at the world-line of an electron with ever increasing resolution, according to Heisenberg, produces nothing but a diffuse haze. This cannot be resolved experimentally because observations at the zeptosecond scale (511 keV) cause pair creation, confounding the issue. But we do not have to assume that electrons vacillate between "actual" positions at measurements and spread-out, uncertain, "potential" positions in between. We can consider isolated interaction events (not necessarily involving "measurements"!) as real, and the electron as a derived concept. A construction of our mind. Residual metaphysical baggage from the classical world. Just as we connect the droplets in the cloud chamber to form a continuous "track".

Rather than a theory of photons and electrons, it may be more appropriate to view QED as a theory of point processes in spacetime. Electrons and photons enter only as "propagators", correlation functions between events.

 

[stevendaryl]

Theorists can create an infinite number of events like "the particle arrives at location $x_ {2731}$ ...". This is not the kind of event I have in mind. I think of events as real and finite in number in a given spacetime region.

I don't understand what you have in mind, but it seems to me that elucidating what they are is an important part of solving the measurement problem.

 

[WernerQH]

I don't understand what you have in mind, but it seems to me that elucidating what they are is an important part of solving the measurement problem.

As I've said before, I don't see the measurement problem. The problem with QM is its ontology, the talk of "quantum objects" with or without well defined properties, or only when "measured". These objects can emerge as special patterns of events in spacetime, just as pixels on your screen may form the letter "Q" without Q-ness being a fundamental property of the screen.

 

[stevendaryl]

As I've said before, I don't see the measurement problem.

Well no offense, but to me, the problem is illustrated by the frustrating vagueness of explanations such as

These objects can emerge as special patterns of events in spacetime, just as pixels on your screen may form the letter "Q" without Q-ness being a fundamental property of the screen.

To me, that’s just mush.

 

[PeterDonis]

this does not imply that correlation functions in position space are meaningless.

I wasn't saying they were. I was only saying that you can't view a vertex in a Feynman diagram as describing an event at a point in spacetime.

 

[stevendaryl]

Well no offense, but to me, the problem is illustrated by the frustrating vagueness of explanations such as
[deleted]

I apologize if my post was rude. Let me try one more time to explain the issue.

Quantum mechanics can be described as a way of calculating probabilities. The question is: probabilities of what? If the answer is “of measurement results”, then that raises the question of what is a measurement result, so that’s the measurement problem. If the answer is something else, then that raises the question of what, precisely, is that something else.

One answer that is at least clear is the Bohmian answer: the basic probabilities in QM are probabilities for particles to be in particular locations. Whether they are observed there, or not.

Another answer that I have heard is that the basic probabilities are for macroscopic collective properties. In the limit as the number of particles goes to infinity, collective properties such as total momentum and center of mass commute, even though single-particle momentum and position do not.

And then the relational interpretation or the quantum Bayesianism interpretation say that the probabilities are subjective.

 

[WernerQH]

I apologize if my post was rude. Let me try one more time to explain the issue.

No offense taken. In a way I find your reaction fairly reasonable. I've been trying for years to make my ideas more precise.

The list of your possible answers is rather short, and I have obviously failed to indicate the general direction of my answer. I'm optimistic that progress can be made through
(1) Studying the mathematics of point processes. Functionals play a key role in this mathematical field as they do in QFT.
(2) The Keldysh closed time-path formalism. It eliminates the need for "measurements". It further indicates that there are at least two types of events (on forward and backward time sheets).
(3) Non-commutative geometry. Alain Connes has derived the general features of the Standard Model from as little as two spacetimes "glued" together, if I interpret it correctly. Unfortunately it is way above my mathematical abilities.

I'm not sure I understand your concern about probabilities. They don't pose real problems in statistical mechanics, and QFT shares many features with statistical mechanics.

 

[stevendaryl]

I'm not sure I understand your concern about probabilities. They don't pose real problems in statistical mechanics, and QFT shares many features with statistical mechanics.

But it doesn’t share the features that make probabilities problematic in quantum mechanics.

Statistical mechanics makes a very specific and understandable use of probabilities: The state of the system is assumed (in some formulations, anyway) to be a point in phase space. The probability distribution (the Boltzmann distribution, for example) gives the probability that the system is in this state versus that state (or more accurately, this neighborhood of phase space, since the probability of being at a specific point is zero).

So that’s what is missing from an interpretation of quantum mechanics: what are the probabilities about?

 

[EPR]

So that’s what is missing from an interpretation of quantum mechanics: what are the probabilities about?

Knowledge? Is there a better candidate for what probabilities are about?

 

[stevendaryl]

Knowledge? Is there a better candidate for what probabilities are about?

That just raises the question: knowledge about what?

 

[kith]

Another answer that I have heard is that the basic probabilities are for macroscopic collective properties. In the limit as the number of particles goes to infinity, collective properties such as total momentum and center of mass commute, even though single-particle momentum and position do not.

Do you have some pointers to where I can read more about this?

It might also be related to the thermal interpretation of @A. Neumaier which I don't really understand yet.

 

[EPR]

That just raises the question: knowledge about what?

Knowledge about observables that the respective quantum field will produce in accordance with the calculated probabilities.

 

[stevendaryl]

Knowledge about observables that the respective quantum field will produce in accordance with the calculated probabilities.

The difficulty with that answer is that the concept of “knowledge about the value of this observable” assumes that the observable has a value. You can’t know information if that information doesn’t exist.

So that answer doesn’t actually answer anything. Does the observable have a value before it is measured? If yes, that’s a hidden variable theory, which is hard to make consistent. If no, then you have the question of how measurement beings these values into existence.

 

[EPR]

The difficulty with that answer is that the concept of “knowledge about the value of this observable” assumes that the observable has a value. You can’t know information if that information doesn’t exist.

So that answer doesn’t actually answer anything. Does the observable have a value before it is measured? If yes, that’s a hidden variable theory, which is hard to make consistent. If no, then you have the question of how measurement beings these values into existence.

We may have to look for clues outside quantum physics for these answers.

It's a relative reality - everything is a worldline moving through spacetime. Observables thus would appear to have values before measurement and they seem to be hidden(hidden variables) before measurement.
You can counter this by asking how conscious experience could arise in a blockworld Universe and I would say that it probably wouldn't. And it probably didn't.

 

[PeterDonis]

everything is a worldline moving through spacetime

This is true in classical relativity, but it's not necessarily true in QM; it depends on which interpretation you adopt. Interpretation-dependent discussion belongs in the QM interpretation forum, not this one.

 

[Demystifier]

The problem with QM is its ontology, the talk of "quantum objects" with or without well defined properties, or only when "measured". These objects can emerge as special patterns of events in spacetime, just as pixels on your screen may form the letter "Q" without Q-ness being a fundamental property of the screen.

Are you saying that position is a preferred observable?

 

[WernerQH]

Are you saying that position is a preferred observable?

Yes. I don't believe that position and momentum can have exactly the same status.

 

[WernerQH]

the features that make probabilities problematic in quantum mechanics

Do you also object to probabilities derived using Fermi's Golden Rule, like decay rates and cross sections? Those should be unproblematic. They always refer to a finite interval of time.

I suspect that you are looking for something that quantum theory does not provide: an "instantaneous" probability characterizing the present "state" of a system, which could replace the Born rule. Schrödinger's equation only gives the appearance of Markovian evolution. It is not the whole truth.

 

[stevendaryl]

I suspect that you are looking for something that quantum theory does not provide: an "instantaneous" probability characterizing the present "state" of a system

No, I specifically said that I'm looking for a clear statement of what events quantum probabilities are probabilities for. I gave several candidate answers, but there are issues with all of them.

The standard quantum recipe says that they are probabilities for measurement outcomes.

 

[Demystifier]

Schrödinger's equation only gives the appearance of Markovian evolution. It is not the whole truth.

What's the rest of the truth?

 

[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?