Quantum Physics via Quantum Tomography: A New Approach to Quantum Mechanics

[A. Neumaier]

I wanted to be able to quote such statements, without explicitly naming their author.

This is against the conventions for good scientific conduct. Hiding such information may be good in a game but not in scientific discourse. If you don't want to name authors use your own words and speak in your own authority!

 

[Ravi Mohan]

Renormalization does not go beyond the limits of quantum theory.

From a physics point of view, everything about renormalization is understood. The missing logical coherence (due to the lack of a rigorous nonperturbative version of renormalization) is a matter for the mathematicians to resolve.

I had a rough reading and I don't see any hints of gravity in your analysis (you know the massless spin 2 (point?) particle).

Your claim "everything about renormalisation is understood" hasn't been demonstrated one way or the other (I think even from Physics POV).

 

[A. Neumaier]

I had a rough reading and I don't see any hints of gravity in your analysis.

Your claim "everything about renormalisation is understood" hasn't been demonstrated one way or the other.

The renormalization problem is independent of gravity, and can be understood independent of it.

The only apparent problem with gravity is its apparent nonrenormalizability, but this is not a real problem as discussed in the link mentioned in post #27.

 

[Ravi Mohan]

The renormalization problem is independent of gravity, and can be understood independent of it.

The only apparent problem with gravity is its apparent nonrenormalizability, but this is not a real problem as discussed in the link mentioned in post #27.

I would like to know that. One lesson I learned is that you cannot renormalise the usual canonical gravity (the Hamiltonian formulation of GR) or the entire "certain" community wouldn't exist.

A page number would be helpful. I wish I had infinite time!

 

[RUTA]

I find this as little surprising as the case of measuring the state of a die by looking at the number of eyes found at its top when the die comes to rest. Although the die moves continuously we always get a discrete integer between 1 and 6.

Similarly, the measurement of a qubit is - by definition - binary. Hence it can have only two results, though the control in the experiment changes continuously.

The die is the counterpart of a "classical bit," we're talking about the qubit, they differ precisely as I (and Koberinski & Mueller) pointed out. That is, it makes no sense to talk about measurements that you would expect to yield 1.5 or 2.3, etc., for a die. But, when measuring a qubit, the measurement configurations of a particular state vary continuously between that yielding +1 and that yielding -1, so one would expect those "in-between" measurements to produce something between +1 and -1, e.g., Stern-Gerlach spin measurements. Instead, you still obtain +1 and -1, but distributed so they average to the expected intermediate outcome, e.g., via vector projection for SG measurements. Your approach simply articulates that fact without offering any reason for why we don't just get the expected outcome to begin with.

 

[A. Neumaier]

e.g., Stern-Gerlach spin measurements. Instead, you still obtain +1 and -1, but distributed so they average to the expected intermediate outcome, e.g., via vector projection for SG measurements.

This is far from true. See the quote at the top of p.12 of the paper summarized by the Insight article, and the book from which this quote is taken.

 

[A. Neumaier]

I would like to know that. One lesson I learned is that you cannot renormalise the usual canonical gravity (the Hamiltonian formulation of GR) or the entire "certain" community wouldn't exist.

This was true in the old days before effective field theories were seriously studied.

But in modern terms, nonrenormalizable does no longer mean ''not renormalizable'' but only ''renormalization defines an infinite-parameter family of theories'', while standard renormalizability means ''renormalization defines a finite-parameter family of theories''. For example, QED is a 2-dimensional family of QFTs parameterized by 2 parameters (electron mass and charge), while canonical quantum gravity defines an infinite-dimensional family of QFTs parameterized by infinitely many parameters (of which the gravitational constant is just the first) .

A page number would be helpful. I wish I had infinite time!

I gave detailed references here: https://arnold-neumaier.at/physfaq/topics/renQG.html

 

[RUTA]

This is far from true. See the quote at the top of p.12 of the paper summarized by the Insight article, and the book from which this quote is taken.

It's exactly true, it's the expectation value for spin 1/2 measurements. I infer from the quote you reference that you therefore disagree with QM. I'm not doing that.

 

[A. Neumaier]

It's exactly true, it's the expectation value for spin 1/2 measurements. I infer from the quote you reference that you therefore disagree with QM.

No. The quote describes the experimental findings of the original paper by Stern and Gerlach. Nobody ever thought this would disagree with QM.

You probably never saw a discussion of the real experiment, only its heavily idealized caricature described in introductory textbooks on quantum mechanics!

 

[RUTA]

No. The quote describes the experimental findings of the original paper by Stern and Gerlach. Nobody ever thought this would disagree with QM.

You probably never saw a discussion of the real experiment, only its heavily idealized caricature described in introductory textbooks on quantum mechanics!

Here is what we cite https://plato.stanford.edu/entries/physics-experiment/app5.html ; it contains reproductions of SG figures and results. There is nothing that contradicts QM spin 1/2 Hilbert space predictions therein. No experiment that I have seen does so and everything that I've said here (as contained in our published papers https://www.mdpi.com/1099-4300/24/1/12 and https://www.nature.com/articles/s41598-020-72817-7) conforms to that fact. If you disagree with that, then you're claiming QM is wrong.

 

[A. Neumaier]

Here is what we cite https://plato.stanford.edu/entries/physics-experiment/app5.html ; it contains reproductions of SG figures and results.

Figure 13 in the reference you cited shows the Stern-Gerlach results. The picture agrees with the description in my quote: The split is not into two separate thin lines at 1 and -1 as you claim but into two broad overlapping lips occupying in each cross section a continuous range, which may be connected or seemingly disconnected depending on where you draw the intersecting line.

There is an intensity minimum in the center of the pattern, and the separation of the beam into two components is clearly seen.

Thus the measurement results form a bimodal continuum with an infinite number of possible values.

 

[RUTA]

Figure 13 in the reference you cited shows the Stern-Gerlach results. The picture agrees with the description in my quote: The split is not into two separate thin lines at 1 and -1 as you claim but into two broad overlapping lips occupying in each cross section a continuous range, which may be connected or seemingly disconnected depending on where you draw the intersecting line.

Thus the measurement results form a bimodal continuum with an infinite number of possible values.

Again, the mathematical description of the outcome is given by spin 1/2 qubit Hilbert space. If you disagree with that, then you are claiming QM is wrong and I am not interested.

 

[Ravi Mohan]

This was true in the old days before effective field theories were seriously studied.

But in modern terms, nonrenormalizable does no longer mean ''not renormalizable'' but only ''renormalization defines an infinite-parameter family of theories'', while standard renormalizability means ''renormalization defines a finite-parameter family of theories''. For example, QED is a 2-dimensional family of QFTs parameterized by 2 parameters (electron mass and charge), while canonical quantum gravity defines an infinite-dimensional family of QFTs parameterized by infinitely many parameters (of which the gravitational constant is just the first) .

I gave detailed references here: https://arnold-neumaier.at/physfaq/topics/renQG.html

Unfortunately I don't care about old or young. If you are inconsistent you are. Nothing wrong in accepting that.

Renormalization is not just about taming the family of field theories (or some dynamics in the Moduli Space so to speak), you need find a right way for Mathematician friends to do their thing.

There is absolutely no consensus on Mathematical definition of free QFT leave alone the interacting ones. The person who was actually trying to do was insulted to highest levels, in these very forums. So yeah it is the weakness of Physics community for not being able to generate enough context and explain the QFT to Mathematicians.

If you are not shook to the core by this fact, I think you should maybe find some other way to propagate your agenda (renormalization problem is independent of gravity). Because first insulting and then using the very same Mathematics for your purpose without responsibility is ...

 

[A. Neumaier]

Again, the mathematical description of the outcome is given by spin 1/2 qubit Hilbert space. If you disagree with that, then you are claiming QM is wrong and I am not interested.

I am claiming that the measurement results form a continuum and the binarization is an idealization. This is in agreement with experiment and with quantum mechanics.

Whether or not you are interested does not matter here.

 

[RUTA]

I am claiming that the measurement results form a continuum and the binarization is an idealization. This is in agreement with experiment and with quantum mechanics.

Whether or not you are interested does not matter here.

There are two distinct measurement outcomes predicted for a qubit and you are claiming the experimental result is a continuum. Therefore, you are claiming the QM prediction is wrong. It's that simple.

 

[A. Neumaier]

Renormalization is not just about taming the family of field theories (or some dynamics in the Moduli Space so to speak), you need find a right way for Mathematician friends to do their thing.

For the right - mathematically rigorous - way see this Insight article!

 

[Ravi Mohan]

Before I delve into them, tell me, how much are they aligned with Wightman axioms?
The fidelity is of no importance here, I just want to see if you can digest both in same context.

 

[A. Neumaier]

There are two distinct measurement outcomes predicted for a qubit and you are claiming the experimental result is a continuum.

Stern and Gerlach obtained in their figure a huge number of distinct measurement outcomes, visible for everyone. Only idealization can reinterpret this as binary measurement outcomes 1 and -1.

By your reasoning, a low energy particle in a double well potential would only take two possible positions!

 

[A. Neumaier]

Before I delve into them, tell me, how much are they aligned with Wightman axioms?
The fidelity is of no importance here, I just want to see if you can digest both in same context.

Causal perturbation theory is consistent with the Wightman axioms. It constructs the Wightman N-point functions and field operators perturbatively in a mathematically rigorous way. The only missing thing to constructing Wightman fields is the lack of a rigorous nonperturbative resummation formula.

 

[Ravi Mohan]

Aso, the renormalization!

 

[Ravi Mohan]

Ok let me point out things as I read
1. What about theories with no expectations of even having an Action?
2. What would you comment on Locality of QFT, within that Insights context?
3. Can you or can you not relate your note to CoBordism formulation?
https://en.wikipedia.org/wiki/Cobordism_hypothesis
4. What failure would you confront when you switch and uplift Poincare invariance with GCT in its full glory?
5. And lastly, for the fun of it, enlighten us "Are the particles in your Insight context pointlike or points?"

 

[A. Neumaier]

1. What about theories with no expectations of even having an Action?

for these, causal perturbation theory is not applicable.

2. What would you comment on Locality of QFT, within that Insights context?

This is built in into the causal approach.

 

[A. Neumaier]

3. Can you or can you not relate your note to CoBordism formulation

I haven't seen work on such a relation but Tomonaga-Schwinger dynamics based on the perturbatively constructed fields should provide a connection.

 

[Ravi Mohan]

The link goes to a nonexistent page.

I haven't seen work on such a relation but Tomonaga-Schwinger dynamics based on the perturbatively constructed fields should provide a connection.

Fixed the link! Sorry about that.

 

[A. Neumaier]

4. What failure would you confront when you switch and uplift Poincare invariance with GCT in its full glory?

Invariance under general coordinate transformations is a consequence of Poincare invariance together with the gauge structure of massless spin 2 particles. This was already shown by Weinberg 1964. Thus no failure is expected, and no need to extend the causal formalism.

5. And lastly, for the fun of it, enlighten us "Are the particles in your Insight context pointlike or points?"

They are approximations emerging from the quantum fields under conditions corresponding to the validity of geometric optics; this makes them definitely not points. See the discussion in Section 7.1 of my paper (and far more details in my 2019 book on coherent quantum mechanics).

 

[vanhees71]

No. The quote describes the experimental findings of the original paper by Stern and Gerlach. Nobody ever thought this would disagree with QM.

You probably never saw a discussion of the real experiment, only its heavily idealized caricature described in introductory textbooks on quantum mechanics!

Which quote are you talking about? On p. 12 of your paper there's the quote by Fröhlich:

The only form of ”interpretion” of a physical theory that I find legiti-
mate and useful is to delineate approximately the ensemble of natural
phenomena the theory is supposed to describe and to construct some-
thing resembling a ”structure-preserving map” from a subset of mathe-
matical symbols used in the theory that are supposed to represent phys-
ical quantities to concrete physical objects and phenomena (or events)
to be described by the theory. Once these items are clarified the theory
is supposed to provide its own ”interpretation”.
J¨urg Fr¨ohlich, 2021 [45, p.238]

with which I fully agree, of course, but that's not referring to the SG experiment.

Of course, when you measure a spin component with the standard ideal SG setup, you don't measure expectation values on a single silver atom but the spin component, which gives either $\hbar/2$ or $-\hbar/2$ as a result with a probability determined by the spin state $\hat{\rho}$ the silver atom is prepared in. When it comes from an oven as in the original experiment, this state is of course $\hat{\rho}=\hat{1}/2$. It's a paradigmatic example, for which a von Neumann filter measurement can be realized.

 

[gentzen]

Which quote are you talking about? On p. 12 of your paper there's the quote by Fröhlich:

This means that you still have v1 of Neumaier's paper. The only quote on p. 12 in v3 is:

The following ’laboratory report’ of the historic Stern-Gerlach experiment stands quite in contrast to the usual textbook ’caricatures’. A beam of silver atoms, produced in a furnace, is directed through an inhomogeneous magnetic field, eventually impinging on a glass plate. [...]
Only visual measurements through a microscope were made. No statistics on the distributions were made, nor did one obtain ’two spots’ as is stated in some texts. The beam was clearly split into distinguishable but not disjoint beams. [...] Strictly speaking, only an unsharp spin observable, hence a POV measure, is obtained.
Busch, Grabowski and Lahti, 1995 [25, Example 1, p.7]

 

[A. Neumaier]

Of course, when you measure a spin component with the standard ideal SG setup, you don't measure expectation values on a single silver atom but the spin component, which gives either $\hbar/2$ or $-\hbar/2$ as a result with a probability determined by the spin state $\hat{\rho}$ the silver atom is prepared in. When it comes from an oven as in the original experiment, this state is of course $\hat{\rho}=\hat{1}/2$. It's a paradigmatic example, for which a von Neumann filter measurement can be realized.

If your interpretation of the measurement results were correct, Stern and Gerlach could have deduced the value of $\hbar$ to infinite precision.

Instead I look at Figure 13 with the actual measurement results of Stern and Gerlach, and see (like Busch et al. in the quote and like everyone who can see) a large number of scattered dots, not two exact numbers involving $\hbar$. Clearly what was measured for each silver atom was position (with a continuous distribution), not spin.

Tu turn these position measurements into a projective spin measurement of $\hbar/2$ or $-\hbar/2$ you need to invoke heavy idealization, including additional theory and uncontrolled approximations.

 

[vanhees71]

Ok, well yes, the original SG experiment did not resolve single-atom results, and it may be well interesting to describe the original SG experiment in terms of the POVM formalism to better understand this formalism. Unfortunately in the quoted book they do this on p. 165ff but in a pretty abstract way instead of (approximately) solving the Schrödinger equation...

 

[A. Neumaier]

Ok, well yes, the original SG experiment did not resolve single-atom results

Can you point to the report of another SG experiment that resolves single silver atoms?

Even then, one only measures atom position and computes from these measurements fairly crude approximations of $\hbar$. It simply isn't a projective (textbook) measurement.

it may be well interesting to describe the original SG experiment in terms of the POVM formalism to better understand this formalism.

You can understand the formalism by reading Sections 2 and 3 of my paper. I did not treat the Stern-Gerlach experiment in detail since a precise description is quite involved. But in Section 3 I discuss in some detail several other measurement situations, which should be enough to get a clear understanding of what the approach means.

Unfortunately in the quoted book they do this on p. 165ff but in a pretty abstract way instead of (approximately) solving the Schrödinger equation...

Many papers and books using POVMs are quite abstract because they employ a measure-theoretic approach rather than simple quantum measures in the sense of my new paper. This is why my paper is a big step forward towards making the approach more understandable to everyone. Still, you need to do some reading to get the correct picture.

 

[Fra]

It results in different emanating beams, though their properties are the same.

Its an equivalence class only in the same irrelevant sense as in the claim that ''momentum is an equivalence class of preparations of particles in a classical source''. Very different equipment can result in particles with the same momentum.

Using mathematical terminology to make such a simple thing complicated is quite unnecessary.

As I understand your paper, it seems one major improvement in your description, is to make mathematically more explicit, the process of inferring the "quantum state" from REAL interactions - rather than considering and imaginary ensemble that is defined outside the formalism?

Ie. the fictive "equivalence class" is replaced by a real construction - as per quantum tomoghraphy - essentially from a sequence or history of interactions. And this works fine, as long as the sources are as you say "stationary" or does not change until the process of tomopgraphy is completed by margin?

Does this sound like a reasonable?

/Fredrik

 

[A. Neumaier]

As I understand your paper, it seems one major improvement in your description, is to make mathematically more explicit, the process of inferring the "quantum state" from REAL interactions - rather than considering and imaginary ensemble that is defined outside the formalism?

Ie. the fictive "equivalence class" is replaced by a real construction - as per quantum tomography - essentially from a sequence or history of interactions. And this works fine, as long as the sources are as you say "stationary" or does not change until the process of tomography is completed by margin?

The real advance is to make the quantum state a property of the source - i.e., of a macroscopic object.

This makes all talk about fictitious stuff (like ensembles, equivalence classes, multiple worlds, or presumable changes of states of knowledge) obsolete, without a change in the operational content of quantum mechanics.

 

[vanhees71]

I've started to read the paper, and I first had the impression, it's now much closer to the real use of QT as a physical theory as done by physicists since 1926, than the previous papers on your "thermal interpretation", but now it seems again, I'm completely misunderstanding its intended meaning. Obviously I misunderstood what you mean by "source". For me a "source" is just some device which "prepares quantum systems", and this can be also a single "particle" or even a single "photon" and not only macroscopic systems.

 

[Fra]

The real advance is to make the quantum state a property of the source - i.e., of a macroscopic object.

This makes all talk about fictitious stuff (like ensembles, equivalence classes, multiple worlds, or presumable changes of states of knowledge) obsolete, without a change in the operational content of quantum mechanics.

Given your ambitions, I guess this makes good sense. It's just that it does not solve the mysteries, at least not for me.

I still see your perspective as as limiting case of a general (yet unknown) theory.

As a macroscopic object is essentially just a part of the classical reality, this to me seems quite close to Bohrs angle to the CI (in contrast to Heisenbergs). You still need a CONTEXT, and this context is classical reality. This is of course a good thing from the perspective of human science... and as the context is the good old classical reality, it becomes more trivial as except for relativity, the observer-observer interaction is more trivial.

But it's a bad thing if you think there is explanatory power to be found by considering the logic of interacting observers. And I am not sure how it helps with fine tuning problems or unification quests. As I understand it, it isn't the ambition either. Then it's fine. I think part of the confusion, is different expectations, which I think what you wrote yourself in post 15 as well.

/Fredrik

 

[A. Neumaier]

I still see your perspective as as limiting case of a general (yet unknown) theory.

I prefer to frame the known in an optimally rational way, rather than to speculate about the unknown.

As a macroscopic object is essentially just a part of the classical reality, this to me seems quite close to Bohrs angle to the CI (in contrast to Heisenbergs). You still need a CONTEXT, and this context is classical reality.

I define classical reality in Section 7.2 of my paper as that part of quantum reality that can be deduced from it in the form of a local equilibrium description. Thus the context is quantum physics itself.

But it's a bad thing if you think there is explanatory power to be found by considering the logic of interacting observers.

Everything in my paper is observer-independent. It doesn't matter who observes, excpt that poor observations lead to poor approximations of the state.