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

[Ravi Mohan]

Well be my guest in explaining it to Natty (Nathan Seiberg)!

 

[A. Neumaier]

Well be my guest in explaining it to Natty (Nathan Seiberg)!

you can send him the link!

 

[RUTA]

I don't see the qubit presenting a mystery. Everything about it was known in 1852, long before quantum mechanics got off the ground.

To understand the mystery of the qubit, consider a measurement of some state that results in outcome O1 every time. Then suppose you rotate your measurement of that same state and obtain outcome O2 every time. We would then expect that a measurement between those two should produce an outcome between O1 and O2, according to some classical model. But instead, we get a distribution of O1 and O2 that average to whatever we expected from our classical model. Here is how Koberinski & Mueller put it (as quoted in our paper https://www.mdpi.com/1099-4300/24/1/12):

We suggest that (continuous) reversibility may be the postulate which comes closest to being a candidate for a glimpse on the genuinely physical kernel of ``quantum reality''. Even though Fuchs may want to set a higher threshold for a ``glimpse of quantum reality'', this postulate is quite surprising from the point of view of classical physics: when we have a discrete system that can be in a finite number of perfectly distinguishable alternatives, then one would classically expect that reversible evolution must be discrete too. For example, a single bit can only ever be flipped, which is a discrete indivisible operation. Not so in quantum theory: the state |0> of a qubit can be continuously-reversibly ``moved over'' to the state |1>. For people without knowledge of quantum theory (but of classical information theory), this may appear as surprising or ``paradoxical'' as Einstein's light postulate sounds to people without knowledge of relativity.

So, your approach captures this averaging nicely and therefore will show how quantum results average to classical expectations for whatever experiment. But, it says nothing about why we don’t just get the value between O1 and O2 directly to begin with. That is what’s “surprising or ‘paradoxical’” about the qubit.

 

[A. Neumaier]

So, your approach captures this averaging nicely and therefore will show how quantum results average to classical expectations for whatever experiment. But, it says nothing about why we don’t just get the value between O1 and O2 directly to begin with. That is what’s “surprising or ‘paradoxical’” about the qubit.

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.

 

[gentzen]

and the other statements, including the first sentence?

John Wheeler

If you write something without giving credits, everyone assumes it is your statement!

Indeed. Even more so, since there was no first question, and no "Quote". Part of my motivation was that I had also read similar statements (that somehow seem to predict your developments) in Herbert Bernard Callen's book on Thermodynamics. I wanted to be able to quote such statements, without explicitly naming their author.

 

[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).