Relational Quantum Mechanics

[PeterDonis]

This is not about accurate position measurements

Excuse me? You said:

Currently, QM does not impose any limit for the accuracy of a position measurement.

So yes, what you're claiming is about accurate position measurements.

I think this is pure speculation.

So is your claim that we can make accurate measurements at sub-Planckian scales. I am perfectly fine with eliminating both claims from this discussion and confining ourselves to scales at which we have some prospect of doing actual experimental tests. But you are the one who brought in sub-Planckian scales, not me.

You already agreed that, in the case of the of a 2-slit experiment it's not actually necessary to detect the photons that carry the relevant which-path information.

No, I said that it's not actually necessary for the "detector" to have any output that humans can read. But it is necessary for a "detector" to be there--to have something at each slit that can in principle provide which-path information. That requires not just "interaction", but a precisely chosen interaction that can provide that information. A rock does not qualify; if it did, we would be using rocks instead of highly expensive detectors to run double-slit experiments--you could just put a rock at each slit and watch the interference pattern disappear. But of course nobody does that, because physicists, unlike you, know that it would be foolish.

 

[AndreiB]

So yes, what you're claiming is about accurate position measurements.

The fact that QM "has only been tested down to length scales about 18 orders of magnitude larger than the Planck length" is not about accurate position measurements of large objects. It's about the de-Broglie wavelength of the accelerated particles. The regime you are invoking is not only about small lengths, but also high energies (required to decrease the associated wavelength). You can use interferometry (like LIGO) to measure positions with much greater accuracy than the wavelength you use.

So is your claim that we can make accurate measurements at sub-Planckian scales.

Yes, since there is no physical principle that makes this impossible. It's a thought experiment.

No, I said that it's not actually necessary for the "detector" to have any output that humans can read. But it is necessary for a "detector" to be there--to have something at each slit that can in principle provide which-path information.

OK, so we diffract some molecules and we try to get the which-path information by illuminating the slits with photons of a wavelength that the molecules can absorb. Do you think that is necessary to detect those photons in order to destroy the interference, or the presence of those photons is enough?

 

[EPR]

Isn't the whole proposition that nearby objects with considerable mass are enough to induce wavefunction collapse on the path of the photons/electrons ruled out by the very double slit experiment, where the slits can act as such bodies(but obviously do not, since results show you need additional detectors to cause wavefunction collapse)?

 

[AndreiB]

Isn't the whole proposition that nearby objects with considerable mass are enough to induce wavefunction collapse on the path of the photons/electrons ruled out by the very double slit experiment, where the slits can act as such bodies(but obviously do not, since results show you need additional detectors to cause wavefunction collapse)?

No, it's not the same thing. The uncertainty principle forbids you from find out the position of the electron accurately enough to determine the slit it went through. In the case of the cat, the uncertainty principle is irrelevant, and its place is taken by the magical box that somehow keeps the cat inside in a superposition that would be impossible without that box. The problem is that you cannot shield gravity with any kind of box so there can be no superposition inside.

 

[EPR]

No, it's not the same thing. The uncertainty principle forbids you from find out the position of the electron accurately enough to determine the slit it went through. In the case of the cat, the uncertainty principle is irrelevant, and its place is taken by the magical box that somehow keeps the cat inside in a superposition that would be impossible without that box. The problem is that you cannot shield gravity with any kind of box so there can be no superposition inside.

Unless you put a detector before one of the slits. Then you know which slit it went through. I don't see your point. People have been marking particles in these types of experiments for decades.
The point is - having a body of mass nearby won't act as a detector no matter what fancy setup you come up with.

 

[AndreiB]

Unless you put a detector before one of the slits. Then you know which slit it went through. I don't see your point. People have been marking particles in these types of experiments for decades.

The desire here is to keep the superposition, not destroy it. In the case of the 2-slit experiment you have the option to detect the path (and see no interference) or not to detect the path (and see interference). In the case of Schrodinger's cat scenario I don't think you have an option. Whatever you do, the cat is "detected" gravitationally from the outside, so you can't have a live/dead cat superposition.

 

[Lord Jestocost]

Whatever you do, the cat is "detected" gravitationally from the outside, so you can't have a live/dead cat superposition.

Schrödinger‘s cat was originally enclosed in a box to avoid any interaction with the outside environment. This is the core idea of the thought experiment!
At heart the problem does not lie with the (dis)appearance of interference terms but with the inability of quantum mechanics to predict single outcomes.
Schrödinger’s reason to devise his ‘cat-in-the-box’ thought experiment and to consider the situation as paradoxical lay in his hope to interpret the wave function as an “objective” wave field. To my mind, he didn’t want to accept the fact “that the formalism of quantum theory does not allow the same degree of objectivation as that of classical physics.”
Quantum mechanics differs from classical physics because the assumption that one of the answers (dead/alive) is "objectively" realized in between observations or measurement is simply impossible. Quantum probabilities are not the probabilities that the cat is dead or alive at a certain instant of time. It’s the probabilities that an observer will find it dead or alive at a certain instant of time.

Carl Friedrich von Weizsäcker on Schrödinger's cat paradox in “The Structure of Physics” (the book is a newly arranged and revised English version of "Aufbau der Physik" by Carl Friedrich von Weizsäcker):

“The answer is trivial: the $\psi$-function is the list of all possible predictions. A probability $1/2$ for the two alternative possibilities (here: "living or dead") means that the two incompatible situations most now be considered equally possible at the instant of time meant by the prediction. There is no trace of a paradox. Schrödinger's reason to consider the situation as paradoxical lay in his hope to interpret the $\psi$-function as an ‘objective’ wave field.”

 

[gentzen]

Quantum mechanics differs from classical physics because the assumption that one of the answers (dead/alive) is "objectively" realized in between observations or measurement is simply impossible.

That statement depends on interpretation, no? In Bohmian mechanics, observations or measurements have no special role, or at least they are not limited to discrete instances in time.

Schrödinger's reason to consider the situation as paradoxical lay in his hope to interpret the $\psi$-function as an ‘objective’ wave field.

True, but that doesn't mean that Schrödinger's hope cannot be achieved. I admit that it is probably more promising to go with the statistical operator instead of the $\psi$-function as an ‘objective’ element (like in consistent histories, ... or ...), but those are just irrelevant details. The basic point is that Copenhagen may not be the last word.

Steven Weinberg in "Lectures on Quantum Mechanics" in section "8.3 Broken Symmetry" seems to "suggest" that often even molecules won't be in strange superpositions of states (even if that superposition would constitute the minimal energy eigenstate), if some related timeinterval far exceeds the lifetime of the universe. Well, a molecule normally has no elaborate mechanics copying a superposition over to those states, so it is not directly comparable to Schrödinger's thought experiment. But the point is that you don't even need to go to a macroscopic cat to come into that conflict between "naive prediction" and actual observation.

 

[Sunil]

Schrödinger‘s cat was originally enclosed in a box to avoid any interaction with the outside environment. This is the core idea of the thought experiment!

Rereading the paper, I disagree. The purpose of box is not explicitly stated, but it is obviously necessary to prevent the cat to run away.

Schrödinger’s reason to devise his ‘cat-in-the-box’ thought experiment and to consider the situation as paradoxical lay in his hope to interpret the wave function as an “objective” wave field.

Yes, this was his point.

Das Typische an diesen Fällen ist,daß eine ursprünglich auf den Atombereich beschränkte Unbestimmtheit sich in grob sinnliche Unbestimmheit umsetzt, die sich dann durch direkte Beobachtung entscheiden läßt.Das hindert uns,in so naiver Weise ein "verwaschenes Modell" als Abbild der Wirklichkeit gelten zu lassen.

 

[AndreiB]

Schrödinger‘s cat was originally enclosed in a box to avoid any interaction with the outside environment. This is the core idea of the thought experiment!

I agree with this. However, no box can shield gravity, so the experiment is not possible, not even in principle. Therefore you cannot learn anything from this thought experiment. You might as well speak about flying carpets.

At heart the problem does not lie with the (dis)appearance of interference terms but with the inability of quantum mechanics to predict single outcomes.

QM predicts single outcomes using Born's rule.

I don't know exactly what Schrodinger intended (I didn't read the paper) but I've heard that he wanted to make fun of Bohr's interpretation.

 

[gentzen]

I don't know exactly what Schrodinger intended (I didn't read the paper) but I've heard that he wanted to make fun of Bohr's interpretation.

Schrödinger intended to explain his current view on the status of quantum mechanics. The cat is only a minor remark, and not the central theme of the paper. The EPR paper had motivated Schrödinger to give an account of entanglement for a general audience, it role in quantum mechanics, and the current status (back then) with respect to how it is understood.

 

[Lord Jestocost]

The purpose of box is not explicitly stated, but it is obviously necessary to prevent the cat to run away.

That's the reason why one has to consider three quantum states: "In fact, the mere act of opening the box will determine the state of the cat, although in this case there were three determinate states the cat could be in: these being Alive, Dead, and Bloody Furious." (Terry Pratchet)

 

[gentzen]

Moreover, in the preparation you can restrict yourself to the particular measurement you are interested in. If you prepare some spin up particles, because for your experiment spin is important but position quite irrelevant, the positions will remain far from being in a pure state simply because this is nothing worth to care about. The state will be almost pure only for the relevant degrees of freedom, say, the spin.
$|\psi_a(a)\rangle\langle \psi_a(a)| \times \hat{\rho}(b,\ldots)$

I didn't talk about irrelevant degrees of freedom either. But it is good to see that you understand that preparing an almost pure state inside a very impure global state is not an issue. I have more the impression that you point out that spin or polarization can easily be prepared in an almost pure state, while I point out that filtering does not prepare the energy of a light source anywhere near as pure as a laser can.

Not sure how far you can go with your "prepared by a preparational measurement" approach, and the strategy to be only interested in the state of a very small subset of the degrees of freedom. Agreed that you can prepare a single qbit. But what about preparing an arbitrary small number of qbits?

 

[*now*]

Just concerning the thread topic, with BMV tests evidential support for quantum gravity or not could soon be within observational reach.

 

[Jarvis323]

Called relational quantum mechanics, it interprets QM by rejecting the idea that quantum systems really exist in isolation absolutely, and says instead that they really only exist as they relate to another system. The interaction between systems is the “real” entity. By taking this approach, a consistent quantum description of an entire world is possible which seems to avoid the problems of other interpretations. The world is a network of interactions. The slogan for how this addresses the measurement problem might be “Everything measures everything else”. I refer you to the Stanford Philosophy Encyclopedia entry for a fuller description.

I am actually curious about the link between Grete Hermann's 1930's relative interpretation of QM, and Rovelli's. It seems she is the originator of relational QM? I find her articulation very elegant and clear. But I wish I could integrate what she is saying into the bigger context, including the modern works such as Rovelli's. Is Rovelli's work fundamentally based on the same idea, only more descriptive and coming with a concrete formulation?

It is an easy read.

Hermann, Grete, and Dirk Lumma. "The foundations of quantum mechanics in the philosophy of nature." The Harvard Review of Philosophy 7.1 (1999): 35-44.

https://www.hcs.harvard.edu/~hrp/issues/1999/Hermann.pdf

 

[physika]

"really only exist as they relate to another system." "the interaction between systems" "network of interactions" “Everything measures everything else”.

...just an interactive dependence; "A" makes "B" existent or "D" makes "K" existent or "Z" makes "J" (whatever) an vicious infinite regress , an endless iteration.

A circular argument.

.

 

[*now*]

I am actually curious about the link between Grete Hermann's 1930's relative interpretation of QM, and Rovelli's. It seems she is the originator of relational QM? I find her articulation very elegant and clear..l

It is an easy read.

Hermann, Grete, and Dirk Lumma. "The foundations of quantum mechanics in the philosophy of nature." The Harvard Review of Philosophy 7.1 (1999): 35-44.

https://www.hcs.harvard.edu/~hrp/issues/1999/Hermann.pdf

Nice introduction to Hermann, Jarvis, a fascinating person whose accomplishments include studying mathematics under Emmy Noether, exchanges with Heisenberg and this-
...” in 1935, Hermann published a critique of John von Neumann's 1932 proof which was widely claimed to show that a hidden variable theory of quantum mechanics was impossible. Hermann's work on this subject went unnoticed by the physics community until it was independently discovered and published by John Stewart Bell in 1966, and her earlier discovery was pointed out by Max Jammer in 1974. Some have posited that had her critique not remained nearly unknown for decades, her ideas would have put in question the unequivocal acceptance of the Copenhagen interpretation of quantum mechanics, by providing a credible basis for the further development of nonlocal hidden variable theories, which would have changed the historical development of quantum mechanics.[1]”
https://en.m.wikipedia.org/wiki/Grete_Hermann

This seems despite her not favouring such views, and while I think Heisenberg reportedly also saw clarity in the view she penned.

 

[CarlB]

I wouldn't call relational a circular argument. It's that to have any information about a quantum state, say a particle, you need something to measure it with and that will be another quantum state or at least a system.

An example is the "candle dance" where the professor holds a candle (or more likely a cup of coffee, the basic idea is to have it be something a bit hazardous so the students will find it more interesting as they suspect that their instructor is a klutz) and walks around it with the candle not rotating. The result is that his arm ends up twisted. Then he walks around again and surprise-surprise his arm untwists. This "explains" why the wave states of electrons take a -1 when rotated by 2 pi (perpendicular to their spin direction) rather than the expectation - i.e. unchanged. And this shows that swapping two identical particles (fermions) can give a -1 to their wave function.

However, the demonstration depends on two objects, the candle and the professor, and this is the relational principle; information about quantum states is actually about their relationship to some other thing.

If someone could show how information about a quantum state could exist in the absence of any interactions with other states, I might find it a good argument against the relational principle. In the absence of such, one must consider all quantum information as relational only. The example Rovelli gives is positional information. He denies the existence of a preferred reference frame so that all positional information is relational only. The assumed position of a single particle system is information that physically does not exist and so, like the absolute reference frame, should not be assumed in the physics.

 

[Fra]

I think the relational idea is good, but the question then, is how you view the relations themselves.

I think the solution to the apparent circularity or chicken/egg situation is to see that it's not just circular reasoning, there is a feedback loop and an evolution. You need some premises or starting point, in order to be able to formulate a question, or a measurement for that matter. But the result from the measurement may modify the starting point, so the future measurment is tuned.

I think Rovellis relational start out wel but, the problem is that even the relations themselves, needs to be relationally inferred, and this would imply IMO at least, an evolutionary view on physical law as well, and a view where symmetries are typically emergent only, rather than constraints. Ie. it takes a third observer to describe the relation between two other observers. But Rovelli never analyses this to completion IMO. Instead he assumes this third observer describes the relation between the other two as per "described by quantum mechanics". Unfortunately that all avoids the foundational problems of QM. The ultimate relational interpretation IMO suggests that QM itself needs reconstruction, as QM as it stands is not relational - it implies a background observer. Rovelli does not solve this in any way.

/Fredrik

 

[CarlB]

<<Ie. it takes a third observer to describe the relation between two other observers. But Rovelli never analyses this to completion IMO. Instead he assumes this third observer describes the relation between the other two as per "described by quantum mechanics".>>

I'm at least sympathetic to this; my feeling is that Rovelli's work is too philosophical and not enough physical. But I agree at heart with his idea; that the only things we should look at are relational in nature. My paper attempting to correct the "not enough physical" problem, "A Relational Analysis of Quantum Symmetry" is still under review at Foundations of Physics now since May 2021. I've never had a paper sit that long without any editorial decision or feedback and I'm wondering why. I'm guessing the problem is that I'm using two math ideas that physicists are not familiar with, Harmonic Analysis and Module theory and my present project is writing some papers explaining those ideas for physicists. Quantum mechanics was developed just after mathematicians invented matrices and used them extensively. Now math has moved on to modules but physics hasn't moved much past matrices. Modules are a nice generalization. And harmonic analysis gives a nice understanding of the relationship between Fourier transforms, symmetry and wave equations.

 

[CarlB]

Schwinger's "Measurement Algebra" is a formulation of QM that is more compatible with Rovelli's relational principle in that it talks about interactions instead of properties of quantum states. He's not avoiding an observer but is taking into account the interaction between the measuring apparatus and the quantum object:

"The classical theory of measurement is implicitly based upon the concept of an interaction between the system of interest and the measurement apparatus that can be made arbitrarily small, or at least precisely compensated, so that one can speak meaningfully of an idealized measurement that disturbs no property of the system. The classical representation of physical quantities by numbers is the identification of all properties with the results of such nondisturbing measurements. It is characteristic of atomic phenomena, however, that the interaction between system and instrument cannot be indefinitely weakened. Nor can the disturbance produced by the interaction be compensated since it is only statistically predictable. Accordingly, a measurement of one property can produce uncontrollable changes in the value previously assigned to another property, and is without meaning to ascribe numerical values to all the attributes of a microscopic system."
https://www.pnas.org/content/pnas/45/10/1542.full.pdf

Schwinger wrote the above in the early 1950s IIRC; my description of the same thing expands it to include thermodynamics, which I think is natural as quantum mechanics is a statistical theory, and also modernized some of the language:
https://file.scirp.org/pdf/JMP_2018032615223977.pdf

 

[Fra]

<<Ie. it takes a third observer to describe the relation between two other observers. But Rovelli never analyses this to completion IMO. Instead he assumes this third observer describes the relation between the other two as per "described by quantum mechanics".>>

I'm at least sympathetic to this; my feeling is that Rovelli's work is too philosophical and not enough physical. But I agree at heart with his idea; that the only things we should look at are relational in nature. My paper attempting to correct the "not enough physical" problem, "A Relational Analysis of Quantum Symmetry" is still under review at Foundations of Physics now since May 2021.

"It is possible to compare different views, but the process of comparison is always a physical interaction, and all physical interactions are quantum mechanical in nature. I think that this simple fact is forgotten in most discussions on quantum mechanics, yielding serious conceptual errors. Suppose a physical quantity q has value with respect to you, as well as with respect to me. Can we compare these values? Yes we can, by communicating among us. But communication is a physical interaction and therefore is quantum mechanical."
-- Rovelli, https://arxiv.org/abs/quant-ph/9609002

I think Rovellis is too fast in the last scentence where things go hazy for me. If we are trying to understand/interpret QM, and we explain it as the view relative to the observers, we can not use the term "quantum mechanical" again to explain "communication" how objectivity is restored, it adds no explanatory value, and seems a bit circular indeed. It's precisely the physical basis and corresponding constraints on this communication we need to reconstruct IMO, to understand the interactions.

My suggestion is to start in the other end. Let's try to describe how two general observers, can possibly establish a communication protocol and then communicate with reasonable reliability. If we instead can instead define possible communication protocols and transceiver microstructures, we can use that to construct from the first principles (ie. communication and information processing principles), QM. This would also be relational, but the strategy is different and more radical. This is the part that I am missing in Rovellis analysis, and where I lost interest. I am guessing your objections to Rovellis philosophy is different. I skimmed your paper and I find no handles on these questions in there.

/Fredrik

 

[Fra]

Unless it wasn

If we are trying to understand/interpret QM, and we explain it as the view relative to the observers, we can not use the term "quantum mechanical" again to explain "communication" how objectivity is restored, it adds no explanatory value, and seems a bit circular indeed. It's precisely the physical basis and corresponding constraints on this communication we need to reconstruct IMO, to understand the interactions.

Unless it was not clear, what I meant was that as Rovelli seems to think he has EXPLAINS communication between general observers by saying "its described by QM" - as if QM was made for that. But part of the discussion here is that some of us think that QM as it stands is not made for this. What Rovelli says would make more sense applied to the yet unknown reconstructed theory of which QM is a limiting case. This is why I feel there is no explanatory value here. Merely reinterpreting things does not solve any of these problems as I see.

Just to raise one simple question: Does it not seems reasonable to expect that the mass of the observer should constrain the possible communication protocols it can run with timley responses? I think Rovelli does not use the physical communication process in it's deepest sense, but more like an informal term. It seems to be QM can at best, describe how two "subatomic" parts interact, but this is then an extrinsic description of their inteaction, from a third observer which is implicitly VERY massive and classical - is it not?

/Fredrik