Is Relational Quantum Mechanics the Key to Understanding Quantum Interactions?

[AndreiB]

Explain to me what you mean by massive bodies, gravitational tides, etc in terms of wavefunctions.

I think you have a wrong understanding about what a theory is. It is an algorithm that takes as input some observations (initial data) and outputs some numbers that need to be related to other observations (predictions).

The observations themselves are as they are, they are neither "quantum" nor "classical".

A wavefunction cannot be observed, hence it cannot play the role of an initial data. The wavefunction can be deduced from observations. In the case of the hydrogen atom you need to know the mass/charge for the electron and proton. once you have those you can calculate the Hamiltonian (assuming the classical Coulombian force) and only then you get the wavefunction. You use the wavefunction to infer the energy levels, and then, you can check the prediction based on spectral observations.

The concept of mass/charge together with the 3D space and time are primitives. They are not explained by the theory. A massive body is an object with mass. A tide is a type of motion of water, itself composed from objects with mass and charge (water molecules)

The framework wasn't devised to explain how the world works but to make predictions.

I agree.

You are using it wrongly to push your circular philosophy.

There is nothing circular here.

There is no deep knowledge why, how and what exists prior to measurements.

So what? Did i ever pretend to know that?

That all observations appear "classical" is not an excuse to use them as an explanation for the appearance of other classical-like behavior.

There are no "classical" or "quantum" observations. You are confused.

Your reasoning and explanations are amount to : there are massive classical bodies... because this is what we observe.

My argument has nothing to do with explaining the existence of "massive classical bodies". I have no idea what made you think so.

 

[PeterDonis]

In the case of the cat in the box, the "which-way detector" is any object with mass that exists outside the box.

Most objects with mass are incapable of detecting the tiny differences in mass distribution that distinguish a live cat from a dead cat, or even the much larger differences in mass distribution inside the Earth. That's why, in order to measure the Earth's mass distribution in detail, we can't just put a bunch of "objects with mass" around; we have to build specialized equipment and launch it in spacecraft and let them orbit the Earth for quite some time.

The only difference is that this object interacts with the cat gravitationaly

Not every gravitational interaction can serve as a "mass distribution detector".

 

[EclogiteFacies]

I know this is late but Rovelli with RQM believes that yes your wife is in a defined position before opening the door. Decoherence plus billions of uncorrelated degrees of freedom wash out relationality. This produces stable facts. Interference is so unbelievably subtle that FAPP there is none. Macro objects under normal circumstances (access to the environment).
Are not in superposition.
RQM is not solipsistic.

Also, I do think Wigner's Friend experiments are disingenuous. Anthropomorphising photons is ridiculous.
Under normal circumstances (excluding MWI) people are not in superposition and these experiments are only applicable for the macroscopic under unbelievably strange idealised circumstances with the use of a magic lab that separates the friend from the entire universe.

It doesn't change day to day life.

 

[AndreiB]

Most objects with mass are incapable of detecting the tiny differences in mass distribution that distinguish a live cat from a dead cat

How "incapable"? We can measure, in principle, the position of such an object with sub-Planckian level accuracy (corresponding to the uncertainty principle applied to a maroscopic object). I'm not saying you are wrong, but I think some sort of calculation needs to be done. I would say that, based on Newton's third law, the disturbance produced on the external object by the change in the cat's mass distribution is of the same order as the change of the mass distribution itself.

Not every gravitational interaction can serve as a "mass distribution detector".

Why?

 

[PeterDonis]

We can measure, in principle, the position of such an object with sub-Planckian level accuracy

We do not know that this is possible, no. Such claims are highly dependent on what quantum gravity theory turns out to be correct.

Why?

For the same reason that, as I've already pointed out, we couldn't just put a bunch of "massive objects" around to measure the Earth's mass distribution. We had to design special equipment and put it aboard satellites with precisely determined orbits and collect data for a long period of time.

 

[AndreiB]

We do not know that this is possible, no. Such claims are highly dependent on what quantum gravity theory turns out to be correct.

Currently, QM does not impose any limit for the accuracy of a position measurement. I have no reason to believe that quantum gravity would change that.

For the same reason that, as I've already pointed out, we couldn't just put a bunch of "massive objects" around to measure the Earth's mass distribution. We had to design special equipment and put it aboard satellites with precisely determined orbits and collect data for a long period of time.

This is a thought experiment. It's not about technology, it's about principles. As a matter of principle there is no difference between a space probe and some random object. It's just not convenient to find such an object and go there to measure its position.

 

[PeterDonis]

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

Currently, QM has only been tested down to length scales about 18 orders of magnitude larger than the Planck length.

I have no reason to believe that quantum gravity would change that.

Um, yes, you do, since quantum gravity is expected by most physicists to predict that the very concept of "length" (and "spacetime" in general) is no longer meaningful at the Planck scale--that our current concept of "spacetime" is an emergent phenomenon at scales much larger than the Planck scale.

As a matter of principle there is no difference between a space probe and some random object.

Yes, there is: a random object is not designed to make a particular very precise measurement. Just as we don't use random rocks as detectors in experiments in general; we use specially designed equipment. To claim that any random object would work just as well is ridiculous.

 

[Sunil]

A wavefunction cannot be observed, hence it cannot play the role of an initial data.

It can and does. Because it can be prepared by a preparational measurement. You measure some A, throw away all cases where $a\neq a_0$ and have prepared a state with a wave function which is an eigenstate of A with eigenvalue $a_0$.
Another way to prepare is simple relaxation. You have atoms in various possibly excited states. You isolate them from influences which can excite them and wait. After some time, the excited states will have emitted photons and returned to the ground state, and you can use the ground state for the initial data.

 

[AndreiB]

It can and does. Because it can be prepared by a preparational measurement.

What you actually see is not a wavefunction, it's the macroscopic disposition of your preparation device. Sure, you can deduce the wavefunction from "classical" observations but you can't "see" a wavefunction directly.

A "pure" version of QM without any reference to "classical" observations is just a piece of mathematics, not physics.

 

[gentzen]

A wavefunction cannot be observed, hence it cannot play the role of an initial data. The wavefunction can be deduced from observations.

It can and does. Because it can be prepared by a preparational measurement. You measure some A, throw away all cases where ...

I have to agree with AndreiB on this one. You can prepare the density matrix of a thermal state, and you can filter that density matrix to become more concentrated around some pure state you want to prepare. But the state will always stay far away from being pure. A laser achieves states whose density matrix is nearly pure. Perhaps the way how this is achieved can be interpreted as using filtering to directly influence a thermal state.

And if you want to measure the density matrix of some prepared state, then you need measurement results for a number of different measurement settings. So believing that you have in any way direct access to the wavefunction is naive.

 

[AndreiB]

Currently, QM has only been tested down to length scales about 18 orders of magnitude larger than the Planck length.

This is not about accurate position measurements, it's about the de-Broglie wavelength of the "probe" particles. LIGO can measure distances of 10^-20 m using lasers with a wavelength of 10^-6 m.

Um, yes, you do, since quantum gravity is expected by most physicists to predict that the very concept of "length" (and "spacetime" in general) is no longer meaningful at the Planck scale--that our current concept of "spacetime" is an emergent phenomenon at scales much larger than the Planck scale.

I think this is pure speculation. I am aware about Nima Arkani-Hamed's arguments that presumably show that spacetime is "doomed". I don't buy his arguments and I don't think he was able to replace spacetime with something more fundamental. But even Nima accepts that measurements of any accuracy can be performed, as long as the accuracy is not infinite. The theories we have at this moment accept a continuous spacetime, and Lorentz invariance requires that nothing special happens at Planck distance.

Yes, there is: a random object is not designed to make a particular very precise measurement. Just as we don't use random rocks as detectors in experiments in general; we use specially designed equipment. To claim that any random object would work just as well is ridiculous.

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. Their detection, sure, requires "specially designed equipment", like a fluorescent screen.

In our case, the rock carries the relevant information, and, by analogy, the "specially designed equipment" is not necessary to suppress the live/cat superposition.

 

[Sunil]

Um, yes, you do, since quantum gravity is expected by most physicists to predict that the very concept of "length" (and "spacetime" in general) is no longer meaningful at the Planck scale--that our current concept of "spacetime" is an emergent phenomenon at scales much larger than the Planck scale.

This maybe what "most physicists expect". But is it relevant?
The part of quantum theory which works and is well-defined is QG as an effective theory:

Donoghue, J.F. (1994). General relativity as an effective field theory: The leading quantum corrections. Phys Rev D 50(6), 3874-3888

It works on the base of the field-theoretic variant of GR, thus, has a background, and breaks full GR symmetry given that it uses harmonic coordinates (but tries to recover symmetry using ghosts).

Yes, there is: a random object is not designed to make a particular very precise measurement. Just as we don't use random rocks as detectors in experiments in general; we use specially designed equipment. To claim that any random object would work just as well is ridiculous.

Depends on the particular experiment. Many statistical experiments especially use random numbers or so to randomize the input, especially in medicine. There is no relation between such random input and precision. The precision of such experiments you can, for example, improve with larger numbers of trials. (But I agree that in this point criticizing the OP is correct.)

 

[Sunil]

I have to agree with AndreiB on this one. You can prepare the density matrix of a thermal state, and you can filter that density matrix to become more concentrated around some pure state you want to prepare. But the state will always stay far away from being pure.

That's only the trivial point that there is no ideal experiment. That it stays "far away" is simply wrong, it may be quite close to the ideal. Close enough to use the wave function as the initial datum for what is done later.

And if you want to measure the density matrix of some prepared state, then you need measurement results for a number of different measurement settings. So believing that you have in any way direct access to the wavefunction is naive.

There would be no need to measure such a density matrix.

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. $|\psi_a(a)\rangle\langle \psi_a(a)| \times \hat{\rho}(b,\ldots)$

So, I don't have to claim some direct access. I claim that one can prepare which can be, with good enough accuracy, described by a well-known wave function for the relevant degrees of freedom.

 

[Sunil]

What you actually see is not a wavefunction, it's the macroscopic disposition of your preparation device. Sure, you can deduce the wavefunction from "classical" observations but you can't "see" a wavefunction directly.

So what? There is no need for this "seeing directly". This may be relevant only for proponents of outdated methodology of science like empiricism where "seeing directly" is somehow important.

A "pure" version of QM without any reference to "classical" observations is just a piece of mathematics, not physics.

The point being? Even the minimal interpretation uses "measurement results" and so implicitly refers to such observations of classical measurement devices.

 

[AndreiB]

So what? There is no need for this "seeing directly". This may be relevant only for proponents of outdated methodology of science like empiricism where "seeing directly" is somehow important.

In my discussion with EPR (see post #89) he asked me:

"Explain to me what you mean by massive bodies, gravitational tides, etc in terms of wavefunctions. without resorting to acts of measurements by other unexplained "classical" objects."

My point was that what EPR wants cannot be done, since the wavefunction cannot be directly observed. My reply has to be understood in this context, it's not that I have something against wavefunctions.

The point being? Even the minimal interpretation uses "measurement results" and so implicitly refers to such observations of classical measurement devices.

EPR is not satisfied with the minimal interpretation. I was replying to him.

 

[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