I What does it take to solve the measurement problem? (new paper published)

[PeterDonis]

Many worlds also have an apparent effective (not true) collapse, similar to Bohmian mechanics.

Calling these both by the same name seems to me to cause far more confusion than it could possibly solve.

 

[PeterDonis]

Pilot wave does not obey non-local dynamics. It is particles that obey non-local dynamics.

I think this is just a difference in choice of words. The pilot wave is how the non-local dynamics that the particles obey is realized: the pilot wave (or "quantum potential") term in the equation if motion is where the non-local dynamics of the particles resides.

 

[Demystifier]

Calling these both by the same name seems to me to cause far more confusion than it could possibly solve.

Well, I'm not responsible for that language, I'm just using standard terminology. Do you have a proposal for better terminology?

 

[PeterDonis]

The Hyperion problem does not exist in Bohmian mechanics because particles are localized objects

Particles are localized objects in standard QM, so I don't see how this helps.

it has nothing to do with the fact that equations of motion for particles are non-local and deterministic.

The fact that the equations of motion are deterministic means that the results of all measurements are predetermined; there is no actual randomness. As you note, the apparent randomness is entirely due to our ignorance of initial conditions--just as in a classical theory. And it is that specific similarity with classical theories that causes there to be no Hyperion problem in Bohmian mechanics, for exactly the same reason that there is no such problem in classical dynamics.

 

[Demystifier]

Particles are localized objects in standard QM

I'm not sure what do you mean by localized here. I mean pointlike, zero-size, which particles in standard QM are certainly not.

 

[PeterDonis]

No, it shouldn't.

I still don't see why not. See below.

Many worlds also have an apparent effective (not true) collapse, similar to Bohmian mechanics. Many versions of Copenhagen talk about collapse very explicitly, as @atyy will confirm. And Bohmians definitely do not say that collapse is a result of ignorance of initial conditions, it is a result of particles entering only one branch of the wave function. It is the randomness of collapse, not the collapse itself, that results from ignorance of initial conditions in Bohmian mechanics.

None of this contradicts the point I was making, which is that collapse is not a real physical process in any of these interpretations.

 

[PeterDonis]

I'm not sure what do you mean by localized here.

I mean that when we observe a "particle", we observe it as a localized thing. We don't observe an electron as "smeared out" over an arbitrary amount of space. We observe it as a dot on a detector screen or something equivalent.

I mean pointlike, zero-size, which particles in standard QM are certainly not.

Ok, this clarifies what "localized" means in the Bohmian interpretation. But I'm not sure what actual work the "pointlike" part does, over and above the weaker notion of "localized" that I described above.

 

[Demystifier]

None of this contradicts the point I was making, which is that collapse is not a real physical process in any of these interpretations.

That is true, but the point is that the collapse does not even need to be a real physical process in order to solve the Hyperion problem. Hossenfelder said that it does, but she was wrong. Effective (not real) collapse a'la Bohm or many worlds is enough.

 

[Demystifier]

Ok, this clarifies what "localized" means in the Bohmian interpretation. But I'm not sure what actual work the "pointlike" part does, over and above the weaker notion of "localized" that I described above.

It provides that the Bohmian particle cannot enter more than one branch of the wave function, which explains why only one branch looks "real", which explains the illusion of collapse.

 

[PeterDonis]

the point is that the collapse does not even need to be a real physical process in order to solve the Hyperion problem

In the Bohmian interpretation, that's true, as I've already said. And since that is your preferred interpretation, I can see why it seems this way to you. But there are other interpretations.

 

[PeterDonis]

It provides that the Bohmian particle cannot enter more than one branch of the wave function

Ah, I see.

 

[Demystifier]

In the Bohmian interpretation, that's true, as I've already said. And since that is your preferred interpretation, I can see why it seems this way to you. But there are other interpretations.

Can you name one interpretation that does not solve the Hyperion problem? I think they all do, whatever Hossenfelder says.

 

[Fra]

I would not state it this way, because if we believe that QM can't explain the observed motion of Hyperion, and by extension of any system that shows classical dynamics beyond the Ehrenfest time, then why would we describe what we are looking for to take its place as "solving the measurement problem", since the measurement problem itself is a problem of QM, and if we accept the first part of her argument, we are discarding QM?

As I understood it, this is one the reason that pure "interpretations" alone are getting us nowhere. I agree on that.

Some sort of modification or revision of QM seems required? That does not mean we literally throw it away and forget about it. Just like QM should have a correspondence limit to CM in the massive objects. The Revised measurement theory should also have a correspondence to QM as it stands for the case of small subsystems and short timescales (where what is short and small is of course a relative notion). That the timescale is important for the paradigm of QM I think it clear also if you consider the processing of inferring the "timeless laws". The timeless laws, are only true for a timescale shorter than their inference time. Any other scenario seems to force us into a cosmological perspective (from the agent).

/Fredrik

 

[Morbert]

See also one of Sabine Hossenfelder's blog entries:
https://backreaction.blogspot.com/2022/05/chaos-real-problem-with-quantum.html

I don't understand her problem with the textbook response. Given some initial state that includes both Hyperion and its environment, the linear evolution of this state in Hilbert state will predict a chaotic evolution of Hyperion in phase space that lasts longer than 20 years. She likens this to a model of a die that gives the right average but the wrong relative frequencies (e.g. predicting the die will return 106 approximately half the time). What is the Hyperion analogue to the 106 case?

Consider Hyperion $H$, its environment $E$, and a device $D$ on Earth that observes Hyperion's evolution and records one of two ouctomes:"Hyperion is chaotic" or "Hyperion is not chaotic". The initial state of such a system is $$\rho_H\otimes\rho_E\otimes\rho_D$$Let's say the system first evolves for 100 years, such that Hyperion and her environment (but not the device) entangle, resulting in the new state $$\rho^{'}_{H+E}\otimes\rho_D$$Then, physicists observe Hyperion using the device over some time interval (say another 100 years) such that the three systems are entagled in some final state$$\rho^{''}_{H+E+D}$$Classically, we would expect the device to record an outcome "Hyperion is chaotic", and indeed that is what QM would presumably predict with probability close to 1. I.e. if the pointer state "Hyperion is chaotic" has some projector $R_c$, then $\mathrm{Tr}\left[R_c\rho^{''}_{H+E+D}\right] \approx 1$

 

[atyy]

Hossenfelder cites Zurek and Berry references which solve the Hyperion problem with decoherence. Then she rejects the solutions, because they only produce entangled states. But then if you don't look at Hyperion, quantum mechanics doesn't say that it's there, so there is no chaotic motion unless one looks at it. If one looks at it, then one would have measurement and collapse (or whatever one wants to call it). So the answer in the standard interpretation is we don't make any statement as to whether Hyperion is there or not when we don't look at it. So in the end, the Zurek and Berry references should solve the problem.

Zurek: https://arxiv.org/abs/quant-ph/0105127

Berry: https://michaelberryphysics.files.wordpress.com/2013/07/berry337.pdf

 

[Lord Jestocost]

Summary: preprint by Jonte Hance and Sabine Hossenfelder on the measurement problem and quantum foundations

Yesterday Jonte Hance and Sabine Hossenfelder published this preprint on the arXiv: https://arxiv.org/abs/2206.10445

What does it take to solve the measurement problem?​

Berthold-Georg Englert in "On Quantum Theory" (The European Physical Journal D, 2013 - Springer):

"One preexisting concept of quantum theory is the event, such as the emission of a photon by an atom, the radioactive decay of a nucleus, or the ionization of a molecule in a bubble chamber. The formalism of quantum theory has the power to predict the probabilities that the events occur, whereby Born’s rule [4] is the link between formalism and phenomenon. But an answer to the question Why are there events? cannot be given by quantum theory.
. . . . . .
Fifth, since neither decoherence nor any other mechanism select one particular outcome (see Sec. 8), the whole “measurement problem” reduces to the question Why is there one specific outcome? which is asking Why are there randomly realized events? in the particular context considered. This harkens back to Sec. 1, where we noted that quantum theory cannot give an answer.
In summary, then, the alleged “measurement problem” does not exist as a problem of quantum theory. Those who want to pursue the question Why are there events? must seek the answer elsewhere." [bold by LJ]

 

[Fra]

Berthold-Georg Englert in "On Quantum Theory" (The European Physical Journal D, 2013 - Springer):

"One preexisting concept of quantum theory is the event, such as the emission of a photon by an atom, the radioactive decay of a nucleus, or the ionization of a molecule in a bubble chamber. The formalism of quantum theory has the power to predict the probabilities that the events occur, whereby Born’s rule [4] is the link between formalism and phenomenon. But an answer to the question Why are there events? cannot be given by quantum theory.
. . . . . .
Fifth, since neither decoherence nor any other mechanism select one particular outcome (see Sec. 8), the whole “measurement problem” reduces to the question Why is there one specific outcome? which is asking Why are there randomly realized events? in the particular context considered. This harkens back to Sec. 1, where we noted that quantum theory cannot give an answer.
In summary, then, the alleged “measurement problem” does not exist as a problem of quantum theory. Those who want to pursue the question Why are there events? must seek the answer elsewhere." [bold by LJ]

The perspective in that paper IMO misses a whole important facet - which at least for me, and from the interacting agent perspective - is the most important one: Unification of interactions and measurements, for the purpose of understanding unification of forces and the nature of causality.

We can say whatever we want, but we still do now have a consistent conceptually coherent unification of QM and GR, and for some, the mesurement problem is most likely entanglet with that problem. Even the conceptual understanding of all other forces WITHOUT gravity, is not satisfactory I think. We have finetuning that you may or may not think is a problem, but I think the fine tuning is "apparent" because we do not fully understand thinks satisfactory (we can only describe it). If one thinks there is no meaning in asking why, that is a personal choice, but I think there is more to understand.

The measurement problem is IMO related to the causality in the following way. Most would agree that an observers action would be depend on what it knows and has at hand, ie. a kind of locality principle. But as any subsystem of the universe (wether classical or not) should by the principle of observer democracy be a valid obserever. Then by equivalence, the rules of inference and choice of actions of such observer, must be indistinguishalbe from the laws of physics and it's causal principles?

This is IMO at the heart of the measurment problem, and if solve it likely will have implications for understanding how the interactions and it's phenomenology are unified, and to see the naturality of things we today see require finetuning because we have learned to describe things, and now understand the full origin of all symmetries.

/Fredrik

 

[bhobba]

That's not her argument. Her argument is:
The long term motion of Hyperion is in agreement with classical chaotic mechanics. Thus to explain it by quantum mechanics we need to show that quantum mechanics reproduces the classical motion for these long time scales, which has not been done so far. This, in turn, is related to the measurement problem.

I just saw Hossnefelder's video, and that was my first reaction - quantum mechanics should reproduce the classical motion over long-time scales. I didn't realise it hadn't been proven yet. Interesting.

Thanks
Bill

 

[bhobba]

In summary, then, the alleged “measurement problem” does not exist as a problem of quantum theory. Those who want to pursue the question Why are there events? must seek the answer elsewhere." [bold by LJ]

Or why when we measure position we get one answer. I think the construction of our measuring apparatus and the definition of position might have something to do with it. The answer is not in QM but in the questions we ask. When not measured we cant say anything - but when measured we certainly can.

Thanks
Bill

 

[Demystifier]

I just saw Hossnefelder's video, and that was my first reaction - quantum mechanics should reproduce the classical motion over long-time scales. I didn't realise it hadn't been proven yet.

The correct statement is that it hasn't been proven yet in an interpretation independent way. Different interpretations reproduce classical motion in different ways, but without an interpretation one cannot get it.

 

[vanhees71]

Then you say that the classical limit is unphysical? Any physically observable phenomenon must be, of course, independent of the interpretation of QT used.

For the most simple case of a single particle in non-relativistic QM, you get the classical limit by the eikonal approximation of the (time-dependent) Schrödinger equation. In the path-integral formulation that's equivalent to the saddle-point approximation and is valid when the typical values of the action around the classical trajectory under investigation are very large compared to $\hbar$. I think there's nothing interpretation-dependent in this argument.

 

[A. Neumaier]

The correct statement is that it hasn't been proven yet in an interpretation independent way.

It (Namely that ''quantum mechanics should reproduce the classical motion over long-time scales'') also hasn't been proven yet in an interpretation dependent way, thus the additional phrase only obscures matters. If you object, please point to a proof.

 

[A. Neumaier]

For the most simple case of a single particle in non-relativistic QM, you get the classical limit by the eikonal approximation of the (time-dependent) Schrödinger equation. In the path-integral formulation that's equivalent to the saddle-point approximation and is valid when the typical values of the action around the classical trajectory under investigation are very large compared to $\hbar$. I think there's nothing interpretation-dependent in this argument.

Yes, and the eikonal approximation is valid only at short times. Nobody so far proved something interesting for very long times, at the constant physical value of $\hbar$.

 

[Demystifier]

It (Namely that ''quantum mechanics should reproduce the classical motion over long-time scales'') also hasn't been proven yet in an interpretation dependent way, thusd the additional phrase only obscures matters. If you object, please point to a proof.

By "proven" I didn't mean in the strict mathematical sense. Different interpretations explain (rather than prove in the strict mathematical sense) it, but it cannot be explained in interpretation independent way.

 

[Demystifier]

Then you say that the classical limit is unphysical? Any physically observable phenomenon must be, of course, independent of the interpretation of QT used.

The classical limit is physical, but we don't fully understand how it arises. That's one of the reasons why we have different interpretations, to explain the classical limit.

For the most simple case of a single particle in non-relativistic QM, you get the classical limit by the eikonal approximation of the (time-dependent) Schrödinger equation. In the path-integral formulation that's equivalent to the saddle-point approximation and is valid when the typical values of the action around the classical trajectory under investigation are very large compared to $\hbar$. I think there's nothing interpretation-dependent in this argument.

This is only part of the story. Decoherence also plays an important role in the classical limit, while the argument above does not involve decoherence.

 

[gentzen]

It (Namely that ''quantum mechanics should reproduce the classical motion over long-time scales'') also hasn't been proven yet in an interpretation dependent way, thusd the additional phrase only obscures matters. If you object, please point to a proof.

I currently do understand how preparation and "interaction" of sufficiently small systems (certainly not the whole universe) can be modeled within Bohmian mechanics. The way how to model measurement is not fully clear to me. (What is unclear to me is that the individual trajectory is not (supposed to be) observable, but maybe "many particle statistics" of trajectories are "supposed to be" observable.)

But even if this would be clarified (for example in a separate thread, or by a reference to some paper explaining this), I guess it would still not be "sufficient proof" for you.

 

[A. Neumaier]

By "proven" I didn't mean in the strict mathematical sense. Different interpretations explain (rather than prove in the strict mathematical sense) it, but it cannot be explained in interpretation independent way.

''proofs'' in the sense of a formal limit $\hbar\to 0$ don't mean much for long times; the time limit for which these limits are valid are of the order of a power of $\hbar$ (times context-dependent constants that producing the right units), and are microscopically small for the physical value of $\hbar$.

This is a manifestation of the fact that different limits (here $\hbar\to 0$ and $t\to\infty$) do not commute in general.

In this sort of questions, this is of primary physical relevance, not only a mathematical detail. Sabine Hossenfelder referred to the real problem, not to the superficial cure.

 

[zekise]

There is no such thing as the measurement problem. This is the creation of some very dated and wrong ideas, picked up by science writers to create some drama in their profession.

In fact observer A can take a measurement of a particle and the particle wave function would not "collapse"!

Imagine we have two observers A and B. A is coherent w.r.t. the environment E and the observer B, and observer B is embedded in E (entangled with E).

A particle arrives in a superposition of states for both A and B. A measures the particle and it "collapses" (an unfortunate word) for A. But the particle has NOT collapsed for B.

The state of the particle depends on who is asking or measuring. There is no such thing as an absolute wave function. A wave function is always between two (or more) parties. Just like velocity. You can't have V(a) the absolute velocity of object a. You can only have V(a, b).

This is the Relational Interpretation of Carlo Rovelli (1994).

Sabine Hossenfelder is still stuck with the measurement problem. Instead of making videos on 5G cell phones, geothermal energy, social matters, she needs to upload a new release of physics.

 

[bhobba]

There is no such thing as the measurement problem.

To me, like probability, it is just an update of knowledge. But it is a subtle issue to do with the ontological status of the quantum state. I am not ready to dismiss it as a total non-issue, I really like Sabine and watch all her videos but must admit she is a bit fixated on it IMHO.

I think Bell's Theorem is a much more important issue to do with properties between observations. Accepting locality does mean quantum objects do not have properties (except the state) between observations, which is a rather startling statement about how the world works. Our world seems to be created by interactions between quantum objects rather than the objects themselves. I think they are real in the sense they are part of a reality independent from us, but not in the sense they have properties all the time (only when measured). It fits in nicely with the QFT view of things IMHO, as it should.

Thanks
Bill

 

[A. Neumaier]

There is no such thing as the measurement problem. This is the creation of some very dated and wrong ideas

The experts in the field don't agree with you. Have you read Schlosshauer's book on decoherence?