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

[gentzen]

This is a claim RUTA makes, but I don't think it is generally accepted.

I think RUTA wants to make more general claims than that. By "conservation laws holding event by event," I explicitly don't mean the quantum intermediate results, but only the measured classical results. If you measure those classical results in a configuration that they have no chance of both satisfying the quantum expectations, and the conservation laws of the classical results for the specific event, then the quantum expectations will "win".

People will use different words to describe this situation, but they will probably agree on what quantum mechanics predicts to happen in that situation.

 

[PeterDonis]

By "conservation laws holding event by event," I explicitly don't mean the quantum intermediate results, but only the measured classical results.

But the measured classical results are only for the measured system. They don't take into account conserved quantities possessed by the measuring apparatus. This means the measured classical results are useless for evaluating conservation laws, because during the measurement the measured system interacts with the measuring apparatus, so the measured system is not a closed system and you should not expect it to satisfy conservation laws in isolation.

If you measure those classical results in a configuration that they have no chance of both satisfying the quantum expectations, and the conservation laws of the classical results for the specific event, then the quantum expectations will "win".

Of course the results will match QM predictions, that's been established by countless experiments. But, as above, that's irrelevant to assessing conservation laws.

 

[gentzen]

But the measured classical results are only for the measured system. They don't take into account conserved quantities possessed by the measuring apparatus.

Agreed. And the measuring apparatus itself is not modeled on the quantum level, it only enters in the form of "boundary conditions" (or some more appropriate word).

This means the measured classical results are useless for evaluating conservation laws, because during the measurement the measured system interacts with the measuring apparatus, so the measured system is not a closed system

Indeed, the idea behind a closed system would be that you don't have to worry about "boundary conditions". But if you perform measurements on the system, then it surely is not a closed system.

and you should not expect it to satisfy conservation laws in isolation.

Indeed, I don't expect this. The violation of conservation laws event by event (in such a situation) is much less surprising than the preservation of conservation laws for the quantum expectations.

 

[PeterDonis]

The violation of conservation laws event by event

To be clear, I don't think there is any actual violation of conservation laws--it's just that if you only look at the measured system, you aren't taking into account all the relevant conserved quantities.

 

[bhobba]

To be clear, I don't think there is any actual violation of conservation laws--it's just that if you only look at the measured system, you aren't taking into account all the relevant conserved quantities.

If there were, there would be something wrong with Noether.

Thanks
Bill

 

[gentzen]

(Edit: I remember a huge table from "Quantenchemie: Eine Einführung" by Michael Springborg, where many relevant physical interpretations of quantities occurring in quantum chemistry computations were given. If I can find it again, I will include it in another reply.)

I found the huge table again:

$n_R$	$n_E$	$n_B$	$n_\Sigma$	Relevanz für:
0	0	0	0	Gesamtenergie
1	0	0	0	Kräfte; Strukturoptimierung
0	1	0	0	Elektrisches Dipolmoment
0	0	1	0	Magnetisches Dipolmoment
0	0	0	1	Hyperfeinstruktur
2	0	0	0	Harmonische Schwingungsfrequenzen und -Moden
0	2	0	0	Elektrische Polarizabilität
0	0	2	0	Magnetische Polarizabilität
0	0	0	2	Kopplung von Spins verschiedener Kerne
1	1	0	0	Infrarot Intensitäten
0	1	1	0	Circulardichroismus
3	0	0	0	Anharmonische Korrekturen zu Schwingungsfrequenzen
0	3	0	0	Erste elektrische Hyperpolarisierbarkeit
1	2	0	0	Raman Intensitäten
4	0	0	0	Anharmonische Korrekturen zu Schwingungsfrequenzen
0	4	0	0	Zweite elektrische Hyperpolarisierbarkeit

Of course, this immediately raises the questions of the meaning of those $n_R$, $n_E$, $n_B$ and $n_\Sigma$ in the header or rather their integer numbers in the rows of the table. The book explains it as follows:

14.15 Experimental quantities​

Many quantities measured in experiment can also be theoretically determined. In particular, the dependences of the total energy on the structure, the spin of the nuclei, and the components of electric and/or magnetic field vectors are important, i. e., quantities like
$$\frac{\partial E^{n_R+n_E+n_B+n_\Sigma}}{\partial R^{n_R} \partial \mathcal{E}^{n_E}\partial \mathcal{B}^{n_B}\partial \Sigma^{n_\Sigma}}.\qquad(14.91)$$
This notation implies that the experimentally relevant quantities are determined by the $n_R$-, $n_E$-, $n_B$-, and $n_Σ$-fold derivatives of the total energy $E$ with respect to the nuclear coordinates, the vector components of the electric field, the vector components of the magnetic field, and the components of the nuclear spin.

(So the table interprets quantities arising in the context of eigenvalue computations. Which makes sense, because those are related to "quasi-equilibrium properties," which are often more relevant than "scattering properties" in chemistry.) The caption of the table then references back to that description in the text:

Table 14.2: Some experimentally determinable quantities obtained by means of derivatives of the
total energies of the type of equation (14.91).

$n_R$	$n_E$	$n_B$	$n_\Sigma$	Relevance
0	0	0	0	Total energy
1	0	0	0	Forces: structural optimization
0	1	0	0	Electric dipole moment
0	0	1	0	Magnetic dipole moment
0	0	0	1	Hyperfine structure
2	0	0	0	Harmonic vibrational frequencies and modes
0	2	0	0	Electric polarizability
0	0	2	0	Magnetic susceptibility
0	0	0	2	Coupling of spins of different nuclei
1	1	0	0	Infrared intensities
0	1	1	0	Circular dichroism
3	0	0	0	Anharmonic corrections to vibrational frequencies
0	3	0	0	First electrical hyperpolarizability
1	2	0	0	Raman intensities
4	0	0	0	Anharmonic corrections to vibrational frequencies
0	4	0	0	Second electrical hyperpolarizability

 

[Demystifier]

That is still a single outcome.

Unless each of them realizes in another "world".

 

[Demystifier]

I don't understand the issue with single outvomes. How can there be anything else? What is a multiple outcome?

The issue is not whether the outcome is single, because it clearly is (except in the many world interpretation), but how QM explains single outcomes. The standard QM avoids a need for explanation because it postulates that a single outcome appears when a measurement is performed. However, the measurement itself in standard QM is usually not described in terms of something more elementary. Instead, measurement is taken as a primitive notion that does not need to be precisely defined. It works fine in practice, but it's not satisfying from a deeper point of view where one wants to introduce a wave function of the measuring apparatus. But when one does that, then wave function of the apparatus and of the measured system should a priori be treated on an equal footing, and from this point of view it is not at all obvious what's special about measurement so that single outcomes appear.

 

[Demystifier]

No, quantum mechanics implies conservation laws event by event.

That's true when both initial and final value of the conserved quantity is measured. But if the initial state is in the superposition of different values, while final measured state has a definite value, then the initial mean value is not equal to the final definite value.

 

[PeterDonis]

if the initial state is in the superposition of different values, while final measured state has a definite value, then the initial mean value is not equal to the final definite value.

In general this is true, but it doesn't mean conservation laws are violated. It just means the system is not a closed system--it interacts with the measuring apparatus during measurement. If a system is not closed, you should not expect it to obey conservation laws in isolation.

 

[vanhees71]

Of course, event-by-event conservation means that you must have a state, for which the conserved quantity takes a definite value.

 

[PeterDonis]

event-by-event conservation means that you must have a state

You will if you include everything that interacts, which means including the measuring apparatus. As @Demystifier points out, we don't currently have a formulation of QM that does that and also explains (instead of just postulating) single outcomes; that means we don't currently have a formulation of QM that allows us to test conservation laws during measurements.

 

[Demystifier]

In general this is true, but it doesn't mean conservation laws are violated. It just means the system is not a closed system--it interacts with the measuring apparatus during measurement. If a system is not closed, you should not expect it to obey conservation laws in isolation.

But the full system, namely measured system and measuring apparatus, is closed. And yet, the final definite energy of the full closed system is not equal to its initial mean energy.

Sure, the conservation law is not violated if one does not compare mean values with definite values. But if one insists that energy is conserved even in this case, then one must accept that the initial state had a definite energy different from the initial mean value, which is tantamount to accepting the existence of hidden variables.

 

[A. Neumaier]

But the full system, namely measured system and measuring apparatus, is closed.

No. it always iteracts with its environment.

 

[Demystifier]

No. it always iteracts with its environment.

Then the full system, namely measured system, apparatus and environment, is closed, and everything I said before applies to this full system.

 

[PeterDonis]

Then the full system, namely measured system, apparatus and environment, is closed, and everything I said before applies to this full system.

Not necessarily; that full system might be in an eigenstate of whatever conserved quantity you are assessing, even if subsystems of it are not.

 

[A. Neumaier]

Then the full system, namely measured system, apparatus and environment, is closed

This full system is the whole universe! How do you propose to measure it?

 

[Demystifier]

Not necessarily; that full system might be in an eigenstate of whatever conserved quantity you are assessing, even if subsystems of it are not.

I would say that the full system cannot be in the full Hamiltonian eigenstate. For if it was, the full wave function would have a trivial time dependence proportional to $e^{-iE_{\rm full}t/\hbar}$, so no decoherence or any other change could happen due to the Schrodinger evolution, which would correspond to a totally dull universe very unlike our own. (BTW such a dull universe is also related to the problem of time in quantum gravity, but that's another issue.)

 

[Demystifier]

This full system is the whole universe! How do you propose to measure it?

By neglecting the influence of environment. In real quantum optics experiments, a measured system is often very well isolated from the environment. The apparatus, of course, is not isolated from the environment, but the exchange of energy between apparatus and environment has a negligible influence on the measured system.

 

[A. Neumaier]

The apparatus, of course, is not isolated from the environment, but the exchange of energy between apparatus and environment has a negligible influence on the measured system.

This is not true.

The interaction of the apparatus with the environment is the essential ingredient in the derivation of decoherence properties for the measured system + apparatus!!!

 

[vanhees71]

But for sure, you don't need the "entire universe", whatever this unobservable entity might be, for that. Also the decoherence of the observed system through interaction with the measurement apparatus is suffcient too.

 

[Demystifier]

The interaction of the apparatus with the environment is the essential ingredient in the derivation of decoherence properties for the measured system + apparatus!!!

No. Since apparatus itself has many degrees of freedom, it is the apparatus that serves as "environment" needed for decoherence of the measured system. The air and other particles around apparatus is not important.

EDIT: Now I saw that @vanhees71 said the same.

 

[Fra]

but how QM explains single outcomes
...
measurement is taken as a primitive notion that does not need to be precisely defined
...
then wave function of the apparatus and of the measured system should a priori be treated on an equal footing, and from this point of view it is not at all obvious what's special about measurement so that single outcomes appear.

I think solving this problem, requires nothing less than understanding the dual perspectives of dynamics as described by a hamiltonian, and the "evolution" describes by agents making measurements on each other. This is exactly the heart of the problem.

One can choose between two problems
(1) complain that the measurement is a primitive notion, but accept an unexplained finetune hamiltonian and hope to have it explain the illustion of measuerment/collapse in some limite

(2) complain that the hamiltonian is not intrinsic, but accept the measurement as primitive and hope to explain the illustion of a hamiltionin in some limit

I choose the second problem because I see a better chance of solving it over the other one.

/Fredrik

 

[Demystifier]

I think solving this problem, requires nothing less than understanding the dual perspectives of dynamics as described by a hamiltonian, and the "evolution" describes by agents making measurements on each other.

So the evolution of agents is not described by Hamiltonian, right? Do you have some concrete model of agent evolution in mind?

 

[Fra]

So the evolution of agents is not described by Hamiltonian, right? Do you have some concrete model of agent evolution in mind?

The simple answer would be yes, if by agent we refer to the intrinsic perspective, it's not described by a fixed Hamiltonian simply because a Hamiltonian itself implicitly encodes information that bypassed proper inference. Instead the evolution of the agent from it's own perspective is simply an evolutionary learning process.

Still I imagine that one agent can have an emergent hamiltonian description, relative to another agent. This is the way in where must be a correspondence. The quest is to understand exactly how and which "hamiltonians" or that are likely abundant in nature.

The traditional method is differential equation based, which is a top down method, based on constraints. I largely consider an agent based model, which are commong in other fields, such as epidemology, social theory and economy. It's a bottom up model, where you simulate interactions of the part as per some sort of evolutionary rules, and see what population scale patterns that emerge. Predictions of these patterns from the model would add explanatory value.

Unless that basic ABM oncept is clear already see this paper (not specific to physics though!)

Validation and Inference of Agent Based Models
"Agent-based model (ABM) is a simulation based modeling technique that aims to describe complex dynamic processes, such as the spread of infectious disease. ABM provides considerable flexibility by explaining the complex dynamic process using simple rules that incorporate characteristics of individual
entities, called agents, and their interactions. Thus, mechanisms which are often difficult or impossible to model directly at the population level can be incorporated at the smaller scale into the development of ABM [Hooten and Wikle, 2010, Grimm and Railsback, 2013]. ABM can capture emergent phenomena resulting from the interactions of agents, and can be used to simulate counterfactual outcomes in hypothetical experiments which are impossible or unethical to conduct in the real world."
-- https://arxiv.org/abs/2107.03619

The idea is simple; simulate interactions of "agents", and identify from the emergent phenomena, emergent dynamical laws. Here the ABM model, has the potential to "explain" what in equation based modelling are constraints as emergent.

I certainly don't have any concrete models that reproduce the standardmodel in a unified manner. Even though that is obviously the goal. If I find it, i promise to publish it ;)

These ideas are not without problems though, but I prefer thoese problems over the alternative.

I have only some concrete toy models, but these are obiously personal theories at this point and even besides off limits here. I need to work on this alot more before I will officially publish it anywhere. But the general guiding principles can I think be understood without the details.

/Fredrik

 

[bhobba]

but how QM explains single outcomes.

It's intuitively obvious you will get a single outcome. But in reality, it is an assumption that needs explanation. It's like QM requires complex numbers - we just don't know. Scientifically it is not an issue since any theory has some foundational assumptions, but why they are true is something only a deeper theory (if it exists) can explain. The only comfort is whatever theory replaces it has the same issue. It's turtles all the way down. About the best you can do is have an intuitive reason why they are true. But then again what is intuitive for you may not be intuitive for others.

Thanks
Bill

 

[bhobba]

The interaction of the apparatus with the environment is the essential ingredient in the derivation of decoherence properties for the measured system + apparatus!!!

And why Hyperion does not 'smear' out of existence. It's like when Einstein asked Bohr, " Do you believe the moon is not there when nobody is looking". The answer is it is being looked at all the time by the environment, even if you consider the CMBR. That is why exactly inertial frames do not exist. But like the idea, a point has no size; it has proven a valuable concept.

Thanks
Bill

 

[martinbn]

The issue is not whether the outcome is single, because it clearly is (except in the many world interpretation), but how QM explains single outcomes. The standard QM avoids a need for explanation because it postulates that a single outcome appears when a measurement is performed. However, the measurement itself in standard QM is usually not described in terms of something more elementary. Instead, measurement is taken as a primitive notion that does not need to be precisely defined. It works fine in practice, but it's not satisfying from a deeper point of view where one wants to introduce a wave function of the measuring apparatus. But when one does that, then wave function of the apparatus and of the measured system should a priori be treated on an equal footing, and from this point of view it is not at all obvious what's special about measurement so that single outcomes appear.

This seems to me to be more about the measurement problem.

 

[martinbn]

It's intuitively obvious you will get a single outcome. But in reality, it is an assumption that needs explanation. It's like QM requires complex numbers - we just don't know. Scientifically it is not an issue since any theory has some foundational assumptions, but why they are true is something only a deeper theory (if it exists) can explain. The only comfort is whatever theory replaces it has the same issue. It's turtles all the way down. About the best you can do is have an intuitive reason why they are true. But then again what is intuitive for you may not be intuitive for others.

Thanks
Bill

My problem is not whether the existing explanations are good or not. I just don't understand the problem here. What is the alternative to "single outcome" in order to ask the question why? You roll a die and one face ends up. What else could it be?

 

[Demystifier]

This seems to me to be more about the measurement problem.

The problem of single outcomes is the measurement problem.

 

[martinbn]

The problem of single outcomes is the measurement problem.

OK, then it's fine. I thought it was another problem, and couldn't see what.

 

[vanhees71]

The problem of single outcomes is the measurement problem.

This is not a problem, just an empirical fact, taken care of by the probabilistic interpretation of the quantum state as a basic postulate of standard (minimal interpretation) QT.

 

[Demystifier]

This is not a problem, just an empirical fact, taken care of by the probabilistic interpretation of the quantum state as a basic postulate of standard (minimal interpretation) QT.

Some physicists would say the same for wave function collapse.

 

[Fra]

But there is a tension between the "empirical facts" between different agents. QM presumes that any valid observer stores their "empirical observations" in a common certain "shared memory" which is the macroscopic world. Ie classical pointer. Modulo Special relativity all valid qm observers should agree or we have a problem.

But if the empirical fact of one observer is in superposition relative to another, then one agent is would make the wrond predictions and expect quantum interference where ther is none.

So we need a fix somewhere?

/Fredrik

 

[Simple question]

It's intuitively obvious you will get a single outcome.

Well, not for WMI'st

It's like QM requires complex numbers - we just don't know.

I always content myself with simple explanation like "Complex numbers are a great way of keeping track of things that have amplitude and phase; that’s why we use them."
But do you mean some more fundamental reasons ?

But in reality, it is an assumption that needs explanation.

Based on the observation that stochastic theories are very powerful and used in a lot of different contexes (not only QM), my question would be: Is there some theoretical work on determining the "minimal properties" that some "domain" must have, that makes it suitable to be correctly (FAPP) but also fruitfully (in term on sheer discovery) modeled by a stochastic theory ?

Whatever the "measurement" does (if it does anything at all) it is probably possible to define it more "mathematically" than words like "collapse" or "update".

 

[vanhees71]

Some physicists would say the same for wave function collapse.

The wave function collapse doesn't solve anything and is unnecessary for phenomenology. In some forms it also contradicts the very construction of microcausality in relativistic QFT.

 

[Demystifier]

The wave function collapse doesn't solve anything

Then why do most physicists use it, in practice?

and is unnecessary for phenomenology.

Agreed, but it nevertheless can be very useful in phenomenology.

In some forms it also contradicts the very construction of microcausality in relativistic QFT.

Agreed again, but in some other forms it doesn't contradict it.

 

[Demystifier]

Whatever the "measurement" does (if it does anything at all) it is probably possible to define it more "mathematically" than words like "collapse" or "update".

Is
$$|\psi\rangle \mapsto \frac{\pi|\psi\rangle}{|| \pi|\psi\rangle ||},
\;\;\; \pi^2=\pi$$
mathematical enough?

 

[Simple question]

Is
$$|\psi\rangle \mapsto \frac{\pi|\psi\rangle}{|| \pi|\psi\rangle ||},
\;\;\; \pi^2=\pi$$
mathematical enough?

Nice. But you'll need to slow down. My last QM course was 30 years ago. Is it how you write the projection postulate ? Or is it the Born rule in disguise ?

I was more thinking along Noether's theorem like math. If probability is conserved, I suppose it is enough to make a similar symmetry arguments.
But measuring position or energy does not need explaining, they come first, in unique instances.
While measuring probability does need explanation, what is the ensemble, what is the probability space/measure.

What are the(or the many) set of minimal properties something need to have a "probability defined" ? Is the law of large number + equilibrium sufficient ? Is it necessary ?
Something else entirely ?

 

[Demystifier]

Is it how you write the projection postulate ?

Yes.

 

[Simple question]

Yes.

Simple answer. I like that

But I was not thinking about replacing "measurement" by "projection", and in the spirit of this thread, not postulate it. So the math I am looking for is more about the "how" a measurement can be done, not just what a measurement is defined as.

So let's say I ask chatGPT: "Find all non-reducible algorithm whose output can be described by the projection postulate."
So if it halts somehow, my expectation would be to have a set of measuring "things" that can be further analysed. Especially what different input space is possible.

Will it find this measuring "apparatus", able to project a ensemble of identically prepared "thingy" into a unique value ? Like a thermometer ?
Must all input be quantiz'able in some way ? Can some of those be continuous ? Can some input be imaginary number ? Must all values be subject to strict conservation law ? What about locality ?

I don't know if I make sense (probably not), but I am looking for the sets of postulate that is sufficient to generate a projection/measurement process (not only in the quantum case, but more generally)

 

[Demystifier]

I don't know if I make sense (probably not), but I am looking for the sets of postulate that is sufficient to generate a projection/measurement process (not only in the quantum case, but more generally)

See e.g. the book https://www.amazon.com/dp/0521485436/?tag=pfamazon01-20
Chapter 8 Theory of experiments.

 

[bhobba]

My problem is not whether the existing explanations are good or not. I just don't understand the problem here. What is the alternative to "single outcome" in order to ask the question why? You roll a die and one face ends up. What else could it be?

When we measure the position of a particle we get one answer. It is logically possible if you had a lot of devices to measure position it can have more than one result. But that is intuitively weird. More importantly, that is not what the experiment shows it is an empirical fact. In my intuitive account, a number is given to each possible result to create an observable. That position has an observable is an empirical fact.

Thanks
Bill

 

[bhobba]

This is not a problem, just an empirical fact, taken care of by the probabilistic interpretation of the quantum state as a basic postulate of standard (minimal interpretation) QT.

I don't think it's a problem either - like you said just an empirical fact. But some worry about it and come up with things like many worlds.

Thanks
Bill

 

[bhobba]

Well, not for WMI'st

Do you think that's intuitive? To be fair; QM has shown intuition is not always reliable, e.g. Bell. If locality is true, it can't have a position until measured. The real measurement problem, if a problem it is, is this interaction-created reality. The only thing you can say about a quantum system until you interact with it is its state - and IMHO, that is like probability - not 'real', just an aid to theoretical calculations. Note I have made several assumptions here with words like IMHO etc. All these are open to challenge. And that is where much of the discussion about QM foundations comes from. Note in my heuristic treatment, I did not put in Bell - that came from the assumptions. That is in itself a bit 'weird.'

Thanks
Bill

 

[Grelbr42]

isn't Hossenfelder on the verge of crackpot soon?

The main sources which are to be discussed in this thread is an arxiv manuscript and a blogpost. I thought only peer-review published work were allowed on this forum? I am just trying to understand

Discussing an arxiv post and your complaint is that we are discussing an arxiv post. Um...

 

[bhobba]

Then why do most physicists use it, in practice?

I don't think most physicists even worry about it, and of those that do there are different views of what the issue is. It's sort of like Hilbert's axiomatisation of Euclidian Geometry. Sure it bypasses issues like a point has position but no size, but I think only pure (or is that puerile - I keep forgetting) mathematicians care. I shouldn't joke like that - I had those tendencies once.

Thanks
Bill

 

[Simple question]

Do you think that's intuitive?

Kind of, even if I don't like it. It is still the most coherent cop-out to evade "the problem", by taking the position that QM only happens in Hilbert space, not in the lab.

To be fair; QM has shown intuition is not always reliable, e.g. Bell. If locality is true, it can't have a position until measured. The real measurement problem, if a problem it is, is this interaction-created reality.

I really like that phrasing. Although I would also consider that "interaction-created reality" also apply to classic theories.

The only thing you can say about a quantum system until you interact with it is its state - and IMHO, that is like probability - not 'real', just an aid to theoretical calculations.

Indeed. Yet I wonder how those "stochastic theoretical framework" can still connect to observation at those "interaction event". Even for more classic one. After all, QM "only" introduce two "un-observable", phase and non-locality (I hope I don't forget some). But it still works fine.

I have more reading to do ...

 

[berkeman]

Thread closed for Moderation...

 

[bhobba]

After discussion with some other mentors I think the thread has run its course, and it is time to close it.

Thanks
Bill