# Measurement problem in classical probability

• atyy
In summary: In experiments in classical statistical mechanics, we need an observer and a system. The observer divides the universe into a part to which he doesn't apply his theory and a part to which he does (the system), chooses what observable to measure, and recognizes when the measurement has occurred. Although every part of the universe can be the part to which he applies his theory, we do not know how to make sense of the whole universe being described by a statistical theory. QM is widely regarded as a fundamental theory due to its limitations on accessing more information through experiments, while classical statistical mechanics does not face this issue. There is also a formulation of classical statistical mechanics, called the Koopman-Von Neuman theory, which has
atyy
This question is inspired by ephen wilb's https://www.physicsforums.com/threads/quantum-theory-of-others.816818/#post-5130620.

In Bohmian Mechanics, everything is exactly as in classical probability theory. How, from the point of view of BM, does the measurement problem arise? Since the measurement problem can arise from a purely classical probability theory, can BM indicate an analogue of the measurement problem in other fields (eg. biology, economics) that use classical probability?

There is no measurement problem because the hidden variables determine the exact trajectory of the particle. There is no probability since everything is fully determined.

Shobah and ShayanJ
Khashishi said:
There is no measurement problem because the hidden variables determine the exact trajectory of the particle. There is no probability since everything is fully determined.

Yes, but if you ignore the trajectories, there is a measurement problem, so the measurement problem is emergent. The question is: under what circumstances does classical probability produce an emergent theory with a measurement problem? Here's an example of emergent theory: starting with a Markovian classical probability theory, if one integrates out some variables, in general one gets a non-Markovian theory.

For example, does classical statistical mechanics have a "measurement problem"?

For the less initiated, What exactly do you mean with measurement problem?

andresB said:
For the less initiated, What exactly do you mean with measurement problem?

In quantum mechanics we need a classical observer and a quantum system. The observer divides the universe into a classical part and a quantum part, chooses what observable to measure, and recognizes when the measurement has occurred. Although every part of the universe can be quantum, we do not know how to make sense of the whole universe being quantum.

Let me try to reformulate your last post for classical statistical mechanics:

In experiments in classical statistical mechanics, we need an observer and a system. The observer divides the universe into a part to which he doesn't apply his theory and a part to which he does (the system), chooses what observable to measure, and recognizes when the measurement has occurred. Although every part of the universe can be the part to which he applies his theory, we do not know how to make sense of the whole universe being described by a statistical theory.

atyy
kith said:
Let me try to reformulate your last post for classical statistical mechanics:

In experiments in classical statistical mechanics, we need an observer and a system. The observer divides the universe into a part to which he doesn't apply his theory and a part to which he does (the system), chooses what observable to measure, and recognizes when the measurement has occurred. Although every part of the universe can be the part to which he applies his theory, we do not know how to make sense of the whole universe being described by a statistical theory.

Yes. The only difference then is that no one is tempted to say that classical equilibrium statistical mechanics is a theory of everything. But with quantum mechanics, it is so tempting, since I can imagine being part of the wave function as long as someone else is the observer.

But in economics, I think I can include myself in the theory? Or maybe the lesson of 2008 was that one can't ...

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atyy said:
But with quantum mechanics, it is so tempting, since I can imagine being part of the wave function as long as someone else is the observer.
In the analogy, the description of the system is the phase space distribution. So is it really tempting to see QM as a fundamental theory because you can imagine including yourself in the system description of someone else?

I think the crucial difference between the two statistical theories is that in the classical case, we can get information about the system by performing measurements until we know all physical properties with certainty.

If we learn something new in pure state QM, we also forget something we knew before we performed the experiment, so we can't get additional knowledge. I would say QM is widely regarded as fundamental simply because we have good reasons to assume that there is no way to access more information in experiments.

atyy said:
But in economics, I think I can include myself in the theory? Or maybe the lesson of 2008 was that one can't ...
You can also include yourself in physical experiments like measuring how fast you are running. I think the point here is that you can't include the part which is responsible for the "watching".

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atyy
kith said:
I think the crucial difference between the two statistical theories is that in the classical case, we can get information about the system by performing measurements until we know all physical properties with certainty.

If we learn something new in pure state QM, we also forget something we knew before we performed the experiment, so we can't get additional knowledge. I would say QM is widely regarded as fundamental simply because we have good reasons to assume that there is no way to access more information in experiments.
.
I think is better to think that is not an issue with our information but a propertiy of the quantum system.

andresB said:
I think is better to think that is not an issue with our information but a properties of the quantum system.
I tend to think this way too, but discussions about interpretations need open minds. This thread was started from the perspective of the de Broglie-Bohm interpretation and there, QM is supplemented with hidden variables.

There is a formulation of classical statistical mechanics in terms of hermitian operators, wavefunctions, Born rule Schrodinger-like equation and etc. It is called the Koopman-Von Neuman theory.

http://arxiv.org/pdf/quant-ph/0301172v1.pdf

Sadly It is a vastly undeveloped and little known formalism, the issues with measurement, entanglement and decoherence have not been well addressed to my knowledge.

If you want too look for a measurement problem in classical statistical mechanics the K-vN theory is probably a good place to start.

ShayanJ and atyy
atyy said:
This question is inspired by ephen wilb's https://www.physicsforums.com/threads/quantum-theory-of-others.816818/#post-5130620.

In Bohmian Mechanics, everything is exactly as in classical probability theory. How, from the point of view of BM, does the measurement problem arise? Since the measurement problem can arise from a purely classical probability theory, can BM indicate an analogue of the measurement problem in other fields (eg. biology, economics) that use classical probability?
The measurement problem in BM is analogous to the measurement problem of dark matter in classical astrophysics. See
http://lanl.arxiv.org/abs/1309.0400 (Sec. 7.1)

bhobba, atyy and ShayanJ
Demystifier said:
The measurement problem in BM is analogous to the measurement problem of dark matter in classical astrophysics. See
http://lanl.arxiv.org/abs/1309.0400 (Sec. 7.1)

I found that paper lucid, instructive, and pretty compelling

Does the idea that massless particles (photons) do not have trajectories, connect to @A. Neumaier photon as global State in H space? And to the entangled boundary in AdS/CFT. I was connecting them as dots.

I just now realized it was yours.

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Jimster41 said:
Does the idea that massless particles (photons) do not have trajectories, connect to @A. Neumaier photon as global State in H space?
I don't know. Where can I find more about the Neumaier global State in H space?

atyy said:
Yes, but if you ignore the trajectories, there is a measurement problem, so the measurement problem is emergent.

No, it appears only if you insist that not trajectory exists. Not if you accept that it exists, but prefer to ignore it.

Jimster41 said:
He posted a link to this over in the "Didactic Sins" Insights thread http://arnold-neumaier.at/ms/lightslides.pdf
The two approaches (his and mine) seem to be somewhat similar in philosophy, but very different in details. We both effectively claim that "there are no photons, only detector clicks", but we use very different arguments for that claim.

julcab12 and Jimster41

## 1. What is the measurement problem in classical probability?

The measurement problem in classical probability refers to the challenge of accurately measuring and predicting the outcomes of events that are influenced by random or uncertain factors. It is a fundamental issue in probability theory and statistics, as it affects our ability to make reliable and precise predictions based on available data.

## 2. What causes the measurement problem?

The measurement problem arises in classical probability due to the inherent randomness and uncertainty present in certain events or systems. This can be caused by a variety of factors such as human error, environmental conditions, or complex interactions between variables.

## 3. How is the measurement problem addressed in classical probability?

In classical probability, the measurement problem is typically addressed through the use of statistical methods and models. These involve collecting and analyzing data, making assumptions about the underlying distribution of the data, and using mathematical techniques to make predictions or draw conclusions about the likelihood of certain outcomes.

## 4. Are there any limitations to addressing the measurement problem in classical probability?

Yes, there are limitations to addressing the measurement problem in classical probability. These include the potential for biased or incomplete data, the challenge of accurately modeling complex systems, and the inherent uncertainty and randomness present in certain events.

## 5. How does the measurement problem impact real-world applications of classical probability?

The measurement problem can have a significant impact on the application of classical probability in various fields such as finance, economics, and science. It can affect the accuracy and reliability of predictions and decision-making processes, potentially leading to incorrect conclusions or costly mistakes.

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