A Measurement problem in the Ensemble interpretation

[atyy]

Ballentine's ensemble interpretation is not even correct quantum mechanics. I wouldn't waste any time on it. The true ensemble interpretation is the Copenhagen interpretation, which of course has a measurement problem.

 

[Mentz114]

[]
To me, treating macroscopic systems as special has to be an ad hoc rule of thumb, and not a fundamental aspect of the theory.
[]
.

Interesting. But I don't think that 'classical' systems are being treated exceptionally. If we define the classical state as the large-number, no-ignorance limit of the quantum state, it becomes a sort of Platonic ideal because there is always some ignorance. This brings all dynamics under the same definition, differing only in the operational ignorance.

 

[stevendaryl]

Interesting. But I don't think that 'classical' systems are being treated exceptionally. If we define the classical state as the large-number, no-ignorance limit of the quantum state, it becomes a sort of Platonic ideal because there is always some ignorance. This brings all dynamics under the same definition, differing only in the operational ignorance.

If the rules of quantum probabilities are formulated in terms of "If you measure such and such, you will get such and such, with such and such probability", then you're making measurement into a different type of interaction, so you are treating macroscopic objects such as measuring devices differently than you treat microscopic objects. Many-worlds in contrast does not assume a macroscopic/microscopic distinction, but on the other hand, it's very hard to understand how probabilities play out in Many-worlds.

 

[Mentz114]

If the rules of quantum probabilities are formulated in terms of "If you measure such and such, you will get such and such, with such and such probability", then you're making measurement into a different type of interaction, so you are treating macroscopic objects such as measuring devices differently than you treat microscopic objects. Many-worlds in contrast does not assume a macroscopic/microscopic distinction, but on the other hand, it's very hard to understand how probabilities play out in Many-worlds.

The laws of physics are not written in terms of probabilities. Otherwise $F=ma$ has no meaning.

If you insist on that I cannot argue, obviously.

 

[stevendaryl]

The laws of physics are not written in terms of probabilities. Otherwise $F=ma$ has no meaning.

If you insist on that I cannot argue, obviously.

Huh?

 

[Mentz114]

Huh?

Well, obviously I can't answer that.

 

[stevendaryl]

Well, obviously I can't answer that.

I meant that I could not make any sense of your response:

The laws of physics are not written in terms of probabilities. Otherwise F=ma has no meaning.

If you insist on that I cannot argue, obviously.

I wasn't insisting on anything in particular, and I certainly wasn't saying that Newtonian physics is written in terms of probability. So I have no idea what prompted that response.

 

[Mentz114]

I meant that I could not make any sense of your response:
I wasn't insisting on anything in particular, and I certainly wasn't saying that Newtonian physics is written in terms of probability. So I have no idea what prompted that response.

I'm sorry maybe I skipped too quickly there.

What do you think is the relationship between 'the rules of quantum theory' and the laws of physics ? You may define the LoP in any rational way you like for this purpose.

 

[PeterDonis]

The laws of physics are not written in terms of probabilities.

How do you know?

Otherwise $F=ma$ has no meaning.

$F = ma$ is not a quantum law, it's a classical law, i.e., it's an approximation that is only valid under certain conditions. So it's irrelevant to this discussion.

 

[PeterDonis]

What do you think is the relationship between 'the rules of quantum theory' and the laws of physics ?

You should answer this since you were the one who introduced the term "the laws of physics". What did you mean by that term?

 

[Mentz114]

You should answer this since you were the one who introduced the term "the laws of physics". What did you mean by that term?

Fair enough. The governing principles of physical theories are conservation laws which are expressed mathematically as invariance of predictions under groups of transformations. Extremized paths in phase/configuration spaces are made from infinitessimal motions which are compounds of the generators of the groups.
I would call these things the LoP for the this discussion.

This is true of classical and quantum theories. The difference is in the Lie algebras of the group generators. In the quantum model the generators do not always commute ( or as Ballentine puts it ) there is indetereminacy ( a kind of ignorance). Actual classical objects (measuring instruments) also have some indeterminacy but are closer to the limiting case ( see my first post) than they are to the microscopic case.

This is why I do not believe that we are treating the measurement problem in a controversial way by asserting that the process is merely one in which amplification and filtering reduces the indeterminacy to make an outcome irreversible.

 

[stevendaryl]

Fair enough. The governing principles of physical theories are conservation laws which are expressed mathematically as invariance of predictions under groups of transformations. Extremized paths in phase/configuration spaces are made from infinitessimal motions which are compounds of the generators of the groups.
I would call these things the LoP for the this discussion.

This is true of classical and quantum theories. The difference is in the Lie algebras of the group generators. In the quantum model the generators do not always commute ( or as Ballentine puts it ) there is indetereminacy ( a kind of ignorance). Actual classical objects (measuring instruments) also have some indeterminacy but are closer to the limiting case ( see my first post) than they are to the microscopic case.

This is why I do not believe that we are treating the measurement problem in a controversial way by asserting that the process is merely one in which amplification and filtering reduces the indeterminacy to make an outcome irreversible.

Your notion of what physics is about is so completely different from mine that I can't really relate them. Conservation laws, symmetry principles, transformations, etc., are tools to be used in physics, but they aren't physics.

 

[Mentz114]

Your notion of what physics is about is so completely different from mine that I can't really relate them. .

I reciprocate those feelings, so I'll let it be. It's not important.

(I'm sorry I accidentally hit the 'Like' button )

 

[stevendaryl]

Your notion of what physics is about is so completely different from mine that I can't really relate them. Conservation laws, symmetry principles, transformations, etc., are tools to be used in physics, but they aren't physics.

To me, physics is: I observe something in the world around me. I come up with a model to describe what I observe. I test that model by seeing what other consequences it has, and seeing if those are born out by observation. If not, I get a new model, or modify the existing one. Repeat.

None of those things--symmetry, conservation, transformations, etc.---is fundamental to the project of physics, which is about describing the world that we live in in a way that is precise enough (mathematically) to make predictions capable of falsification.

 

[Mentz114]

To me, physics is: I observe something in the world around me. I come up with a model to describe what I observe. I test that model by seeing what other consequences it has, and seeing if those are born out by observation. If not, I get a new model, or modify the existing one. Repeat.

None of those things--symmetry, conservation, transformations, etc.---is fundamental to the project of physics, which is about describing the world that we live in in a way that is precise enough (mathematically) to make predictions capable of falsification.

Is that not the same thing as trying to find some laws of physics. If you find some theory that agrees with experiment and applies to nearly all cases - is that a law ?

We come back to your objection concerning the measurement problem. What law or principle that you hold is being dishonoured if we treat an apparatus as macroscopic ? None of my principles can be violated by any physical process, or any choice made by any agency at any time or place. Those are good principles.

 

[stevendaryl]

We come back to your objection concerning the measurement problem. What law or principle that you hold is being dishonoured if we treat an apparatus as macroscopic ? None of my principles can be violated by any physical process, or any choice made by any agency at any time or place. Those are good principles.

I don't understand what you're talking about. The point I was making is that if a measurement apparatus is made up of electrons, protons, neutrons interacting through electromagnetic interactions, then it would seem to me that whatever rules for how those particles behave would logically imply everything there is know about how the measurement apparatus behaves. Conversely, if we have some rules about macroscopic measurement devices that does not follow from properties of electrons, protons, etc., then it seems to me that we have missed something in our modeling of the behavior of the latter.

I suppose you can take a completely phenomenological point of view, which is that the only things that are real are macroscopic objects, and electrons, protons, etc., are just mathematical fictions useful for calculating the behavior of the actual physical objects.

 

[Mentz114]

I don't understand what you're talking about. The point I was making is that if a measurement apparatus is made up of electrons, protons, neutrons interacting through electromagnetic interactions, then it would seem to me that whatever rules for how those particles behave would logically imply everything there is know about how the measurement apparatus behaves. Conversely, if we have some rules about macroscopic measurement devices that does not follow from properties of electrons, protons, etc., then it seems to me that we have missed something in our modeling of the behavior of the latter.

I suppose you can take a completely phenomenological point of view, which is that the only things that are real are macroscopic objects, and electrons, protons, etc., are just mathematical fictions useful for calculating the behavior of the actual physical objects.

With the slight rephrasing you've applied I agree in principle except I don't think the disconnect between the model we use for the macroscopic part and the model of the microscopic bit exists.

 

[vanhees71]

Your notion of what physics is about is so completely different from mine that I can't really relate them. Conservation laws, symmetry principles, transformations, etc., are tools to be used in physics, but they aren't physics.

This is a very strange view. For me to figure out the symmetry principles (or any other general description of what we consider "fundamental laws of nature") is the very goal of what's called physics, which consists of both observations and theoretical mathematical analysis.

Further, according to our current understanding, the "classicality" of macroscopic systems (including measurement devices, which are nothing special but just also macroscopic systems) is well compatible with quantum theory and nothing else than the "Law of Large Numbers", i.e., if you have $N$ degrees microscopic degrees of freedom figuring additively into a macroscopic variable $X$ (like, e.g., the total energy of a gas which consists of $N/3$ monatomic particles) one has $\Delta X/|X| \sim 1/\sqrt{N}$. If $N$ is large the fluctuations (both quantum an thermal) are small.

Measuring a microscopic system is due to the interaction with a macroscopic system which takes a well-defined macroscopic value for its pointer position, and that's why we measure one and only one value for the microscopic system, no matter whether the value was determined or not. If it was not determined, all we can know having maximal possible information (i.e., if the micro system is prepared in a pure state) are the probabilities for the occurance of each possible value of the measured observable, given by Born's rule. So there is no measurement problem as soon as you accept the principle probabilistic behavior of Nature. It's at the same time consistent with the observed indeterministic behavior of microscopic observables and the apparently deterministic one of macroscopic observables. It's just elementary statistics!

 

[stevendaryl]

This is a very strange view. For me to figure out the symmetry principles (or any other general description of what we consider "fundamental laws of nature") is the very goal of what's called physics, which consists of both observations and theoretical mathematical analysis.

Symmetry principles aren't the goal. The goal is modeling the world. If the world obeys certain symmetry principles, then of course, we should find out what they are, but finding out symmetry principles isn't the goal.

Measuring a microscopic system is due to the interaction with a macroscopic system which takes a well-defined macroscopic value for its pointer position,

That is the heart of the measurement problem. Why do macroscopic systems have well-defined macroscopic values?

 

[stevendaryl]

With the slight rephrasing you've applied I agree in principle except I don't think the disconnect between the model we use for the macroscopic part and the model of the microscopic bit exists.

That would be great, if it were true. But it seems like wishful thinking to me. If the physics doesn't distinguish between macroscopic and microscopic, then it should be possible to formulate the theory completely in microscopic terms, and then the macroscopic facts would be derivable. So if your theory of quantum mechanics starts with "When you measure blah, blah, blah..." then you've already distinguished macroscopic from microscopic or measurements from other interactions. It should be possible, if measuring devices were treated no differently than microscopic systems, to restate the theory without mentioning measurements or macroscopic systems.

 

[stevendaryl]

Further, according to our current understanding, the "classicality" of macroscopic systems (including measurement devices, which are nothing special but just also macroscopic systems) is well compatible with quantum theory and nothing else than the "Law of Large Numbers", i.e., if you have $N$ degrees microscopic degrees of freedom figuring additively into a macroscopic variable $X$ (like, e.g., the total energy of a gas which consists of $N/3$ monatomic particles) one has $\Delta X/|X| \sim 1/\sqrt{N}$. If $N$ is large the fluctuations (both quantum an thermal) are small.

I don't think that reasoning is correct. What you're suggesting is that the law of large numbers by itself is enough to explain why there are never macroscopic superpositions? The law of large numbers is only valid if you have a large number of independent systems with the same distribution of values of an observable, then the averages over all the systems will have a smaller variance than the values on the individual systems. But that's not what's going on when we perform a measurement and get a definite value.

 

[Mentz114]

I don't think that reasoning is correct. What you're suggesting is that the law of large numbers by itself is enough to explain why there are never macroscopic superpositions? The law of large numbers is only valid if you have a large number of independent systems with the same distribution of values of an observable, then the averages over all the systems will have a smaller variance than the values on the individual systems. But that's not what's going on when we perform a measurement and get a definite value.

[my emphasis]
Do you know what is happening when a measurement is made ? Your statement makes at least one implicit assumption that can be challenged.

 

[vanhees71]

I don't think that reasoning is correct. What you're suggesting is that the law of large numbers by itself is enough to explain why there are never macroscopic superpositions? The law of large numbers is only valid if you have a large number of independent systems with the same distribution of values of an observable, then the averages over all the systems will have a smaller variance than the values on the individual systems. But that's not what's going on when we perform a measurement and get a definite value.

The averaging is over a large number (of order $10^24$) of microscopic observables making up a macroscopic one.

 

[bhobba]

None of those things--symmetry, conservation, transformations, etc.---is fundamental to the project of physics, which is about describing the world that we live in in a way that is precise enough (mathematically) to make predictions capable of falsification.

It's exactly what Feynman said - nothing more - nothing less:


However Noether provided an invaluable tool in making those 'guesses'.

What came first - the guess or its experimental proof? The logic of those guesses is sometimes so compelling you are shocked if it's wrong. Even Feynman realized it. He came up with some beautiful theory (ie guess) that experiment was against at the time. He decided to wait rather than abandon it. By his dictum he should have scrapped it - but it was just so beautiful. He was right - later experiments proved it.

It really is a strange thing. As one person expressed it, and even wrote a book with the title, there is fire in the equations. Trying to get to the bottom of it has led to some rather interesting views such as those of Penrose.

Me - I am with Gell-Mann:


Thanks
Bill

 

[stevendaryl]

It's exactly what Feynman said - nothing more - nothing less:


However Noether provided an invaluable tool in making those 'guesses'.

What came first - the guess or its experimental proof? The logic of those guesses is sometimes so compelling you are shocked if it's wrong. Even Feynman realized it. He came up with some beautiful theory (ie guess) that experiment was against at the time. He decided to wait rather than abandon it. By his dictum he should have scrapped it - but it was just so beautiful. He was right - later experiments proved it.

It really is a strange thing. As one person expressed it, and even wrote a book with the title, there is fire in the equations. Trying to get to the bottom of it has led to some rather interesting views such as those of Penrose.

Me - I am with Gell-Mann:


Thanks
Bill

Yeah, there have been lots of examples where looking for a compelling theory galloped way ahead of experiment, and the experiments confirmed the beautiful theory was right. Some examples:

• I think it's true that Maxwell introduced the "displacement current" because it fixed flaws in the mathematical appearance of his equations, rather than because there was any evidence for it.
• General relativity was really driven by Einstein's desire for a theory that elegantly incorporated gravity and Special Relativity, not because of evidence. The evidence came soon afterwards.
• Antiparticles and electron spin were predicted by Dirac's equation, which was motivated by an attempt to reconcile quantum mechanics with relativity (spin had already been discovered, but it comes naturally out of the Dirac equation).

Of course, in recent years, there have been quite a few counter-examples, where the pursuit of an intellectually-pleasing theory turned out not to have any empirical support. I'm thinking the various GUT theories, supersymmetry, string theory.

 

[Mentz114]

Yeah, there have been lots of examples where looking for a compelling theory galloped way ahead of experiment, and the experiments confirmed the beautiful theory was right. Some examples:

• I think it's true that Maxwell introduced the "displacement current" because it fixed flaws in the mathematical appearance of his equations, rather than because there was any evidence for it.
• General relativity was really driven by Einstein's desire for a theory that elegantly incorporated gravity and Special Relativity, not because of evidence. The evidence came soon afterwards.
• Antiparticles and electron spin were predicted by Dirac's equation, which was motivated by an attempt to reconcile quantum mechanics with relativity (spin had already been discovered, but it comes naturally out of the Dirac equation).

Of course, in recent years, there have been quite a few counter-examples, where the pursuit of an intellectually-pleasing theory turned out not to have any empirical support. I'm thinking the various GUT theories, supersymmetry, string theory.

None of this is relevant. You guys have galloped off on some by-way.

It is preposterous to say that symmetries and conserved charges and currents are irrelevant in Physics when it is on these principles that the SM is made.
No physical theory which does not conform will be any use.

I give up.

 

[stevendaryl]

None of this is relevant. You guys have galloped off on some by-way.

Well, your comments about symmetry were pretty far off-topic to start with, so it's a little strange for you to complain about relevance.

It is preposterous to say that symmetries and conserved charges and currents are irrelevant in Physics

I didn't say they were irrelevant. I said:

None of those things--symmetry, conservation, transformations, etc.---is fundamental to the project of physics, which is about describing the world that we live in in a way that is precise enough (mathematically) to make predictions capable of falsification.

 

[stevendaryl]

The averaging is over a large number (of order $10^24$) of microscopic observables making up a macroscopic one.

But the law of large numbers is not just about any situation involving large numbers. It's specifically (from Wikipedia):

In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times.

If we use a macroscopic device to measure, say, the spin of an electron, the 10^{24} is not the number of times we perform the experiment. So the law of large numbers is not obviously relevant.

 

[Mentz114]

Well, your comments about symmetry were pretty far off-topic to start with, so it's a little strange for you to complain about relevance.
:

I wanted to know why you keep asking 'why can macroscopic objects not form superpositions ?'. You say that the 'rules of quantum mecanics demand it'.

Which rule says that ? How was that rule derived ?

 

[stevendaryl]

I wanted to know why you keep asking 'why can macroscopic objects not form superpositions ?'. You say that the 'rules of quantum mecanics demand it'.

Which rule says that ? How was that rule derived ?

I think it's good form not use to quote symbols unless you're quoting. It's not fair to ask me to defend a statement that you just made up (such as "symmetries and conserved charges and currents are irrelevant in Physics").

Anyway, according to quantum mechanics, states obey the principle of superposition: If |A\rangle is a state, and |B\rangle is a state, then \alpha |A\rangle + \beta |B \rangle is a state. Are you asking where that rule is stated? It's part of the definition of a Hilbert space.