Measurement problem in the Ensemble interpretation

[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.

 

[Mentz114]

It's exactly what Feynman said - nothing more - nothing less:
[..]
Me - I am with Gell-Mann:


Thanks
Bill

If we're down to quoting authority - Steven Weinberg said

Our job as physicists is to see things simply, to understand a great many
complicated phenomena in a unified way, in terms of a few simple principles.

 

[Mentz114]

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.

Apologies, I hope I didn't distort the meaning.

Ok, thanks. A purely mathematical statement then, with no support from any physical principle.

[aside]
To anyone who finds these things interesting I commend this learned paper. I don't claim to have read it all nor agree with everything the author asserts.

http://philsci-archive.pitt.edu/878/1/PSA2002.pdf

Laws, Symmetry, and Symmetry Breaking; Invariance, Conservation Principles, and Objectivity

John Earman
Dept. of History and Philosophy of Science
University of Pittsburgh

 

[bhobba]

If we're down to quoting authority - Steven Weinberg said

But finding those - well let's just say even its greatest exponent, Einstein, hell even slightly lesser lights like Von-Neumann, guys likely even better than Weinberg (and that's saying something) is a slow slow process with a lot of false twists and turns. As Feynman said a trick, like say positivism, used early on by Einstein, works just once - after that everyone knows it and tries it. If it works, which it rarely does again, but if it does progress is made and everything falls away. If it doesn't, and this is usually the case, a different approach is required. Want a Nobel? Figure out the approach that works. Good luck.

But as to your question - the answer is known - symmetry. But to understand it you need quite a bit of study or simply accept what you have been told.

Thanks
Bill

 

[vanhees71]

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

Ok, then why do you think classical physics works so well for macroscopic matter? The ensembles you cite are Gibbs ensembles, but the law of large number says that we measure almost with certainty a definite value for a macroscopic variable given the very small relative standard deviation of this variable of order $\mathcal{O}1/\sqrt{N}$. So you can within this relatively negligible uncertainty predict the value for this macroscopic variable. That's how, in my understanding, the apparent deterministic nature of classical physics is principally explained within the statistical interpretation.

If we measure the spin of an electron (within a neutral atom ;-)) in an SG apparatus we measure its position with a photo plate, which is the macroscopic object. What we call "position", is a very coarse grained macroscopic region consisting of very many atoms/molecules. Within that resolution we can say the "electron hit the photoplate at a definite place". That the position is related to the spin observable is due to the entanglement of the spin component determined by the directdion of the magnetic field with position.

 

[stevendaryl]

Ok, then why do you think classical physics works so well for macroscopic matter?

I think the answer is complicated. I think it has to do with the fact that decoherence will spoil interference effects between macroscopic states with different values of macroscopic observables. Without interference effects, we are free to think of quantum probabilities as classical probabilities, reflecting uncertainty about which of several alternatives is actually the case. So that's why Copenhagen (or the minimal interpretation) seems to work so well, because it is consistent to think of macroscopic probabilities as reflecting ignorance in a way that it is not consistent to interpret microscopic amplitudes.

So the whole structure works, to the extent that we can make a clean distinction between macroscopic and microscopic variables. But it's somewhat schizophrenic, since we are applying a different interpretation to probabilities depending on how large the system is.

 

[vanhees71]

Hm, but you can use quantum statistics to calculate the properties of, say, an ideal gas to get the classical results in the limit, where you can approximate the Bose-Eisntein or Fermi-Dirac statistics with the modified classical Maxwell-Boltzmann statistics (with modified I mean the notorious factor $1/N!$ borrowed from the indistinguishability of particles from QT). Even if you keep the full quantum statistics, the macroscopic quantities which are indeed very coarse grained (total energy $U$, temperature, chemical potential(s),...) you get very small fluctuations due to the fact that $N$ is large. Of course you get quantum effects, if the gas becomes degenerate (low temperatures, high densities), among them early achievements of "old quantum mechanics" like the specific heat at low temperatures, the microscopic understanding of the 3rd Law and so on.

Of course, decoherence is also an important point. Here you can even get semiclassical behavior of microscopic objects when interacting with macroscopic objects, as was already realized in Mott's famous article on why $\alpha$ prticles in a clould chamber seem to run on straight-line trajectories.

 

[zonde]

It should be possible, if measuring devices were treated no differently than microscopic systems, to restate the theory without mentioning measurements or macroscopic systems.

Why do you think it should be possible?
Measuring devices are just bigger more complicated "particles". If you take away Born rule, QM can not say anything about microscopic particles. Why it should say anything about measuring devices?

 

[stevendaryl]

Why do you think it should be possible?
Measuring devices are just bigger more complicated "particles".

That's my point. If measuring devices are just complicated systems, and measurements are just complicated interactions, then the Born rule shouldn't treat measurements differently than any other interactions. But it does: The Born rule says "If you measure a quantity, you get an eigenvalue of the corresponding operator, with such-and-such probability."

 

[zonde]

That's my point. If measuring devices are just complicated systems, and measurements are just complicated interactions, then the Born rule shouldn't treat measurements differently than any other interactions. But it does: The Born rule says "If you measure a quantity, you get an eigenvalue of the corresponding operator, with such-and-such probability."

You apply Born rule to measurements only. You do not apply Born rule to other interactions. At least this is my understanding.

And my point is that Born rule treats microscopic reality differently too. Before you apply Born rule you don't describe particles. You describe modes not particles.

 

[AlexCaledin]

As long as ensemble interpretation refuses to talk about single measurements, it cannot say anything about the measurement problem.

- but what if the EI is applied to the whole spacetime-universe? Then, there is the Ensemble of "prepared" universes, each one having its definite observable history (Bohmian trajectory) - quite definite past and future - but "we" are uncertain as to what universe we are in - and we are in the process of getting knowledge about that - and then every measurement is simply a little increment of our knowledge.