I The thermal interpretation of quantum physics

  • #691
A. Neumaier said:
The official description of the thermal interpretation of quantum physics can be found in my just finished papers
A. Neumaier said:
When performing on a quantum system a measurement of an operator A with a physical meaning, one gets an approximation for its value. The thermal interpretation treats this value as an approximation not of an eigenvalue of A but of the q-expectation of A, the formal expectation value defined as the trace of the product of A with a density operator describing the state of the system. This deviation from the tradition has important theoretical implications.

To understand.

The q-expectation of A is the expectation value of the eigenvalues of A, based on an infinite number of measurements, right? Isn't it counterfactual?

1564738423688.png


Mean value of an observable in a given state :
1564738765680.png

...

/Patrick
 
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  • #692
microsansfil said:
The q-expectation of A is the expectation value of the eigenvalues of A, based on an infinite number of measurements, right?
No. The q-expectation of ##A## is the number ##\langle A\rangle:=Tr~\rho A##. Neither eigenvalues nor measurements are involved in this definition.

To get an interpretation in terms of eigenvalues one has to work hard - namely up to a derivation of the spectral theorem, and then one must derive a representation this short and concise definition in terms of an integral over the spectrum. Nothing like that is needed in the thermal interpretation.

To get an interpretation in terms of measurements one needs even more, as the notion of measurement is not even mathematical. Thus one needs to invoke Born's rule. But this rule is not assumed in the thermal interpretation; it is derived there as an approximate rule, valid under the appropriate conditions.
 
  • #694
microsansfil said:
Does thermal interpretation lead to a questioning of the postulates of quantum mechanics? such as
[Eigenvalue link and Born's rule]
and replace them with more "primitive" postulates?
It replaces the two postulates mentioned by the weaker postulate that the measurement results deviate from the q-expectation by at most a small multiple of the uncertainty.

This weaker postulate is universally valid, while the traditional eigenvalue link and Born's rule are valid only for small systems with rational eigenvalues.
 
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  • #695
This is simply not true! Standard quantum theory works very well for large systems, and eigenvalues are of course usually not rational (in which units anyway, an angular momentum is rational in units of ##\hbar## but oviously not in units of ##h=2 \pi \hbar##).

What's measured doesn't depend on the state the system is prepared in but only on the construction of the measurement device. You have to distinguish between the statistics of observables in a given quantum state and the statistics describing the accuracy of the measurement device. Of course to understand your measurement device you also need in addition the systematical errors.

So, whether you measure the "q-expectation value" in a given state or not depends on the experimental setup.

If your measurement device is constructed such that it is accurate enough, you'll always find eigenvalues of the operators describing observables. Of course then the measured value must be in the discrete spectrum of the observable operator. If you measure the spin component of a particle accurate enough, you'll alsways find one of the discrete values ##\sigma \hbar## with ##\sigma \in \{-s,\ldots,s \}##, no matter in which state the particle is prepared in. This may be the expectation value in this state or not, depending on the specific state the system is prepared in.

When measuring a continuous observable, of course you always have a finite accuracy. This accuracy again doesn't depend on the state the system is prepared in but on the construction of the measurement device.
 
  • #696
vanhees71 said:
eigenvalues are of course usually not rational (in which units anyway, an angular momentum is rational in units of ##\hbar## but obviously not in units of ##h=2 \pi \hbar##).
Of course - though recently, ##h## (not ##\hbar##) was defined to be rational!

But measurements usually produce not too high precision rational numbers. Thus the ''third postulate'' in post #693 is usually at least slightly violated in measurements of observables corresponding to operators with irrational eigenvalues.

The thermal interpretation postulates the (by the theorem in Section 2.6 of Part III) strictly weaker property mentioned in post #694, hence is more cautious than the traditional postulates that the measured value is an eigenvalue, obtained with the probability given by Born's rule. Being strictly weaker, it remains valid in all cases where the traditional postulates apply.

But the new postulate does not produce the nonsense claim that the in the early days of quantum mechanics quite inaccurate spin measurements provided as result one of the eigenvalues ##\pm\hbar/2## of the angular momentum component ##S_z##. They provided only (compared to today) crude approximations to these eigenvalues.
 
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  • #697
Sure, it's always true that measurements are only as accurate as the measurement device are constructed to measure. Of course, in a physical theory, the corresponding statistical and systematical error analysis is not worked in. That wouldn't make much sense since that would mean you'd have to formulate a separate theory for any measurement device. This is precisely something you do not want in formulating a theory that is supposed to be generally valid. Of course, for any experiment to compare with the general theory you have to do a careful analysis of the statistical and systematic errors in order to be able to decide (objectively!) whether the result of your measurements/experiments/observations is in accordance with a generally valid theory or not.

No mater, however you interpret ##\langle A \rangle = \mathrm{Tr}(\hat{A} \hat{\rho})## within the formalism of QT, it doesn't contain the specifics of a measurement device.
 
  • #698
Hi,

I searched in vain for a peer-reviewed publication of thermal interpretation of quantum physics. There was no peer review of thermal interpretation?

/Patrick
 
  • #699
microsansfil said:
I searched in vain for a peer-reviewed publication of thermal interpretation of quantum physics. There was no peer review of thermal interpretation?
The material is too new. Peer reviewed publication takes time.
 
  • #700
microsansfil said:
Hi,

I searched in vain for a peer-reviewed publication of thermal interpretation of quantum physics. There was no peer review of thermal interpretation?

/Patrick
I'm very curious, whether this idea will ever pass peer review... Nowdays that's not too unlikely though...
 
  • #702
  • #703
mattt said:
Is there a free draft? Thanks.
The book is mainly based on the five free preprints mentioned in the edited post #1 (together with a preprint on coherent spaces). These cover the general content of the book, and in particular the essence of the thermal interpretation, but in a less final form. In particular, some arguments were improved or polished based on the feedback from the discussion here on PF.
 
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  • #704
A. Neumaier said:
authoritative exposition of the thermal interpretation.
What do you mean by "authoritative"? Isn't that a qualification that only readers can give?
 
  • #705
I would rather say, "authorative" means that's the version the author declares to be complete, expressing the subject according to his intention (at least at the time of publication).
 
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  • #706
Demystifier said:
What do you mean by "authoritative"? Isn't that a qualification that only readers can give?
It means that this is the officially published definition of the thermal interpretation. Only the author of an interpretation can say whether it is authoritative. This is in contrast to the Copenhagen interpretation and the many worlds interpretation, whose content is different dependent on whom you ask, since there is no unique defining document.
 
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  • #707
vanhees71 said:
I would rather say, "authorative" means that's the version the author declares to be complete, expressing the subject according to his intention (at least at the time of publication).
According to google, that word doesn't exist.
 
  • #708
A. Neumaier said:
It means that this is the officially published definition of the thermal interpretation. Only the author of an interpretation can say whether it is authoritative. This is in contrast to the Copenhagen interpretation and the many worlds interpretation, whose content is different dependent on whom you ask, since there is no unique defining document.
Searching on google, I couldn't find such a meaning of the word "authoritative". But I found this: https://piedmont.libanswers.com/faq/135714
 
  • #709
Demystifier said:
Searching on google, I couldn't find such a meaning of the word "authoritative".
Well, google is not a dictionary. You should consult for example

https://en.wiktionary.org/wiki/authoritative, where the intended meaning is the first one listed:

authoritative (comparative more authoritative, superlative most authoritative)
  1. Arising or originating from a figure of authority The authoritative rules in this school come not from the headmaster but from the aged matron.
Clearly the creator of a concept is a figure of authority for this concept. Or look at

https://www.ldoceonline.com/dictionary/authoritative, where one can read an example sentence with a similar usage as mine:

• The results provide the most authoritative and conclusive evidence to date of some enduring inequities in participation in such facilities.
 
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  • #711
Demystifier said:
According to https://en.wiktionary.org/wiki/authority#English authority refers to a book or quotation that settles an argument. Now what does "settles" mean? If it means settles as far as the author is concerned, then it's OK.
The word authority has not a single, narrow meaning, so taking just one of its uses as ''the'' meaning is ill-advised. According to https://en.wiktionary.org/wiki/authority#English, authority refers to

1. (uncountable) The power to enforce rules or give orders.

Surely, the creator of a concept has the power to enforce the rules of usage of the concept; in a scientific context, this is called a definition.

In the present case I used the word to express that the book defines (and in this sense settles) the meaning of the term ''thermal interpretation''.

At least in more detail than the meaning of the terms ''Copenhagen interpretation'' or ''Many Worlds interpretation'' is settled. I didn't want that the thermal interpretation suffers the same fate as these ill-circumscribed interpretations.
 
  • #712
A. Neumaier said:
In the present case I used the word to express that the book defines (and in this sense settles) the meaning of the term ''thermal interpretation''.

At least in more detail than the meaning of the terms ''Copenhagen interpretation'' or ''Many Worlds interpretation'' is settled. I didn't want that the thermal interpretation suffers the same fate as these ill-circumscribed interpretations.
Well, if the thermal interpretation will become popular in the future (which is certainly something that you want) then it will be hard to avoid some modifications and distortions by other writers.
 
  • #713
Demystifier said:
According to https://en.wiktionary.org/wiki/authority#English authority refers to a book or quotation that settles an argument. Now what does "settles" mean? If it means settles as far as the author is concerned, then it's OK.
It settles an issue for the author first. In extreme cases it settles the issue only for the author ;-).
 
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  • #714
Demystifier said:
Well, if the thermal interpretation will become popular in the future (which is certainly something that you want) then it will be hard to avoid some modifications and distortions by other writers.
Yes, but anyone can go back to the authoritative source. There things are specified precisely. Anything in science can be misunderstood, but if the definitions are useful and clear enough they will survive this.
 
  • #717
ftr said:
There is no probability in TI?
There is probability in TI, just no fundamental one.
 
  • #718
A. Neumaier said:
There is probability in TI, just no fundamental one.
Yes, that is what I meant "no fundamental". I believe (you can correct me) that the quantum computers are based on the notion of fundamental property of QM.
 
  • #719
ftr said:
I believe (you can correct me) that the quantum computers are based on the notion of fundamental property of QM.
No. All past work on quantum computers assumes the standard machinery of quantum mechanics and is independent of interpretation issues.
 
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  • #720
A. Neumaier said:
No. All past work on quantum computers assumes the standard machinery of quantum mechanics and is independent of interpretation issues.
Are you saying that TI is just plain old interpretation and has no significant practical value of any sort other than "explaining".
 

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