What Do Most Physicists Call the Quantum-To-Classical Cut?

[bhobba]

Hi All

This is just a dumb question. I have usually called the the Quantum/Classical cut the Von-Neumann cut because Von-Neumann's classic text was the first serious QM book I read - nearly 40 years ago now - seems like yesterday. Recently I noticed in some of the papers I have been reading they call it the Heisenberg cut. What would be the term physicists generally use? Or does it even matter?

Thanks
Bill

 

[Demystifier]

Perhaps Bohr cut, because he took it more seriously than the others?

Anyway, either there must a spooky cut or a spooky cat (the Schrödinger's one). At Halloween, a physicist may scare his neighbors by knocking at the door and saying: Cut or cat!

 

[vanhees71]

I'd just abandon it from any discussion in physics texts, but for the use at Halloween it's great ;-)).

 

[A. Neumaier]

Recently I noticed in some of the papers I have been reading they call it the Heisenberg cut. What would be the term physicists generally use?

It is always called the Heisenberg cut, or just cut. Heisenberg introduced it in his famous 1927 paper with the uncertainty relation 5 years before von Neumann's book. (Edit: Actually, Heisenberg introduced it at the 1927 Como conference; see post #22 below.)

 

[PAllen]

It is always called the Heisenberg cut, or just cut. Heisenberg introduced it in his famous 1927 paper with the uncertainty relation 5 years before von Neumann's book.

I have also only seen Heisenberg cut, if a proper name is attached to it. As in "you place the Heisenberg cut where you want it".

 

[EPR]

I have also only seen Heisenberg cut, if a proper name is attached to it. As in "you place the Heisenberg cut where you want it".

Sure. The HUP is about knowledge, not about physical values. The context of the cut is knowledge.

 

[bhobba]

I'd just abandon it from any discussion in physics texts, but for the use at Halloween it's great ;-)).

As you know I am not a fan of it either but that is another thread. This is just about terminology. As you know I am reading those philosophy/history of science papers from academa.edu. The philosophy part I am not that keen on, but the history part I am finding interesting. It's like Feynman said - students get a physicists view of the history handed down to them from their professors. What an actual historian of physics thinks is another matter. Just going through the history of MW right now - very interesting. Wheeler was Everett's supervisor and was a good friend of Bohr. Wheeler was quite positive towards the idea, but Bohr not quite so much. Gell-Mann was one of the founders of the related decoherent histories and wondered if Feynman knew of Everett's work while he was developing it. It's not known for sure, Feynman and Wheeler were fairly close, being his ex supervisor, so I think he probably did.

Thanks
Bill

 

[Lord Jestocost]

According to the following description by Landsman, I personally would call the "cut" the "Heisenberg/von Neumann cut".

N.P. Landsman in “Between classical and quantum”:

“………Namely, from the point of view of von Neumann’s measurement theory (see Subsection 2.5) the Heisenberg cut is just a two-step example of a von Neumann chain, with the special feature that after the quantum-mechanical interaction has taken place, the second link (i.e. the apparatus) is described classically. The latter feature not only supports Bohr’s philosophical agenda, but, more importantly, also suffices to guarantee the applicability of the ignorance interpretation of the mixed state that arises after completion of the measurement.⁷² All of von Neumann’s analysis of the arbitrariness of the location of the cut applies here, for one may always extend the definition of the quantum-mechanical object by coupling the original choice to any other purely quantum-mechanical system one likes, and analogously for the classical part. Thus the two-step nature of the Heisenberg cut includes the possibility that the first link or object is in fact a lengthy chain in itself (as long as it is quantum-mechanical), and similarly for the second link (as long as it is classical).⁷³”

 

[vanhees71]

As you know I am not a fan of it either but that is another thread. This is just about terminology. As you know I am reading those philosophy/history of science papers from academa.edu. The philosophy part I am not that keen on, but the history part I am finding interesting. It's like Feynman said - students get a physicists view of the history handed down to them from their professors. What an actual historian of physics thinks is another matter. Just going through the history of MW right now - very interesting. Wheeler was Everett's supervisor and was a good friend of Bohr. Wheeler was quite positive towards the idea, but Bohr not quite so much. Gell-Mann was one of the founders of the related decoherent histories and wondered if Feynman knew of Everett's work while he was developing it. It's not known for sure, Feynman and Wheeler were fairly close, being his ex supervisor, so I think he probably did.

Thanks
Bill

If you are at the history, I'd been interested to remember, where I read that Heisenberg got the physics of his uncertainty relation wrong first, and Bohr had to correct him. If you stumble across them, could you post the references of the corresponding papers?

The story about Everett's dissertation is also a pretty sad one, and Wheeler didn't play a very good role in this issue.

 

[A. Neumaier]

If you are at the history, I'd been interested to remember, where I read that Heisenberg got the physics of his uncertainty relation wrong first, and Bohr had to correct him.

It is mentioned at the end of Heisenberg's 1927 paper, I believe.

 

[A. Neumaier]

According to the following description by Landsman, I personally would call the "cut" the "Heisenberg/von Neumann cut".

N.P. Landsman in “Between classical and quantum”:

“………Namely, from the point of view of von Neumann’s measurement theory (see Subsection 2.5) the Heisenberg cut is just a two-step example of a von Neumann chain, with the special feature that after the quantum-mechanical interaction has taken place, the second link (i.e. the apparatus) is described classically. The latter feature not only supports Bohr’s philosophical agenda, but, more importantly, also suffices to guarantee the applicability of the ignorance interpretation of the mixed state that arises after completion of the measurement.⁷² All of von Neumann’s analysis of the arbitrariness of the location of the cut applies here, for one may always extend the definition of the quantum-mechanical object by coupling the original choice to any other purely quantum-mechanical system one likes, and analogously for the classical part. Thus the two-step nature of the Heisenberg cut includes the possibility that the first link or object is in fact a lengthy chain in itself (as long as it is quantum-mechanical), and similarly for the second link (as long as it is classical).⁷³”

This justifies the name von Neumann chain but confirms that the cut itself is due to Heisenberg alone.

 

[vanhees71]

It is mentioned at the end of Heisenberg's 1927 paper, I believe.

This one?

https://link.springer.com/article/10.1007/BF01397280

 

[A. Neumaier]

This one?

https://link.springer.com/article/10.1007/BF01397280

This is what I had in mind. Cannot check now whether it indeed contains the remark - should be at the end.

 

[EPR]

Everyone should be able to perform this experiment at home and observe the cut where quantum rules become dominant.

 

[bhobba]

If you are at the history, I'd been interested to remember, where I read that Heisenberg got the physcs of his uncertainty relation wrong first, and Bohr had to correct him. If you stumble across them, could you post the references of the corresponding papers?

I heard of it first on good old Wikipedia:
https://en.wikipedia.org/wiki/Heisenberg's_microscope
You have confirmed it on a number of occasions so I take it as at least part of what Feynman calls the physicists version of the history.

And yes I would like to see an actual historian of science/physics version.

Thanks
Bill

 

[Lord Jestocost]

This justifies the name von Neumann chain but confirms that the cut itself is due to Heisenberg alone.

Subtleties count! The "von Neumann cut" differs a "little bit" from the "Heisenberg cut". As Henry P. Stapp puts it in "Attention, Intention, and Will in Quantum Physics":

"Heisenberg's transition from 'the possible' to 'the actual' at the dumb measuring device was shown to be a superfluous and needless complication by von Neumann's analysis of the quantum process of measurement (von Neumann, 1932, Chapter VI). I shall discuss that work later, but note here only the key conclusion. von Neumann introduced the measuring instruments and the body/brains of the community of human observers into the quantum state, which is quantum theory's only representation of 'physical reality'......".

 

[vanhees71]

I heard of it first on good old Wikipedia:
https://en.wikipedia.org/wiki/Heisenberg's_microscope
You have confirmed it on a number of occasions so I take it as at least part of what Feynman calls the physicists version of the history.

And yes I would like to see an actual historian of science/physics version.

Thanks
Bill

Yes, this version is indeed the wrong Heisenberg argument that the uncertainty relation is about measurement, but it's about preparation, and that was, as I've read in some book on the history of QM (I'm not sure whether it was a scientific or a popular-science book or paper), what Bohr immediately corrected after having read the paper by Heisenberg, which he published without having discussed it with Bohr before though he was still affiliated at the Bohr institute. I bring it always as a caveat that one should not talk about "the Copenhagen interpretation". There are at least two flavors developed in parallel in Copenhagen around 1926-27, namely Bohr's and Heisenberg's version though of course in general they were closely discussing it intensely. For me it's also the prime example for the danger of trying to understand physics without math by rather philosophical arguments in the unsharp non-mathematical language, even if it's at a high level of philosophy.

 

[A. Neumaier]

The "von Neumann cut" differs a "little bit" from the "Heisenberg cut".

This even more justifies not to call the Heisenberg cut after von Neumann.

 

[A. Neumaier]

I'd been interested to remember where I read that Heisenberg got the physics of his uncertainty relation wrong first, and Bohr had to correct him.

It is mentioned at the end of Heisenberg's 1927 paper, I believe.

https://link.springer.com/article/10.1007/BF01397280

Nachtrag bei der Korrektur. Nach Abschluss der vorliegenden Arbeit haben neuere Untersuchungen von Bohr zu Gesichtspunkten geführt, die eine wesentliche Vertiefung und Verfeinerung der in dieser Arbeit versuchten Analyse der quantenmechanischen Zusammenhänge zulassen. In diesem Zusammenhang hat mich Bohr darauf aufmerksam gemacht, dass ich in einigen Diskussionen dieser Arbeit wesentliche Punkte übersehen hatte. Vor allem beruht die Unsicherheit in der Beobachtung nicht ausschliesslich auf dem Vorkommen von Diskontinuitäten, sondern hängt direkt zusammen mit der Forderung, den verschiedenen Erfahrungen gleichzeitig gerecht zu werden, die in der Korpuskulartheorie einerseits, der Wellentheorie andererseits zum Ausdruck kommen. Z.B. ist bei Benutzung eines gedachten $\Gamma$-Strahlmikroskops die notwendige Divergenz des Strahlenbündels in Betracht zu ziehen; diese erst hat zur Folge, dass bei der Beobachtung des Elektronenortes die Richtung des Comptonrückstosses nur mit einer Ungenauigkeit bekannt ist, die dann zur Relation (1) führt. Ferner ist nicht genügend betont, dass die einfache Theorie des Comptoneffekts in Strenge nur auf freie Elektronen anwendbar ist. Die daraus folgende Vorsicht bei Anwendung der Unsicherheitsrelation ist, wie Prof. Bohr klargestellt hat, unter anderem wesentlich für eine allseitige Diskussion des Übergangs von Mikro- zu Makromechanik. Schliesslich sind die Betrachtungen über die Resonanzfluoreszenz nicht ganz korrekt, weil der Zusammenhang zwischen der Phase des Lichtes und der der Elektronenbewegung nicht so einfach ist, wie angenommen.

 

[A. Neumaier]

Yes, this version is indeed the wrong Heisenberg argument that the uncertainty relation is about measurement, but it's about preparation

The paper

• Paul Busch, Pekka Lahti and Reinhard F. Werner, Proof of Heisenberg’s error-disturbance relation, Physical Review Letters 111 (2013), 160405.

rigorously establishes Heisenberg's view as valid in spite of Bohr's informal criticism:

the slogan ‘‘no measurement without disturbance’’ has established itself under the name of the Heisenberg effect in the consciousness of the scientifically interested public [...] Here we show that [...] Heisenberg-type inequalities can be proven that describe a tradeoff between the precision of a position measurement and the necessary resulting disturbance of momentum (and vice versa).

See also

• Masanao Ozawa, Heisenberg’s original derivation of the uncertainty principle and its universally valid reformulations, Current Science (2015): 2006-2016.

 

[atyy]

So Heisenberg's reference to "Übergangs von Mikro- zu Makromechanik" is supposed to be the cut? I guess that is more like "micro-macro transition".

 

[A. Neumaier]

So Heisenberg's reference to "Übergangs von Mikro- zu Makromechanik" is supposed to be the cut?

No, the cut was first defined by Heisenberg at the 1927 conference in Como (Proceedings of the 1927 Como conference, in the discussion of Bohr's lecture):

Um zur Beobachtung zu gelangen, muss man also irgendwo ein Teilsystem aus der Welt ausschneiden und über dieses Teilsystem eben 'Aussagen' oder 'Beobachtungen' machen. Dadurch zerstört man dort den feinen Zusammenhang der Erscheinungen und an der Stelle, wo wir den Schnitt zwischen dem zu beobachtenden System einerseits, dem Beobachter und seinen Apparaten andererseits machen, müssen wir Schwierigkeiten für unsere Ansschauung erwarten. [...] Jede Beobachtung teilt in gewisser Weise die Welt ein in bekannte und unbekannte oder besser: mehr oder weniger genau bekannte Grössen.

 

[A. Neumaier]

I guess that is more like "micro-macro transition".

Yes, in his uncertainty paper he only considers this transition. It is nowadays called the emergence of classicality. Since Zeh's work, it is usually treated by means of decoherence.

 

[vanhees71]

Weren't the Como lectures given by Bohr?

https://doi.org/10.1007/BF01504968https://doi.org/10.1038/121580a0

 

[A. Neumaier]

Weren't the Como lectures given by Bohr?

The conference consisted of a number of lectures plus extended discussion, which were part of the Proceedings. Following the Como lecture by Bohr,

N. Bohr,
The Quantum Postulate and the Recent Development of Atomic Theory,
Lecture delivered on Sept. 16, 1927 in Como.
Published in: Nature, April 14 (1928), 580--590.

the subsequent discussion features Heisenberg's quote given in my post #22:

W. Heisenberg, in:
Discussione sulla communicazione Bohr, pp. 589--598 in:
Proc. Int. Conf. Physicists, Como 1927.