Symmetry considerations between observer and observed in QM

[spaghetti3451]

The following is taken from page 101 of Warren Siegel's textbook 'Fields.'

Another example is quantum mechanics, where the arbitrariness of the phase of the wave function can be considered a symmetry: Although quantum mechanics can be reformulated in terms of phase-invariant probabilities, currents, or density matrices instead of wave functions, and this can be useful for some purposes of exposing physical properties, formulating and solving the Schrodinger equation is simpler in terms of the wave function. The same applies to “local” symmetries, where there is an independent symmetry at each point of space and time: For example, quarks and gluons have a local “color” symmetry, and are not (yet) observed independently in nature, but are simpler objects in terms of which to describe strong interactions than the observed hadrons (protons, neutrons, etc.), which are described by color-invariant products of quark/gluon wave functions, in the same way that probabilities are phase-invariant products of wave functions.

(Note that in quantum mechanics there is a subtle distinction between observed and observer that can obscure this symmetry if the observer is not invariant under it. This can always be avoided by choosing to define the observer as invariant: For example, the detection apparatus can be included as part of the quantum mechanical system, while the observer can be defined as some “remote” recorder, who may be abstracted as even being translationally invariant. In practice we are less precise, and abstract even the detection apparatus to be invariant: For example, we describe the scattering of particles in terms of the coordinates of only the particles, and deal with the origin problem as above in terms of just those coordinates.)

I am having problems understanding the second paragraph. I have an intuitive understanding of the difference between observer and observed. The detection apparatus, for example, is an observer, isn't it?

What does one mean when one says that an observer is invariant under a symmetry?

 

[Demystifier]

What does one mean when one says that an observer is invariant under a symmetry?

For instance, I am right-handed which allows me to distinguish between left and right, so I am not invariant under chiral symmetry. But I have no idea what my phase $e^{i\varphi}$ is, so I am invariant under phase symmetry.

 

[spaghetti3451]

Is the detection apparatus part of the observer, or is it part of the observed?

 

[Demystifier]

Is the detection apparatus part of the observer, or is it part of the observed?

Great question! I would say it is a part of the observed, but sometimes by "observer" physicists really mean "the apparatus". So if the writer is sloppy and careless about such conceptual/philosophical issues (which real physicists usually are), one should decipher from the context what the writer really meant.

 

[spaghetti3451]

In the first sentence of the second paragraph, the writer writes

(Note that in quantum mechanics there is a subtle distinction between observed and observer that can obscure this symmetry if the observer is not invariant under it.

I don't really see why the distinction between observer and observed is subtle at all. Isn't it clear that the detection apparatus and the particles at play are part of the observed and the experimenter is the observer?

Am I missing a subtle point here?

 

[Demystifier]

In the first sentence of the second paragraph, the writer writes

I don't really see why the distinction between observer and observed is subtle at all. Isn't it clear that the detection apparatus and the particles at play are part of the observed and the experimenter is the observer?

Am I missing a subtle point here?

The distinction is not subtle in classical physics, but it becomes subtle in quantum physics. What you are missing is probably the whole branch of quantum physics known as the measurement problem.

 

[spaghetti3451]

Why does both the observer and the observed have to be invariant under a set of transformations in order for that set of transformations to qualify as a symmetry?

Why is the symmetry obscured if the observer is not invariant under the symmetry?

 

[Demystifier]

Why does both the observer and the observed have to be invariant under a set of transformations in order for that set of transformations to qualify as a symmetry?

Why is the symmetry obscured if the observer is not invariant under the symmetry?

A transformation is called a symmetry of the system if (and only if) the system is invariant under the transformation. So if the system is not invariant, then it is not called symmetry.

By the way, the concept of symmetry in physics is quite elementary. If you are not familiar with it, perhaps the Warren Siegel's 'Fields' is not the best place to start with studying QFT.

 

[spaghetti3451]

A transformation is called a symmetry of the system if (and only if) the system is invariant under the transformation. So if the system is not invariant, then it is not called symmetry.

By the way, the concept of symmetry in physics is quite elementary. If you are not familiar with it, perhaps the Warren Siegel's 'Fields' is not the best place to start with studying QFT.

I have taken a course in group theory and know the meaning of symmetry. What I was really confused about is if the observer is part of the system or not, and hence whether the observer needed to be invariant under those symmetry transformations (which already apply to the observed) Thanks for clarifying my confusion.

Siegel writes that, in order to ensure that the symmetry is not obscured by the subtle distinction of observed and observer, the observer can be chosen such that it is invariant. To exemplify his case, he writes that the detection apparatus can be included as part of the quantum mechanical system, while the observer can be defined as some remote recorder, who may be abstracted as even being translationally invariant.

Are we really the arbiter on who we decide is the observer and who is the observed?

 

[Demystifier]

Are we really the arbiter on who we decide is the observer and who is the observed?

Are you familiar with the Wigner's friend problem? If not, you might start with googling about that.

 

[secur]

Wigner's position was that consciousness causes collapse of the wave function, and his gedanken was meant to illustrate that. Indeed, that's the obvious answer to failexam's concerns. Since you recommend "Wigner's friend", Demystifier, can we assume you agree with Wigner that consciousness collapses the wave function?

 

[Demystifier]

Since you recommend "Wigner's friend", Demystifier, can we assume you agree with Wigner that consciousness collapses the wave function?

No we can't. But I am open to discussion of various possibilities. Sometimes wrong ideas are more worth of discussion than the right ones.

 

[bhobba]

Wigner's position was that consciousness causes collapse

Point of clarification. Towards the end of his career he did a 180% about face after reading some early work on decoherence by Zeth. He realized it has many many problems - which of course it does. It doesn't disprove it of course - by the extreme difficulties are much clearer in the computer age.

An irony is Von Neumann was one of the early advocates of it and he was one of the early pioneers of computers.

Thanks
Bill

 

[bhobba]

the observer can be chosen such that it is invariant.

That's an interpretation thing. We have interpretations where the observer is central, where its not required, where observers are concious, where it is not - all sorts of interpretations exist. Since they can't be distinguished assume any you like to simplify your analysis - its equally valid regardless.

If this observer thing worries you (it doesn't me) chose Bohmian Mechanics where everything is objectively real.

Thanks
Bill

 

[A. Neumaier]

Are we really the arbiter on who we decide is the observer and who is the observed?

Those who discuss something about physics are always the persons who decide what the subject of the discussion is. in particular, they decide about which system they talk, and what they are going to observe. Thus it is the context of a statement (or, the person who makes the statement) that determines what is observed and what is the observer. They point to some part of Nature and say - let this be our system. and to another part of Nature (possibly themselves) and say - let this be the observer. if it is not specified precisely you have to figure it out from the contex, and if the context leaves it ambiguous then nit is ambiguous and you have to invoke the error correcting facilities acquired during your education to make a choice - like everywhere in life.

Specifying the system (i.e., the observed) is defining what is often called the Heisenberg cut. it singles out from Nature a system to be modeled by quantum mechanics. In most real work involving quantum physics the system is taken as small as possible - which enhances tractability. Everything outside the system - in particular its measurement - is treated by omission or by very simplified heuristic arguments. The typical example is the Born rule that tells what happens in certain kinds of deal measurements. (My description ignores for simplicity quantum cosmology where the whole universe is treated as a quantm system.)

The only deviation form the rule that the system is taken as small as possible is when one wants to analyze the emasurement process itself in terms of quantum mechanics. In this case, the system modeled consists of a tiny subsystem to be measured and a detector (measurement apparatus) coupled to this tiny subsystem. This system is far more complicated but can be analyzed under simplifying conditions to justify things like the Born rule, state reduction, Lindblad dynamics for open systems, and the like.

I am having problems understanding the second paragraph. I have an intuitive understanding of the difference between observer and observed. The detection apparatus, for example, is an observer, isn't it? What does one mean when one says that an observer is invariant under a symmetry?

What Warren Siegel refers to is that one can change one's viewpoint of what one regards as the system, and include into the system everything not invariant under a symmetry. This is like analyzing the measurement - instead of describing the small system where the observation breaks the symmetry one thinks of the small system plus the detector (and everything else that may make up the observer) as a larger system. This system is then invariant under the universal symmetries - you can translate, rotate, boost the joined system and you get an equivalent system. Alternatively, you abstract completely from the observer [by regarding it as an abstract object submitted to the same symmetries as the small system] and treat the small system as forming a complete, tiny universe - again having the universal symmetries.

The parenthetical paragraph that you had quoted states precisely this alternative and nothing else - though in different, perhaps somewhat opaque words.