Seeking clarity on the physical definition of an observer

[okabe rintarou]

TL;DR

Seeking clarity for a high school student on the physical definition of an observer, decoherence in MWI, and the mathematical laws preventing cross-timeline traversal.

I am an 18-year-old student waiting for my Class 12 results, and I've been doing some conceptual reading into Quantum Foundations (specifically referencing 1926 wave mechanics and 1957 Relative State formulation). I have three specific questions I'd love to ask a professional:

1) In the Schrödinger equation, how is the 'observer' strictly defined physically? Why did the von Neumann information-based interpretation lose its mainstream status?

2) Regarding the Many-Worlds Interpretation (MWI), how does the math of decoherence physically ensure that branches become orthogonal/separated?

3) From a purely theoretical standpoint, which specific physical laws (Thermodynamics, Causality, etc.) mathematically prevent information or matter from reaching or traveling to a different decohered timeline?

Thank you for your time and guidance!

 

[PeroK]

Regarding questions 2 and 3, one suggestion is to read Feynman's book on QED:The Strange Theory of Light and Matter. It doesn't cover decoherence, but the way light behaves quantum mechanically to produce the classical wave phenomena of reflection, refraction and diffraction gives a valuable insight into how the mathematics of decoherence works.

 

[gentzen]

1) In the Schrödinger equation, how is the 'observer' strictly defined physically?

Good answers to this question can be found in "Quantum Theory: Concepts and Methods" by Asher Peres (https://en.wikipedia.org/wiki/Quantum_Theory:_Concepts_and_Methods)
and "Quantum Mechanics: A Modern Development" by Leslie E. Ballentine (https://en.wikipedia.org/wiki/Ensemble_interpretation#cite_note-BallentineBook-11)
Both are in tradition of Niels Bohr, quite direct in case of Asher Peres, and what you get if you take Bohr's positions to a logical conclusion in case of Ballentine.

Why did the von Neumann information-based interpretation lose its mainstream status?

???
Why do people ascribe all sorts of things to von Neumann?
Anton Zeilinger is the famous person advocating for information-based interpretations. No idea what you mean by "mainstream status".
Perhaps you are thinking about the version of Copenhagen defended by Werner Heisenberg and Rudolf Peierls?

 

[PeterDonis]

Moderator's note: Thread moved to the QM interpretations subforum.

 

[bhobba]

As an 18-year-old, QED has been suggested as a good place to start (and I agree).

The following video suggests the next books to read (but are above what I would expect of the usual 18-year-old, although certainly not beyond their capability if you want to go deeper):



The next would be Ballentine, as mentioned in a previous answer, but it is graduate-level and should be read after the recommendations in the above video. Perhaps a bit too advanced for an 18-year-old - but giving it a look and seeing what you can glean would be OK.

One thing sometimes not appreciated about QM is that, as you progress to more advanced material concepts at the less advanced level, how to put it, are 'tweaked' a bit. The great Richard Feynman, well known as a great teacher, lamented this, but try as he might, he could not figure out how to avoid it.

Von Neumann's classic Mathematical Foundations of QM (not to be read until you have done a course in functional analysis) is where the idea of 'consciousness' causing collapse originated. If you do look at it, understand his (scathing) comments on the Dirac Delta function have all now been resolved. At your level, the book to get on how it was done, and also highly recommended as something every mathematician and physicist should know, is:

https://www.amazon.com.au/Theory-Distributions-Nontechnical-Introduction-ebook/dp/B01DM26TPW.

His analysis showed that the Quantum Classical cut could be placed anywhere, and, for reasons he explained, he placed it at the level of human consciousness. This led to the consciousness-causes-collapse interpretation, which popular books still flirt with but is well out of favour these days, with most considering it mystical nonsense (as do I). It never really caught on, and prominent adherents like Wigner changed their mind after early work on decoherence. These days, the term "observation" is usually synonymous with decoherence.

In many worlds, the assumption is that after decoherence, each possible outcome is a separate world. However, as Murray Gell-Mann explains, the issue of their reality is to some extent just a semantic difference between real and potentially real, with each treated on equal footing:



If you think they are real, you are led to Many Worlds. If you think they are potentially real, you are led to Decoherent Histories.

However, I need to mention that we now know that ordinary QM is wrong and has been replaced by Quantum Field Theory (QFT), which incorporates relativity. Most people think QM is the limiting case of QFT, but, to my surprise, a recent paper I read shows that this is not the case. That has thrown the cat really amongst the pigeons and suggests the issues with QM are not quite what is usually thought. This is just by the by; it really is at the graduate level, and the details go beyond the level of this thread. Plus, it is only of any value to nuts like me interested in such things - no need to worry about it at your level. Remember what I mentioned, as you become more advanced, things get 'tweaked' a bit.

If you believe in the reality of many worlds, the assumption is that they are always separate; there is no law involved.

My view is, once you have read the books in the YouTube video I posted, the best book about quantum interpretations is:
https://www.amazon.com.au/Fields-Their-Quanta-Quantum-Foundations-ebook/dp/B0DLNLLG7Y

A bit pricey and a minority interpretation (which is a bit strange, as it's basically just a literal interpretation of QFT), but it has the advantage of making usual issues like wave-particle duality and what is a particle, trivial.

Thanks
Bill

 

[PeterDonis]

a semantic difference between real and potentially real

Is that like the difference between all dead and mostly dead?

 

[bhobba]

Is that like the difference between all dead and mostly dead?

It is surprising how much of what we discuss is, to a large extent, semantics. I know we don't discuss philosophy here, but many of Wittgenstein's ideas centred on this (yes, I know he started as an aeronautical engineer). His mentor Bertrand Russell was 7th wrangler. Those were the days when philosophers knew at least some science (many still do).

However, some philosophers went down a 'peculiar' path best read about in the book by the mathematical physicist Alan Sokal: 'Beyond the Hoax: Science, Philosophy and Culture'

Thanks
Bill

 

[gentzen]

Why did the von Neumann information-based interpretation lose its mainstream status?

???
Why do people ascribe all sorts of things to von Neumann?

OK, I guess I know how your mistake happened. At the end of the The Information Philosopher page for John von Neumann, Bob Doyle had explained the connection to his information physics, but without a clear separation from the extracts of John von Neumann thoughts:

Information physics places the cut or boundary at the place and time of information creation. It is only after information is created that an observer could make an observation. Beforehand, there is no information to be observed.

And Gemini (google's AI) misinterpreted Bob Doyle's writing beyond any basis in reality:

Legacy​

Today, von Neumann is celebrated by movements like Information Philosophy, which views the universe not just as a collection of matter and energy, but as fundamentally built from information structures. [1, 2]

• Dive deeper into his conceptual framework on the Information Philosopher Profile.
• Read about his evolving intellectual journey toward computation theory in this arXiv Study on Von Neumann's Philosophical Shift.

Bob Doyle (The Information Philosopher) is not bad, he is a useful source of information. It is unfortunate that minor document structuring and formating mistakes get ridiculously amplified by AI, but not really his fault.

 

[gentzen]

1) In the Schrödinger equation, how is the 'observer' strictly defined physically?

On the mathematical level of the Schrödinger equation, 'preparation' (~= initial values) and 'measurement' are defined as mathematical operations. It could also make sense to explicitly define 'control' as a combination of 'measurement' and 'classical action taken in response to measured result' (~= time dependent Hamiltonian) on that mathematical level.

The more controversial question is how to interpret 'observer' in our actual physical world. It is relatively uncontroversial that an 'observer' doesn't need to be a "human" or a "conscious being". But beyond that minimal consensus, opinions vary widely:

It is not the "human" part which upsets me about the word "observer". It is the suggested absence of "interaction" and "altering"/"influencing" capabilities. The word "observer" suggest a passive viewer of some "TV show" or "cinematic movie", not an active participant in some "massively multiplayer online game".

Or maybe more aptly, it suggests an old time astronomer like in Newton's times watching the planets, moons, and stars without any possibility to alter their course. It does not suggests a modern NASA scientist designing swing-by (gravity assist) maneuvers to steal a tiny amount of the energy of some planet or moon to let his spacecraft save fuel.

Of course, the course of the planet or moon is not significantly altered, but the course of the spacecraft is. You could model the spacecraft itself as an agent, because it has thrusters which are effectively controlled by intentions (i.e. final causes). It can also make sense to only model the ground station as an agent, because the communication delay to the spacecraft might be important. But beyond that, the usefullness and explanatory value of the model would rather decrease if you try to remove agents even further.

 

[martinbn]

In the Schrödinger equation, how is the 'observer' strictly defined physically?

What exactly do you mean by that?!

 

[jeffn1]

My $.02 for what its worth:

The term "observer" has caused so much confusion. The word "observer" implies a conscious, biological entity looking at a result. Art Hobson emphasizes that wave function collapse and measurement are entirely physical, mind-independent processes.

For Hobson, a "measurement" is simply what happens when a microscopic quantum system interacts and becomes nonlocally entangled with a macroscopic macro-device—a detector.

A detector does not have to be a piece of laboratory equipment like a Geiger counter. In nature, a grain of sand or an atmospheric molecule acting as an interacting medium serves as a detector. No human intervention is needed to finalize the physics.

 

[Sambuco]

Art Hobson emphasizes that wave function collapse and measurement are entirely physical

It is worth noting that this statement about wave function collapse is interpretation-dependent. In fact, this is true only for some $\psi$-ontic "interpretations" that invoke an objective collapse, such as Ghirardi-Rimini-Weber (GRW), or constinuous spontaneous localization (CSL). I use quotation marks because, by modifying the Schrödinger equation, such formulations are often considered alternative theories rather than interpretations.

Lucas.

 

[bhobba]

It is worth noting that this statement about wave function collapse is interpretation-dependent.

True.

But Art is referring to the collapse of the quantum field, which the state is an approximation to (the non-relativistic limit of QFT is not ordinary QM). Certainly, it is possible that the quantum field is, like the state, just a computational aid, but since particles are excitations in the quantum field, the reality of particles becomes debatable. They, of course, may not be 'real', but that would seem to be a minority position amongst physicists (in fact, I don't know of any who believe that).

Thanks
Bill

 

[Matterwave]

His mentor Bertrand Russell was 7th wrangler. Those were the days when philosophers knew at least some science (many still do).

Thanks
Bill

I recently read Bertrand Russell's History of Western Philosophy. His ending section on QM was horrendously outdated. He was using concepts mostly from the 1910s when he wrote the book in 1945.

I don't think he kept up to date with the physics TBH. Or if he did, he presented only the view which fit his worldview best.

 

[Sambuco]

Certainly, it is possible that the quantum field is, like the state, just a computational aid, but since particles are excitations in the quantum field, the reality of particles becomes debatable. They, of course, may not be 'real', but that would seem to be a minority position amongst physicists (in fact, I don't know of any who believe that).

I believe it's possible to think of QFT as a tool that, given information about the occurrence of a certain past event, allows us to predict the probability of a future event. These events could be described in terms of system variables taking on definite values, while fields would allow us to calculate the transition probabilities between events.

Lucas.

 

[Matterwave]

Certainly, it is possible that the quantum field is, like the state, just a computational aid, but since particles are excitations in the quantum field, the reality of particles becomes debatable.

The bolded part seems to me to be quite a simplification. In a free, non-interacting, QFT, particle states are created by some creation operator $\hat{a}_p^\dagger$ (using momentum representation in place of a general one) acting on the vacuum state in Fock space. The field operators are, generally, integrals (sums if you work with a discrete representation) of the creation and annihilation operators and looks something like this:

$$\hat{\phi}(\mathbf{x}) = \int \frac{d^3p}{(2\pi)^3} \frac{1}{\sqrt{2E_{\mathbf{p}}}} \left( \hat{a}_{\mathbf{p}} e^{i\mathbf{p} \cdot \mathbf{x}} + \hat{a}_{\mathbf{p}}^\dagger e^{-i\mathbf{p} \cdot \mathbf{x}} \right)$$

When you hit a vacuum state with a field operator, you get a single particle state because the annihilation operator part ($\hat{a}_p$) annihilates the vacuum and you're left with the creation operator part.

And then one asks "yeah but, the universe has interactions in it" and you find, due to Haag's theorem, that the full interaction theory's vacuum state can't even be the same thing as your free vacuum state.

If I may take off my physicists-hat for a moment and muse a little -- I simply don't know how to read an ontology -- particles or not, fields or not -- off of QFT. I realize QFT gives incredibly accurate predictions of experimental results, but perhaps some weakness in me prohibits me from viewing it through the lens of a fundamental theory. I am fully ready to accept that this is a deficiency in my own understanding and not one in the theory. It's just, no matter how many QFT books I try to go through, I get stuck here haha.

 

[PeterDonis]

When you hit a vacuum state with a field operator, you get a single particle state

No, you don't, you get a superposition of a continuous infinity of different single particle states with different momenta, because of the integral. That's one of the problems with giving QFT operators a physical interpretation. Creation and annihilation operators are "cleaner" in terms of particle states, but they're not Hermitian; field operators are Hermitian, but what they produce when you apply them to the vacuum state doesn't look like anything we actually observe. (And that's without even opening the other can of worms you refer to, to do with Haag's Theorem.)

 

[Matterwave]

No, you don't, you get a superposition of a continuous infinity of different single particle states with different momenta, because of the integral.

Gotcha. I still lacked precision in my statements. By "single particle state" I just meant a state which would have eigenvalue $1$ for the number operator:

$$\hat{N} = \int \frac{d^3p}{(2\pi)^3} \hat{a}_{\mathbf{p}}^\dagger \hat{a}_{\mathbf{p}}$$

Thanks for the correction! I'm very glad to be corrected here because it helps me reduce my misconceptions.

 

[PeterDonis]

By "single particle state" I just meant a state which would have eigenvalue $1$ for the number operator

Unfortunately, as I said, such a state, if it's obtained by applying the field operator you wrote down to the vacuum, doesn't look anything like what we would expect a "single particle state" to look like; instead it looks like a continuously infinite superposition of them.

 

[bhobba]

Very nice discussion.

Kudos.

Just as an aside, a link to the prototype QFT, What Is A Photon, so those unfamiliar can get a general idea:

https://digitalcommons.usu.edu/cgi/viewcontent.cgi?article=3211&context=physics_facpub

Note that no 'ordinary QM' theory of a photon exists since EM is already relativistic. QFT must be used.

Thanks
Bill

 

[QuarkyMeson]

No, you don't, you get a superposition of a continuous infinity of different single particle states with different momenta, because of the integral. That's one of the problems with giving QFT operators a physical interpretation. Creation and annihilation operators are "cleaner" in terms of particle states, but they're not Hermitian; field operators are Hermitian, but what they produce when you apply them to the vacuum state doesn't look like anything we actually observe. (And that's without even opening the other can of worms you refer to, to do with Haag's Theorem.)

A continuous superposition of momentum eigenstates can still be a one-particle state, no?

 

[PeterDonis]

A continuous superposition of momentum eigenstates can still be a one-particle state, no?

If your only requirement to call something a "one-particle state" is that it's an eigenstate of the number operator @Matterwave wrote down with eigenvalue $1$, yes. But it's a state that looks nothing like what we normally think of as a "particle", since it has no definite momentum, nor even a narrow spread of momentum that would make it look approximately like a particle.

It's true that all this is a matter of words, not physics. But that seems to be what this thread is about in general.

 

[QuarkyMeson]

If your only requirement to call something a "one-particle state" is that it's an eigenstate of the number operator @Matterwave wrote down with eigenvalue $1$, yes. But it's a state that looks nothing like what we normally think of as a "particle", since it has no definite momentum, nor even a narrow spread of momentum that would make it look approximately like a particle.

It's true that all this is a matter of words, not physics. But that seems to be what this thread is about in general.

Fair.

My take on OPs questions:

TL;DR: Seeking clarity for a high school student on the physical definition of an observer, decoherence in MWI, and the mathematical laws preventing cross-timeline traversal.

I am an 18-year-old student waiting for my Class 12 results, and I've been doing some conceptual reading into Quantum Foundations (specifically referencing 1926 wave mechanics and 1957 Relative State formulation). I have three specific questions I'd love to ask a professional:

1) In the Schrödinger equation, how is the 'observer' strictly defined physically? Why did the von Neumann information-based interpretation lose its mainstream status?

2) Regarding the Many-Worlds Interpretation (MWI), how does the math of decoherence physically ensure that branches become orthogonal/separated?

3) From a purely theoretical standpoint, which specific physical laws (Thermodynamics, Causality, etc.) mathematically prevent information or matter from reaching or traveling to a different decohered timeline?

Thank you for your time and guidance!

1. It doesn't say anything about it at all. SE describes unitary evolution of a state vector under a Hamiltonian. I'm assuming those are just words to you now.

I don't know much about von Neumanns interpretations, just the footnote that his earlier proof on hidden variables was wrong and later corrected by Bell. Any interpretation he might have based on the understanding at the time is probably similarly flawed. We have almost an additional 100 years of theory development.

2. Imagine a particle in a superposition of spin up and spin down. As long as nothing interacts with it in a way that reveals which component it is in, the two components remain coherent, and a suitable experiment can make them interfere.

Now send the particle through a Stern–Gerlach apparatus. The magnet correlates spin with position, the spin-up component follows one path and the spin-down component follows another. By itself, this separation is not yet decoherence. Decoherence occurs when the surroundings interact differently with the two paths. Air molecules, photons, and the detector funbits then carry information about which path was taken.

The combined state of the particle and environment becomes entangled. The environmental state associated with the spin-up path becomes almost orthogonal to the environmental state associated with the spin-down path. As a result, interference between the two components becomes essentially impossible to observe by measuring the particle alone.

The coherence has not been destroyed from the total quantum state. It has been spread into correlations between the particle and the environment. In principle, interference could be recovered by erasing the path information and reversing those correlations, but for a macroscopic detector and environment this is effectively impossible.

In the many-worlds interpretation, the two components are described as approximately separate branches. They behave like independent histories because interference between them is negligibly small. However, the claim that both branches literally exist is an interpretational statement, not something implied by decoherence alone.

3. The SE is linear, so a superposition evolves as a superposition of the evolved components. After decoherence, those components become correlated with different states of the environment and evolve almost independently. The only way to detect the relative phase between them is to make them interfere again.

For a macroscopic event, however, the two components differ not only in the particle itself but also in the states of enormous numbers of photons, air molecules, detector funbits, and other environmental degrees of freedom. Reversing all of those correlations well enough to restore interference is allowed in principle, but effectively impossible in practice.

 

[Matterwave]

Very nice discussion.

Kudos.

Just as an aside, a link to the prototype QFT, What Is A Photon, so those unfamiliar can get a general idea:

https://digitalcommons.usu.edu/cgi/viewcontent.cgi?article=3211&context=physics_facpub

Note that no 'ordinary QM' theory of a photon exists since EM is already relativistic. QFT must be used.

Thanks
Bill

The section of this text maybe most fitting for the current discussion is section 6.10