Do measurements modify angular momentum and energy?

[Jarek 31]

TL;DR Summary

Spin corresponds to angular momentum - isn't it modified in measurement of spin?
If so, what happens with this difference of angular momentum?

While physics is generally believed to be CPT symmetric, there are processes for which such symmetry is being questioned - especially the measurement.

One of examples of (allegedly?) going out of QM unitary evolution is atom deexcitation - we can save its reversibility by remembering about change of energy, which requires carrier for this energy e.g. photon - getting reversible:
excited atom <-> deexcited atom + photon

The question is if can we save reversibility of measurement in analogous way?
e.g.: unpolarized spin <-> measured spin + e.g. photon carrying angular momentum difference

Spin corresponds to angular momentum, so doesn't its measurement mean change of angular momentum?
In other words, while angular momentum of measured spin is clear, can it be the same before the measurement?
In magnetic field e.g. Stern-Gerlach there is also involved energy change: like in Zeeman V=-mu\cdot B.

If so, what is happening with this difference of angular momentum, energy?

 

[jambaugh]

The measurement process, which is a recording of the quantum system's measured value as a classical state, is thermodynamic in nature (you must amplify the system's "signal" and refrigerate your measuring device) and thus breaks the T symmetry. Remember that measurement occurs outside of the unitary evolution of the system being measured. You can expand your system definition but once you encompass the whole measuring device you will necessarily need a non-sharp description and trace over inaccessible component systems namely the functional heat sink (i.e. photons speeding away from the observer off into space.)

Utilizing a photon to measure an atom doesn't actualize the measurement until the photon itself gets measured. Up to that point, the photon is merely entangled with the post-interaction atom.

As to your titular question, If you measure the same component of spin in succession you will not get a different result unless there was an intermediate interaction. That interacting mechanism will be where the change in angular momentum came from/went.

Note, however, that if you measure a distinct component (after previously measuring one component) then that component will not be well defined as different components do not commute. You can't say that the angular momentum changed nor can you say it didn't. To say either goes against complementarity. Each is an ill-defined statement for a quantum mechanical system. (On par with saying e.g. momentum and position can simultaneously be defined.)

 

[Jarek 31]

Thermodynamics, statistical physics are effective models - using the maximal entropy principle/Boltzmann ensemble to predict expected behavior for large number of objects.
In contrast, more fundamental are conservation laws, like of energy, momentum, angular momentum e.g. from Noether theorem ... also CPT theorem being at heart of QFT.
So, in my knowledge, thermodynamics cannot violate energy, momentum, angular momentum conservation laws?

Here the final particle with measured spin has fixed angular momentum.
If initial particle would have the same angular momentum, wouldn't it mean that it had the same spin direction?

Sure, in e.g. sequential Stern-Gerlach experiment, second measurement in the same direction should not change spin direction, angular momentum.
But what about the first measurement - of originally unpolarized beam of particles?

Remember that measurement occurs outside of the unitary evolution of the system being measured.

Indeed that's the source of the problem.
Atom deexcitation is naively also "outside of the unitary evolution" as producing photon to environment.
But including this environment in quantum consideration, is it really still non-unitary?
It becomes reversible: excited atom <-> deexcited atom + photon

There is this general view that non-unitarity comes from not included environment - cannot be also applied to measurement?

 

[PeterDonis]

There is this general view that non-unitarity comes from not included environment - cannot be also applied to measurement?

If you apply this idea--that when you include the environment, the overall evolution is always unitary--to measurement, you end up with the many worlds interpretation. As long as you're ok with that interpretation, yes, you can apply this viewpoint to measurement. (Note that discussion of interpretations belongs in the interpretations subforum, not this one.)

 

[Jarek 31]

I personally don't like MWI and wanted to focus on conservation laws here - repair non-reversibility analogously to atom deexcitation:

excited atom <-> deexcited atom + photon
unpolarized spin <-> measured spin + e.g. EM wave carrying angular momentum difference

Cannot these two be seen as analogous?
The issue is that such hypothesized e.g. EM wave carrying angular momentum difference, maybe also energy - do current experiments exclude such possibility?
If no, maybe a dedicated experiment could search for them?
Maybe we shouldn't think about localized optical photon here, but e.g. much more diffiult to verify cyllindrically symmetric EM wave like from linear antenna?

 

[PeterDonis]

repair non-reversibility analogously to atom deexcitation:

Neither of your examples "repair non-reversibility", because once you send off a photon or an EM wave you can't catch up with it, so the process is not reversible.

Both of your examples do illustrate that, in order to properly evaluate conservation laws, you have to include everything involved in the process that carries the conserved quantity. But that has nothing to do with reversibility.

 

[PeterDonis]

The issue is that such hypothesized e.g. EM wave carrying angular momentum difference, maybe also energy - do current experiments exclude such possibility?

No, they do the opposite, they tell you that conservation laws are always satisfied, so if you are missing some of a conserved quantity, it means you haven't yet included everything that is involved in the process.

The only thing your examples ignore is the possibility of states that do not have a well-defined value of a conserved quantity. For example, your "unpolarized spin" state--is it an eigenstate of angular momentum with eigenvalue zero, produced by some definite preparation procedure that yields that state? Or is it a mixed state where you don't know how the spin was prepared? In the latter case the initial state will not have a well-defined value of spin, so there's no way to assess conservation of angular momentum.

 

[Jarek 31]

Neither of your examples "repair non-reversibility", because once you send off a photon or an EM wave you can't catch up with it, so the process is not reversible.

The "excited atom <-> deexcited atom + photon" is basic reversible atomic process: toward right you wait for deexcitation, toward left you e.g. excite with laser.

For "unpolarized spin <-> measured spin + e.g. EM wave carrying angular momentum difference" toward right you perform measurement, toward left absorption of EM wave.

"unpolarized spin" state--is it an eigenstate of angular momentum with eigenvalue zero

After spin measurement the angular momentum is nonzero, so you agree this process modifies angular momentum?
If so, shouldn't the difference be radiated e.g. as an EM wave?

 

[PeterDonis]

After spin measurement the angular momentum is nonzero

Assuming you're measuring something like an electron, yes; the electron will end up in either the "up" or "down" spin eigenstate about the axis being measured.

you agree this process modifies angular momentum?

If the angular momentum was previously in an eigenstate with a different value, yes. Otherwise the question is not well-defined.

 

[Jarek 31]

So let us imagine Stern-Gerlach setting, in classical view I would say:

- there is flying magnetic dipole ("tiny magnet") initially pointing a random direction,
- in external magnetic field there appears torque tau =mu x B causing precession ( https://en.wikipedia.org/wiki/Larmor_precession ),
- precessing magnetic dipole means additional kinetic energy and oscillating magnetic field - unless mu x B = 0, what happens for parallel or anti-parallel alignment,
- so it radiates this abundant energy (e.g. through this oscillating magnetic field) and aligns in parallel or anti-parallel way - as in measurnment.

If the above is proper intuition (?), this "radiates abundant energy" makes it analogous to "excited atom <-> deexcited atom + photon".

 

[PeterDonis]

The "excited atom <-> deexcited atom + photon" is basic reversible atomic process: toward right you wait for deexcitation, toward left you e.g. excite with laser.

For "unpolarized spin <-> measured spin + e.g. EM wave carrying angular momentum difference" toward right you perform measurement, toward left absorption of EM wave.

These are both time-asymmetric processes whose time reverses are also valid processes. Is that what you mean by "reversible"?

 

[Jarek 31]

Indeed reversible as if there exists reverse process, applying time symmetry it is still valid.
CPT theorem says that applying CPT symmetry to any process, we should get a valid process.

Naively, measurement does not have a valid reverse (or CPT) process, my point is that it can be repaired if remembering about change of angular momentum/energy - which have to be compensated like during deexcitation.

 

[PeterDonis]

it can be repaired if remembering about change of angular momentum/energy

No, that in itself doesn't "repair" non-reversibility. To make quantum measurements reversible, you would need to adopt an interpretation like the MWI in which measurements are unitary processes.

 

[Jarek 31]

All the time I am writing about repairing (e.g. for CPT theorem) as:

unpolarized spin <-> measured spin + e.g. EM wave carrying angular momentum difference

With what exactly do you disagree with?
You agree that mean angular momentum before is zero, after is nonzero?
If so, don't conservation laws say that this difference should go somewhere e.g. as EM wave?
If so, applying T symmetry: this EM field is absorbed by polarized spin, leading to different initial spin.

 

[PeterDonis]

All the time I am writing about repairing (e.g. for CPT theorem) as:

unpolarized spin <-> measured spin + e.g. EM wave carrying angular momentum difference

As you write it here, this is not a reversible process, because you have "measured spin" there and measurement is not CPT symmetric (unless you adopt an interpretation like the MWI).

(Note that I didn't notice the "measured spin" part before, when I responded in post #11, so my statement there that both of the processes you wrote down have time reverses that are valid processes was incorrect.)

You agree that mean angular momentum before is zero, after is nonzero?

I already responded to this in post #9.

 

[jambaugh]

[...]
Indeed that's the source of the problem.
Atom deexcitation is naively also "outside of the unitary evolution" as producing photon to environment.
But including this environment in quantum consideration, is it really still non-unitary?
It becomes reversible: excited atom <-> deexcited atom + photon

There is this general view that non-unitarity comes from not included environment - cannot be also applied to measurement?

As long as you include the full field outside the atom then yes it remains unitary. But the reversibility means that the experimenter must maintain control of the entirety of that piece of the environment. The experimenter can for example observe the deexcitation within a cavity with perfectly conducting walls. You will note then that the overall behavior is then also cyclic over the long term with the energy oscillating between atom excitation-deexcitation and field photon count increasing and decreasing. The exact "state" of the composite system is then in a superposition of the states you wish to measure. No measurement has then been made.

You can measure that extended system in such a way that it will reveal the measurement of the atomic state of the initial system since as it is set up the field state and atom state are entangled (e.g. |e,0> + |d,1> for |excitation state, photon number> ).

Before you can ask questions about unitarity and whether a measurement occurs you must first unambiguously define what exactly is the system. To invoke the full quantum treatment there is the tacit assumption that you also have free control of that system i.e. are able to couple an external measuring device to any observable you would wish to measure.

I think the "problem" people see with measurement is in thinking they can keep expanding (hence redefining) "the system" while leaving questions of "the observables" "a measurement" and so on unchanged. Yes, you can carry out a delayed measurement with an arbitrary daisy chain of "clones" of the original system thereby creating a representative secondary quantum system (the last in that chain) entangled with the original "measured" system so that measuring Y for the representative equates to measuring X for the original. But the measurement as such hasn't occurred until that classically copyable record exists. You could measure a complementary Y' observable and destroy any ability to determine X.

Finally, I would point out that, in my Copenhagenist's interpretation, both the sharp quantum description and more classical stochastic description of the systems are of the same categorical nature. They both phenomenologically express a class of systems and not a singular system "state of reality" i.e. they are forms of probability distributions. The distinction is only (imnsho) that the assumption that these probability distributions are a measure of an objective set of physical states ceases to be correct for the quantum systems. Decoherence is the physical description of us then being able to ignore the non-objective quantum actuality underneath due to the inevitable thermodynamic aspects of a measurement process.

An SG magnet setup by itself does not measure electron spin, it rather correlates spin with transverse momentum. To carry out the experiment we have to "refrigerate" the entry electron's transverse motion to be relatively localized in position and relatively fixed in momentum. After the passage, the electron propagates enough for the transverse position to entangle with the earlier momentum and expand enough so that the difference is significantly greater than the Heisenberg uncertainty necessary since we've localized both momentum and position. But you are still talking about a quantum electron with position and spin entangled until you get your big entropic particle detector out and get the electron to induce a messy avalanche of other particles in a scintillation crystal or through a gas near its breakdown voltage or cause an ion trail in a supersaturated cloud chamber etc.

Up until that point the system has typically evolved unitarily and is in principle reversible and has not been measured.

 

[jambaugh]

Regarding MWI. To my (Copenhagenist's) mind it is literally correct and essentially wrong.

Classically we use a "reality description" of physical phenomena (a reality of objects in objective states). Quantum nature (under CI) asserts a phenomenological "actuality description". (actuality = what happens, reality = what is).

With this in mind "realities" are models we build to match the phenomena we observe. At the gross classical scale we live this is a very very good way to describe most things. When we started looking too closely though, it broke down and we developed QM.

Now there is already a many-worlds interpretation in classical mechanics but we don't bother as it is intuitively obvious. I am going to flip a coin and I imagine (build a world model) where it lands heads-up and I pay for dinner or it land tails-up and you pay for dinner. I then describe a 50% one "world" 50% other world representation of the future.

We flip, we look, and oops I'm paying. My probability distribution describing future behavior of the coin "collapses" to a 100% one "world" 0% other world description. You can argue that "no not we have certainty" but I argue that I am expressing that certainty only I'm using the same format as before when we did not have that certainty so that before and after descriptions are compatible with other statements we may make. I.e. I seek to avoid category errors due to change in format. You can ignore the 0% case but it is a "2nd world" in our many worlds "interpretation" of my description. It was before and it still is afterwards. If you include me (and you) in the description there are still two worlds for the outside observer 50% us seeing the coin and me buying dinner, 50% us seeing the coin and you buying dinner. But we understand that these are many worlds of possibilities. The actuality is that we each use the realty model that matches our experience and forget about the other. It's not "out there somewhere" any more than the model we do actually use is "out there somewhere" as it's only a model. In actuality, stuff happened.

Now replace the coin with a previously x-spin +1/2 electron's z-spin measurement. Given the fact that during measurement the evolution of our e-coin will cease to be unitary due to external interactions (measuring device i.e. the "flip") so I begin with a "many-worlds" description of the e-coin with 0% x-spin -1/2 and 100% x-spin +1/2. I change frames for that initial description to that of a 50% spin z +1/2 and 50% spin z -1/2 plus some off diagonal components. I then evolve it so those off diagonal components are eliminated by the measurement process. Still 2 worlds in a 50% vs 50% pair of possibilities. The same 2 worlds as in the classical coin flip as seen by the external observer before asking us what happened. Still two models of what may have actualized.

The weirdness comes in the fact that we can map one pair of "worlds" in a state of certainty to another world in a superposition of certainties by changing our frame of observables. But adding worlds doesn't resolve this weirdness. It's just how things happen.

 

[PeterDonis]

Since the OP has been banned, this thread is closed.