# Events in Quantum Theories

• I
Gold Member
TL;DR Summary
An experimenter can use QM to compute probabilities for possible experimental outcomes (events) so long as the experimenter chooses a measurement basis. Decoherence will select a preferred basis for the experiment, but does not explain why events associated with that basis occur vs events associated with other bases. I believe the resolution to this issue can be found in the subtle difference between "complementary" and "mutually exclusive".
This thread picks up a discussion between myself and @A. Neumaier in another thread. In particular, this comment:
A. Neumaier said:
What does it mean in quantum terms for a detector to produce an event? To give your POVM a meaning you need to refer to the classical description of the experiment done to identify the projectors with real events. This is what I mean with classical.

First some basic background. If we consider the usual presentation of a destructive measurement of an observable ##A = \sum_i a_i|a_i\rangle\langle a_i|## of system ##s## by detector ##D##, we have the evolution $$U(t)|\psi_0,D_\Omega\rangle = \sum_ic_iU(t)|a_i,D_\Omega\rangle = \sum_ic_i|D_i\rangle$$where ##|\psi_0\rangle## and ##|D_\Omega\rangle## are initial states of the system of measurement and detector respectively, and ##|D_i\rangle## are orthonormal states on ##\mathcal{H}_s\otimes\mathcal{H}_D##.

We can then build an event algebra from a sample space of outcomes built in turn from a projective decomposition of the identity $$I_{s+D} = \sum_i|D_i\rangle\langle D_i|$$The probability for the occurrence of outcome ##D_i## is $$p(D_i) = \mathrm{tr}(|D_i\rangle\langle D_i|U(t)|\psi_0,D_\Omega\rangle\langle \psi_0,D_\Omega|U^\dagger(t))$$But QM doesn't insist upon the decomposition. Take for example some complementary observable ##B=\sum_ib_i|b_i\rangle\langle b_i|## that the device doesn't measure. We can write the same evolution as $$U(t)|\psi_0,D_\Omega\rangle = \sum_ic_iU(t)|b_i,D_\Omega\rangle = \sum_ic_i|D'_i\rangle$$We then consider the projective decomposition
$$I_{s+D}=\sum_i|D'_i \rangle \langle D'_i|$$and QM will return probabilities for these "outcomes" occurring. Interactions with the environment will explain why this decomposition is not a decomposition into pointer states of the detector, but it doesn't explain why events constructed from this decomposition don't occur.

Normally this is where a Heisenberg cut is introduced. The device is classical, and the projective decomposition ##\sum_i|D_i\rangle\langle D_i|## reproduces the classical characteristics of the device that the experimenter reads off as data. I think this is fine, as I am not aware of any instance where such a procedure is ambiguous. But there is an alternative approach. The outcomes ##\{D'_i\}## are complementary to ##\{D_i\}##, but complementary is subtly different from mutually exclusive. An example of mutually exclusive outcomes would be ##D_i## and ##D_j## where ##j\neq i##, an example wouldn't be ##D_i## and ##D'_j##. An observer making note of one of the events ##\{D_i\}## doesn't preclude any of the events ##\{D'_i\}##. Instead we say a description that includes an observer making note of one of the events ##\{D_i\}## preculdes a description that includes an event from ##\{D'_i\}##. QM does not select one description as more correct than the other. Instead, the experimenter selects one description as more useful than the other: namely, the description that includes the pointer observable they are capable of reading.

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Fra

Gold Member
QM does not select one description as more correct than the other. Instead, the experimenter selects one description as more useful than the other: namely, the description that includes the pointer observable they are capable of reading.
If so, then the experimenter herself, i.e. her capability of reading, cannot be explained by QM. In other words, this means that QM is incomplete.

physika
Gold Member
If so, then the experimenter herself, i.e. her capability of reading, cannot be explained by QM. In other words, this means that QM is incomplete.
We could in principle include the observer in our model Hamiltonian. It would be a challenge, but it would also be a challenge in classical physics. Once we did, the dynamics of our theory would determine what detector properties can be selected by the environment and propagated to, and can be made intelligible by, the observer.

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Gold Member
We could in principle include the observer in our model Hamiltonian. It would be a challenge, but it would also be a challenge in classical physics. Once we did, the dynamics of our theory would determine what detector properties can selected by the environment and propagated to, and can be made intelligible by, the observer.
I don't think that it is really necessary to include the observer in the model. In most cases it is sufficient to include a macroscopic apparatus, or simply the environment. In this way decoherence theory makes concrete predictions about the preferred basis in practice, not merely in principle.

PeroK
Gold Member
I don't think that it is really necessary to include the observer in the model. In most cases it is sufficient to include a macroscopic apparatus, or simply the environment. In this way decoherence theory makes concrete predictions about the preferred basis in practice, not merely in principle.
I'm not sure what you mean by her capability of reading can't be explained by QM. In the same way that the dynamics between the apparatus and the system of measurement ensure the pointer states record observable ##A##, dynamics would also explain why she can read the pointer states and not the a non-pointer state like ##|D'_i\rangle##

CoolMint
Decoherence is not enough to explain single outcomes. The microchip industry is dealing with these issues as just having decoherence does not remove leaks across gates.
Measurement is what brings single outcomes on top of decoherence however measurement cannot be introduced into leaky 2nm chips. At present at least.
Measurement is what kills quantumness very effectively.

physika
Fra
QM does not select one description as more correct than the other. Instead, the experimenter selects one description as more useful than the other: namely, the description that includes the pointer observable they are capable of reading.
As i see it, the quantum mechanical description always has an implicit observer. So in your example I see the choice of basis of the experimenter as part of defining the state of the observer. The environment including its "choices" define the quantum picture.

/Fredrik

Simple question
Fra
We could in principle include the observer in our model Hamiltonian.
But this is a change of position. This implicitly means describing the original observer from the perspective of another ("bigger") observer. That other observer have similar choices, so it pushes the problem out to an asymptotic one instead of dealing with the core issue.

/Fredrik

Gold Member
I'm not sure what you mean by her capability of reading can't be explained by QM.
I don't think that it can't be explained by QM, indeed I think it can. But it looked to me that one of your claims implied that it can't. In the next post you explained that it doesn't follow, with which I agreed, but I also pointed out that observers (her ability of reading) are not really important because the preferred basis can be explained even without invoking observers.

So to make the long story short, to explain the preferred basis, I think it is misleading to invoke a reference to observers. Not because they can't be invoked, but because it makes the discussion look more complicated than it really is.

CoolMint
As i see it, the quantum mechanical description always has an implicit observer. So in your example I see the choice of basis of the experimenter as part of defining the state of the observer. The environment including its "choices" define the quantum picture.

/Fredrik

When the observer gets entangled with the quantum system, they become one system. We can't just assume we are not entangled with the environment as this leads to contradiction.
This is the crux of the hard interpretational issue surrounding QM and measurement.
Everything is indefinite and entangled, yet when you take a look around, it appears it is not.
Who is wrong? QM or human intuition?

Fra
If so, then the experimenter herself, i.e. her capability of reading, cannot be explained by QM. In other words, this means that QM is incomplete.
In this particular sense I agree. But I think its not the ambition of the observer to "explain itself". How could it possibly?

This is why I come to the stance that the situation is one of incremental learning. The only for an observer to "put itself to test" is to enter the quantum game. The enviroment will tear apart any unfit agents. QM is then seen as rational inference - given the unavoidable incompleteness.

/Fredrik

Fra
When the observer gets entangled with the quantum system, they become one system. We can't just assume we are not entangled with the environment as this leads to contradiction.
This is the crux of the hard interpretational issue surrounding QM and measurement.
Everything is indefinite and entangled, yet when you take a look around, it appears it is not.
Who is wrong? QM or human intuition?
The one looking around has one reduced view only. The view where all is entangled... who is that observer? What is its mass for example? What i think is wrong is "views" based on fictive perspectives of asymptotic observers. QM is not corroborated for those observers at that scale so nothing need to violated qm in its domain of validity. This has more todo with taking principles outside the domain of empirical support and see what absurd situationams that may happen in principle.

/Fredrik

Gold Member
I don't think that it can't be explained by QM, indeed I think it can. But it looked to me that one of your claims implied that it can't. In the next post you explained that it doesn't follow, with which I agreed, but I also pointed out that observers (her ability of reading) are not really important because the preferred basis can be explained even without invoking observers.

So to make the long story short, to explain the preferred basis, I think it is misleading to invoke a reference to observers. Not because they can't be invoked, but because it makes the discussion look more complicated than it really is.
What I'm trying to address in this thread is the insufficiency of decoherence in explaining the occurrence of events in QM implied by the preferred basis, rather than the preferred basis itself. I.e. You can cite Zurek et al to show how environment selects a basis, but a skeptic would say "So what? QM can still return probabilities for events constructed from other bases". Associating real events with the preferred basis in QM is not automatically justified, and I understood this to be the ad hoc character A. Neumaier was referring to. From the tl;dr
Decoherence will select a preferred basis for the experiment, but does not explain why events associated with that basis occur vs events associated with other bases.

mattt, gentzen and Demystifier
Gold Member
What I'm trying to address in this thread is the insufficiency of decoherence in explaining the occurrence of events in QM implied by the preferred basis, rather than the preferred basis itself.
I agree that decoherence alone is insufficient. Something more has to be assumed. This is also well explained in https://arxiv.org/abs/1210.8447.

Gold Member
I agree that decoherence alone is insufficient. Something more has to be assumed. This is also well explained in https://arxiv.org/abs/1210.8447.
That is true, but it seems to me that Morbert wants to explain something else. Doesn't that paper just points out that a Hilbert space by itself does not define a spacetime structure? (Or rather an "enviroment"-structure to be used as input for the construction of a prefered basis by decoherence.) That the claim that such a structure would emerge from a Hilbert space + a Hamiltonian is just as ridiculous as to claim that a σ-algebra + a probability measure + a permutation on the ground set would be enough in classical physics to define a spacetime structure?

Morbert on the other hand accepts that a spacetime (or "enviroment") structure is given, and that this gives you some preferred basis. But his point is that this is still not enough to get unique measurement results (especially not with respect to that still somehow arbitrary basis).

Demystifier, mattt and Morbert
Gold Member
Morbert on the other hand accepts that a spacetime (or "enviroment") structure is given, and that this gives you some preferred basis. But his point is that this is still not enough to get unique measurement results (especially not with respect to that still somehow arbitrary basis).
Yeah. I'm starting from the position that, once a sample space is taken for granted, a unique outcome occurs. The mutual exclusivity of elements in a sample space is respected, as QM says the probability of two outcomes from the same sample space occurring is 0 (##\mathrm{tr}(\Pi_i\Pi_j\rho) = 0, i \neq j##). The problem is outcomes belonging to different sample spaces are not mutually exclusive, and it's here where uniqueness of outcome becomes an issue. (And unlike in classical physics, you can't resolve the issue by adjusting the granularity of your sample space).

 - reading back over my original post, I conflate event with outcome, which is unfortunate, but hopefully didn't cause too much confusion

Fra and gentzen