High School Where does a quantum experiment *begin*?

[vanhees71]

To add to David Lewis's post above, the whole of this quote from vanhees71 is wrong.

In short, I object to attacks on Many-Worlds or Bohmian Mechanics (or other approaches to the measurement problem) based on incorrect Minimal Interpretations.

I don't have an opinion on many worlds. I never understood its point. Just to claim the universe splits at each measurement or observation into many unobservable new universes, is just empty. It's nothing physically observable. Otherwise it doesn't provide anything new concerning the observable predictions of QT. Bohmian mechanics is similar. It introduces trajectories of particles in non-relativistic quantum theory that are not observable either. There's no merit to calculate them. Also there is no convincing Bohmian interpretation for relativistic QFT.

 

[Demystifier]

There is no accepted proof that collapse is the same as the classical Bayesian update (without "nontrivial" additional assumptions).

In fact, there is a proof of something opposite. The PBR theorem and its variations shows that wave function is something more than (the square root of) epistemic probability.

 

[Demystifier]

The collapse in the usual meaning of textbooks claims that the interaction of the measured system with the measurement device (a local interaction according to local relativistic QFT) acts instantaneously over the entire space,

It would be nice to have an exact quote from some standard textbook. Could you give some?

 

[Demystifier]

I don't have an opinion on many worlds. I never understood its point. Just to claim the universe splits at each measurement or observation into many unobservable new universes, is just empty. It's nothing physically observable. Otherwise it doesn't provide anything new concerning the observable predictions of QT. Bohmian mechanics is similar. It introduces trajectories of particles in non-relativistic quantum theory that are not observable either. There's no merit to calculate them. Also there is no convincing Bohmian interpretation for relativistic QFT.

Classical general relativity does something similar. It claims that behind horizon (either black-hole horizon or cosmological horizon) there is a lot of space (perhaps even infinite space in the cosmological case) which is completely unobservable to us. Does it mean that spaces behind horizons of classical general relativity are physically meaningless?

 

[Demystifier]

It's a bit like Ballentine - the nominal claim to support the minimal interpretation, but not the actual support of it.

Promoting minimal interpretation is like promoting non-existence of free will. You can promote it in abstract discussions of the deepest principles of nature, but as a human being you cannot think that way in all situations of practical interest. Whether one promotes it or not may depend on the level of discussion (fundamental vs practical).

Think of the sentence
"I decided to write a new argument why free will does not exist."
and note that it makes sense because it involves thinking at two different levels.

Similarly, the statement
"I have written a paper where I explain why minimal interpretation is good. The paper is in the tray."
makes sense for a similar reason.

 

[ddd123]

In fact, there is a proof of something opposite. The PBR theorem and its variations shows that wave function is something more than (the square root of) epistemic probability.

Could the Bayesian inference be intended as referring to measurement outcomes instead of the physical underlying states (whether psi is ontic or epistemic)? In that case the PBR theorem doesn't apply.

 

[Demystifier]

Could the Bayesian inference be intended as referring to measurement outcomes instead of the physical underlying states (whether psi is ontic or epistemic)? In that case the PBR theorem doesn't apply.

Nobody said that psi cannot be used as a Bayesian tool. It can. But the PBR theorem shows that psi contains also something more than that. This is like showing that swiss knife is something more than a knife, which does not stop you from using it only as a knife.

 

[vanhees71]

It would be nice to have an exact quote from some standard textbook. Could you give some?

In nearly any introductory textbook you find the collapse postulate, i.e., it says that if you make a measurement of an observable $A$ and find a value $a$ which is necessarily in the spectrum of the representing self-adjoint operator $\hat{A}$ and if $|a,\beta \rangle$ is a complete orthonormal basis of the eigenspace to $a$ and the system as been prepared in the state represented by $|\psi \rangle$, then after the measurement the system is immediately in the state
$$|\psi' \rangle = \sum_{\beta} |a,\beta \rangle \langle a,\beta|\psi \rangle.$$

 

[vanhees71]

Classical general relativity does something similar. It claims that behind horizon (either black-hole horizon or cosmological horizon) there is a lot of space (perhaps even infinite space in the cosmological case) which is completely unobservable to us. Does it mean that spaces behind horizons of classical general relativity are physically meaningless?

That's a good question. It's not observable in principle. So it's irrelevant for physics. Whether or not the prediction of GR that these regions of space time exist, cannot be checked by experience. That doesn't invalidate GR as long as anything predicted that's observable is not ruled out by observation.

 

[martinbn]

There is a difference though. In general relativity the space-time may contain causally disconnected regions, but the space-time itself is connected. At least those if physical interest. In the many world interpretation it seems that the worlds are completely disjoint.

 

[Demystifier]

In nearly any introductory textbook you find the collapse postulate, i.e., it says that if you make a measurement of an observable $A$ and find a value $a$ which is necessarily in the spectrum of the representing self-adjoint operator $\hat{A}$ and if $|a,\beta \rangle$ is a complete orthonormal basis of the eigenspace to $a$ and the system as been prepared in the state represented by $|\psi \rangle$, then after the measurement the system is immediately in the state
$$|\psi' \rangle = \sum_{\beta} |a,\beta \rangle \langle a,\beta|\psi \rangle.$$

Yes, but exact words are very important in this context. For instance, in the explanation above you don't mention that collapse has anything to do with interaction, while in another post you do. Similarly, in the explanation above you use the word "immediately", while some textbook may not use that word. It also matters whether one talks about "measurement" or about "observation". Depending on the exact words, the connotations may take different flavors.

 

[Demystifier]

In the many world interpretation it seems that the worlds are completely disjoint.

Not really. First, they are fully connected in the past. Second, even in the future the overlap of the two worlds exponentially decreases with time, so it is very small but not exactly zero. Third, even this exponential law is only an approximation, and after a very very long time (essentially the Poincare recurrence time for the many-body Schrodinger equation) the two worlds may join together again.

One of the most frequent misconceptions about many worlds is that this interpretation postulates that wave function splits at measurements. In reality, there is no such postulate. The only explicit postulate is the Schrodinger equation, while the split is derived from the Schrodinger equation.

 

[martinbn]

That confuses me. What exactly is a world in MWI? I assumed it is literally a space, so after the measurement there is a family of disjoint spaces. For example take a particle that has wave function that is the superposition of localized in region A and localized in region B. I make a measurement and detect it in region A. What is the description in MWI? I thought it is that now there are two separate particles in two separate spaces each in the corresponding region.

 

[Demystifier]

That's a good question. It's not observable in principle. So it's irrelevant for physics. Whether or not the prediction of GR that these regions of space time exist, cannot be checked by experience. That doesn't invalidate GR as long as anything predicted that's observable is not ruled out by observation.

Fair enough. But then also other worlds of MWI and unmeasurable trajectories of Bohmian mechanics (BM) do not invalidate MWI and BM, as long as anything predicted by MWI and BM that's observable is not ruled out by observation. You will ask: Yes, but what's the motivation for introducing other words or unobservable trajectories in the first place? And my answer is: What's the motivation for introducing spaces behind the horizon in the first place?

 

[Demystifier]

That confuses me. What exactly is a world in MWI? I assumed it is literally a space, so after the measurement there is a family of disjoint spaces. For example take a particle that has wave function that is the superposition of localized in region A and localized in region B. I make a measurement and detect it in region A. What is the description in MWI? I thought it is that now there are two separate particles in two separate spaces each in the corresponding region.

No. In MWI, particles do not have wave functions. In fact, particles do not exists at all in MWI. According to MWI, there is only a wave function and nothing but the wave function. Only one wave function, not many wave functions. However, evolution by Schrodinger equation is such that wave function often splits into branches, such that the overlap between the branches is very small. When the overlap is small, then each branch can approximately be thought of as an object by its own, not depending on the existence of other branches. In this case, each branch can approximately be thought of as a separate "world". That's what the world in MWI is.

 

[martinbn]

No. In MWI, particles do not have wave functions. In fact, particles do not exists at all in MWI. According to MWI, there is only a wave function and nothing but the wave function. Only one wave function, not many wave functions. However, evolution by Schrodinger equation is such that wave function often splits into branches, such that the overlap between the branches is very small. When the overlap is small, then each branch can approximately be thought of as an object by its own, not depending on the existence of other branches. In this case, each branch can approximately be thought of as a separate "world". That's what the world in MWI is.

What is the relation of this to experiments and observation? Can you phrase the example above in MWI? Also what happened to space and time? When you say that there is only a wave function and nothing else, it seems meaningless.

 

[Demystifier]

What is the relation of this to experiments and observation? Can you phrase the example above in MWI?

Can you be more specific, which example do you have in mind?

Also what happened to space and time? When you say that there is only a wave function and nothing else, it seems meaningless.

Well, like any other function in mathematics, the wave function is a map from a domain D to a codomain C. The space and time are in D. (I'm sure you will appreciate such a Bourbaki-like answer. )

 

[vanhees71]

Well, for a N-body system the wave function's domain is $\mathbb{R}^{6N+1}$ and $C=\mathbb{C}$.

 

[martinbn]

Can you be more specific, which example do you have in mind?

Well, like any other function in mathematics, the wave function is a map from a domain D to a codomain C. The space and time are in D. (I'm sure you will appreciate such a Bourbaki-like answer. )

The example from #103.

 

[Demystifier]

Well, for a N-body system the wave function's domain is $\mathbb{R}^{6N+1}$ and $C=\mathbb{C}$.

No, it's $\mathbb{R}^{3N+1}$.
And even $C=\mathbb{C}$ is not correct for systems with spin.
(I know you know that, I'm just splitting hairs. )

 

[martinbn]

(I know you know that, I'm just splitting hairs. )

But do you split worlds or not?

 

[Demystifier]

But do you split worlds or not?

Me? No. I'm just explaining what do world splitters do.

 

[vanhees71]

True. Sorry, but I still don't get why I should introduce "many worlds". While causally disjoint regions of GR spacetime are unavoidable, I don't need unobservable many worlds in QT to make physics out of the mathematical formalism. You have a plethora of examples in theoretical physics, where you have unobservable mathematical elements, e.g., the vector potential in classical electrodynamics. It's unobservable (and thus "unphysical") but simplifying the calculations, but I think we are splitting hairs indeed, and we are once more far from discussing relevant physics, which brings me again to my idea to split off the philosophical discussions of the qmech subforum.

 

[Demystifier]

While causally disjoint regions of GR spacetime are unavoidable, I don't need unobservable many worlds in QT to make physics out of the mathematical formalism.

But multiple wave-function branches with a negligible overlap are a prediction of Schrodinger evolution for systems with many degrees of freedom. They are unavoidable just as disjoint regions of GR spacetime are unavoidable. The only controversial part is whether all these mathematical branches are ontic or epistemic. In minimal interpretation they are epistemic. In MWI they are ontic. In Bohmian interpretation they are something in between. But as mathematical objects they are an unavoidable part of the theory in all interpretations.

 

[vanhees71]

I don't care whether it's ontic or epistemic. For me mathematical objects in physical theories are epistemic anyway. It's completely irrelevant for physics.

 

[Demystifier]

The example from #103.

That's in fact a standard example to describe the idea of MWI. I will assume that you are familiar with the bra-ket notation.

The measured system in the superposition can be written as
$$|\psi\rangle = |\psi_A\rangle + |\psi_B\rangle$$

But this cannot be a full description, because there is also a macroscopic measuring apparatus. The measuring apparatus can be in 3 different states:
$|\phi_0\rangle$ - the apparatus does not show any result (e.g. because it is turned off).
$|\phi_A\rangle$ - the apparatus shows that the "particle" is in region $A$.
$|\phi_B\rangle$ - the apparatus shows that the "particle" is in region $B$.
These 3 states are macroscopically distiniguishable so their overlaps are negligible, e.g.
$$\langle\phi_A|\phi_B\rangle \approx 0$$

Taking the measuring apparatus into account, the full state at the initial time $t_0$ is
$$|\Psi(t_0)\rangle = (|\psi_A\rangle + |\psi_B\rangle) |\phi_0\rangle $$
At this point there is no yet "world splitting". But at later time $t_1$ the state evolves into
$$|\Psi(t_1)\rangle = |\psi_A\rangle |\phi_A\rangle+ |\psi_B\rangle |\phi_B\rangle $$
The macroscopic branches $|\Psi_A\rangle =|\psi_A\rangle |\phi_A\rangle$ and $|\Psi_B\rangle =|\psi_B\rangle |\phi_B\rangle$ have a negligible overlap
$$\langle\Psi_A|\Psi_B\rangle \approx 0$$
so they can be thought of as separate "worlds". That's the essence of MWI.

 

[Demystifier]

I don't care whether it's ontic or epistemic. For me mathematical objects in physical theories are epistemic anyway. It's completely irrelevant for physics.

But then space behind the horizon in GR is epistemic, other worlds in MWI are epistemic, and non-measurable trajectories in BM are epistemic. By what general criteria is the first more "physical" than the second or the third?

 

[vanhees71]

Physical is what's observable.

 

[Demystifier]

Physical is what's observable.

So neither space behind cosmological horizon of GR nor other worlds of MWI are physical. Yet, somehow you feel that space behind horizon is more "acceptable" than other worlds of MWI. Still, you cannot explain why exactly do you feel so. Am I right?

 

[martinbn]

That's in fact a standard example to describe the idea of MWI. I will assume that you are familiar with the bra-ket notation.

The measured system in the superposition can be written as
$$|\psi\rangle = |\psi_A\rangle + |\psi_B\rangle$$

But this cannot be a full description, because there is also a macroscopic measuring apparatus. The measuring apparatus can be in 3 different states:
$|\phi_0\rangle$ - the apparatus does not show any result (e.g. because it is turned off).
$|\phi_A\rangle$ - the apparatus shows that the "particle" is in region $A$.
$|\phi_B\rangle$ - the apparatus shows that the "particle" is in region $B$.
These 3 states are macroscopically distiniguishable so their overlaps are negligible, e.g.
$$\langle\phi_A|\phi_B\rangle \approx 0$$

Taking the measuring apparatus into account, the full state at the initial time $t_0$ is
$$|\Psi(t_0)\rangle = (|\psi_A\rangle + |\psi_B\rangle) |\phi_0\rangle $$
At this point there is no yet "world splitting". But at later time $t_1$ the state evolves into
$$|\Psi(t_1)\rangle = |\psi_A\rangle |\phi_A\rangle+ |\psi_B\rangle |\phi_B\rangle $$
The macroscopic branches $|\Psi_A\rangle =|\psi_A\rangle |\phi_A\rangle$ and $|\Psi_B\rangle =|\psi_B\rangle |\phi_B\rangle$ have a negligible overlap
$$\langle\Psi_A|\Psi_B\rangle \approx 0$$
so they can be thought of as separate "worlds". That's the essence of MWI.

But this is just quantum mechanics. The interpretation is supposed to say what a world is and what it means for them to be thought as separate.

It seems that these are just words, which are useless and misleading.