Where is the quantum system prior to measurement?

[jbergman]

Out of curiosity, is that statement formally true?

Assume $|L>$ be the state of an particle passing left slit and $|R>$ the right one. Then the projection operator onto the state $\frac {1} {\sqrt 2} (|L> +|R>)$ suffices the axiomatic requirements for an observable. Therefore we can (at least formally) measure that observable and thus in theory give an answer within the framework of the theory.

I believe you are correct. In other words, we can create an observable to measure whether or not the photon went through both slits or not.

Peter Shor discusses that here, https://physics.stackexchange.com/a/6861

 

[PeterDonis]

we can create an observable to measure whether or not the photon went through both slits or not.

That's not what the given observable measures. It measures whether the photon went through both slits in phase, or out of phase. The orthogonal state is $\frac{1}{\sqrt{2}} \left( \ket{L} - \ket{R} \right)$, so a "yes" measurement on the given observable means "went through both slits in phase" and a "no" measurement means "went through both slits out of phase". Neither one means "went through only one slit".

In other words, whether or not the photon "went through both slits" depends on what observable you choose to measure. If you choose to measure a "which-slit" observable, i.e., one in which a "yes" measurement means $\ket{L}$ and a "no" measurement means $\ket{R}$, then the photon went through just one slit. If you choose to measure the observable described by @Killtech, then the photon went through both slits.

 

[PeterDonis]

Peter Shor discusses that here, https://physics.stackexchange.com/a/6861

Shor is saying the same thing I said in post #142.

 

[vanhees71]

You can of course measure through which slit a single photon goes. However then you have to mark each photon somehow to imprint the corresponding which-way information.

One way to realize it is to start with a source of $\varphi=0$-polarized (where the photon momentum is assumed to be in $z$ direction and $\varphi$ is the angle of the polarization vector, which is in the $xy$-plane to the $x$ axis) photons and putting quarter-wave plates oriented $\pm \pi/4$ wrt. the $x$ axis. Then a photon going through the left slit is left-circular (helicity $h=+1$) and a photon going through the right slit is right-circular ($h=-1$) polarized. Thus indeed now you have an entanglement between the helicity of the photon and through which way it went:
$$|\psi \rangle=\frac{1}{\sqrt{2}} (|L,h=1 \rangle + |R,h=-1 \rangle).$$
The probability for registering the photon at a position $x$ on a far-distant screen is given by the correspondingly propagated state ket
$$|\psi' \rangle=\frac{1}{\sqrt{2}}(|\vec{k},h=1 \rangle + \exp[\mathrm{i} \phi(x)]|\vec{k},h=-1 \rangle ).$$
Here $\vec{k}$ is the momentum of the photon if it's registered at position $x$ behind the screen and $\phi(x)=k x d/L$ the phase shift between a photon's probability amplitudes going through the left or right slit. Since now the photon states with helicities $\pm 1$ are perpendicular to each other there is no interference term between "going through the L or R slit", i.e., there's no two-slit interference pattern (only a single-slit interference pattern, not taken into account in this schematic treatment).

If you just don't put the quarter-wave plates at the slits, the state at the screen is
$$|\psi' \rangle=\frac{1+\exp(\phi(x))}{|1+\exp(\phi(x))|}|\vec{k}, \varphi=0 \rangle$$
and you get an interference term.

That's an example what Bohr called the complementarity between having which-way information and thus in some very loose sense "particle properties" (no two-slit interference pattern) or having no which-way information and ("wave properties") (two-slit interference pattern).

 

[Lynch101]

Bohmian mechanics does, yes. But not MWI. MWI says that "the state of the system" is the wave function, period. That's all there is.

Ah yes, my apologies. I was thinking that because MWI was a fully deterministic interpretation that it implied that particle had well-defined positions at all times, but MWI says that branching occurs upon measurement.

And this, by itself, is just a statement of opinion, even for EPR. Others might have different opinions. There is no way to resolve such a dispute, so arguing about it is rather pointless.

It's not simply a matter of opinion. It's the application of basic principles of 3D modeling to the experimental set-ups and making inferences/deductions about the implications.

If an interpretation doesn't conform to these basic principles then this tells us something about its compatibility with the 3D model.

 

[vanhees71]

But that's a different and in my opinion the only physically sensible statement: The position of quantum systems are only determined by experimental setups (macroscopic detectors). All you can say about the quantum system's position before using this setup to measure it all you know, given the quantum state, the probability distribution for detecting the quantum system at the location defined by this measurement apparatus.

An extreme example are single-photon Fock states: Since the photon itself has no position observable in the usual sense all you know about it being prepared in such a single-photon Fock state is the probability to measure it at a location determined by the photon detector (e.g., a CCD cam/pixel detector, where the position is defined by the pixels, also defining the spatial resolution, which is always finite).

 

[Lynch101]

Again, the only system a physicist commits to is the preparation and the measurement outcome. You are supposing some additional process made intelligible by e.g. some physical state $\lambda$, distinct from the preparation $\rho$, which has a direct ontological interpretation at all times between the preparation and measurement.

Physicists also commit to the propagation of causal influences at a finite speed, don't they?

Let's put the system itself to one side for a moment. We can try to add it back in at the end.

We can start by creating a 3 dimensional model, basically just a model with the XYZ axes. We can then represent the experimental set-up within that model i.e. the preparation device, the screen with the slits, and the measurement apparatus. For this model to be representative of 'the physical reality' i.e. the physical experimental set-up in the lab, there must be something corresponding to 'the slits' in the screen at the noumenlogical level.

In our 3D model we can represent the 3D region where the preparation device is, together with the spatially separated 3D region where the measurement apparatus is. We can attempt to represent everything else in the universe within the 3D model. Essentially, if something operates within 3D dimensions we can represent it in our model, since our model doesn't allow anywhere to hide in those 3 dimensions.

Identifying the 3D regions, corresponding to the measurement apparatus and the preparation device, in our model we can ask the question. If something/anything starts in the finite 3D region of the preparation device and ends up in the 3D region of the measurement device, how does it get there? Well, it could just instantaneously go from preparation device to measurement apparatus, however, our 'no FTL propagation' prohibits this.

So, if it can't instantaneously go from one 3D region to the other, it must propagate, with a finite speed in the intervening 3D region.

Thinking about our screen now and how we represent it in the 3D model. We can represent it as a line which acts as a barrier between the two regions. When we do this, according to our model, there is no way to get from one region to another. When we put 'slits' in the 'screen' there are now possible routes between the two regions.

Given that there is nowhere to hide in our 3D model, something which starts in one region and ends up in the other, must follow some unique path through the intervening 3D region.Now, where does our quantum system fit into this? If we remain agnostic on the unique route taken, then our 3D model cannot be complete. If we say that it does not take a unique route then it doesn't fit within our 3D model and it must be propagating in other dimensions or instantaneously from one region to the other.

 

[Lynch101]

In case I understand you correctly, you are believing that a “complete” theory must provide some picturization as, for example: “… for something to get from the physical preparation device to the physical measurement device it must take a path through the intervening 3D region in the 'physical reality'.”

Why?

P. A. M Dirac in “THE PRINCIPLES OF QUANTUM MECHANICS” (third edition, page 10) :

"...the main object of physical science is not the provision of pictures, but is the formulation of laws governing phenomena and application of these laws to the discovery of new phenomena. If a picture exists, so much the better; but whether a picture exists or not is a matter of only secondary importance. In the case of atomic phenomena no picture can be expected to exist in the usual sense of the word 'picture', by which is meant a model functioning essentially on classical lines.“

The object of physical science may not be to draw pictures, however, we can still draw pictures and ask how the physical world conforms to those pictures - and make deductions/inferences accordingly.

If we model the universe in 3 dimensions, and our model is complete, we should be able to represent everything in the universe in 3D. From this 3D model we can infer rules about how anything operating within 3 dimensions must behave. Adding a 'no FTL propagation' principle we can say, for anything - operating within 3 dimensions - to propagate (with a finite speed) from one 3D region to another it must follow some unique path through the intervening 3D region. This is just what a 3D picture says must be the case.

If we do not, or can not specify the unique route taken by something which starts in the 3D region of the preparation device and ends up in the 3D region of the measurement device then either our model is not a complete description of 'the physical reality' i.e. what is happening in the physical experimental set-up or, the system which propagates from the preparation device to the measurement apparatus does not do so in 3 dimensions.Note: this unique path does not have to conform to our intuitive ideas of the system having a single, well-defined value at all times. It could be a mutli-valued path, it could occupy the entire 3D region, or any other such unique path. Remaining agnostic on this is what renders a description incomplete.

 

[Lynch101]

I think there are some interesting questions here but I am not sure I agree with your framing of them in terms of complete and incomplete.

Really, what you are positing is that a complete theory must provide some physical explanation of the wave function outside of the context of measurements.

In the double slit experiment, we cannot "measure" whether a particle passes through one slit or both slits. We only know that if we measure the particle going through a slit then the interference pattern disappears.

It might be better to say that a complete 3D model must specify the unique path taken by the system from one spatially separated region to another. At the very least, it must allow that some unique path (through the intervening 3D region) is taken.

Remaining agnostic would render it an incomplete 3D model.

So all we really know is that the wave function describes the probabilities we will measure for an ensemble of particles prepared in the same state.

Anything beyond that is speculation.

We don't need to speculate about the rules of our 3D model.

Where something begins in one 3D region and ends up in another, spatially distant 3D region and where no FTL propagation is permitted, it must take some unique route through the intervening 3D region. Remaining agnostic on what route is taken renders a 3D model incomplete. Saying that no unique route is taken implies other dimensions.

The minimal statistical interpretation appears to remain agnostic.

 

[WernerQH]

If we do not, or can not specify the unique route taken by something which starts in the 3D region of the preparation device and ends up in the 3D region of the measurement device then either our model is not a complete description of 'the physical reality' i.e. what is happening in the physical experimental set-up or, the system which propagates from the preparation device to the measurement apparatus does not do so in 3 dimensions.

I admire your persistence. It may not be obvious to you, but ironclad logic loses its force when a flawed assumption is included. You have achieved reductio ad absurdum of the idea that quantum theory can be understood in terms of quantum "objects" (or what you call "systems"). Probably you'll never be able to make sense of quantum theory.

 

[gentzen]

Remaining agnostic on what route is taken renders a 3D model incomplete.

then either our model is not a complete description of 'the physical reality'

I admire your persistence. It may not be obvious to you, but ironclad logic loses its force when a flawed assumption is included. ... Probably you'll never be able to make sense of quantum theory.

My impression is that Lynch101 ignores the connection of "complete description" with the original thermodynamical riddles: If there were a more complete description, then there must be more local degrees of freedom, but then you have to explain why those local degrees of freedom don't show up in the entropy.
OK, an atom actually has internal degrees of freedom, so why are those invisible in the entropy? Because their excitation energy is so high that they would only start to contribute to the entropy in a really really hot plasma.
But those unique paths he wants the interpretation to describe, why would those not constitute degrees of freedom, and why would those not show-up in the entropy?
OK, the de Broglie-Bohm interpretation actually has such paths, so why are those invisible in the entropy? Because those are not local degrees of freedom.

 

[Lynch101]

I admire your persistence. It may not be obvious to you, but ironclad logic loses its force when a flawed assumption is included. You have achieved reductio ad absurdum of the idea that quantum theory can be understood in terms of quantum "objects" (or what you call "systems"). Probably you'll never be able to make sense of quantum theory.

In effect all I have done is set out some very basic principles of 3D modelling. From this we can deduce/infer certain rules which must apply to anything which operates within such a model. One such rule relating to the propagation of anything from one region to another spatially separated region.

For a complete 3D model we should be able to represent everything in the universe at all times. If we don't specify i.e. remain agnostic on the unique path/route of propagation taken by anything within our 3D model then we are left with an incomplete 3D model. If we say that no unique path is taken, then either that 'thing' is not in the universe or it operates in other dimensions.

 

[PeterDonis]

It's not simply a matter of opinion. It's the application of basic principles of 3D modeling to the experimental set-ups and making inferences/deductions about the implications.

This claim about "basic principles of 3D modeling" is just your opinion.

Physicists also commit to the propagation of causal influences at a finite speed, don't they?

No. Not all interpretations of QM require causal influences to "propagate".

 

[PeterDonis]

I admire your persistence. It may not be obvious to you, but ironclad logic loses its force when a flawed assumption is included. You have achieved reductio ad absurdum of the idea that quantum theory can be understood in terms of quantum "objects" (or what you call "systems"). Probably you'll never be able to make sense of quantum theory.

And this seems like a good note on which to close the thread.