Locality and Wave Function Collapse Implications

[The Head]

OK, so I'm trying to work out a few ideas regarding locality. I've studied at the undergrad level in the past (including quantum), but with professors that slaved away at proving math constructs and never bothered to indulge in clarifying the context of any concepts, so I'm pretty weak here.

From how I understand the Copenhagen Interpretation, the wave-function does not exist physically in space-time before a measurement (it rejects realism), otherwise the principle of locality would be violated when the wave-function collapses due to measurement. And I take this to mean that this is why locality isn't violated when we consider entangled particles.

If that's all reasonably correct, my question is, if the wave-function isn't something physically real and is just a mathematical tool to help us figure out probabilities, then what is the measurement device actually interacting with? We have physical things that cause collapse of a non-physical entity into a physical, localized particle (e.g., a photon).

For example, in the case where a photon could go traverse one of two distinct paths, it goes through both in a way in the form of a wave/probability distribution. Is energy actually moving through both paths, and this is what interacts with the detector? Or perhaps it's something else that causes collapse.

Appreciate any help. Trying to make this as concrete as possible.

 

[atyy]

You can treat the wave function as physically real. However, you don't have to believe that it is physically real, ie. you treat it as physically real for the purpose of making correct predictions of the probabilities of measurement outcomes.

In the standard interpretation of quantum mechanics, an observer or measurement device is required. The observer and measurement device are real real, and the wave function is fake real. A measurement outcome occurs when the measurement device interacts with the wave function. The absurd thing is not the reality of the wave function per se (which is open to interpretation), but the idea that we need to give the observer or measurement device a special status, when intuitively it should just be another physical system. Trying to remove the special status of the measurement device is called the "measurement problem".

Bohmian Mechanics is a conjecture, but fairly coherently worked out way of seeing how the measurement problem might be solved for non-relativistic quantum mechanics.

 

[jfizzix]

To answer whether or not the energy is actually moving through both paths at once is a challenge to say the least, as the only think quantum physics is equipped to describe is the measurement statistics of experiments.

However, there are only four possibilities: (first path, second path, both paths, neither path).

We can rule out (first path, second path) by performing interference experiments where we change the length of a given path and change the interference pattern. If the interference pattern changes when we change the length of a path, the light must be going through it.
We can also rule out (neither path) by designing the experiment so that the two paths are the only possible paths for light to travel from source to detector.

By process of elimination, we have that the light must travel both paths at once. At least, we have this, so long as our assumptions entering into this make sense. Trying to use simple arguments like this on quantum-mechanical concepts is iffy, since the question only has a definite answer of an experiment can be conceived that can test it.

 

[The Head]

Thanks very much for both of your replies. Regarding the question of what the measuring device is actually interacting with, is the measurement problem responsible for being unable to answer this? If so, I suppose responding to this question really only exposes one's beliefs on locality and realism.

It makes sense that we could treat the WF as real, but in the case that it's not actually a physical thing, I am pretty mystified about what could potentially be going on. It's an intriguing concept, but really begs the question of what could be interacting.

After just seeing the math for so often and repeating the process frequently, I began to believe it meant something that made sense. But looking at it with fresh eyes, I'm missing something fundamental. Not sure if that's because the answer isn't available yet or I'm simply not getting it.

 

[atyy]

Thanks very much for both of your replies. Regarding the question of what the measuring device is actually interacting with, is the measurement problem responsible for being unable to answer this? If so, I suppose responding to this question really only exposes one's beliefs on locality and realism.

It makes sense that we could treat the WF as real, but in the case that it's not actually a physical thing, I am pretty mystified about what could potentially be going on. It's an intriguing concept, but really begs the question of what could be interacting.

After just seeing the math for so often and repeating the process frequently, I began to believe it meant something that made sense. But looking at it with fresh eyes, I'm missing something fundamental. Not sure if that's because the answer isn't available yet or I'm simply not getting it.

You have to remember that the wave function is in Hilbert space (or "everywhere"), ie. an object that has a wave function is not typically assigned a position in space. However, the measurement apparatus is treated "classically" or "intuitively", so it has a position in space. I think it is fine (for all practical purposes) to think of the wave function as real, and to imagine that the measurement occurring when the measurement appratus interacts with the wave function, but you have to remember that the wave function is not "there" in space.

Famous article by Bell about the measurement problem:
https://m.tau.ac.il/~quantum/Vaidman/IQM/BellAM.pdf

 

[atyy]

From how I understand the Copenhagen Interpretation, the wave-function does not exist physically in space-time before a measurement (it rejects realism), otherwise the principle of locality would be violated when the wave-function collapses due to measurement.

The reason to be ambivalent about the reality of the wave function is not locality. There are 2 sorts of locality: local realism and signal locality. Local realism is dead, whether the wave function is real or not. Signal locality is preserved, whether the wave function is real or not.

The ambivalence about the reality of the wave function stems from the idea that measurement has a special status in QM, and that it makes predictions only about measurement outcomes. So if QM must be used by an observer, then maybe there is no wave function if there are no observers.

The absurdity of measurement-induced collapse contributes to the ambivalence.

However, strictly speaking, the standard interpretation does not care whether the wave function is real or not. It will work either way. And the problem of measurement is in the standard interpretation whether you believe the wave function to be real or not.

 

[The Head]

The reason to be ambivalent about the reality of the wave function is not locality. There are 2 sorts of locality: local realism and signal locality. Local realism is dead, whether the wave function is real or not. Signal locality is preserved, whether the wave function is real or not.

The ambivalence about the reality of the wave function stems from the idea that measurement has a special status in QM, and that it makes predictions only about measurement outcomes. So if QM must be used by an observer, then maybe there is no wave function if there are no observers.

The absurdity of measurement-induced collapse contributes to the ambivalence.

However, strictly speaking, the standard interpretation does not care whether the wave function is real or not. It will work either way. And the problem of measurement is in the standard interpretation whether you believe the wave function to be real or not.

Thank you once again for the thoughtful reply. I'm letting these concepts sink in (slowly). and will read the Bell article.

Regarding measurement, you mention the possibility of a WF requiring observers. Is this separate from something that simply interacts with the WF, like a measuring device with no computation displayed? From what I can tell, a measurement being made does not require something (consciously) observing to collapse the WF. Or is the statement you're making with observers slightly stronger in this case?

 

[atyy]

Thank you once again for the thoughtful reply. I'm letting these concepts sink in (slowly). and will read the Bell article.

Regarding measurement, you mention the possibility of a WF requiring observers. Is this separate from something that simply interacts with the WF, like a measuring device with no computation displayed? From what I can tell, a measurement being made does not require something (consciously) observing to collapse the WF. Or is the statement you're making with observers slightly stronger in this case?

QM does not state what exactly a measurement device or an observer is. The special status of a measurment device is needed in QM, because there are no measurement outcomes or events that really happen, in the sense that they are invariant occurrences in spacetime in the sense of classical special relativity until a measurement has occurred. You can see this in the Born rule, which begins "When a measurement of an observable occurs ...".

Since an event is something that really happens in the sense of classical special relativity, it is associated with some notion of "macroscopic irreversibility" or "macroscopic definiteness" or a "definite outcome" as opposed to before a measurement we don't know whether the cat is dead or alive, or in some strange superposition of dead and alive. In the formalism, this is enforced by the irreversibility of wave function collapse when we need to calculate the probabilities of successive events.

However, the wave function collapse itself is not an invariant event in the sense of classical special relativity, since the same probabilities for events that are invariant can be calculated in different frames, even though each frame places the collapse on a different slice of spacetime. So if the wave function is real, it can be real in only one frame, which means it would be an invisible aether. See Figure 1 of https://arxiv.org/abs/0706.1232.

 

[martinbn]

I clarifying question. What is an invariant event?

...an invariant event in the sense of classical special relativity...