Does the bomb experiment do a measurement?

[Rene Dekker]

TL;DR Summary

The Elitzur–Vaidman bomb experiment allows detecting the "live" status of a "bomb" without anything interacting with it. Can a similar mechanism be used to measure a quantum property without affecting it?

In short, the Elitzur–Vaidman bomb experiment consists of a Mach–Zehnder interferometer, where a bomb is placed in one of the paths (I used the wikipedia description https://en.wikipedia.org/wiki/Elitzur–Vaidman_bomb_tester, and Sabine Hossenfelder's video: )
The bomb can be live or a dud. When it is a dud, any photon passes right through it. If it is live, then any photon hitting it will cause it to explode.
Due to the setup in the interferometer, it is actually possible to detect that the bomb is live with no photon interacting with it (the photon "takes the other path").

In general that sounds like a way to measure something without affecting it, which is supposed to be impossible in quantum mechanics. Therefore my question:
If we would use, instead of the bomb, some particle in a superposition of states. What would happen to the particle in that case, would it collapse into a determinate state? That is, would the non-interaction with the photon count as a measurement that collapses the wave function?

 

[Demystifier]

In general that sounds like a way to measure something without affecting it, which is supposed to be impossible in quantum mechanics. Therefore my question:
If we would use, instead of the bomb, some particle in a superposition of states. What would happen to the particle in that case, would it collapse into a determinate state? That is, would the non-interaction with the photon count as a measurement that collapses the wave function?

In the bomb experiment, we measure a classical macroscopic property of the bomb. Macroscopic properties are not affected by measurement because macroscopic properties are redundant, in the sense that the same information is repeated many times, so if you destroy information once you still can see the information. For example, suppose that you have a macroscopic object, made of many atoms, at a well defined macroscopic position. If you change the position of one of the atoms, it will not significantly affect the position of the object as a whole.

And this answers your question. If the bomb was replaced with a single particle in a quantum state, it would not work as for the macroscopic bomb. Either the state of the particle would "collapse" (which is analogous to the bomb explosion), or the test photon would not be affected by the particle at all, so we would not get any new information about the particle (which makes the particle different from the bomb, because in the bomb case we can learn that the bomb is working even though it didn't explode).

Note, however, that the "collapse" does not happen due to interaction between photon and the particle. Their interaction creates entanglement between them, but not the collapse. The "collapse" happens in the photon detector, where a macroscopic apparatus (the detector) measures the "position" of the photon. By measuring the state of the photon we also learn about the state of the particle, and it is this learning that that we call "collapse" of the particle state.

 

[Nugatory]

In general that sounds like a way to measure something without affecting it, which is supposed to be impossible in quantum mechanics.

When we speak of the E-V bomb tester making a “measurement” we’re using the word in a different sense than when we speak of “measurement” in quantum mechanics. So there’s no contradiction with any principle of quantum mechanics here, just another example of the gap between common usage and the specialized vocabulary of QM.

If we would use, instead of the bomb, some particle in a superposition of states. What would happen to the particle in that case, would it collapse into a determinate state? That is, would the non-interaction with the photon count as a measurement that collapses the wave function?

Every particle is always in a superposition of states in some basis, and the post-collapse state of a quantum system is no less “determinate” than the pre-collapse state - it’s just a different determinate state. So the “what would happen?” question cannot be answered without a more complete specification of the experimental setup and what we’re measuring. However, collapse is by definition the result of an interaction so we can say that if there is no interaction there is no collapse and no measurement.

That last sentence uses the word “measurement” with its specialized meaning, not in the sense that you used it in your original post.

(Edit to add: and this thread attracts no response for almost twelve hours and then Demystifier and I both post responses within minutes of one another…. )

 

[Rene Dekker]

In the bomb experiment, we measure a classical macroscopic property of the bomb. Macroscopic properties are not affected by measurement because macroscopic properties are redundant, in the sense that the same information is repeated many times, so if you destroy information once you still can see the information. For example, suppose that you have a macroscopic object, made of many atoms, at a well defined macroscopic position. If you change the position of one of the atoms, it will not significantly affect the position of the object as a whole.

And this answers your question. If the bomb was replaced with a single particle in a quantum state, it would not work as for the macroscopic bomb. Either the state of the particle would "collapse" (which is analogous to the bomb explosion), or the test photon would not be affected by the particle at all, so we would not get any new information about the particle (which makes the particle different from the bomb, because in the bomb case we can learn that the bomb is working even though it didn't explode).

Note, however, that the "collapse" does not happen due to interaction between photon and the particle. Their interaction creates entanglement between them, but not the collapse. The "collapse" happens in the photon detector, where a macroscopic apparatus (the detector) measures the "position" of the photon. By measuring the state of the photon we also learn about the state of the particle, and it is this learning that that we call "collapse" of the particle state.

Thanks for the answer. To paraphrase, you say that the photon wave function travels both paths, and is therefore entangled with the particle wave function. Due to that entanglement, the wave function of the particle will collapse when the photon is measured.
Is that a correct summary?

 

[Rene Dekker]

When we speak of the E-V bomb tester making a “measurement” we’re using the word in a different sense than when we speak of “measurement” in quantum mechanics. So there’s no contradiction with any principle of quantum mechanics here, just another example of the gap between common usage and the specialized vocabulary of QM.

Well, the photon appearing in the right detector still gives us which-path information of the photon. And that in turn, gives information about whether it is theoretically possible for the photon to interact with the bomb. I don't understand how that conceptually differs from a direct (QM) measurement on the bomb.

Every particle is always in a superposition of states in some basis, and the post-collapse state of a quantum system is no less “determinate” than the pre-collapse state - it’s just a different determinate state. So the “what would happen?” question cannot be answered without a more complete specification of the experimental setup and what we’re measuring. However, collapse is by definition the result of an interaction so we can say that if there is no interaction there is no collapse and no measurement.

So are you saying that the particle wave-function would not collapse in this experiment, even though we extract information about the particle?

(Edit to add: and this thread attracts no response for almost twelve hours and then Demystifier and I both post responses within minutes of one another…. )

Maybe you two where entangled with each other?

Appreciate the answer.

 

[Demystifier]

Thanks for the answer. To paraphrase, you say that the photon wave function travels both paths, and is therefore entangled with the particle wave function. Due to that entanglement, the wave function of the particle will collapse when the photon is measured.
Is that a correct summary?

Yes.

 

[Rene Dekker]

Yes.

Great, thanks, I understand it better now.

 

[Nugatory]

I don't understand how that conceptually differs from a direct (QM) measurement

What you are describing is inferring properties of a macroscopic system (the bomb) from observations we've made. That is one traditional natural language meaning of the word "measurement", and it's what we're talking about when you say the E-Z bomb tester "measures" the bomb.

A direct quantum mechanical measurement is something that is represented mathematically as projecting the state (an abstract mathematical object in a complex infinite-dimensional Hilbert space) of the quantum system under measurement onto a subspace of that Hilbert space. That's something different.

It is an unfortunate historical accident that quantum physics has coopted the word "measurement" in this way, and it's not the only one - we see similar problems with "particle", "wave", "observation", "observer", "spin" - none of these mean what they do in normal conversation.