# Collapse of Wavefunction

This is with respect to the Elitzur–Vaidman bomb-tester. Where the of wavefunction of photon is going to collapse is not known accurately. It is said that a given photon takes both paths in the Mach-Zehnder interferometer and MAY collapse if it meets an obstacle (Bomb).

few questions:

1. Photon can take any path,can go even outside interferometer, and not necessarily a straight line. Is this correct ?
2. Is the description 'photon takes both paths' accurate ? Is it not just our inability predict with 100% accuracy where the photon is ?
3. Even if we agree that photon takes both paths and decides to collapse at one location, does the collapse have a physical meaning ?

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The way I see it: the bomb simply affects the wave function, and it is not too difficult to calculate how it affects it. That's all and that's simple. What more do we need?

Demystifier
Gold Member
The way I see it: the bomb simply affects the wave function, and it is not too difficult to calculate how it affects it. That's all and that's simple.
I agree with that.

What more do we need?
Problems appear when one attempts to identify the photon with its wave function. What we need is to understand what exactly the relation between the two is. Unfortunately, different interpretations of QM offer different answers. The EV bomb is an example where the differences between various interpretations become particularly clear.

Photon is an excited state (of a particular kind) of a quantized electromagnetic field.

Demystifier
Gold Member
Photon is an excited state (of a particular kind) of a quantized electromagnetic field.
A state is a state in a Hilbert space. A wave function is also (a representation of) a state in a Hilbert space. So, are you saying that photon should be identified with its wave function?

DrChinese
Gold Member
This is with respect to the Elitzur–Vaidman bomb-tester. Where the of wavefunction of photon is going to collapse is not known accurately. It is said that a given photon takes both paths in the Mach-Zehnder interferometer and MAY collapse if it meets an obstacle (Bomb).

few questions:

1. Photon can take any path,can go even outside interferometer, and not necessarily a straight line. Is this correct ?
2. Is the description 'photon takes both paths' accurate ? Is it not just our inability predict with 100% accuracy where the photon is ?
3. Even if we agree that photon takes both paths and decides to collapse at one location, does the collapse have a physical meaning ?
I think you have to take the superposition as the wave state being "real" i.e. physical. So what does that make the collapse? I wish I knew. If the collapse were physical, then what is the cause? After all, we know that an observation can be erased. So that implies there is no cause if the collapse can be reversed and the superposition restored.

If collapse is not physical, then I guess that means we live in one of many worlds. Or?

A state is a state in a Hilbert space.
Mathematical representation of a state is in a Hilbert space. State itself is different from its mathematical representation. Much like 3n vector representing positions of a system of n particles is different from the instantaneous configuration of the system of n particles.

After all, we know that an observation can be erased. So that implies there is no cause if the collapse can be reversed and the superposition restored.

If collapse is not physical, then I guess that means we live in one of many worlds. Or?
And thats a physical observation....not theoretical one...

so maybe things are even crazier than we so far suspect...such as maybe there ARE some violations of causality....but for the time being many worlds seems more likely to me...

After all, we know that an observation can be erased.
I'm sure an observation cannot be erased. After all you cannot observe the photon twice...

DrChinese
Gold Member
I'm sure an observation cannot be erased. After all you cannot observe the photon twice...
You can measure the polarization of a photon by running it through a polarizing beam splitter. This can be done repeatedly, prior to the ultimate absorption/detection of the photon. And even then, it is possible to absorb the photon into a lattice structure and re-emit later with original characteristics.

So I would say that the dividing line is quite gray.

You can measure the polarization of a photon by running it through a polarizing beam splitter. This can be done repeatedly, prior to the ultimate absorption/detection of the photon. And even then, it is possible to absorb the photon into a lattice structure and re-emit later with original characteristics.

So I would say that the dividing line is quite gray.
I would argue that every polarization beam splitter is just preparing the state of the photon. The detection is the real measurement. Also, can you actually detect that the photon is absorbed in the lattice without disturbing its original characteristics?

Also, can you actually detect that the photon is absorbed in the lattice without disturbing its original characteristics?
When you use radar to measure speed of a car - you disturb the original characteristics of the car. So, the question is not whether but how much.

When you use radar to measure speed of a car - you disturb the original characteristics of the car. So, the question is not whether but how much.
Damn, never occurred to me that a car can be polarized and absorbed in a lattice and then re-emitted.

Anyway I was thinking that we are talking about photons, where "how much" is the whole thing you try to measure.

Also, can you actually detect that the photon is absorbed in the lattice without disturbing its original characteristics?
So, if you question was not about disturbing its original characteristics (every measurement of everything does it) - what was your question?

After all, we know that an observation can be erased.
I'm sure an observation cannot be erased. After all you cannot observe the photon twice...
And even then, it is possible to absorb the photon into a lattice structure and re-emit later with original characteristics.
Here I assumed this means it is possible to detect the photon and then re-emit it with original characteristics. Otherwise the statement is unrelated to the process of observation.

The detection is the real measurement. Also, can you actually detect that the photon is absorbed in the lattice without disturbing its original characteristics?
So, if you question was not about disturbing its original characteristics (every measurement of everything does it) - what was your question?
It was about the statement that an observation can be erased. See the beginning.

DrChinese
Gold Member
I would argue that every polarization beam splitter is just preparing the state of the photon. The detection is the real measurement. Also, can you actually detect that the photon is absorbed in the lattice without disturbing its original characteristics?
As I say, you can call the absorption event the end of the line... after all, this is the point that seems to be irreversible. But actually it wouldn't be if there was absorption and re-emission at a later time from a lattice. And yes, recent experiments have entangled particles being stored and later retrieved with entanglement intact. Pretty amazing stuff. Anyway, it seems that if you constructed a setup - somehow - in which the outcome paths were indistinguishable... that whether there was photon absorption or not wouldn't matter.

As I say, you can call the absorption event the end of the line... after all, this is the point that seems to be irreversible. But actually it wouldn't be if there was absorption and re-emission at a later time from a lattice. And yes, recent experiments have entangled particles being stored and later retrieved with entanglement intact. Pretty amazing stuff. Anyway, it seems that if you constructed a setup - somehow - in which the outcome paths were indistinguishable... that whether there was photon absorption or not wouldn't matter.
I still don't understand. How can you be sure that the photon was actually absorbed?
Say, you have a setup with something emitting photons and then some kind of strange material that you claim can absorb a photon and then re-emit it with the original characteristics. You switch on the light and then I observe what?

DrChinese
Gold Member
I still don't understand. How can you be sure that the photon was actually absorbed?
Say, you have a setup with something emitting photons and then some kind of strange material that you claim can absorb a photon and then re-emit it with the original characteristics. You switch on the light and then I observe what?
Here is an example of the concept: http://arxiv.org/abs/0911.3869

"Quantum storage of light in a collective ensemble of atoms plays an important role in quantum information processing. Consisting of a quantum repeater together with quantum entanglement swapping, quantum memory has been intensively studied recently. Conventional photon echoes have been limited by extremely low retrieval efficiency and short storage time confined by the optical phase decay process. Here, we report a storage time-extended near perfect photon echo protocol using a phase locking method via an auxiliary spin state, where the phase locking acts as a conditional stopper of the rephasing process resulting in extension of storage time determined by the spin dephasing process. We experimentally prove the proposed phase locked photon echo protocol in a Pr3+ doped Y2SiO5 in a quasi phase conjugate scheme, where the phase conjugate gives the important benefit of aberration corrections when dealing with quantum images."

After a while, you realize the end of the line is simply a line you draw somewhere.

Here is an example of the concept: http://arxiv.org/abs/0911.3869

"Quantum storage of light in a collective ensemble of atoms plays an important role in quantum information processing. Consisting of a quantum repeater together with quantum entanglement swapping, quantum memory has been intensively studied recently. Conventional photon echoes have been limited by extremely low retrieval efficiency and short storage time confined by the optical phase decay process. Here, we report a storage time-extended near perfect photon echo protocol using a phase locking method via an auxiliary spin state, where the phase locking acts as a conditional stopper of the rephasing process resulting in extension of storage time determined by the spin dephasing process. We experimentally prove the proposed phase locked photon echo protocol in a Pr3+ doped Y2SiO5 in a quasi phase conjugate scheme, where the phase conjugate gives the important benefit of aberration corrections when dealing with quantum images."

After a while, you realize the end of the line is simply a line you draw somewhere.
Well, but they have detectors APD1 and APD2 that actually detect the photons. No detection took place in the crystal. Thus the photon was detected only at one place, not two.

Excited to see so much discussion.

I agree with arkajad that we can calculate how it collapses. But my questions were :

1. Photon can take any path,can go even outside interferometer, and not necessarily a straight line. Is this correct ?

2. Is the description 'photon takes both paths' accurate ? Or is it just our inability to predict with 100% accuracy where the photon is ?

Any material on this would also be appreciated.

DrChinese
Gold Member
Well, but they have detectors APD1 and APD2 that actually detect the photons. No detection took place in the crystal. Thus the photon was detected only at one place, not two.
From our perspective, that seems true. But from the perspective of the lattice, absorption took place. After all, it's state was stored there for a period of time. Then, a photon was emitted with the original characteristics. Was it the same one? I'm not so sure how that can be answered without a degree of ambiguity.

DrChinese
Gold Member
2. Is the description 'photon takes both paths' accurate ?
I would say that is the most reasonable description.

From our perspective, that seems true. But from the perspective of the lattice, absorption took place. After all, it's state was stored there for a period of time. Then, a photon was emitted with the original characteristics. Was it the same one? I'm not so sure how that can be answered without a degree of ambiguity.
No doubt. But you have no measurement. You have no number to tell where (x,y,z) it was absorbed. So, putting that material will tell you nothing about if there is interference pattern. Say, you don't know what is there double-slit or not, which-path or not. you only have the opportunity to put a screen and observe. if you put real screen you will know whet is there, if you put that meta material you will not. So, it is not an observation.

zonde
Gold Member
Excited to see so much discussion.

I agree with arkajad that we can calculate how it collapses. But my questions were :

1. Photon can take any path,can go even outside interferometer, and not necessarily a straight line. Is this correct ?
In any practical situation - yes, it can go outside interferometer but it will not contribute to the result.

2. Is the description 'photon takes both paths' accurate ? Or is it just our inability to predict with 100% accuracy where the photon is ?
Description 'photon takes both paths' is wrong. Particle is something localized by definition. Of course you can scale down to when you can't talk about localization of particle any more and for photon this scale is around it's wavelength. As interferometer scale is well above this limit that it's not an issue.

But you can say 'wavefunction takes both paths'.