Elitzur -Vaidman bomb experiment
Starting off, you might wonder what an Elitzur Vaidman bomb is .The Elitzur Vaidman bomb tester uses a light sensitive bomb with a tube containing a photon detector in it.To detonate it, you’d send a photon through the tube, the detector detects it and the bomb explodes. On the other hand if the bomb is defective ie a dud, the photon goes in, detector doesn’t work and the photon comes back out.
With time, bombs decay and the detectors don’t work anymore. The question that Elitzur and Vaidman present is whether there’s a way to certify that the bomb is working or not, without setting it off.
Quantum mechanics forces us to rethink our attitude towards counterfactual conditionals such as this.
That is, you can use quantum mechanics to find out what would have happened if you’d done something,when classically it seems impossible!
Elitzur and Vaidman have proposed a measurement scheme that, using the quantum superposition principle, allows one to detect the presence of an object, a bomb in this case-without interacting with it.This bomb testing uses a Mach Zehnder interferometer that operates with a single photon at a time.
This experiment has its origins in the double-slit experiment and other complex experiments which inspired it, such as the Schrödinger’s cat and Wheeler’s delayed-choice experiment
For this experimental setup we need four components:Mirror, 50/50 beam splitters and two detectors.Now as we know in quantum mechanics, superpositions exist which means if we send one single photon through the beam splitter, there’s a 50% chance that the photon will go through or get reflected off the beam splitter. In reality it is going to get in a superposition between these two states. Which means it’s going to be reflected and transmitted through the beam splitter at the same time.
To build the setup, we place a light source that shoots single photons at a time in front of a beam splitter.This gives us two paths of light,V and U. We now place a mirror angled at 45 degrees at each of these paths.If we follow the paths of the photons after being reflected, they meet up again at the right corner where another beam splitter is placed. Finally we place the detectors ahead of it. Using the same concepts as in the double slit experiment, we place the detectors such that there is constructive interference at detector D1 and destructive interference at detector D2.
What would happen if there was an obstacle on path V? This would prevent the photon from travelling through this path V and therefore will not be able to interfere with itself at the beam splitter.
If we replace the obstacle in the above case with a bomb,we’d have the Elitzur Vaidman experiment. If the bomb is defective, the photon will go right through it and interference will only happen at detector D1.
On the other hand,if our bomb is real,no interference is seen.
Here’s where the main point of the experiment comes in.Let’s say we have a bomb and we don’t know if it real or fake and we place it in our experiment.
There’s only three possible outcomes to our experiment:
First outcome is detector D1 clicks.This gives us no information. Detector D1 clicks if there is an obstacle and if there isnt one in path V.
The second outcome is: no detector clicks.For this to happen, the photon must scatter off something. And the only thing that could scatter a photon in this experiment would be the obstacle. Which means it hit the bomb and the bomb explodes.
The third outcome is where the photon goes through path U and hits the beam splitter and is reflected off of it into detector D2.The only way a photon hits detector D2 is if the path V is interrupted.This confirms the presence of a real bomb in path V without detonating it.
From quantum mechanics formalism, we get the following probabilities:
P(|2⟩)=P(D2 Clicks) = 1/4
P(|1⟩)=P(D1 Clicks) = 1/4
P(|scattered⟩)=P(No clicks) = 1/2
In this case, we did not interact with the bomb at all yet we were able to gain information from it!This is the sort of thing that bothered Einstein and Schrodinger about quantum mechanics.If we think about explanations for this, we really don’t know.In the many worlds interpretations from Everett,in this world if we were able to find information from the bomb without touching it,there has to be another world where the bomb exploded.
Kwiat,in 1996 showed that using better methods, you can reduce the percentage of wasted working bombs to almost to 0%. And taking the idea even further, Richard Jozsa and Graeme Mitchison,in 1999 showed that you could get a quantum computer to do a calculation for you without even turning it on!
The idea of receiving information about a system without interacting with it would have never crossed a classical physicist’s mind before the quantum revolution. Even with the rise of quantum mechanics, phenomena like entanglement allowed us to obtain instantaneous information about another particle without interacting with it. What sets it apart is that for entangled systems, you would need to already have some knowledge about the system. For instance, you must know that the particle is entangled. In this experiment , an idea is presented where it is shown to be possible to learn about a system, without any previous knowledge about it.
The Copenhagen interpretation revolves around “The measurement” part of the experiment. Physicists backed this interpretation for a long time as it is intuitive to think that by measuring a system, we are altering it, and therefore changing its state. Through the idea presented above, we now know we are able to measure the state of a system without any interaction at all with. This implies that instead of a bomb we could place a particle in a superposition of blocking path |v⟩ and not blocking path |v⟩. We run this experiment and successfully collapse the wavefunction of such particle without interacting with it at all.From this we understand that the ”collapse” of a wavefunction is something much deeper than what we thought, it can be collapsed instantaneously from light years away, without interacting with it in the present or past(just like entanglement does).Whatever interpretation you may believe in, this experiment only shows us that ideas that once could have been deemed impossible, can become possible later on, as we try to understand our universe further.
