What if an Entangled Photon Gets Destroyed?

Most recent answer: 10/03/2013

Q:
I have a question about (quantum mechanics) entanglement. If a photon – that is entangled with another photon – gets destroyed, what happens to it's partner photon? Does it expire also? Is there any way for two photons that are entangled to meld together into one?
- Deanna (age 38)
Los Angeles
A:

Hi Deanna,

Great questions.

First, it's important to understand that entanglement is a somewhat general term. Photons can be entangled in many ways: they might exhibit quantum correlations in frequency, polarization, trajectory, etc.

Let's take a specific case: say you have two photons entangled in energy. For example, you could take a photon with 3 eV of energy and split it into two photons using some tricky experimental techniques. These two photons can have undetermined energies, so that if you measure any one of them, it might have any amount of energy less than 3 eV! This number will be random: you can't predict what energy each of the photons will have until you measure. However, if you measure both photons separately and add the two energies, you will always find that they sum to 3 eV! That's the mysterious "quantum correlation."

Now, to answer your question. If you took one such photon, and somehow destroyed it, what would happen to its entangled partner? Well, no matter what process you use to destroy it, it turns out you won't find anything interesting. The particle certainly isn't "harmed" by the death of its partner, and if you measure its energy, you'll still get some random undetermined value less than 3 eV. You'll never be able to measure its partner's energy, so you won't notice that the sum of the two energies was 3 eV. All you've done by destroying the partner is thrown away some information.

There are ways to combine two photons into one; it's a difficult process known as second harmonic generation. You could in principle do this to two entangled photons, although I don't think anything particularly exciting would happen. For example, if they were entangled in energy, then the photon they combined to create would have 3 eV of energy, as you would expect.

Hope that helps demystify entanglement a bit!

Cheers,

David Schmid


(published on 10/03/2013)

Follow-Up #1: Time dilation with entangled photons

Q:
If there are two entangled particles, and on of them is kept stationary and the other is accelerated near c, what does it mean for the two in regards to time dilation? Suppose I could entangle a massive system for a long time in the form of two clocks. With a third unentangled, but synchronized clock present ads well. And suppose I could accelerate one of the entangled clocks to relativistic speeds for some duration. Would the stationary clock when observed show time had passed according to the moving clock, or according to a identical, but not entangled, local stationary clock?
- Anahn (age 73)
Cambridge, MA
A:

Based on your question, I think you have a misconception of entanglement. Specifically, it sounds like you are imagining two entangled clocks as devices which always read the same time. If such devices were constructed, you would indeed have problems with relativity. Many people make this sort of mistake; they assume that entangled particles always have some property which is identical for each in the pair. (I've marked you as a follow-up to another such question.)

However, in reality, entanglement doesn't quite work like that. Instead, two particles entangled in property X exhibit very strong (stronger than can be explained classically... for brevity I'll call these "quantum" correlations) correlations between the results of separate measurements on property X. The measurement results "x" don't have to be equal, they just have to be quantum correlated. For example, perhaps the sum of x1 and x2 (the two measurement outcomes for particles 1 and 2) is always a fixed number, as is often the case for entanglement in energy. If a particle of energy 10 eV decays into two particles of indeterminate energies e1 and e2, then energy conservation says that their energies will be entangled, such that e1+e2 = 10 eV.

Now, you can't actually have a clock that is entangled, so what is the nearest thing to your question? Well, you could consider two particles with spins which rotate evenly in time. Now, just like a clock, you could "tell time" from the direction that the spin (like hands of a clock) were pointing. You could further have their spins start in an entangled state, so that neither spin pointed in a definite direction, but measurement results of spin s1 and s2 would always be the same direction, giving the same time.

This is the closest physical analogy to your question. So, what happens if you take one particle and accelerate it to relativistic speeds, so it sees time dilation with respect to its partner? Simple: its spin (clock time) lags behind the other (from a laboratory frame). There isn't a paradox here, because entanglement doesn't ensure that the spins are equal, it just fixes the measurement results on spins to be correlated, which they still are: the measured lag between them is a direct function of the time dilation. 

Hope that makes sense, and make sure to check out the above question as well!

David Schmid

 


(published on 10/31/2013)