What Happens When Entangled Photons get Redshifted?

Suppose two photons are entangled with respect to their energy (wavelength). The combined energy of the two photons is 3eV. We bottle up one of the photons so that it is bouncing between two mirrors. Further suppose that the energy of the bottled photon is measured to be 1.5eV (coincidentally half of the combined energy of the entangled pair). The other photon we send off to a distant galaxy 1B light-years away. When the second photon reaches the target galaxy, 1.1B years later due to the expansion of the universe, a scientist there measures its energy in a detector. Would this photon also measure 1.5eV, like it's partner, since it would have experienced energy loss (red-shift) due to expansion as it traveled? What about it's partner photon back in the source galaxy? Is it the case that red-shifted photons from distant galaxies actually have less energy (i.e. shorter wavelengths) than when they originally started their journey, or does it just appear that way to us because we are receding away from the source galaxy (and they from us)? In other words, if it were possible to instantaneously measure the second photons wavelength from the source galaxy where it started, would it not still appear to have the same energy as when it left? Thank you!
- Ralph Knight (age 44)
Florida, USA

There are two kinds of redshift that affect light from distant galaxies, so let's briefly discuss that first. There's a Doppler shift from relative motion, which can actually be a blueshift if a galaxy in our local group happens to be moving towards us (as the Andromeda galaxy is). There's also the redshift from the expansion of space in the universe, which always makes wavelengths longer. This redshift is not due to relative motion between reference frames. Interestingly, the space between galaxies can expand faster than the speed of light without violating any laws of physics. [Although it's not so clear what the speed of expansion of space means, the accelerating expansion can make a galaxy that used to be visible go outside our horizon. /mw]

Photons which have been redshifted due to the expansion of the universe do indeed have less energy than when they started their journey. Where does that energy go? No one really knows. (One idea is that the energy becomes gravitational potentional energy—.)

Photons which have been redshifted due to relative motion (or gravitational redshift) just appear to have different energies in different reference frames, and there's no mystery about whether energy is conserved—the kinetic energy and potential energy of the measurement devices and photons in different reference frames take care of that.

Okay, now for the entangled photons. You can think of entangled photons as belonging to the same "quantum state." You can move the pieces of this quantum state far apart, but they'll still behave as one. Neither photon has a definite energy until you measure one of them; only the whole state has a total energy. (And if you measure the trapped photon before you send its partner off to a distant galaxy, you'll break the entanglement.) If one of the photons loses energy, which it will as it gets redshifted by the expansion of the universe, the whole state loses energy—it will have something less than 3 eV. The energies of the two photons will add up to this new total.

This is all assuming that the expansion of the universe doesn't cause decoherence between the two photons, which would make the entanglement break down. In the lab, we can shift the frequency of one photon in an entangled pair with an acousto-optical modulator while keeping the entanglement intact. Redshift from the expansion of the universe probably wouldn't be any different, but so far no one knows for sure. 

Rebecca H.

(published on 10/14/2015)