# Superposition of Time Evolutions

## Main Question or Discussion Point

Superposition of Time Evolutions

My Pathetic Explanation:
A photon can be in a superposition of states by going through a beam-splitter (thus you have interference). Yakir Aharonov says you can make an object experience a superposition of time (actually Time Evolutions, or how it ages).
He does this in a thought experiment. He starts by creating the gravity equivalent of a beam-splitter. Out of his hat he pulls out a quantum indeterminate gravity force. This means a gravity force which can be high or low as determined by some quantum event. We all know that time slows for something close to a strong gravity force ,such as a spaceship near the event horizon of a black hole. So if you tie the strength of the gravity to a quantum event then the gravity can be both low and high , at the same time, essentially causing interference just like a photon can travel both paths when going through a beam-splitter causing interference.
The result is that the object in the experiment can age either faster ,slower, or negativly than is experienced in our reference frame. Of course, statistically it only works 1 out of 10,000 times tried. But he makes mention that it could also work with a superposition of speed. A spaceship going close to the speed of light also experiances time slower. So if you could make an object experience a quantum indeterminate speed you could perform the same experiment.
The idea is to create a superposition of time (for the object) rather than the usual superposition of position in space as is usually the case.
If you don't understand my rather bad explanation than read the much more eloquent explanation in the first link below by John G. Cramer.

My Question:
OK, assuming I understand any of this, and assuming "Superposition of Time Evolutions" actually works. Would it be possible to recreate the experiment using photons rather than a physical object? There are many current experiments claiming to be able to slow light way down. Thus you have photons traveling at C and photons that travel much slower. Apply a quantum indeterminate switch and you have recreated the experiment.

I see several problems right off the bat:
1. Photons traveling at C don't age. All photons travel at C. So a photon can't experience time differently, much less a superposition of time.
2. Most would say just delaying a photon as it goes through a medium is not really slowing it at all. You are just delaying it's output. So there is no change in how it experiences time.
3. Because photons are being absorbed and emitted as it goes through a medium, such as glass, you arn't really getting the same photon out the end.
4. One could say that all photons are the same and indistinguishable and thus this experiment doesn't apply. Apples and oranges. Besides the aspect of speed, photons are not things that can experience time. Hmmm, read that somewhere. I don't pretend to understand it. Perhaps it means that because photons can occupy the same place at the same time and have the same quantum state that they are indistinguishable. Not sure.

However:
1. Photons are affected by gravity. They are pulled towards a strong gravity source. So arn't they experiencing a time effect also?
2. Just because a photon doesn't age that doesn't mean it can't be changed through time, as in applying a polarizing filter. So we can change a photon as it travels through time.

Anyone have any ideas or comments? Is the idea of using photons untenable? Can you tink of any other way to actualy do the experiment (without a black hole or exotic energy/matter). Thoughts?

References:

Quantum Time Travel by John G. Cramer
http://www.npl.washington.edu/AV/altvw45.html

AAVP Effect:
"Superposition of Time Evolutions of Quantum System and a Quantum Time Translation Machine", Yakir Aharonov, Jeeva Anandan, Sandu Popescu, and Lev Vaidman, Physical Review Letters 64, 2965 (1990).