I understand that it is always better to check experimentally.

 

Given that...

A particle and anti-particle pair of equivalent mass are created from an amount of energy equivalent to at least twice the mass of the particle or antiparticle. This energy, say a gamma photon, was previously affected by a gravitational field in accordance with its mass-equivalent energy. After the particle and anti-particle come back together and annihilate, energy conservation dictates that the equivalent amount of energy is produced, i.e. the same gamma photon. This photon continues to be affected by the previous gravitational field.

Is it possible that the matter and anti-matter particles were affected differently by the gravitational field and so the re-created photon is in a different trajectory about the gravitational field, thus invalidating energy /momentum conservation ?

 

Or is ALPHA actually testing the equivalence principle of GR, i.e. energy is equivalent to inertial mass but maybe not to gravitational mass ?

You get two photons in annihilation, and the production takes place near a nucleus, in order to conserve momentum which also takes a small amount of the energy. So the situation is not quite as you describe. I'm not sure how you would systematically correct for such perturbations to make a precise measurement.

It wouldn't worry me if the new photon pair had a momentum different from the original photon, because the gravitational field introduces one more actor that interacts with the already mentioned particles. The mass that creates the field would equal the momentum difference out.

 

This in addition to the nucleus that provides the electric field, usually - which would also absorb momentum. Some experiments achieve to produce pairs from two photons in vacuum, far from any nucleus, in rare events.

OK It was a too quickly put together thought experiment, spurred by reading the other thread. Lets consider, instead, virtual particles.

 

Is it impossible for a single photon to be travelling along a geodesic and spontaneously produce a virtual particle/ant-particle pair ? Now the virtual particle pair could have the wrong energy because of Hisenberg borrowing ( I made up that term ), but when they annihilate after a brief period, they must reproduce the initial energy and momentum of the original photon exactly. A gain any difference in the trajectory of the virtual particles would be manifest in a difference in the final photon's energy and momentum.

 

In effect, virtual anti-particles that act differently gravitationally, provide a mechanism for violating conservation laws.

A photon's energy and momentum is going to be different anyway as it travels and samples a different gravitational potential (frequency changes by about a part in 10¹⁶ per vertical meter near the earth) owing to relativity. This is confirmed in the Pound-Rebka experiment (and subsequent tests). So an effect has to be a deviation from this change.

 

So, how big? If the particle and antiparticle behave differently and thus the momentum of one changes differently, this would shift the frequency of the photon and/or steer it. For the latter, one needs to know big of an effect are we talking about, and compare that to how well one might be able to collimate the photons used. If you can only do a microradian, then you aren't going to be able to detect a steering shift smaller than 10^-6 unless you can think of something very clever.

 

Pound-Rebka style experiment put limits on the frequency shift, because the results agree with relativity. Though I think the followup was good to about 1% (Pound and Snider?)

Thanks for the info, swansont.

It's an interesting question. It's certainly possible someone has a different approach that gives better results and I'm just unaware of it. It's not my sub-field.