Assuming that energetic gamma photons travelling in free space at the speed of light have no influence on time and gravity (to my best knowledge no one ever measured a time dilation or gravitational effect caused by a photon or ray of photonic light in free space). If the photon generates an electron and a positron pair, since the matter particle (electron) applies gravitational force and time dilation, from conservation of time and gravity consideration, can we assume that the anti-matter particle (positron) will apply anti-time-dilation (i.e. time runs faster) and apply anti-gravity (i.e. gravity repels)? please read the following paper : http://vixra.org/abs/1609.0047
The gravitational properties of light are not in question. No direct measurements but enough indirect ones.
Light has inertial mass, from the $E=mc^2$ equivalence. One of the first two tests of General Relativity (I think 1918) was that light is bent as it travels near the Sun, due to its gravitational attraction. This bending of light near heavy bodies has been observed and confirmed lots of times. From conservation of momentum and the equivalence of inertial and gravitational mass the light also attracts the Sun or anything else it comes close to. It's just too small to measure
It is known that for the early time after the Big Bang and inflation (if there was one, as evidence indicates but not 100% agreed) the universe was too hot and was radiation dominated, with light and highly relativistic particles prevalent. The expansion of the universe was consistent with the radiation (estimated as massless particles like the photon) causing the gravitational field then present. Early on the expansion decelerates because of it. After some time the universe cooled enough that matter became more and more prevalent. And as it expanded more also the dark energy.
There are other good reasons to think so. If it is not true energy and matter would also not convert into each other.
The gravity of antimatter is hard to measure, but there are some plans to do so. But we do 'see' the gravity of the energy difference between hydrogen and its fusion products, and the rest is photons and neutrinos. I am not sure if the mass loss of the radiated photons from the sun has been measured.
There's probably other good reasons but those are pretty easy to see.
Interesting question, though some of the assumptions may be wrong.
Light is energy and it has both the mentioned effects. The reason that there may not be experiments, is that the speed of light, and gravity is same. Due to this, measuring the effects may not be feasible. Because light and its associated gravitational effects both come together, and pass at the same time. Moreover, the effects would be very small to measure. For measurable effects, you have to be very close to a star, but in that case, you can not turn off the star light to measure the difference.
The two particles created out of photon (assuming it did happen) will have same (rest+kinetic) energy as the photon had. Their combined gravitational effect will be same as that of the photon, but they would not move as fast relative to an observer. That is why we can measure gravitational effects of matter.
Net energy of two particles should be same as that of the photon assuming there was no third thing created in the process.
Touching on a topic in comments under Bob Bee's answer -
It is not matter, or anti-matter that creates gravity. It is the interaction of empty space with them that causes curving (gravity). Space curves in a similar manner in presence of both - matter, and anti-matter.
Another way to think is - energy curves space (which is gravity). Anti matter, and matter, both are rest energy equivalent per E = mc$^2$. So, there is no difference between the two as far as gravity is concerned.
This isn't quite an answer, but instead is a gedankenexperiment which tries to convince you that light does attract things gravitationally. It should be a comment but is far too long.
For this experiment imagine a large container whose inside walls are perfect mirrors (see below for a modification). In this container is a quantity of flammable material and enough oxygen to allow it all to burn, and a timer which will ignite the material. The container is perfectly sealed.
So, initially weigh the container (with its contents). Now, wait until the timer has gone off and long enough after that that all the material has burned. Weigh the container again.
Now note two things:
- the container has perfectly reflective walls and is perfectly sealed, so no energy or matter has escaped from it;
- the material has dumped energy into the environment inside the container, in the form of light.
Now, we know (and have very good evidence for this) that, in burning, the material has converted some (tiny fraction) of its mass to energy. So the matter in the container now has slightly less mass than it did.
So, after the burning is finished, is the mass of the container and its contents less, more or the same?
- If it is less, where has the mass gone?
- (I won't bother with the more case.)
- If it's the same, then where is the mass that was lost from the burnt material?
Well, of course, it is the same, and the extra mass is in the soup of energy that now fills the container. Light does indeed influence things gravitationally.
- In real life we can't make the walls perfectly reflective, and some light leaks out: we'd have to account for this loss, which we could do by careful measurement of the emissions from the container.
- A better way of doing this experiment involves using a nuclear weapon instead of burning things, as the mass-to-energy conversion is far higher. But nuclear weapons emit things like neutrinos, which leak out and are hard to take account of. Still, this is how these experiments are done in practice, where I come from anyway.