Not a big assumption at all. Gravity is believed to be a property of space as opposed to a property of matter. That is, a satellite orbiting around the Earth is really going in a straight line but space is curved.
Seen that way it’s just insane that any kind of matter could fall up. See
> a satellite orbiting around the Earth is really going in a straight line but space is curved.
This is not quite how it works, I think. The gravity of the Earth isn't high enough to cause space to curve around in a circle, and the path of the satellite depends on its orbital velocity. If it fired a rocket forwards to reduce speed, it would fall towards the Earth, but that's not due to a change in space curvature.
The paths taken by light will follow the curvature, however. That would give a very small deflection for light passing near the Earth.
The gravity of Terra is exactly enough to cause the curved orbit. You are just missing how shallowly curved it really is, by squashing out the time part of spacetime. In 4 dimensional spacetime, the circle is (to simplify a little) really a helix, because it does not return to its starting point, and it's very stretched out along the time axis. (Or very narrow along the space axes, depending from how one choses one's units.) The curvature only looks greater because you are discounting how much greater length of time it extends across in order to do all of that curving that gets it all of the way around Terra.
The curvature is quite small but is responsible for orbital motion in the steady state condition. I don't think the parent comment was suggesting that space would "curve into a circle" unless you are implying something else specifically.
All ideal orbits, with no other forces involved, are equivalent to geodesics. However that only applies in true free fall. Actual orbits decay due to tiny non-ideal characteristics which have a cumulative effect or stochastic "butterfly effect"-like characteristic over long periods of time. For example in the ideal case, as soon as a satellite fires maneuvering thrusters, it is not following a geodesic for the time that the rockets are active. After the maneuver is completed, a new steady state condition can be calculated piecewise and then it's following a geodesic again. Another example is the ideal state of a satellite being in a low orbit that decays due to friction with the atmosphere, for which there are good estimates but not exact predictions. Due to the friction, there is a tiny acceleration (which happens to become larger over time) and this makes it follow something that starts close to a geodesic but deviates from it.
The quantity coupled to the curvature is the stress-energy tensor. In local coordinates, this can be represented as a (1+n)x(1+n) matrix where n is the number of spatial dimensions, with components given by
[mass density, mass flux = momentum density]
[energy flux, stress]
Photons are massless, but still carry momentum and energy, so they do gravitate.
A negative mass particle would repel a positive mass particle but be attracted by a positive mass particle so the two would accelerate to ever increasing speeds but the positive and negative kinetic energy would cancel out so energy would still be conserved.
If photons had mass they would attract each other as well.
Gravitational lensing is pretty strong proof that photons follow the curvature of space affected by a gravitional field. If photons had mass themselves they would not follow straight lines in free space but they'd clump together over astronomical distances and long periods of travel. Though there is a way to get them to act in unison which gives some pretty odd effects:
Photons do interact with each other gravitationally. It's not as simple as just attracting each other - the Newtonian limit doesn't work here - but parallel photon beams going in opposite directions, for instance, will be deflected towards each other.
But photons traveling in (almost...) the same direction (such as the photons that arrive at some destination after gravitational lensing do not gravitationally attract.
I thought photons also contributed to the curvature of spacetime because they have momentum (and thus energy). I would expect it to be a pretty miniscule contribution, though.
Hm... just an interested layperson here but would that not require some kind of mechanism by which the photon sheds some of that momentum? Which would seem to be pretty hard if it really is an 'elementary' particle. Unless 'photon === graviton' and you find photons shedding other photons!
I'm a layman as well, but I think photons can effectively lose energy in various ways, one of them being the well-known redshift effect. And one of the main causes of redshifting is photons climbing out of a gravitational well (this is called a gravitational redshift).
However, whether that translates to a loss in momentum is a bit more fuzzy and I really can't tell whether it does or doesn't. Although I'm far from being a physicist, so hopefully someone more knowledgeable chimes in to enlighten us...
But I'm curious: what is your reasoning for asking whether photons have a mechanism to lose momentum as a consequence of them affecting the curvature of spacetime? It's not at all obvious to me the relationship between these two concepts.
> However, whether that translates to a loss in momentum is a bit more fuzzy and I really can't tell whether it does or doesn't.
Yes, redshifted photons lose momentum. Momentum (really the stress-energy tensor) is conserved locally, and along trajectories that preserve the metric, but global momentum conservation in GR isn't even well-defined.
If they don't lose momentum then there is no interaction (in order for any kind of interaction you need to lose some energy). Momentum is pretty much all a photon has and it could conceivably toss off much lower energy photons to shed that momentum.
Seen that way it’s just insane that any kind of matter could fall up. See
https://en.wikipedia.org/wiki/Equivalence_principle
anti-matter falling up would be as crazy as superluminal neutrinos (which I have to admit I almost want to believe)