Simple question: If photons have no mass what is there for gravity to attract, e.g. black holes?
They have mass because they travel at the speed of light – they would only have no mass if they were travelling slower than that.
Photons are actually traveling in straight lines, even near a black hole. The mass of the black hole makes space curve, and the photos appear to curve as they actually travel in a straight line through curved space.
Even with Newtonian gravity, we expect massless objects to be accelerated by gravity. The acceleration due to gravity is not a function of the mass of the object. The force of gravity depends on the mass, but in exactly the same way that acceleration in general is. That is, gravitational mass is the same as inertial mass.
To throw a few equations about, the force of gravity is
F = G M m / R^2
with G the gravitational constant, M the mass of the source of gravity, m the mass of the object in question, and R^2 the square of the distance between them.
The acceleration of the object is
a = F / m = G M / R^2
The mass of the object divides out. (Don’t bother me with m=0 complaints; this is physics, not mathematics.)
Of course, Newtonian physics is only an approximation, but as a naive initial look, it tells us we shouldn’t expect the mass of an object to affect its acceleration due to gravity.
This is an interesting subject.
Two photons traveling along parallel to each other do attract because they both carry energy. However, they also carry momentum and this momentum creates an equal and opposite gravitomagnetic force, so net the system of two photons doesn’t have mass.
On the other hand, if they are not traveling parallel then there is no canceling gravitomagnetic force, and the system does have mass, and there is an attraction.
This is sort of a mishmash of SR and GR.
Could you expand on that a little bit?
Setting c = 1, Einstein’s equation relating mass energy and momentum is:
m[sup]2[/sup] = E[sup]2[/sup] - p[sup]2[/sup]
m = mass
E = energy
p = momentum
When the photons are running in non parallel directions they have a zero momentum frame where the momentum = zero, and therefore m = E.
When the photons are running in parallel directions E = p and therefore m = zero.
Sorry I misread you’re question. In GR mass is replaced by the stress energy tensor and among other things mass is replaced by mass/energy.
I think the simplest way to say it is that if the invariant mass of the two photons is zero, then there is no attraction. The scattering cross section is proportional to the invariant mass of the system. So anti-parallel photons scatter, parallel photons do not scatter, because the CM energy is zero.
The pithy answer was touched on by Ring above: in relativity, mass is equivalent to energy, and so gravity affects an object depending on its energy content as well as its mass content. (And its momentum content and internal pressures and strains as well.)
This is kind of misleading as your phrased it. Massless objects must travel at the speed of light. Massive objects cannot. If you’re saying that “a photon travelling at less than the speed of light would have no mass”, there’s a sense in which that’s true, using the notion of “relativistic mass”. But very few physicists ever use the notion of relativistic mass any more; most people view it as more elegant to say that a particle has one mass, its rest mass, and it’s just that the momentum and energy of the particle depend differently on the particle’s speed when v approaches c.