Confusion in energy-mass equivalence: Why would gravitational effects remain the same even when you move at high speeds?

Question

It is said that most of what we call "mass" of nucleons are in fact from the kinetic and binding energies of quarks, and that the rest mass of quarks, from the higgs mechanism is much smaller compared to the nucleon.

There are other examples, like the binding energy of a nucleus, that show how energy contributes to the mass of things in the subatomic world.

My problem arises from the fact that it is also said that the gravitational effects are not really affected by how fast the object goes. Thus, a object won't get infinitely attracted to a planet even it goes at the speed near light. This seemed different from the previous examples, since in those cases the energy did affect the mass(in the classical way), which is basically what builds us up.

What would be a appropriate way of understanding this discrepancy? Thank you for your time in advance.

Answer 1

Newton's formula of gravity is an approximation which is only valid in a non-relativistic regime. To model gravitational effects of and on relativistic objects one must use the Einstein field equations (EFE). In those equations the source of gravity is not energy alone, but something called the stress-energy tensor which includes terms for energy, momentum, stress, and pressure.

For a single body, the curvature of spacetime as described by the EFE is frame independent, so you will get the same curvature near a body whether you consider it to be at rest or moving at 99.9999% of the speed of light. Crudely speaking, the momentum terms of the stress-energy tensor have opposite sign to the energy term, and so "cancel out" the higher energy for a moving body.

Note that if you consider a two body system the gravity between them does depend on their relative motion, since there is an invariant component to that relative motion. But it's not as simple as just applying Newton's formula to the relativistic mass. If the bodies are at rest relative to one another (or nearly so) then Newton's formula works fine, but if they are moving at high speed relative to one another it gets much more complicated. Roughly speaking there's a greater gravitational attraction between them than Newton would predict, just as (for example) light is deflected more by the Sun that Newton's laws predict.