I’m not so sure even gravity can act instantaneously, but is also limited by the speed of light.
The speed of gravitational waves in the general theory of relativity is equal to the speed of light in a vacuum, c. Within the theory of special relativity, the constant c is not only about light; instead it is the highest possible speed for any interaction in nature. Formally, c is a conversion factor for changing the unit of time to the unit of space. This makes it the only speed which does not depend either on the motion of an observer or a source of light and / or gravity. Thus, the speed of “light” is also the speed of gravitational waves, and further the speed of any massless particle.
Gravity isn’t instant, and turns out to propagate at exactly the speed of light.
Gravity isn’t best viewed as a straight-line, instantaneous force connecting any two points in the Universe. Instead, Einstein put forth a picture where space-and-time are woven together in what he visualized as an inseparable fabric, and that not only masses, but all forms of matter and energy, deformed that fabric. Instead of the planets orbiting because of an invisible force, they simply move along the curved path determined by the curved, distorted fabric of spacetime.
This conception of gravity leads to a radically different set of equations from Newton’s, and instead predicts that gravity not only propagates at a finite speed, but that speed — the speed of gravity — must be exactly equal to the speed of light.
So, no information can travel instantaneously.
But then Einstein showed that time is relative. It changes with speed and in the presence of gravity. One of the ramifications of that is that you can’t have simultaneous actions at a distance. So information of any kind has a finite speed, whether it’s a photon — the light-carrying particle — or a graviton, which carries the force of gravity.
“In relativity, there is a ‘speed of information’ — the maximum speed that you can send information from one point to another,” says University of Wisconsin-Milwaukee physicist Jolien Creighton, an expert on general relativity and member of the LIGO team that first spotted gravitational waves.