What is the Speed of Gravity?

“The only problem with the speed of light, is it gets here too early in the morning.” –Danny Nevrath

One of the most common questions I get asked is whether gravity is instantaneous, or whether there’s a speed limit to how fast the force of gravity can travel.

It’s a good question! After all, we know how fast light travels, and if the Sun were to suddenly wink out of existence, we’d still receive light from it for just over 8 minutes after it disappeared! But what about gravity, and the Earth’s orbit? Would the Earth simply fly off in a straight line, like a twirled poi ball the instant a string broke?

Or would it continue to move in its planetary for some time, and perhaps suffer some more interesting effects? Believe it or not, this is one of the most severe differences between Newton’s old school theory of gravity and Einstein’s General Relativity. According to Newton, you have two masses separated by a distance, and that determines the force. You take one of those masses away, and the force instantly goes away. End of story.

But in general relativity, things are much more intricate, and incredibly interesting. First off, it isn’t mass, per se, that causes gravity. Rather, all forms of energy (including mass) affect the curvature of space. So for the Sun and the Earth, the incredibly large mass of the Sun dominates the curvature of space, and the Earth travels in an orbit along that curved space.

If you simply took the Sun away, space would go back to being flat, but it wouldn’t do so right away at every point. In fact, just like the surface of a pond when you drop something into it, it snaps back to being flat, and the disturbances send ripples outward!

In Einstein’s theory of gravity, these ripples move at the speed of light, not instantaneously.

This is a really amazing idea, and leads me to ask another question. Think about it; if the Earth was stationary, it would feel the ripples in one way, but if the Earth were moving over the surface of space, wouldn’t it feel the ripples differently?

It turns out, that while Newton doesn’t care what your velocity is, Einstein does. The Sun, as it is right now, won’t have its gravity affect Earth for another 8+ minutes, and the gravity that the Earth feels right now pulling it towards the Sun is actually pulling it towards where the Sun was 8+ minutes ago! (Weird, isn’t it?)

The Earth, of course, since it’s also moving, kind of “rides” over such a ripple, so that it comes down in a different spot from where it was lifted up. It looks like we have two effects going on: velocity affects gravity, and so do changing gravitational fields.

So, in theory, we know that the speed of gravity should be the same as the speed of light. But the Sun’s force of gravity out here, by us, is far too weak to measure this effect. In fact, it gets really hard to measure, because if something moves at a constant velocity in a constant gravitational field, there’s no observable affect at all. What we’d want, ideally, is a system that has an object moving with a changing velocity through a changing gravitational field. What would that take?

Something intense, like two neutron stars orbiting each other extremely close together! Occasionally, we get very lucky, and a neutron star emits very regular blips of light, pulsing with incredible precision: this makes it a pulsar! If one of these neutron stars is a pulsar aimed at us, we can test whether gravity moves at the speed of light or not!

Incredibly enough, we’ve discovered multiple independent binary pulsars with this exact configuration!

Not only is the gravitational source (star #1) moving, but the other object (star #2) is changing its velocity, as it changes its direction in orbit around the gravitational source! Remarkably, this effect causes the orbit to ever-so-slowly decay, which leads to time changes in the pulses!

The predictions from Einstein’s theory of gravity are incredibly sensitive to the speed of light, so much so that even from the first binary pulsar system, PSR 1913+16 (or the Hulse-Taylor binary), we have constrained the speed of gravity to be equal to the speed of light with an error of less than 1%!

While we’d love to be able to detect these gravitational waves directly, rather than make an indirect measurement, we’re likely going to have to wait until close to 2030. Why? We’ll need to have LISA up and running, where it’s capable of detecting a system like this and directly measuring the speed of gravitational radiation.

But until then, indirect measurements of very rare pulsar systems like this give us the tightest constraints, and tell us that the speed of gravity is between 2.993 x 108 and 3.003 x 108 meters per second, which is an amazing confirmation of general relativity and a terrible difficulty for alternative theories of gravity! (Sorry, Newton!) And now you know not only what the speed of gravity is, but where to look to figure it out!