# How does general relativity eliminate the Newtonian action at a distance? By the mediation of which "carriers"?

I found in Wikipedia the following statement

From a Newtonian perspective, action at a distance can be regarded as: "a phenomenon in which a change in intrinsic properties of one system induces a change in the intrinsic properties of a distant system, independently of the influence of any other systems on the distant system, and without there being a process that carries this influence contiguously in space and time.

Later on, I see at the same site,

This problem has been resolved by Einstein's theory of general relativity in which gravitational interaction is mediated by deformation of space-time geometry. Matter warps the geometry of space-time and these effects are, as with electric and magnetic fields, propagated at the speed of light.

I am not good at general relativity so I am asking the following: since celestial objects are in permanent movement, do they permanently emit gravitational waves? If so, they should lose energy permanently. Shouldn't this loss affect their trajectory? Or, alternatively, is it a negligible loss comparing with the loss by other types of radiation (e.m. radiation, particle radiation, etc.)?

A practical example: imagine that an object comes from afar, e.g. an asteroid approaching the Earth. As long as it travels through "empty space*, it is not accelerated (at least, not by the Earth). But, getting closer to Earth there is a moment, or a time-interval, when the asteroid begins to feel the Earth's presence, and begins to accelerate. How so?. I understand (if I understand correctly at all) that during body's non-accelerated movement, there is no radiation exchanged between it and the Earth. Then how does the asteroid begin to feel the Earth's presence? By the mediation of which carriers?

• It is a standard exercise to find the energy radiated from a two-body system. For the sun-earth system if I recall correctly to energy loss is of the order of magnitude that the orbital radius decreases by an atomic radius over the lifetime of the sun. I'm uncertain about the details but you get the idea of how tiny the effect is for our solar system. Jan 20, 2015 at 16:37
• Yes, energy is permanently lost by gravitational waves, due to the fact that the Earth's circular movement around the sun creates a time-variant quadrupole moment in the mass. The effect is vanishingly small, as Robin Ekman says. Jan 20, 2015 at 17:54
• Since the earth goes around in a circle, the net momentum flux is zero, since the gravitational radiation flux in january is in an opposite direction from the flux in july. It turns out that you CAN get net momentum transfers to the gravitational field in the case of colliding black hole binaries, though, where the last orbit is only a half orbit, and the black holes can get "pushed" to velocities exceeding the escape velocity from the galaxy they're in. Jan 20, 2015 at 20:44
• why are you talking about asteroids? the energy/momentum is transferred directly to the gravitational field. Over the course of a whole year, the net momentum transfer averages to zero. Jan 20, 2015 at 21:17
• AH. That bit is best not thought of as a gravitational wave. Think of it as a static gravitataional field that the Earth drags around with it as it moves. It orbits the sun, just like the Earth. And it's out there because it's always been out there. Jan 20, 2015 at 21:38

The massive body that is moving changes the gravitational field (or the metric) around it. This change happens at the speed of light and the delay can be (and was experimentally) detected. The carriers of the information of this change are believed to be gravitons (some particles that nobody detected so far, although there are various reasons to believe on their existence). The propagation of graviton can be considered (like in the case of photon) a gravitational wave (or electromagnetic wave in case of photon).

The emission of gravitational wave does take energy. In some rapid and very very massive systems this can lead to substantial loss of energy. The obvious example to check was a binary neutron star system. Russell A. Hulse and Joseph H. Taylor, Jr measured it first on a newly discovered type of a pulsar (neutron stars) and got themselves a Nobel prize 1993. This was also an indirect confirmation of the existence of gravitational waves (the direct measurement has not$^{*}$ been done yet, although there are several GW detectors around the world).

$^*$Update: Gravitational waves have been directly detected, cf. https://en.wikipedia.org/wiki/List_of_gravitational_wave_observations

Gravitational waves are emitted by oscillating quadrupoles (and higher moments). Compare this to electromagnetism where EM radiation is emitted by oscillating dipoles.

So an isolated body travelling along in space will not emit gravitational waves and won't lose energy. I can't offhand think of any physically plausible oscillating gravitational dipoles, but they wouldn't lose energy either.

As Robin says in a comment, the obvious example of an oscillating gravitational quadrupole is two masses in orbit around each other. These do radiate energy, and indeed this has been measured for binary neutron stars. However even in such an extreme system the amount of energy radiated is small. It's measurable only because we have two very compact, very massive objects orbiting each other with high angular frequency. For normal cosmological objects like binary stars, solar systems, galaxies etc, the rate of gravitational wave emission is so low as to be completely negligable.

• Imagine that an object comes from afar, like an asteroid. As long as it travels through "empty space*, it is not accelerated. But, getting closer to Earth it becomes accelerated (the quadrupole of which you speak?) How, it's ununderstandable to me, feels the asteroid the presence of the Earth? When the acceleration begins it's O.K. I believe that there is radiation, but at a certain moment in its non-accelerated movement, the body feels the Earth's presence. How? Jan 20, 2015 at 17:11
• @RobinEkman : can you see my comment to JohnRennie? Can you give some thought on it? Jan 20, 2015 at 17:12
• Do you know if this argument relies on some weak-field limit in which gravitational waves are treated as being solutions to a linear wave equation, and which propagate in something close to a flat background, or is this argument sufficient to prove that gravitational effects are bounded by future light cones even in the general case where curvature can be large and gravitational waves can behave in nonlinear ways? (like the 'geons' I described in this answer) Jan 21, 2015 at 0:46

I'm not a PhD in physics either or even a physicist for that matter, however, it's my understanding that all moving bodies in space will lose kinetic energy continuously over time.

For example, let's say the universe consists of a vast vacuum and one moving planetary body. That body will continually lose kinetic energy over time. Why? I'm not sure. Perhaps virtual particles would have something to do with it.

According to cosmological theory, the universe will eventually suffer heat death. There will be no motion except perhaps atomic motion. Again, I'm not a physicist.

http://www.newscientist.com/article/mg20927994.100-vacuum-has-friction-after-all.html#.VL6G7mwo6Cg

• Einstein didn't mention virtual particles. And though, in the Wikipedia article it's written clearly - the problem has been resolved by Einstein's theory of general relativity. Jan 20, 2015 at 16:45
• "it's my understanding that all moving bodies in space will lose kinetic energy continuously over time": this is a mis-understanding. The (real) Isaac Newton had this very clear in mind when he wrote the first law of motion. If you "wannabee" Newton, you'd better read it Jan 21, 2015 at 21:19