# Classical gravitational wave

Consider the electric field surrounding an electron. The electron moves. A wave propagates at $c$ reflecting the electron's movement. This is an electromagnetic wave. Consider a mass. Classically surrounded by a gravitational field. The mass moves. The field deforms and it propagates at $c$.

• Is this not a gravitational wave?

• Why do people talk as if only general relativity predicted gravitational waves?

• Compare Maxwell's equations for electromagnetism (with time derivatives of the fields) and Poisson equation for gravity (with no time derivatives). – AccidentalFourierTransform Jan 18 '16 at 6:40
• The catch is that classical gravity works instantaneously, not at c. This would still produce a "wave" with infinite velocity and infinite wavelength, if you would see it that way. – busukxuan Jan 18 '16 at 6:53

## 2 Answers

Newtonian gravity doesn't predict anything traveling at speed $c$ as neither the constant $c$ nor any constants you can use to make the constant $c$ even appear in Newtonian Gravity.

Maxwell has $\epsilon_0$ and $\mu_0$ from which you can make $c$. And General Relativity and Special Relativity have $c$ directly as a constant of the theory. But Newtonian Gravity has no speed, it only has one constant, $G,$ and the units of $G$ are $\mathrm{kg^{-2}N}.$

You're not wrong! Gravitational waves do occur classically, and that's because general relativity is a classical theory! In Newtonian gravity, the gravity field doesn't "deform," nor does it have a speed - it's just a force that acts at a distance, instantaneously. So you're entirely correct - that is one way that gravitational waves could be created.

• There are two senses of classical here. You are using classical as an opposite to quantum, and in that sense general relativity is a classical (smooth, not quantized) theory. The other sense is classical Newtonian mechanics and gravity as opposed to general relativity. In that sense, there are no gravity waves in classical mechanics because gravity propagates instantaneously. I think OP was using classical in the second sense. – Ross Millikan Jan 18 '16 at 7:09
• Right - but in the Newtonian classical sense, there's not a whole lot of sense in talking about propagating gravitational waves. So my answer says "yes, in the typical usage of the word classical, you're right," but "no, not in Newtonian gravity." – Sam Blitz Jan 18 '16 at 7:11
• I guess I need to hone my question. Not like Newton but a student of Newton who understands (believes) that information cannot be transmitted to another person (where ever they are) at infinite speed. So if the mass m moves it will take time before the information of that movement is propagated. I agree c has no role so call it d. So this hypothesis added on to Newtonian gravity surley produces a gravity wave but has nothig to do with General Relativity? I suppose that is my point. This is my first StackE Q so forgive me if I am not with the protocol. – Robbydcm Jan 18 '16 at 8:48
• @Robbydcm: Newtonian mechanics, including gravity, assumes a universal time coordinate everywhere and that gravitational effects travel at infinite speed. It also presumes that the speed of light is influenced by source velocity. You can't pick and choose. You could try to formulate an alternate gravity theory that has finite transmission speed, but you would have to be careful not to cause a contradiction. Probably you have seen the derivation of all of special relativity from the constant speed of light. It is all interrelated. – Ross Millikan Jan 18 '16 at 14:55
• I think this answer is incorrect because gravitational waves are not created if only the mono- and dipole moments are non-vanishing (it is well-known that the leading contribution to radiation depends on the quadrupole moment). – Danu Feb 16 '16 at 16:25