S PEED OF G RAVITY by Robert Nemiroff Michigan Tech

Physics X: About This Course Officially "Extraordinary Concepts in Physics" Being taught for credit at Michigan Tech o Light on math, heavy on concepts o Anyone anywhere is welcome No textbook required o Wikipedia, web links, and lectures only o Find all the lectures with Google at: "Starship Asterisk" then "Physics X" o

S PEED OF G RAVITY Does gravity propagate at the speed of light? It is clear that gravitational radiation propagates at c, although this has never been directly experimentally confirmed, since gravitational radiation has not yet been directly detected. But what about gravity itself?

S PEED OF G RAVITY S PEED OF G RAVITY : H ISTORY Newton (1680s) assumes that the speed of gravity is infinite. o This fits all contemporary observations. Laplace (1805) tries to fit Newton's theory with a wave mechanism where the speed of gravity was equal to the speed of light o Failed. Laplace then estimated that gravity moves ~106 times faster than light.

S PEED OF G RAVITY S PEED OF G RAVITY : H ISTORY Lorentz (1904) creates ether theory where gravity propagates at light speed. o Laplace problem fixed. o Precession of Mercury too small. Many more people propose many gravitational theories. Einstein proposes General Relativity (1915) o In GR gravity propagates a light speed.

A BERRATION OF L IGHT You see two stars before you in the distance. You start moving rapidly toward them. What do you see? 1. The stars appear to move apart. 2. The stars appear to move together. 3. The stars appear the same. 4. The stars get out of the way just to be safe.

A BERRATION OF L IGHT 2. The stars appear to move together. This is a known effect from special relativity. This is caused by the finite speed of light. This is in addition to the Doppler - color effect where the stars in front would appear more blue, while the stars behind would appear more red.

A BERRATION OF L IGHT You are placed in a circular orbit around the Sun. Because of aberration, does the Sun appear precisely 90 degrees from your orbital motion? 1. Yes, that is necessary for a circular orbit. 2. No, aberration makes the Sun appear slightly ahead of you. 3. No, aberration 'leaves the Sun behind' and makes the Sun appear slightly behind you.

A BERRATION OF L IGHT 2. No, aberration makes the Sun appear slightly ahead of you. The faster you orbit, the more the Sun will appear ahead of you.

A BERRATION OF L IGHT OK, the Sun appears slightly ahead of you. Does sunlight push you back, creating a "drag force" as you orbit the Sun. 1. Yes, that sounds reasonable. 2. No, that would cause the Earth to fall into the Sun. 3. No -- the Sun, being over there, cannot create a force over here.

A BERRATION OF L IGHT 1. Yes, that sounds reasonable. This is called the Poynting-Robertson effect and is a primary reason (for example), why dust particles fall into the Sun. The effect on the Earth, although real, is very small.

A BERRATION OF G RAVITY OK, the Sun appears slightly ahead of you. Does the gravity of the Sun also appear slightly ahead of you? 1. Yes, since sunlight and gravity move at the same speed. 2. No, gravity is immune to this effect. 3. Does this mean the Solar System is unstable?

A BERRATION OF G RAVITY 2. No, gravity is immune to this effect. Although few direct experiments have been done, the stability of the Earth's orbit puts limit on aberrational effects. As detailed in Carlip (2000), in Einstein's general relativity, there are velocity dependent terms that cancel the aberration effect. The calculation is complex but demanded by conservation of angular momentum, although the emission of gravitational radiation will make the cancellation inexact. Carlip (2000)

A BERRATION OF G RAVITY It is therefore possible to see someone in one direction, and feel the force of its pull from a different direction! Strange!

A BERRATION OF AN E LECTRIC F IELD Does a charged object orbiting an oppositely charged object see an aberrated electric field? 1. Yes, all electromagnetic effects will feel aberration. 2. No, electric fields are (also) immune to this effect.

A BERRATION OF AN E LECTRIC F IELD 2. No, electric fields are immune to this effect. There is no aberration of an electric field. This is an observed fact. Given Noether's theorem, any field that is invariant over in time will conserve energy (locally) and hence will not show aberration. When worked out in detail, velocity dependent terms come in to cancel the effect of the finite speed of propagation of a changing electric field.Noether's theorem