Newton’s equations give the speed of gravity as infinite. For example, in Cartesian coordinates, suppose a gravitating mass 2M is at the origin up until time t=0. At that time, the mass splits into two masses of mass M, one going in the +x direction at speed v the other in the -x direction at speed v. For times greater than 0, the gravitational potential is given by the sum of the two gravitational potentials:
At any distance, the above depends on t so the gravitational potential (and it is easy to show the gravitational force) is instantaneously changed at all distances from the origin. The speed of gravity is therefore infinite in Newton’s theory.
The name of this blog is “Mass”, but I really haven’t made many posts on the subject of physics. The reason is that I do not yet understand mass, and don’t have a great desire to explain pieces of things that I think I know but that are not well motivated to the reader. But a recent post on Backreaction on the subject of the GZK cutoff has motivated me to write on some of the anomalies seen in ultra high energy cosmic rays.
Cosmic rays are events in the atmosphere that are caused when a very high energy “primary particle” leaves the vastness of empty space and collides with the crowded environment of our planet’s atmosphere. A series of collisions turn the primary particle into a shower of debris. Primary particles with very high energies are extremely rare and so only experiments that examine very large regions of the atmosphere can hope to be lucky enough to see them.
Such an experiment must cover hundreds of square kilometers, it is not possible for the experiment to see the primary particle. The primary particle disintegrates at high altitude, it is only the shower of debris that the experiments can measure. For this reason, there is some question as to the nature of the primary particles.