Notes on Relativity and Cosmology - Physics Department, UCSB

170 CHAPTER 7. RELATIVITY AND THE GRAVITATIONAL FIELD
Instead, the movement of the charge modifies the field only where the charge
actually is. This makes a ‘ripple’ in the field which then moves outward at the
speed of light. In the figure below, the black circle is centered on the original
position of the charge and is of a size ct, where t is the time since the movement
began.
+
Thus, the basic way that Maxwell’s equations get around the problem of instant
reaction is by having a field that will carry the message to the other charge (or,
say, to the planet) at a finite speed. Oh, and remember that having a field that
could carry momentum was also what allowed Maxwell’s equations to fit with
momentum conservation in relativity. What we see is that the field concept is
the essential link that allows us to understand electric and magnetic forces in
relativity.
Something like this must happen for gravity as well. Let’s try to introduce a
gravitational field by breaking Newton’s law of gravity up into two parts. The
idea will again be than an object should produce a gravitational field (g) in the
spacetime around it, and that this gravitational field should then tell the other
objects how to move through spacetime. Any information about the object
causing the gravity should not reach the other objects directly, but should only
be communicated through the field.
Old: F = m1m2G
d 2
New: F on m1 = m 1 g,
g = m2G
d .
7.2 Some observations
I should mention that these notes will address our new topic (General Relativity)
from a somewhat different point of view than your readings do. I do not mean