More Notes on Relativity and Gravity
What is the point of relativity? (translating between non-absolute measurements to restore a sense of objectivity: movie analogy)
The key "dictionary" for doing the translation is a set of laws, including that the speed of light is the same in all frames.
(Why is that true? Well, light is massless, so "goes as fast as it can", it's built right into spacetime.)
Useful spacetime picture, since in relativity the two are weaved together.
Twin paradox: what breaks the symmetry that they both should think the other is younger? (proper acceleration)
How does breaking that symmetry rectify the situation? (relativity of simultaneity)
What if there is a gravitational field that does it, there's no proper acceleration then, right? (right, equivalence principle,
so it must mean that time slows down in a gravity field)
How does changing the flow of time make gravity work? (it creates spacetime curvature, think of it as space itself falling)
So to recap the main points of relativity:
It changes how we think about spatial lengths and time intervals-- we used to think those were absolutes, we now think
we reckon them differently for moving objects than for stationary objects. However, there's no change in how we think about
our own proper lengths and proper times-- the lengths and times that are in our own reference frame (stationary to us).
Also, we have simple rules of translation between different observers, so that's what we mean by the "same reality."
It changes what we think gravity is. We used to think gravity was a force (so appears in Newton's second law, F=mA),
but with Einstein, our picture has
changed dramatically. We now think it is a change in the meaning of straight paths in space-time (so appears in Newton's
first law, about what objects with no forces on them do, which is move in a "straight line" at the "same speed", both of
which take on new meanings in Einstein's modified space-time). We already thought that way for observers seeing the
world from an accelerating reference frame, so thinking about gravity in that same way is called "the equivalence principle."
One way to picture what gravity is doing is to imagine that it slows time for things closer to a source of gravity. That also
has the effect of (in this picture) making space itself "fall in" toward that object. This is often called "spacetime curvature,"
but that can be hard to picture, so this other way of thinking may work better for you. Note that it neatly explains why all
objects follow the same path under gravity-- they are just moving through the same "falling space and slowing time", it's not an
effect on the objects at all!
Review of course:
Three main parts: what is science (astronomy version), what are the key discoveries in our solar system (and
how were they made), and what is
our place in the grand scheme of the rest of the universe (and the potential for life there).