Hey it's professor Dave, I want to tell
you about general relativity.
We just spent a good amount
of time learning Einstein's theory of
special relativity, which he developed in
1905. This and other publications of that
year put him on the map as a force to be
reckoned with. A decade later in 1916, he
published his general theory of
relativity, which described the geometry
of space itself, and revolutionized the
way we think of the gravitational force.
An adequate description of general
relativity requires extremely
complicated math that goes far beyond
the scope of these tutorials, so we won't
even try to touch it from that approach.
But we can still briefly describe some
of the conceptual implications of the
theory that will dramatically change
your perception of the universe, so let's
see what Einstein had to say.
For centuries we thought that the universe
obeyed Euclidean geometry. This is the
kind from high school geometry class
where parallel lines never intersect, the
angles of a triangle add up to 180
degrees, and all kinds of other
geometrical perfections hold true. With
general relativity, Einstein showed that
this is not the case. Just the way you
can distort the shapes drawn on a piece
of paper by bending the paper, space
itself is distorted or bent around
massive objects. That is to say that just
the way that bending a piece of paper
results in a two dimensional plane
becoming wrapped around a third spatial
dimension, the three spatial dimensions
of space are wrapped around a fourth
spatial dimension, according to the
distribution of matter in the universe,
as mass is the property that causes
space to bend in this way. This is
physically impossible to visualize, so
don't worry when you find that you can't do it.
Our brains can only comprehend three
spatial dimensions, and so the best we
can do is to employ analogies, like the
bending of the piece of paper, and
understand that space does the same thing,
illustrated in an image like this, where
a two-dimensional representation of
space-time is curved around a star or
planet. This does not accurately depict
the true curvature of space, it is simply
the best we can do. These conclusions
describe the universe as non-Euclidean.
Parallel lines can indeed cross if they
move through curved space-time. Einstein
derived this theory in an attempt to
expand special relativity, which applies
only to inertial reference frames, to
include all reference frames, which is
why it is called general relativity.
One result of this is the idea that the
source of an acceleration has no effect
on the force imparted, such that a ship
in deep space accelerating at 9.8 meters
per second squared would impart a force
on someone inside that would feel
exactly like the gravitational pull on
the surface of the earth. Because we now
understand that space is warped around
massive objects, we see that general
relativity is a big improvement on
Newton's law of universal gravitation in
terms of a satisfactory theory of
gravity. Newton outlined aspects of the
gravitational force, but he didn't know
exactly what gravity is or how it
propagates. Now we can regard it as the
warping of space that deflects the path
of other objects, like a bowling ball
pressing down on a membrane. This
curvature creates what we know of as
gravity, being that massive objects tend
to fall towards more massive objects, and
this explains the orbits of the planets
around the Sun, as well as the falling of
objects towards Earth, without having to
resort to a magical field force
imparting action at a distance. Space is
therefore no longer an empty expanse
just the way that time is not a detached
parameter. These two constructs are
actually part of the same thing.
They comprise the space-time fabric.
Space-time tells matter how to move, and
matter tells space-time how to curve.
General relativity, just like special
relativity, enjoys a tremendous amount of
corroboration by experiment. One necessary
result of the theory is that light
should follow curved paths around
massive objects, and a famous experiment
observed light from a distant star
curving around the Sun during a solar
eclipse, whereby the blocking of the
sun's light allowed us to directly
observe the light from the star behind,
which appeared in a shifted location.
When light is deflected around more
compact objects like black holes, the
light from the more distant object can
bend around the mass in a way that
results in multiple images of the object.
This phenomenon is called gravitational
lensing, and it is a common astronomical
observation. General relativity predicts
and explains all kinds of other
observable phenomena, like anomalies in
the orbit of the planet Mercury, and
things like neutron stars and black
holes, which we will cover in the
astronomy course. But as strong as the
theory of general relativity is, it is
not complete, because it has not merged
with the particle world. That is to say,
we do not yet know how general
relativity can be reconciled with
quantum physics. To understand this
problem, we need to do a comprehensive
survey of all particles, so that we know
exactly what we are dealing with, so
let's move forward now.
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