Theory of Relativity
Special Theory of Relativity
(Space, Time, and Motion)
- Principle of relativity: All
observers not acted on by forces experience the same laws (an
assumption, and we also assume that they move with constant velocity).
- Constancy of speed of light:
All observers measure the same speed for light (a fact!).
- Consequences: Time dilation and length
contraction; Increase of effective mass with speed, E = mc2; Mixing of space
and time, replaced by spacetime.
- What does this have to do with black
holes? Special relativity works well as long as
gravity can be considered as a very weak force, and if we only observe
what happens in relatively small regions; But otherwise, you have to
add spacetime curvature...
General Theory of
- Equivalence Principle: Gravity
affects all objects in the same way; it cannot be distinguished from
what you feel when you are just accelerating. It is a fictitious
force like the centrifugal one, why is why it affects everything
the same way.
- Thought experiment: In a closed
elevator, could you distinguish acceleration from gravity?
- What does this tell us?
Spacetime is curved and objects in free fall don't follow straight line
paths, this is the fictitious gravity; The real forces are the ones
that make us deviate from free fall; Curvature of spacetime tells matter
how to move.
- What causes the curvature? The global
shape of spacetime may force it to be curved, plus matter/energy tells
spacetime how to curve locally.
- The main idea: If gravity is
caused by spacetime curvature and affects all objects the same
way, it must affect light too (no matter what Newton's theory
- Have we seen this? Yes,
from apparent shifts in the positions of stars when their light passes
near a massive object, from images of distant galaxies seen through
gravitational lenses, and from gravitational redshift of light from
stars (the mass of Sirius B was measured this way!).
- Extreme situations: Curvature
may cause light to be bent so much that it is trapped near the massive
object, inside a region from which not even light can escape: A black
- Other effects: If
spacetime can be curved, we should be able to see other effects too...
- What are gravitational waves? Ripples
in the fabric of spacetime.
- Do we know they are out there? Yes,
we have indirect evidence from the fact that the binary pulsar is
gradually losing energy.
- How can we detect them? Several interferometer
detectors, such as LIGO and VIRGO, are now operational; (Also search
by monitoring spacecraft such as Cassini); other detectors are being
- On Earth: Gravity makes time slow down, and the GPS would not work if
general relativity was not taken into account.
- Near Earth: The fabric of spacetime
twists like a vortex around a rotating body, making both orbits and
spins of objects wobble (by tiny amounts!).
[Astronomers are seeing evidence for this in the flickering of X-rays coming
from near massive black holes.]
- In the Solar System: Since gravity affects lengths and times, orbits don't have
exactly the shape that Kepler and Newton predicted.
- Wormholes? If the shape of spacetime
can change, there is the theoretical possibility of shortcuts to
remote places, as well as time travel...
- Can the whole universe be curved? This
is also a fact! It is also possible that there are small extra
dimensions! See what we know about cosmology...
page by luca bombelli <bombelli at olemiss.edu>,
modified 29 sep 2012