General Relativity
(This page still under construction)
In special relativity, we learnt about how space and time is actually intertwined. We have also learnt that the laws of Physics are the same in all inertial reference frames (including Maxwell’s Equations!).
How about accelerating reference frames? What happens to the laws of physics for a ‘stationary’ observer as compared to an observer in a freely falling frame? Is it even possible for us to have a ‘stationary’ observer?
We will start by looking at Newton’s model of gravity.
Newton’s Universal Law of Gravitation
Before we start considering a freely falling frame, let us take a step back and look at Newton’s Universal Law of Gravitation. When Newton imagined that the force that is pulling the apple to the surface of the earth is the same force which keeps the planets in orbit around the Sun, it was revolutionary!
Textbook Chapter 6.6 (p. 185-189) and 6.7 (p. 189-192)
There is a gravitational force between any two objects in the universe.
The strength of this attractive force is proportional to the product of the objects’ masses
The strength of this force decreases with the square of the distance between the objects.
While Newton came up with a good mathematical model (which also helped to show that it makes more sense to consider earth orbiting the sun than to have the sun orbit around the earth), he was not quite able to explain how such a force of attraction arose.
Newton formulated his law of gravitation around 1690. It stood for more than 200 years before Einstein came about with his General Theory of Relativity around 1910.
Questions on this section? Go to Newton’s Law of Gravitation
General Theory of Relativity
Following from Special Relativity, we go back to considering reference frames – this time, accelerating reference frames. Let’s begin with an illustration (Slightly modified from p.140-142 of Ref [2]). Consider two elevator cars:
(1) sitting at rest on the surface of the Earth;
(2) situated in outer space completely removed from the effects of any gravitational field, and is being accelerated upwards with a constant acceleration, g, equal to the acceleration of the particle falling near the surface of the Earth.
We claim that an observer in one of these cards would not be able to determine which car she was situated because her experiences in both cars would be identical. She would experience a gravitational pull towards the floor of the elevator in both cars. If the observer dropped two balls (one iron and one wooden ball), both will fall at exactly the same rate in the first elevator and also, at the exact same rate in the second elevator.
Principle of equivalence: the phenomena in an accelerating frame of reference are identical to those in a gravitational field [2].
Note: The principle of equivalence is also based on the equivalence of gravitational and inertial masses.
Bending of light
Let us go back to the elevator example [2]. Using the second elevator car, if a beam of light propagates perpendicular to the direction of the acceleration and enters the elevator from one wall, it will exit at a point below the one it had entered. By the principle of equivalence, Einstein argued that a beam of light can also be bent by a gravitational field!
Gravity as geometry
The bending of light suggests that gravitational effects are not confined to massive particles. Einstein proposed that the gravitational interaction between masses is not about one exerting a force upon another. Instead, he proposes that the presence of matter causes the spacetime continuum to curve. This means that what we use to consider as “free fall” is when a mass will travel along the shortest possible path in this curved four-dimensional space.
In a curved space, the shortest path is not a straight line! It is a curved path known as a geodesic. Essentially, all particles will move along this geodesic paths in spacetime unless there are other forces acting on it.
Comparing the models
Recall what we learnt about spacetime diagrams in special relativity. Let’s watch an animation and complete the worksheet given.
Activity
Astrophysical Implications
Einstein’s theory has some astrophysical implications. Many of these predicted consequences under the theory have also been experimentally proven. Some of these phenomenon puzzled mankind for decades, and has been explained by Einstein!
Gravitational Lensing (bending of light) http://www.youtube.com/watch?v=hL0UqcTExxI
Perihelion advance of Mercury’s Orbit (not able to explain using Newton’s Law of Gravitation!)
http://demonstrations.wolfram.com/MercurysPerihelionPrecession/
Many more…
Spectral shift
Gravitational time dilation
Black Holes
More links to help you…
General Relativity & Gravity: http://youtu.be/0rocNtnD-yI
Introduction to Newton’s Law of Gravitation: http://youtu.be/Xcel427Ezl0
Wikipedia: http://en.wikipedia.org/wiki/Introduction_to_general_relativity
http://en.wikipedia.org/wiki/General_relativity
References
College Physics Textbook
Wikipedia.
[1] Foster, J. & Nightingale, J. D. (2006). A short course in general relativity (3rd ed.). New York, USA: Springer.
[2] Logan, R. K. (2010). The poetry of physics and the physics of poetry. Singapore: World Scientific Printers.
[3] Perimeter Institute of Theoretical Physics. (2011). 03 Perimeter inspirations: revolutions in science [DVD]. Ontario, Canada.