## Thursday, 9 July 2009

### Spacetime and Energy

Spacetime and Energy:
Special relativity and E=mc2 led to the most powerful unification of physical concepts since the
time of Newton. The previously separate ideas of space, time, energy and mass were linked by
special relativity, although without a clear understanding of how they were linked. The how and why remained to the domain of what is called general relativity, a complete theory of
gravity using the geometry of spacetime. The origin of general relativity lies in Einstein's attempt to
apply special relativity in accelerated frames of reference. Remember that the conclusions of
relativity were founded for inertial frames, i.e. ones that move only at a uniform velocity. Adding
acceleration was a complication that took Einstein 10 years to formulate.
Equivalence Principle:
The equivalence principle was Einstein's `Newton's apple' insight to gravitation. His thought
experiment was the following, imagine two elevators, one at rest of the Earth's surface, one
accelerating in space. To an observer inside the elevator (no windows) there is no physical
experiment that he/she could perform to differentiate between the two scenarios. An immediate consequence of the equivalence principle is that gravity bends light. To visualize
why this is true imagine a photon crossing the elevator accelerating into space. As the photon
crosses the elevator, the floor is accelerated upward and the photon appears to fall downward. The
same must be true in a gravitational field by the equivalence principle. The principle of equivalence renders the gravitational field fundamentally different from all other
force fields encountered in nature. The new theory of gravitation, the general theory of relativity,
adopts this characteristic of the gravitational field as its foundation.