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Summary Special Relativity
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Summary of Special Relativity in the subject of Modern Physics.
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Module 1: Modern Physics1. Special Relativity
Relativity: the study of how different observers measure the same event.
Classical relativity:
- limited but are good approximations for large, slow-moving objects.
- Galileo and Newton: first correct version of classical relativity.
Modern relativity is divided into 2 parts:
- General Relativity: deals with observers who are undergoing acceleration.
- Special relativity: deals with observers who are moving at a constant
velocity.
Einstein's First Postulate
The laws of physics are the same and can be stated in
their simplest form in all inertial frames of reference.
The laws of physics include only those that satisfy this postulate.
- the definitions of relativistic momentum and energy must be altered to fit.
Outcome: E = mc 2
An inertial frame of reference is a reference frame in which a body at
rest remains at rest and a body in motion moves at a constant speed in
a straight line unless acted on by an outside force (i.e. constant velocity).
- The simplest frames of reference are those that are not accelerated nor
rotating.
Newton's first law, the law of inertia, holds exactly in such a frame.
The laws of physics seem to be simplest in inertial frames, and they should be
the same in all inertial frames, since there is no preferred frame and no
absolute motion.
E.g. When flying in a plane at a constant altitude and speed, physics seems to
work exactly the same as if you were standing on the surface of the Earth.
However, in a plane that is taking off, the net force on an object, F, is not
equal to ma. Instead, F = ma plus a fictitious force.
Inertial a=0 Ball stays at rest
MB
accelerating Ball moves to the back of the plane
Accelerated
Md
, Einstein's Second Postulate
The speed of light c is a constant, independent of
the relative motion of the source.
Late in the 19th century, the major tenets of classical physics were well
established. Two of the most important were the laws of electricity and
magnetism and Newton's laws.
In particular, the laws of electricity and magnetism predict that light
travels at c = 3.00 x 108 m/s in a vacuum, but they do not specify the frame
of reference in which light has this speed.
There was a contradiction between this prediction and Newton's laws, in
which velocities add like simple vectors. If the latter were true, then two
observers moving at different speeds would see light traveling at different
speeds.
If such a motion were possible then:
- the wave would be stationary relative to the observer.
- it would have electric and magnetic fields that varied in strength at
various distances from the observer but were constant in time.
This is not allowed by Maxwell's equations. Law of physics
C= 1
EM
An object with mass cannot travel at speed c.
- This conclusion implies that light in a vacuum must always travel at speed c
relative to any observer.
- Maxwell's equations are correct, and Newton's addition of velocities is not
correct for light.
Michelson-Morley experiment:
The Michelson-Morley experiment demonstrated that
the speed of light in a vacuum is independent of the
motion of the Earth about the Sun.
The eventual conclusion derived from this result is that light, unlike mechanical
waves such as sound, does not need a medium to carry it. Furthermore, the
results implied that the speed of light c is independent of the motion of the
source relative to the observer. That is, everyone observes light to move at
speed c regardless of how they move relative to the source or one another.
Misconception: constancy of the speed of light
The speed of light is a constant c = 3.00 x 108 m/s in a vacuum.
- the effect of the index of refraction from The Law of Refraction, the
speed of light is lower in matter.
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