Relativity
Objective: at the end of the lesson you should be able to
1. Discuss concept of relativity
2. Explain inertia frame of references
3. Discuss morley view to relativity
4. Discuss wave speed
A. Frames of Reference
Physical systems are always observed from some point of
view. That is, the displacement, velocity, and acceleration of a particle are
measured relative to some selected origin and coordinate axes. If a different
origin and/or set of axes is used, then different numerical values are obtained
for r, v and a even though the physical event is the same. An
event is a physical phenomenon which occurs at a specified point in space and
time.
1. Inertial Frames of Reference
a. Definition
An inertial frame is one in which Newton’s “Laws” of Motion
are valid. Moreover, any frame moving with constant velocity with respect to an
inertial frame is also an inertial frame of reference. While r and v would have
different numerical values as measured in the two frames, F= ma. in
both frames.
b. Newtonian relativity
Quote: The Laws of Mechanics are the same in all inertial
reference frames. What does “the same” mean? It means that the equations and
formulae have identical forms, while the numerical values of the variables may
differ between two inertial frames.
c. Fundamental frame
It follows that there is no preferred frame of reference—none
is more fundamental than another.
2. Transformations Between Inertial Frames
a. Two inertial frames
Consider two reference frames—one attached to a cart which
rolls along the ground. Observers on the
ground and on the cart observe the motion of an object of mass m.
PART b
Michelson-Morley
a.
Wave speeds
Midway through the 19th century, it was
established that light is an electromagnetic (E-M) wave.
Maxwell showed that these waves propagate through the vacuum
with a speed 8 c ≈ 3x10 m/sec.
Now, wave motion was well understood, so it was expected
that light waves would behave
Exactly as sound waves do. Particularly the measured wave
speed was expected to depend on the Frame of r In the S-frame, the speed of
sound is u in the S’-frame the speed is u′
The source and the Medium
are at rest in the S-frame. We find (measure) that u v in conformity with Newtonian
or Galilean relativity. We may identify a “preferred” reference frame, the
frame in Which the medium is at rest.
b.
Michelson-Morley
Throughout the latter portion of the 19th
century, experiments were performed to identify that Preferred reference frame for light waves. The
questions were, what is the medium in which Light waves travel and in what reference frame
is that medium at rest? That hypothetical medium Was given the name luminiferous ether (æther).
As a medium for wave propagation, the ether Must be very stiff, yet offer no apparent
resistance to motion of material objects through it. The classic experiment to detect the ether Is
the Michelson-Morley experiment. It Uses interference to show a phase shift Between
light waves propagating the Same distance but in different directions. The whole apparatus (and the Earth) is Presumed
to be traveling through the Ether with velocity, v. A light beam From the
source is split into two beams Which reflect from the mirrors and are Recombined
at the beam splitter— Forming an interference pattern which is Projected on the screen. Take a look at the
two light rays as observed in the ether rest frame.
The sideward ray: The
time required for the light ray to travel From the splitter to the mirror is obtained From
this.
- Lecturer : Agatha Oyiogu