Relativity
A.1 The Beginnings of Relativity
Physics Guide
Understandings:
•
Reference frames
•
Galilean relativity and Newton’s postulates concerning time and space
•
Maxwell and the constancy of the speed of light
•
Forces on a charge or current (A.2)
Applications and skills:
•
Using the Galilean transformation equations
•
Determining whether a force on a charge or current is electric or magnetic in a given
frame of reference (A.2)
•
Determining the nature of the fields observed by different observers (A.2)
Reference Frames
Reference frames
•
A co-ordinate system in which measurements of distance and time can be
made (IB def)
•
Depending on the frame of reference, Newton’s laws may not hold. Can you
think of how?
•
Newton’s Laws require an “Inertial” frame of reference, usually defined with
respect to the object or the classical x,y co-ordinate carthesian system where y
is vertical position and x is horizontal position of the environment
Example wrt the object
Example wrt the environment
Definition:
An inertial
reference frame is
one that is either
at rest or moving at
constant speed in a
straight line.
Fictitious Forces
Galilean relativity
Galileo (yes, that one) said that there is no special position,
rotation or velocity, they are all defined relative to each other
Imagine you’re asleep on a train during a very smooth journey.
You wake up and see another train car outside your window. Is
it moving? Are you moving?
Galilean relativity
S is a rest frame (the lady), S’ is a
frame travelling at a constant
velocity uwrts which is the train. Both
frames are at the same position at
t=0
The image to the left is at some time
t later.
The train (and person on it) appear
to be travelling a velocities uwrts and
vwrts
From S’, the lady appears to be
moving with the same velocity in
the other direction.
If the man on the train walks
forward then
x=x’+vt
Note: Since time is absolute then ∆𝑡′ = ∆𝑡 is also true
u=u’+v
So switching between coordinate
systems is easy (just be careful of
the signs, these are vectors after all)
Newton’s postulates concerning time
and space
Time is absolute
“Absolute, true and mathematical time, of itself, and from its own nature flows equably without
regard to anything external, and by another name is called duration: relative, apparent and common
time, is some sensible and external (whether accurate or unequable) measure of duration by the
means of motion, which is commonly used instead of true time ...”
So the time interval in any frame of reference is the same
Space is absolute
“Absolute space, in its own nature, without regard to anything external, remains always similar and
immovable. Relative space is some movable dimension or measure of the absolute spaces; which our
senses determine by its position to bodies: and which is vulgarly taken for immovable space ...
Absolute motion is the translation of a body from one absolute place into another: and relative
motion, the translation from one relative place into another .”
Hence in any inertial frame (i.e not accelerating), any observations must be the same
(i.e difference is position is the same therefore the velocity calculated will be the same)
Maxwell and the constancy of the
speed of light
Maxwell’s Equations (integral form)
Don’t worry, they’re not on our
course, (although maybe number 3
looks familiar…)
Notice that in the fourth equation, we have
two constants, one is c and the other is
which is the magnetic permeability of free
space, and is also related to c.
The fundamental speed of light is built into
the defining equation showing the
relationship between electric and magnetic
fields, specifically the term relating to a
time varying electric field.
Nature of Science
Paradigm shift:
The fundamental fact that the speed of light is constant for all
inertial observers has far-reaching consequences about our
understanding of space and time. Ideas about space and time that
went unchallenged for more than 2,000 years were shown to be
false.
The extension of the principle of relativity to accelerated frames of
reference leads to the revolutionary idea of general relativity that
the mass and energy that spacetime contains determine the
geometry of spacetime. (discussed in A.5)