SPECIAL THEORY OF RELATIVITY
WHAT IS RELATIVITY?
THE TWO FRAMES OF REFERENCE
INERTIAL FRAME OF
REFERENCE
NON-INERTIAL FRAME OF
A reference frame in
which an object stays
either at rest or at zero
acceleration unless
another force acts upon it.
A reference frame in which is in
accelerated motion with respect to
an inertial frame of reference.
REFERENCE
NEWTONIAN MECHANICS AND
ELECTRODYNAMIC THEORY
• Before 1905, all the laws of physics surround
gravity and electromagnetism. Both in these topic
is the well-known principle called Galilean
Relativity, where the Newtonian Mechanics agrees
with, but not with Maxwell’s Electrodynamic theory.
• Galilean Relativity states that the laws
concerning motion (dynamics) of a body are the
same in all the inertial frames of reference.
TIME FRAME OF REFERENCE
• The speed of light (c), as predicted, in an
inertial time frame of reference moving with
relative velocity is:
c = c’ + u
• Speed of light in inertial reference frame (c);
speed of light in the moving frame(c’); velocity
of the moving frame (u)
TIME FRAME OF REFERENCE
• Equation 2 is given where 𝑢𝑜 is the
permeability in free space and 𝑒𝑜 is the
permittivity in free space, which led to
now accepted speed of light of 3.0 × 10𝟖 .
c=
𝟏
1
𝐶= 𝑢 𝑒
0 0
= 3.0 × 10𝟖
SPECIAL RELATIVITY
• The theory of special relativity gives two
postulates dealing with inertial frame of
reference only. That is why it is called “special”
because it only deals with special cases where
motion is uniform. Hence, the motion it
explains is when it is travelling in a straight
line at a constant speed. But, when motion
starts to accelerate, the General Theory of
Relativity will be applied.
KEY PRINCIPLE IN SPECIAL THEORY
OF RELATIVITY
PRINCIPLE OF RELATIVITY
• The laws of physics are all the same in all
inertial frame of reference.
PRINCIPLE OF LIGHT SPEED CONSTANCY
• The speed of light in a vacuum is constant for
all observers, regardless of their motion
relative to the source.
CONSEQUENCES OF SPECIAL
RELATIVITY
TIME DILATION
• Time slows down for anything moving.
• The faster the object moves, the more the
time is affected.
• An inertially moving clock runs slowly than the
one at rest.
TIME DILATION
• CALCULATE FOR DILATED TIME INTERVAL
∆𝑡0
∆𝑡 =
𝑣2
1− 2
𝑐
• Dilated time interval (∆𝑡) or the time measured by
a non-moving observer. Proper time interval (∆𝑡0 )
or the time measured by an observer inside the
moving reference frame. Speed of a relative motion
(v) and (c) is the speed of light.
LENGTH CONTRACTION
• The faster the objects are moving, the shorter
the lengths.
• As they approach the speed of light, their
length contracts to zero. The length of objects
moving at relativistic speeds undergoes a
contraction along the dimension of motion.
∆𝑥 = (∆𝑥0 )
𝑣2
1− 2
𝑐
• Contracted length (∆𝑥); proper length (∆𝑥0 );
speed of relative motion (v); speed of light (c)
MASS INCREASE
• The faster the object is moving, the more its mass
is increasing. The mass of an object moving at a
speed approaching the speed of light in vacuum is
greater than its mass at rest relative to the
observer.
∆𝑚0
∆𝑚 =
𝑣2
1− 2
𝑐
• Relativistic mass (∆𝑚); rest mass (∆𝑡0 ) or the time
measured by an observer inside the moving
reference frame. Speed of a relative motion (v) and
(c) is the speed of light.