2. Relativity
According to classical mechanics space, time
and mass are constant, these are not relative.
Einstein said that space, time and mass are not
constant or absolute, these are relative. This
theory of Einstein is called theory of relativity.
There are two parts in the theory of relativity.
3. i) Special or restricted theory of relativity: The
special theory of relativity developed in 1905
treats problems involving inertial frames of
reference, which are frames of reference
moving at constant velocity with respect to one
another.
ii) General theory of relativity: The general
theory of relativity, proposed by Einstein in
1915 treats problems involving inertial frames
of reference accelerated with respect to one
another.
4. Frame of Reference: A coordinate system relative to which the
measurements are taken is known as frame of reference.
5. Frame of Reference are two types:
I. Inertial Frame of Reference:
II. Non - Inertial Frame of Reference :
i) Inertial Frame of Reference: A coordinate system in which Newton’s
first law (i.e. law of inertia) is valid is known as inertial frame of
reference.
ii) Non - Inertial Frame of Reference: A reference frame which is at rest
or moving with constant velocity is inertial reference frame, while the
accelerated frame is known as non-inertial frame of reference
6. The Galilean transformation and The
Lorentz transformation
The Galilean transformation and the Lorentz
transformation are two different sets of equations
used to relate coordinates between different inertial
frames of reference in the context of classical
mechanics and special relativity, respectively. They
describe how space and time coordinates change when
transitioning from one frame to another, specifically
when there is relative motion between the frames.
7. Galilean transformation
Equations:
𝑥′ = 𝑥 − 𝑣𝑡
𝑦′ = 𝑦
𝑧
𝑧 ′ = 𝑧
𝑡
𝑡 ′ = 𝑡
The Galilean transformation was developed by Galileo Galilei in the
17th century and was used to describe the transformation of
coordinates between two inertial frames in classical mechanics. It
applies when relative velocities between frames are much less than
the speed of light, making it suitable for everyday experiences at
non-relativistic speeds.
8. Lorentz transformation
Equations:
𝑥′ =
𝑥−𝑣𝑡
√1−
𝑣2
𝑐2
𝑦′ = 𝑦
𝑧′ = 𝑧
𝑡′ =
𝑡0
√1−
𝑣2
𝑐2
The Lorentz transformation is a fundamental part of Albert Einstein's theory
of special relativity, developed in the early 20th century. It is used to
describe how coordinates transform when dealing with relative velocities
close to the speed of light, making it applicable at relativistic speeds.
