Lecture Physics A2: Einstein’s special relativity - PhD. Pham Tan Thi present the content statement for special relativity, Reference Frame and Inertial Frame, newton relativity or Galilean invariance/transformation, twin paradox,...
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Nội dung Text: Lecture Physics A2: Einstein’s special relativity - PhD. Pham Tan Thi
- Einstein’s Special Relativity
Pham Tan Thi, Ph.D.
Department of Biomedical Engineering
Faculty of Applied Sciences
Ho Chi Minh University of Technology
- Contents
• Statement for Special Relativity
• Reference Frame and Inertial Frame
• Newton Relativity or Galilean Invariance/Transformation
• A need of “Ether” (a Medium for propagating Light)
• Michelson-Morley Experiment
• Lorentz - FriztGerald Proposal
• The Problem of Simultaneity
• Lorentz Transformation
• Consequence of Lorentz Transformation
• Twin Paradox
- Classic Picture for Relative Motion
- Consider a Situation
Reference #1 Reference #2
- Consider a Situation
Reference #1
Speed of light
0.5c
- 0.5c
From the girl’s point of view on the platform, that light would not
look like it is going faster than the speed of light. It would just look
like it is moving at exactly the speed of light
- Classical and Modern Physics
Classical Physics Modern Physics
Large, Slow moving Object Small, Fast moving Object
• Newtonian Mechanics • Relativistic Mechanics
• Electromagnetism and Waves • Quantum Mechanics
• Thermodynamics
10% of c
- • Below 10% of the speed of light, c, classical mechanics holds
(relativistic effects are minimal)
• Above 10%, relativistic mechanics holds (more general theory)
SPECIAL THEORY OF RELATIVITY
Aims to answer some burning questions:
• Could Maxwell’s equations for electricity and magnetism
be reconciled with the laws of mechanics?
• Where was the ether?
- History
Albert Einstein surprised the world in 1905 when
• He theorized that time and distance cannot be measured
absolutely
• They only have meaning when they are measured relative to
something
Einstein published his theory in two steps:
• Special theory of relativity (1905) ➔ How space and time are
interwoven
• General theory of relativity (1915) ➔ Effects of gravity on space &
time
What is “relative” in relativity?
• Motion … all motions is relative
• Measurements of motion (and space & time) make no sense
unless we are told what they are being measured relative to
What is “absolute” in relativity?
• The laws of nature are the same for everyone
• The sped of light, c, is the same for everyone
- What is Relative?
• A plane flies from Nairobi to Quito at 1,650 km/hr
• The Earth rotates at the equator at 1,650 km/hr
• An observer…
✦on the Earth’s surface sees the plane flies westward overhead
✦at a far distance sees the plane stands still and the Earth rotate
underneath it
- Origin of Special Theory of Relativity
Albert Einstein
(1879 - 1955)
• In 1905, Albert Einstein changed our
perception of the world forever.
• He published the paper on the
electrodynamics of a moving body
• In this, he presented what is now
called the Special Theory of Relativity Albert Einstein, Ann. Phys.
17, 891 (1905).
- Einstein’s Discussion
✴What was the background to this work?
✴What was the new idea that he proposed?
✴How was this experimentally confirmed?
✴How does this influence our thinking today?
- The Special Theory of Relativity
• The laws of Physics are known to be unchanged
(“invariant”) under rotations.
• A rotation mixes the space coordinates but does not
change the length of any object.
• So there should be a linear transformation.
- The Special Theory of Relativity
• Special Relativity extends this invariance to certain
transformations of space and time together.
• Collect the space coordinates (x,y,z) as well as time t into a four
component vector.
• c is the speed of light. According to Relativity, it is the same in
every reference frame.
• Relativity states that all laws of physics are invariant under those
linear transformations:
4
X
xi → Mij xj
j=1
which leave x2 + y2 + z2 - c2t2 unchanged
• This quantity is like a “length” in space-time, rather than just
space.
- The Special Theory of Relativity
We will now examine the physical meaning of this statement, as
well as how it came to be proposed by Einstein.
- Electrodynamics
Gauss’ Law
• The crisis that motivated
Einstein’s work was related ~ ⇢
r·E =
to the laws of electricity and "0
magnetism, or Gauss’ Law for Magnetism
Electrodynamics
• These laws were known, ~ =0
r·B
thanks to Maxwell, and
embodied in his famous Faraday’s Law
equations. @ ~
B
~ =–
r⇥E
@t
Ampere’s Law
@ ~
E
~ = µ0 J~ + µ0 "0
r⇥B
@t
- Electrodynamics
These equations depend on the speed of light, c.
• In what frame is this speed to be measured?
• It was thought that light propagates via a medium called “ether”,
much as sound waves propagate via air or water.
• In that case, the speed of light should change when we move with
respect to the ether - just as for sound in air.
• So c would be the speed of light as measured while one is at rest
relative to the ether.
- Reference Frames
Two or more objects which do not move relative to each other
share the same reference frame.
• they experience time and measure distance & mass in the same
way
Objects moving relative to the other are in difference reference
frames
• like the plane and ground
• they experience time and measure distance and mass in different
ways
- Reference Frames
A reference frame in physics, may refer to a coordinate system or
set of axes within which to measure the position, orientation, and
other properties of object in it.
Inertial frames Non-Inertial frames
• in which no accelerations are observed • that is accelerating with respect to
in the absence of external forces an inertial reference frame
• that is not accelerating • bodies have acceleration in the
• Newton’s laws hold in all inertial absence of applied forces
reference frames
- Inertial Reference Frame
• A reference frame is called an inertial frame if Newton
laws are valid in that frame.
• Such a frame is established when a body, not subjected to
net external forces, is observed to move in rectilinear
motion at constant velocity.
NEWTONIAN PRINCIPLE OF RELATIVITY
• If Newton’s law are valid in one reference frame, then they are
also valid in another reference frame moving at a uniform
velocity.
• This is referred to as the Newtonian Principle of Relativity or
Galilean Invariance
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