Lecture physics a2 einstein’s special relativity phd pham tan thi

• 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 RELATIVI

Einstein’s Special Relativity

Ho Chi Minh University of Technology

• 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

Consider a Situation

Reference #1

0.5c

Speed of light

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

0.5c

Classical and Modern Physics Classical Physics

Large, Slow moving Object

• Newtonian Mechanics

• Electromagnetism and Waves

• Thermodynamics

Modern Physics Small, Fast moving Object

• Relativistic Mechanics

• Quantum Mechanics

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?

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…

underneath it

Origin of Special Theory of Relativity

• 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 (1879 - 1955)

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

• Relativity states that all laws of physics are invariant under those linear transformations:

which leave x2 + y2 + z2 - c2t2 unchanged

• This quantity is like a “ length ” in space-time, rather than just

space.

xi

4

X

j=1

Mijxj

→

We will now examine the physical meaning of this statement, as well as how it came to be proposed by Einstein.

The Special Theory of Relativity

• The crisis that motivated

Einstein’s work was related

to the laws of electricity and

magnetism, or

Electrodynamics

• These laws were known,

thanks to Maxwell, and

embodied in his famous

equations.

r · ~ E = ⇢

"0

r · ~ B = 0

r ⇥ ~ E = – @ ~ B

@t

r ⇥ ~ B = µ0J + µ ~ 0"0 @ ~ E

@t

Gauss’ Law

Gauss’ Law for Magnetism

Faraday’s Law

Ampere’s Law

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

set of axes within which to measure the position, orientation, and

other properties of object in it.

Inertial frames

• in which no accelerations are observed

in the absence of external forces

• that is not accelerating

• Newton’s laws hold in all inertial

reference frames

Non-Inertial frames

• that is accelerating with respect to

an inertial reference frame

• bodies have acceleration in the absence of applied forces

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

• If Newton’s law are valid in one reference frame, then they are also valid in another reference frame moving at a uniform

velocity

Galilean Invariance

NEWTONIAN PRINCIPLE OF RELATIVITY