**Special Relativity**

Reference Frame

Example

Based upon Newton’s First Law, Inertial reference frame: when the person or object relative to the object in motion is in uniform velocity or at rest

Mickelson-Morley Experiment

The Relativity Principle

Concept of Space-time

x

y

z

Space

Time

Sitting at your desk, how fast are you moving?

Relative to the ground: Zero. You’re not moving relative to the frame of reference of the ground.

Relative to the sun: 2.97e4 m/s! That’s a pretty big difference, but since the Earth is orbiting the sun at this speed, an observer standing on the sun would say that you are moving at 2.97e4 m/s.

Both of these answers are correct in their own frame of reference.

The laws of physics don’t change, even for objects moving in inertial (constant speed) frames of reference.

Light travels through empty space with a definite speed of 3.0 x 10^8 m/s, regardless of the light source or the observer.

Simultaneity

What is Simultaneity?

Simultaneous: two events occurring at the same time

In Newtonian physics, simultaneity was absolute

According to Einstein, simultaneity is relative

What do you think?

Let’s find out…

The Train Experiment

Conclusion

Two events that are simultaneous to one observer are not necessarily simultaneous to another observer, moving relative to the first.

Time Dilation

What is time dilation?

Time is not a universal constant.

Two factors influence time dilation: speed and distance.

It only becomes noticeable at speeds closely approaching the speed of light, and do not, therefore, form any part our everyday experience.

The Twin Paradox

Length Contraction

Just as time slows down at very high speeds, length contracts at a very high speed too.

The formula that binds the relationship between proper length and contracted length can be derived by looking at a situation similar to the one for time dilation.

Mass Increase

Not only does the speed of an object impact factors like time and length, it also changes the mass of the object.

The derivation of the mass increase formula is based on the Newtonian concept of conservation of momentum.

Life of Albert Einstein

Einstein was asked if he would accept the position of being the second president of Israel. Einstein, age 73, declined the offer.

Twenty-one years after writing his Special Theory of Relativity, Albert Einstein invented a refrigerator that operated on alcohol gas.

Albert Einstein never received a Nobel Prize for special relativity. It was actually for the photoelectric effect.

Just after Einstein died in 1955, the recently discovered element with atomic number 99 was given the name ‘einsteinium’ in his honour.

Derivation

Significance

The length contraction is only significant when the object is moving at speed that which is a significant fraction of the speed of light.

The contraction occurs in the direction of the motion of the object.

Simple Definition

Einstein realized that space and time have to be treated equally in order for the laws of physics to be the same in all frames of reference (i.e. to all moving observers). This leads to a picture of a four dimensional space in which the three spatial dimensions and time make up the space. He called this space-time to signify that time and space are equal partners. Space-time has a geometry which determines how people moving through it observe the laws of physics and it is this geometry that makes up for the motion effects allowing all moving observers to agree on the speed of a light beam

Hafele-Keating Experiment

The Hafele–Keating experiment was a test of the theory of relativity. In October 1971

Took four cesium-beam atomic clocks aboard commercial airliners. They flew twice around the world, first eastward, then westward, and compared the clocks against others that remained at the United States Naval Observatory.

Why was it done, and what would it explain?

Velocities

Light

Galilean Relativity

9 m/s

21 m/s

30 m/s

Relative to the Bus

Relative to the Ground

1860s, James Clerk Maxwell

= C

The conclusion is that "Light travels at c."

Light

C

ether

This was also used to explain how light is able travel from the sun and other stars to the Earth through what would otherwise be empty space. The ether fills that empty space so light can wave along it. As the story goes, if you are at rest relative to the ether, you will measure the speed of light as 300 000 000 m/s, But if you are moving relative to the ether. You will see light traveling at a different speed.

Albert Michelson and Edward Morley

During the 1880s two American men, Michelson and Morley, wanted to discover an "absolute reference frame".

Source

Beam Splitter

Mirror

Mirror

Detector

Ether Wind

Conclusion?

Inertial frame of reference

You the observer is at rest or moving at a constant velocity

Example

Constant Velocity

Non-Inertial frame of reference

Non-inertial reference frame: when a person/object relative to the object in motion is accelerating

You the observer is accelerating

Example

Accelerating

*In this frame of reference Newtonian physics cannot explain the movement of an object

It's when an object is observing another object in motion. But different people in different positions and points of view can witness the exact same event and still interpret it differently.

Inter convertibility of Mass and Energy

Introduction

If you recall, in the equation, work done = ΔEk= Ek2- Ek1, the object’s mass is assumed to be constant.

In the situations with the very high speeds however, this assumption can no longer be made. Therefore, the Newtonian equation for kinetic energy is not valid anymore.

What is the Equation?

At velocities close to that of the speed of light, mass and energy are inter convertible.

Called by some the most famous equation of all time:

E=mc^2

This equation means that mass can be converted to energy and vice versa.

Sample Problem

Examples

In radioactivity radium disintegrates to emit energy, in accordance with the equation.

For medical purposes through the use of radioactive substances.

Earth’s crust is kept warm by processes which use E=mc^2

The warmth that we feel from the sun is the result of this process

BY:

The Designer/Creator

The Mathematician

The Historian

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