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EINSTEIN'S SPECIAL THEORY OF RELATIVITY

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Faizan Khan

on 16 January 2015

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Transcript of EINSTEIN'S SPECIAL THEORY OF RELATIVITY

In 1905, Einstein proposed an explanation.
The Special Theory of Relativity, in two parts:
The relativity principle:
All of the laws of physics are valid in all inertial frames of reference
The consistency of the speed of light :
Light travels through empty space with a speed of C=3.00x108 m/s, relative to all inertial frames of reference
EINSTEIN'S SPECIAL THEORY OF RELATIVITY
Due to the movement Om concludes himself that the light doesn't flash simultaneously
Two events that are simultaneous in one frame of reference are in general not simultaneous in a second frame moving with respect to the first; simultaneity is not an absolute concept.
Each inertial frame of reference with a different velocity takes its own 'slice' of spacetime.
In the second experiment the train is moving past Os at a high speed.
The distance the beams of light travel are equal relative to Os or Om.
For Os, the scenario is the same and the lamps flash simultaneously.
In the time interval it takes the light flash to travel to Om from each lamp, Om will have moved a slight distance to the right. Therefore when Om sees the flash from L2, Om has not yet seen the flash from L1. Observing Om is halfway between the soot marks on the train, Om concludes L2 flashed before L1.


Example: observer Os is standing on a railway platform in the middle of two lamp posts, each lamp post is connected to the same circuit. The lamps come on at the same time when the switch is closed .
Let's assume the lamps do not stay on when current is applied but flash and explode sending out soot and broken glass.
Light from the each flash travel in all directions at the speed of light.
Simultaneity is the occurrence of two or more events at the same time.
But different from Newton's universal time scale, in Einstein's theory of relativity, the measurement of time depends on the reference frame in which they are made.


Simultaneity

No change in interference pattern!
The experiment failed to show what was expected.
It was performed over and over at different points in orbit with the unchanged result that the speed of light in all directions remained the same.
Therefore, ether does not exist!
But how is the speed of light constant in different reference frames?
What made Einstein's theory so revolutionary is that it considers the measurement of the speed of light to be constant by definition, in other words it is a law of nature.

Einstein said this happens because there is something unexpected about length and duration. He thought that as the Earth moves through space, all measurable durations change, ever so slightly.

For example, any clock used to measure some duration will give a duration off by exactly the right amount so that the speed of light remains the same
If a velocity is constant in all directions from one frame of reference, then if we look at the velocity in different directions from a second frame of reference, we can determine the relative velocities of the frames of reference
If light travels through a Aether, then by measuring the speed of light in different directions, we should be able to determine our velocity relative to the Aether
The Special Theory of Relativity was developed and explained by Albert Einstein in 1905 because of weaknesses in Newtonian physics
Special theory of relativity

Frames Of Reference

Replaced absolute time with the speed of light
Asserted the equivalence of mass and energy (E=mc^2)
Challenged the wave theory of light, suggesting that light could also be regarded as a collection of particles. This helped to open the door to a whole new world – that of quantum physics.
Profound insight of the motion of particles
Demonstrated how to calculate Avogadro’s number and the size of molecules
Published the paper of “General Relativity”
Used general relativity theory to model the behavior of an entire universe
Won the Noble Prize in 1921
Considered one of the most influential physicist in the history of mankind


Time Dilation is the slowing down of time in a system, as seen by an observer in motion relative to the system.


Time Dilation

Os and Om are at the midpoint of the lamp posts. The distance the beams of light travel are equal, so the light arriving from each lamp is simultaneous.
The second observer Om sitting in a stationary train also concludes that the light from first lamp is simultaneous with the light from the second

Relative Motion of Objects
PART 1 : FRAMES OF REFERENCE AND RELATIVITY
PART 2: RELATIVITY OF TIME, LENGTH AND MOMENTUM
To illustrate, let's perform a thought experiment with two observers measuring different time intervals for the same sequence of events from two different frames of reference.
PART 3- MASS AND ENERGY
INTRODUCTION
From previous chapters, you may be familiar about the conservation of energy law which states:
In any given situation, no energy is destroy nor created, but it only changes form.
To understand this concept further we must look at energy itself: When a force is applied on an object, work is done, thus increasing its kinetic energy.

The Speed Limit:
Einstein proposed the famous "speed limit" that no material object can have a speed that is equal to, or greater than that of light.
Experiments Done to Prove Time Dilation:

Atomic Clocks:
-Four atomic clocks were flown around the world twice , once eastward, once westward, on regular passenger planes.
-Predicted time loss in time were 40 +/- 23 ns for eastward journey, and 275 +/- 21 ns for westward.
-Actual time loss were 59 +/- 10 ns for eastward journey, and 273 +/- 7 ns for westward.

Muons:
-Unstable particles which has a lifespan of 2.2 us.
-Accelerated to 0.994c into circular accelerator at CERN in Switzerland, in 1976.
-hypothesis that muons should only last 14 to 15 trips around the ring before they decay.
-muons actually did not decay until 400th trip, approximately 30 times longer.

NEWTONS FAMOUS EQUATION
When speeds become relativistic, (according to the theory of relativity), we must use a different approach to energy.
It was Einstein who claimed that: The total energy connected to an object of rest, the mass (m), moving at speed(v) relative to an inertial frame exists as:

Where E is Total energy, m is the mass and c is the speed of light.
If the object remains at rest in its inertial frame, then v is zero and the total energy is basically:
In the development of the mass-energy formulas Einstein anticipated two things:
There may be forces or interfaces in nature that perhaps convert mass into more acquainted forms of energy or vice versa. *
* This may be further explained by applying laws of energy along with Einstein's relativity theory.
Rest mass is a specific form of energy complied with all massive objects.
Real-Life applications of Einstein's Propositions
KEY POINTS COVERED IN THIS CHAPTER
In conventional or classical mechanics, mass and energy are preserved independently.
However in Einstein's theory of special relativity these laws are universalized to become one combined law; the conservation of mass-energy, which states:
That both mass along with energy are very much the same.
Rest mass is a form of energy that is convertible to several common forms of energy.
Einstein also concluded that:
Twin Paradox:

-Albert Einstein's famous thought experiment.
-One of the two identical twins travel on a spaceship at near light speed towards another planet and back to Earth.
-When he returns, his identical twin will be older than him, due to time dilation.
Length Contraction:

Consider the following scenario:
A spaceship making a trip from Planet A to Planet B, which is separated by a distance Lo apart and traveling at a speed v measured.
For captain in the spaceship, the journey occur at one single place. The captain can thus assign a proper-time duration "To" using a single clock on the spaceship. So the captain finds the distance between the two planets to be L = v x To
But for observers on the planets, the journey occurs at two different places, so they can assign a duration "t" to the two-event process consisting of the takeoff and the landing and would find the distance separating the events as Lo= v x t
Relativistic Momentum
We know that momentum a very important concept in Physics, and we know the equation to be p=mv. But in subatomic physics, it involves collision of particles traveling in relativistic speed, so it's important to know about relativistic momentum.

Through Newtonian concept of conservation of momentum, Einstein showed that momentum of an object is


This equation shows that as v approaches c, momentum approaches infinity.
Key Points Covered in This Chapter
-Time dilation is the slowing down of time in a system, as seen by an observer in motion relative to the system.
-Expression for time dilation is

-Proper length is Lo is length of an object, measured by an observer at rest relative to the object.
-Length contraction only occur in direction of motion.
-The expression regarding length contraction is
-Relativistic momentum is used for objects traveling at or more than 1/10th of the speed of light.
-Expression regarding relativistic momentum is
Motion
Newton's Laws
1. Law of Inertia

2. F = ma

3. For every action there is equal and opposite
reaction

Easily observed in low speed motion phenomenons



Einstein's Theory Of relativity
It analyzes motion of objects at high speeds, approaching the speed of light

Electrons & Photons
Our perspective of motion
An arbitrary origin and set of axes from
which to measure motion
Relativity
Earth is our most common frame of reference
Inertial Frame of reference
An example would be the motion of throwing a ball straight up from on top of a moving object

From the moving object's Frame of reference, the ball have taken a straight up and down path

From Earth's frame of reference, the ball seems to have traveled a projectile type of motion, in which it has a horizontal velocity
Non inertial Frame of Reference

It is a frame of reference that is accelerating relative to an inertial frame
e.g traveling in an accelerating vehicle
From the vehicle's frame of reference, we experience force when the car undergoes acceleration
From earth's frame of reference our motion obeys the law of inertia
In other words, a non inertial frame of reference, is a frame of reference, in which the law of inertia is not obeyed
Key Statements
In an inertial frame of reference, law of inertia applies
The laws of Newton's mechanics are only valid in an inertial frame of reference
Newton's mechanics apply equally in all inertial frame of references
There are no absolute velocity in Newtonian mechanics
According to Einstein, time interval
measurements depend on the reference frame
in which they are made
Newton's universal time scale

1 s you = 1 s all observers
Fusion in the sun ( hydrogen atoms squeeze together to form heavier atom, a process called nuclear fission). Release in energy causes corresponding loss of mass

Meson (subatomic particle) decay, complete disappearance ( so looses all of its rest mass). In the masses place appears electromagnetic radiation (energy is equivalent to mass lost)

In classical mechanics, velocities in different frames of reference is additive.

But wait! Maxwell's equations show the speed of light to be 3.00 x 10^6 m/s!
Scientists at the time proposed light propagates as a wave through a 'Luminiferous Aether'
Our measured speed of light should be different depending on our relative speed to this medium
The best-known experiment of this kind was done by A. A. Michelson and E. W. Morley in 1887
Light provided from a sodium lamp was focused into a narrow beam and split into two using a half-silvered mirror
Using mirrors, each half was sent through a long path, then recombined to form a diffraction pattern.
At different points in the Earth's orbit, our velocity relative to the Aether should change
Therefore, each beam would traverse in different times, and the interference pattern should shift
The Life Of Albert Einstein
Early Years
Albert Einstein was born on March 14 1879, In a small German town named Ulm. He also achieved his early education here. In 1896, Einstein begins attending ETH, a swiss polytechnical school. After graduating from ETH, the education board deemed him unqualified for any further education.
Einstein, Age 3 (1882)
Einstein, Age 14 (1893)
The Breakthrough
In 1901, Einstein accepts a job as a clerk at the swiss patent office in Berne. It was in 1905 that Einstein began publishing his works, and he is finally recognized for his feats. He published three papers in 1905: First, his quantum theory explanation of photoelectric effects, which awarded him a Nobel prize. Second, he took a mathematical approach to his explanation of the motion of particles in a fluid, which is commonly known as “Brownian Movement”. Thirdly, his revisions to what we know of energy, time, and length. By 1909, Einstein’s works were greatly recognized, and he was offered numerous university posts, such as then-named Kaiser Wilhelm physical institute (now named Max Planck Institute).
The Road To Greatness
Come 1915, Einstein published his General Theory of Relativity. This theory picks up where conventional Newtonian mechanics leaves off. Within the theory was his prediction of light being deflected by gravitational fields, which was proven true in 1919. Now Einstein is world-renowned, and is being recognized as one of the greatest scientists of the 20th century. In 1930, he went on vacation to California, and decided to permanently reside there due to the uprise of Hitler’s Nazis. In 1933, he accepted a post at Princeton, which was his last 22 years of his life was spent. In this time, he searched endlessly to compose a theory that united electromagnetic and gravitational fields into one, which he called the “Unified Field Theory”. This was never achieved, due to the lack of technology and many factors were unknown, such as forces of nature. Modern day scientists are working at the “Superstring Theory”, which proposes that all forces and particles are united by tiny, supersymmetric strings. Einstein was also skeptical of Werner Heisenberg’s theory, which proposed a subatomic universe which was based on probability. It is from this that Einstein is quoted; “God does not play dice”. With the creation of nuclear fission in 1939, Einstein saw his famous prediction of mass being converted to energy prove true. It was also then that Einstein wrote to US President Franklin D. Roosevelt, encouraging him to surpass Nazi Germany in nuclear weapons research. Roosevelt agreed, and the Manhattan Project was born.
Einstein Age 25 (1904)
Einstein, after receiving the Nobel prize (1921)
Einstein, In a portrait taken at Princeton (1935)
Last Years
Once the bomb was developed and working, Einstein wrote another letter to the President, who was now Harry S. Truman, pleading not to use the atomic bombs. Truman ignored the plea, and in 1945, the two atomic bombs were dropped on Japan. This sent the world into the “Nuclear Era”. Despite his collaboration in the research and development of the atomic bombs, Einstein was a pacifist, and only wanted to show the Japanese the atomic bomb as a demonstration, not drop it on them. On April 18, 1955, the world experienced the death of a great Physicist, Albert Einstein.

Einstein, 1947
2
CHAPTER 4- THE LIFE AND TIMES OF ALBERT EINSTEIN
Einstein's Theory of Relativity
Analyzes the effects of motion at high speeds, approaching the speed of light
Such as the motion of electrons & photons
THE END
It analyzes the motion relative to the
frame of reference
in which its made
Key Statements
3
. Nuclear power plant

Nuclear fission is uranium nucleus, breaks into two or more pieces releasing energy. During process some mass converted into energy

Sun’s power output=4x1026Watts

4.1x10^9 kg/s  energy / sec

QUESTION:-
The heat of combustion of coal is approximately 3.2 3 107 J/kg. If 1.0 kg
of coal is burned, what change would the release of energy in light and warmth make in the mass of the coal compared with the mass of the products of combustion? Using DE 5 (Dm)c 2 for an original rest mass of 1.0 kg of coal?
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