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Einstein's Theory of Relativity

SASP Presentation April 2011

Graham Perrin

on 4 May 2011

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Transcript of Einstein's Theory of Relativity

Einstein's Theory
of Relativity The Life of Einstein
Special Relativity Time dialation is cool =D
What is the Theory of Relativity? What is Time Dilation?
Time dilation is a concept that Albert Einstein had proposed about the relativity of time when travelling near the speed of light.
When travelling near the speed of light which is 3.00 x 10 m/s
General Relativity Special Relativity (1905) "Put your hand on a hot stove for a minute, and it seems like an hour. Sit with
a pretty girl for an hour, and it seems like a minute. That's relativity."
- Albert Einstein
Einstein's Theory of Relativity postulates that the passage of time is affected by the speed at which a body travels. It also seems to slow down in other situations...such as the sunset to sunset fast... Frame of Reference
The Special Theory of Relativity
Time Dilation
Length Contraction
Relativistic Momentum
E = mc² Two branches of relativity: The Special Theory of Relativity is a theory that Albert Einstein propose for the relative speed when an object is moving near the speed of light or moving the same as the speed of light. Simultaneity E = mc² Twin paradox
There are two twin brothers. On their thirtieth birthday, one of the brothers goes on a space journey in a superfast rocket that travels at 99% of the speed of light. The space traveller stays on his journey for precisely one year, whereupon he returns to Earth on his 31st birthday. On Earth, however, seven years have elapsed, so his twin brother is 37 years old at the time of his arrival.
This is due to the fact that time is stretched by factor 7 at approx. 99% of the speed of light, which means that in the space traveller’s reference frame, one year is equivalent to seven years on earth. Yet, time appears to have passed normally to both brothers, i.e. both still need five minutes to shave each morning in their respective reference frame. The Special Theory of Relativity One of the biggest questions in physics regards the properties of light
Scientists throughout the 20th century attempted to explain why light travels at a constant speed no matter what medium and length of time it travels
1905, Einstein proposed a revolutionary explaination in the form of Special Relativity
Comprised of two postulates:
1) The Relativity Principle: all the laws of physics are valid in all inertial frames of reference
2) The Constancy of the Speed of Light: light travels through empty space with a speed of
c = 3.00x10 m/s, relative to all inertial frames of reference
The first postulate is an extension of Newtonian relativity, proposing all the laws of physics, including those that govern electricity, magnetism, and optics, are all in the same inertial frames
The second postulate is less comprehensive as it defies the common notions of relative motion
One would expectthat in different frames of reference whether flying in an airplane or even sitting on a couch, the relative speed of light would change
The reason light speed being constant is unexpected is due to the fact most physical objects in the world “add” their speeds together
It is for this reason Einstein believed the relative speed of light should not change and that the same value, c = 3.00x10 m/s will be obtained despite changes in reference
Einstein’s proposed theory eliminated the dilemma found in Maxwell’s equations in which the speed of light predicted was not the speed of a special or absolute frame of reference, but the speed of any inertial frame

Eintstein originally named the "Special Theory of Relativity" as "The Special Theory of Invarience". In a sense, "invarience" describes his theory much better than the word "relativity". Perhaps it was to retain some "consistency" in naming his theories... Fun Fact: Q: A passenger of a car travelling at 50 km/h throws a ball out the window at 20 km/h towards
you. What is the speed of the ball?
A: One would expect the ball to travel at 70 km/h (speed of the car + speed of the throw) relative
to the frame of reference (yourself). This is in fact what truly happens.

Q: Similarly if the car is approaching you and decides to turn on the headlights, what would the
speed of light be?
A: The speed of light would remain the same since the speed of the car in addition to the speed of
the light beam from the headlights hardly makes any noticable difference! This is the reason
why the speed of light is considered constant as no Earthly objects can travel at a speed
significant enough to surpass light speed. If this was to be true, the mass would be infinite.
Think About It... While in physics you have learned gravity is a kind of force exerted on an object, Einstein made the revolutionary suggestion gravity is not a force like other forces, but is a consequence of space-time (the 3rd and 4th dimensions) not being flat, but curved or warped, by the distribution of mass and energy in it
In general relativity, objects/bodies always follow straight lines in 4-D space-time, but they nevertheless appear to us as moving along curved paths in 3-D space
This is known as geodesics, a path between two nearby points that are "straight lines” occurring on a “curved space”
The mass of the sun curves space-time in such a way that although Earth follows a straight path in 4-D space-time, it appears to us as a circular orbit in 3-D space
Not only planets must follow geodesics, but light rays as well
Current knowledge tells us light always travels at a constant speed, 3.00 x 10 m/s no matter what medium and length of time it travels
Light therefore doesn’t bend itself, but travels along warps in space appearing to being bent
Thus general relativity predicts light is bent by gravitational fields
Another prediction is that time should appear to run slower near a massive body like Earth
This is caused by the relation between energy of light and its frequencies (the higher the energy, the higher the frequency)
As light travels through Earth’s gravitational field, it loses energy and so frequency decreases
To someone travelling at such frequency, time appears to slow down dramatically
This phenomenon is responsible for the belief time travel is possible

General Relativity (1915) 8 8 Length Contraction
Time Dilation Relativistic Momentum Momentum is one of the most important concepts of physics
Recall Newton’s laws can be stated in terms of momentum which is conserved whenever there is no external, unbalanced force present in a system
Einstein developed an equation based on the Newtonian concept of Conservation of Momentum as given by:

The magnitude of p increases as speed increases according to the above relationship
The rest mass m of an object is its mass in the inertial frame in which the object is at rest and is the only mass that can be uniquely defined
It is impossible for an object of nonzero rest mass to be accelerated to or beyond the speed of light
p is the magnitude of the relativistic momentum
m is the mass of the object
v is the speed of the object relative to the observer at rest (frame of reference)
Length Contraction
Length contraction, according to Hendrik Lorentz, is the physical phenomenon of a decrease in length detected by an observer in objects that travel at any non-zero velocity relative to that observer.
This contraction (more formally called Lorentz contraction or Lorentz–Fitzgerald contraction) is usually only noticeable at a substantial fraction of the speed of light; The contraction is only in the direction parallel to the direction in which the observed body is travelling.
This effect is negligible at everyday speeds, and can be ignored for all regular purposes. Only at greater speeds it becomes important. At a speed of 13,400,000 m/s, the length is 99.9% of the length at rest and at a speed of 42,300,000 m/s still 99%. As the magnitude of the velocity approaches the speed of light, the effect becomes dominant.
The equation for Length Contraction is very similar to the Time Dilation equation with just some minor diffrences. In the length contraction equation, the contracted length is smaller than the proper length. Unlike time dilation, where the dilated time is larger than the proper time.
Time Dilation
One of the most enthralling aspects of Relativity is its new understanding of time. The term time dilation means the change in time through different frames of reference for a person travelling nearly the speed of light.
When traveling nearly the speed of light, your sense of time does not change, all you heart beats and everything that is travelling nearly the speed of light feels normal to you.
Take an anaology of you being in the train, if you close all windows and the train is moving at constant velocity, would you know that you're moving? Of course not. even if you bounce the ball up and down and what you will see is that the ball's path is directly vertically to you which would take about 4s if you time it. But when someone else that is in a stationary frame of reference observes you and the ball, instead of seeing the ball go a direct path up and down, the person sees the ball go up and down in a zig zag pattern and when the person times it, its actually roughly 6s.
Why is this? Well since the person observing you sees the ball going in a zig zag pattern, its distance to travel to keep up with the speed of the train is alot more than what you see. Therefore the longer the distance, the longer time. this is what time dilation is. Check out the awesome video to see how things work out. Is the equation for time dilation simple?
Like most equations you learn in physics, they are pretty simple to use in mathematical calculations.
The equation for time dilation is:

The Twin Paradox
There are two twin brothers. On their thirtieth birthday, one of the brothers goes on a space journey in a superfast rocket that travels at 99% of the speed of light. The space traveller stays on his journey for precisely one year, whereupon he returns to Earth on his 31st birthday. On Earth, however, seven years have elapsed, so his twin brother is 37 years old at the time of his arrival.
This is due to the fact that time is stretched by factor 7 at approx. 99% of the speed of light, which means that in the space traveller’s reference frame, one year is equivalent to seven years on earth.
Yet, time appears to have passed normally to both brothers, i.e. both still need five minutes to shave each morning in their respective reference frame.
What is SImulataneity in Special Relativity?
Two events occur at the same time but varies to people according to the frame of references that they experience the events.
According to the special theory of relativity, it is impossible to say in an absolute sense whether two events occur at the same time if those events are separated in space.
Where an event occurs in a single place—for example, two lightning bolts hitting both ends of the car, one person that is in a different frame of reference which is stationary will see that the two lightning bolts hit at the same time. However, the person that is in motion would see each bolt hitting at different times.
Which person is wrong about the lightning bolt? Neither is wrong because they are right in there own frame of reference. Check out the video for visual explanation! Recall the definition of momentum must be changed for relativistic speed if the conservation of momentum law is to remain true
Similarly, if conservation of energy law was to remain continuous, the definition of energy must also be revised
Einstein suggested that the total relativistic energy associated with an object of rest mass m, moving at a speed v relative to an inertial frame is:

If the object happens to be at rest in this inertial frame, where v is thus equal to zero, the total relativistic energy is simply:

With this equation, Einstein proposed two things: rest mass is a form of energy associated with all massive objects and that forces or interactions in nature may transform mass into varying forms of energy or vice versa
This proposal became what is known as the Conservation of Mass-Energy, the principle that rest mass and energy are equivalent
No, Einstein did NOT use the process of elimination to figure out his famous equation. While widely misconceived Einstein was involved in the creation of the atomic bomb, Einstein himself played no role in its development nor had any knowledge of it at the time. Rather, Einstein is credited to being the one who provided its theoretical framework, demonstrating through his equation that even the smallest mass, such as an atom, can generate immense quantities of energy. Fun Fact: Frame of Reference Thanks for Watching! Still utterly confused? Want to learn more? Here are some additional sources we hope will satisfy either situation: Literary Sources: Online Sources: http://www.osti.gov/accomplishments/nuggets/einstein/speedoflight.html
Nelson Physics 12
A Brief History of Time (Stephen Hawking) 8 8 A Frame of Reference can be defined as an arbitrary set of axes in which the change in position of a moving object can be measured
In more simple terms, it is simply “where a person (or other observer) happens to be standing”
To account for the motion of any object, a frame of reference must be used
Important to note there is no such thing as an absolute frame of reference in our universe
When referred to as absolute, it is meant no place in the universe is completely stationary
Since everything is moving, motion is relative to a frame of reference
Keep in mind even though you are not moving with respect to the Earth’s surface, you are moving with the Earth
Earth is commonly chosen as this reference point which thus gave rise to Newtonian physics
All of Newton’s laws, including gravitation theory and kinematics relies on a transition between two varying frames of reference:
a) Inertial Frame of Reference: a frame of reference that has no acceleration. Newton’s first law,
The Law of Inertial, holds in such a frame in which no fictitious forces arise
b) Non-Inertial Frame Reference: a frame of reference that experiences acceleration. The law of
inertia does not apply and fictitious forces arise
Each describe space-time, with time being dependent, in which depending on the type of reference frame, dictates the behaviour of motion
Such frames of reference are important based on the principle of space-time, what are considered to be “the third and forth dimensions” respectively
When one of these dimensions fail to exist, no dimensions are present and thus a frame of reference cannot be formulated
Therefore, a frame of reference allows one to analyze the behaviour of a motion over time as it travels in a given space

Albert Einstein (1879–1955) was born in the small town of Ulm, Germany, where he also received his early education. He showed little intellectual promise as a child, except in mathematics. He attended university in Switzerland but was not considered qualified to go on to graduate school or to secure a university post.
In 1901, he accepted a job as a clerk in the patent office in Berne, where he worked until 1909. In 1905, Einstein published papers that described three important new concepts in physics. The first, in quantum theory, was his explanation of the photoelectric effect. The second, published two months later, was his mathematical interpretation of the random motion of particles in a fluid, behaviour known as “Brownian movement.” The third, his most celebrated, set out special relativity, profoundly revising our conceptions of time, length, and energy.
By 1909, Einstein’s work had been widely recognized, and he was offered university posts, first at the University of Zurich and, in 1913, at the prestigious Kaiser Wilhelm Physical Institute in Berlin (later renamed the Max Planck Institute). In 1915, he published his general theory of relativity. This broader theory predicted further effects not forecast by Newtonian mechanics.
In 1930, Einstein went to California as a visiting professor. He subsequently chose to make his stay in the United States permanent because of the rise of Hitler and the Nazis in Germany. In 1933, he accepted a post at the Institute for Advanced Studies at Princeton, where he stayed until his death in 1955. For the last twenty-two years of his life, he searched in vain for a theory that would unite all gravitational and electromagnetic phenomena into a single, all-encompassing framework, a “unified field theory.” Einstein never realized his dream, in large part because a number of essential properties of matter and the forces of nature were unknown at the time
In 1939, Einstein was to see his famous prediction that mass could be changed into energy realized experimentally, with the achievement of nuclear fission by Otto Hahn and Lise Meitner in Germany. Various scientists persuaded Einstein, as the most influential scientist in the United States, to write to President Franklin D. Roosevelt, urging him to pre-empt Nazi Germany in nuclear weapons research. The enormous Manhattan Project was begun, and atomic bombs were produced. Gravitational Doppler Shift
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