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Relativity Theories

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Relativity Theories

The Principle of Relativity

In physics, the concept of relativity is not new.

Galilean Relativity means that the laws of mechanics are the same in all constant velocity (inertial) reference frames.

Although motion often appears relative, it’s logical to identify a “background” reference frame from which absolute motion could be measured.

OBSERVER AT REST

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Newton and others believed that space itself provided the reference frame for measuring absolute motion.

Albert Einstein developed a new theory of relativity that abolishes the concept of absolute space (and absolute time)!

OBSERVER MOVING

AT CONSTANT VELOCITY

The End of Classical Physics

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James Clerk Maxwell explained how light and all other electromagnetic waves are composed of self-propagating alternating electric and magnetic fields.

The electromagnetic waves were believed to exist in the “luminiferous ether” of space, which had peculiar qualities:

It allows EM waves to travel very fast

- 300,000,000 m/s or 186,000 ft/s or 671,000,000 miles per hr!

It has low inertia (very “lightweight”)

It permeates all space

It is the “background” for measuring absolute motion in the universe

The Michelson-Morley Experiment

In 1887Albert Michelson and Edward Morley attempt to measure the motion of the Earth relative to the “ether wind”.

Relative velocity in a stream

Relative velocity through the ether

Michelson-Morley interference pattern

The test yielded a “null hypothesis”, meaning no ether wind was detected.

In 1907, Michelson wins the Nobel Prize in Physics, mostly for this famous “failed” experiment.

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Postulates of Special Relativity

Postulate #1

All laws of physics (mechanics and electricity & magnetism) are the same in all uniformly moving frames of reference.

All motion is relative, not absolute

Postulate #2

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The speed of light in is independent of the motion of the source or the motion of the observer.

Stationary charges make electric fields, but moving charges also make magnetic fields

The observer sees the same speed of light c each time

These two observers measuring the speed of light observes the exact same speed!

Time Dilation

Time is not absolute, but is relative, and depends on motion.

Motion in space alters motion in time.

To a stationary observer a moving clock runs slower that an identical stationary clock.

A LIGHT CLOCK

LIGHT CLOCK OBSERVED IN A ROCKET SHIP

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LIGHT CLOCK OBSERVED FROM THE EARTH

Time Dilation & the Lorentz Factor

Time dilation is determined with algebra and geometry!

The factor γ(“gamma”) is called the Lorentz factor, and γ ≥ 1

“proper time” t0 is the time measured in the reference frame where two events occur at the same location in space. It is incorrect to call this “rest time” because rest is relative!

Time Dilation & the Lorentz Factor

The Twin Paradox

A classic mental test of Special Relativity involves twins, one who stays on Earth, while the other travels in a spaceship and then returns home. The twin who travels will have aged less than the twin who stays at home!

For example, if the twin who travels moves at half the speed of light, the twin at home will be 15% older when they meet again!

Why does this happen? Doesn’t each see the other’s “clock run slow”? No! – the frames of reference are not the same – one twin has a single time frame on Earth, the other has two time frames, one for each one-way trip!

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Length Contraction

As objects move through spacetime, space as well as time undergoes changes in measurement. The lengths of objects are contracted when they move by us at relativistic speeds.

How does the length appear to each observer? Both see each other’s meter stick contracted!

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“proper length” L0 is measured in the reference frame of the object. It’s incorrect to call this “rest length” -rest is relative!

Spacetime

No longer are the three dimensions of space unrelated to the one dimension of time. Relativity links them together as spacetime, a four dimensional quantity.

Spacetime Diagrams

Earth-Moon spacetime

Relativistic Momentum

The revision of Newtonian mechanics includes momentum. At relativistic speeds, the product of mass and velocity increases without limit.

path for γmv

path for mv

relativity calculator

This means that particles act as if their mass increases when their velocity increases. It also means it’s impossible for something with mass to be pushed enough to acquire the speed of light, c.

STANFORD LINEAR ACCELERATOR (SLAC)

Energy/Mass Equivalence

Einstein not only linked space and time, he also linked mass and energy. Mass has “energy of being” (in effect a kind of potential energy) that is called rest energy.

Perhaps the most famous equation of the 20th century is the energy/mass equivalence equation:

Nuclear physics

elementary particle

physics provide the

experimental proof of Einstein’s most celebrated equation!

Energy is released in fusion of light elements, and in fission of heavy elements

Kinetic Energy, Rest Energy, Total Energy

The famous equation linking mass and energy is called “rest energy”.

EXAMPLE: A muon (rest mass 2.4 x 10-28 kg) travels at 0.8c. What is its kinetic energy? Compare to a “classical calculation” (½mv2)

Einstein showed that relativistic kinetic energy is

Total relativistic energy is

What is the total energy of the muon?

Equivalence Principle

The “special theory of relativity” is limited to constant velocity reference frames. A more “general theory” applies to accelerated reference frames and links acceleration to gravity.

Newton’s universe animation

Einstein realized that an accelerated frame of reference is equivalent to a gravitational field.

Einstein’s universe animation

Freefall down and acceleration up are equal!

Dropping a ball while in freefall vs. rest

This principle applies to all physical phenomena including optical, electromagnetic, as well as mechanical.

General Theory of Relativity

Einstein’s ideas led to a new meaning of gravity. Since acceleration can mimic gravity, then gravity is not a force but a curvature of spacetime.

A good summary is “matter tells spacetime how to curve, and curved spacetime tells matter how to move.”

A few years after the general theory is published, deflected light from a star is measured during a total solar eclipse, confirming the general theory.

Earth warps spacetime; curved spacetime binds the Moon in orbit.

Gravity B Probe: “Testing Einstein’s Universe”

General theory merges spacetime with energy/mass

Light is bent by the sun’s mass, or rather by it’s curved local spacetime