Transcript The Development of Relativity

Einstein and the
Development of Relativity
Light- The Gateway to
Relativity
The Field Concept of Light
Around 1850, Foucault (foo-koh’)
measured the speed of light to be
about 3 x 108 meters/second.
Michael Faraday – magnetism
creates electricity and electricity
creates magnetism.
James Clark Maxwell – light
cycles with a magnetic field
creating an electronic field and
an electronic field creating a
magnetic field.
Maxwell’s 8 equations unify
magnetism and electricity while
describing electromagnetic
radiation.
Problems With Prevailing
Theory
Seemingly endless supply of
energy from radium.
Several problems with aether, a
transparent, hard, elastic solid,
that offered no resistance to the
movement of matter through it.
Maxwell’s equations showed
light was the same speed for
all reference systems.
Ernst Mach challenged ideas that
could not be proved such as:
Atoms
Aether
Absolute motion (he said that all
motion was relative)
Absolute time
Absolute space
All of Newtonian mechanics,
because it assumed absolute time
and space.
Michelson’s and Morley’s
“failed” experiments
Michelson’s and Morley’s
“failed” experiment
Using mirrors, he split a single
light beam into two identical
beams and sent them out ninety
degrees to each other.
The light beam sent in the
direction of the earth’s motion
should travel faster than light sent
at right angels to the earth’s
motion.
The beams traveled the same
speed regardless of orientation to
the movement of the earth.
Impossible Result
If we were moving away from light
at ¼ the speed of light, the light
should only strike us at ¾ the
normal speed of light.
If we were traveling towards the
light at ¼ the speed of light, the
light should strike us at 1¼ times
the normal speed of light.
The Michelson-Morley experiment
proved that light strikes us at the
same speed, regardless of our
motion relative to the light source.
The Galileo/Newton/common
sense view of velocity must be
wrong.
Could Newtonian Physics be
saved?
Lorentz-Fitzgerald contraction –
proposal that an object became
shorter in the direction of travel
(the math worked perfectly to
explain the result).
This preserved the concepts of
aether and of absolute space and
time.
Einstein didn’t agree with this
interpretation- the theory had no
basis, and was not testable.
Einstein’s Explanation
Time is different for different
observers, like the clock tower –
time changes with speed.
Lightning strikes a train – not
simultaneous for different frames
of reference.
As relative velocity increases,
time and distance both decrease
by the same percentage;
therefore…
The speed of light (ratio of
distance/time does not change)
Special Theory of Relativity
Equations
If v=80% the speed of light, 1 m
becomes .6m, 1 kg becomes 1.67 kg,
and 10 sec become 16.7 sec.
The Space-time Arrow
Arrow length = speed through
space + speed through time.
Length of arrow never changes.
If you’re stationary, all of your
speed is through time.
As you approach the speed of
light, the speed through space
section increases and the speed
through time decreases and
slows.
The length of arrow is the speed
of light.
E = mc2
E is energy in Joules, m is mass
in kg, c is the speed of light (3 x
108 m/sec).
1 Joule = 1 kg m2/sec2
Energy and mass are
interchangeable, different forms
of the same thing.
The total energy of an object is
given by its mass.
Published 3 months after the
Special Theory of Relativity.
New paradigm
The universe is no longer a rigid
grandfather clock ticking away.
It is dynamic, elastic, and
dependent on the reference frame
of the observer.
Time, distance, velocity, and even
mass are no longer absolute
“It’s all relative!”
Difficulty in accepting theory
Relativity is difficult to accept
because it lies outside our range
of experience.
It violates our “common sense.”
Einstein quote: “Common sense
is that prejudice learned before
the age of eighteen.”
1905 – Einstein’s miracle year
Explained photoelectric effect –
start of Quantum Theory.
Explained Brownian Motion – first
hard evidence for atoms.
Special Theory of Relativity –
replaced Newtonian Mechanics.
Problems with Special Relativity
It only dealt with constant
velocities.
Did not cover acceleration.
Did not cover gravity.
Newton’s gravity was
instantaneous, while Einstein’s
universe had a speed limit.
General Relativity
Just as the speed of light was the
springboard for Special Relativity…
Gravity would be the springboard for
General Relativity.
Freefall did not feel like acceleration
(like being accelerated in a car).
Equivalence Principle
Situations that felt the same and
acted the same, in terms of physics,
were the same.
Freefall was equivalent to
weightlessness.
Acceleration was equivalent to
gravity.
Gravity bends light
Rocket ship – light thought
experiment
As the rocket ship is accelerated,
light will bend as it travels.
Since acceleration is equivalent to
gravity, gravity will also bend light.
Gravity slows time
Two clock – rocket thought experiment
The clock at the rear is being accelerated
towards the light ray image of the front
clock.
The front clock appears to be running
faster than the rear clock.
Conclusion – acceleration slows time.
Therefore, gravity also slows time.
Minkowski’s Space-Time
4-dimensional coordinate system
(3 space and 1 time).
Reworked the Pythagorean
Theorem into four dimensions.
Absolute interval – The shortest
line in space-time.
All observers can agree on the
absolute interval.
World line – line of person or
object during existence.
Curved space-time
Imagine a spinning vinyl record.
The outer edge covers more
distance per revolution than the
center.
The velocity of the outer edge is
greater than the center, therefore
it will shrink more than the center.
The record becomes dome
shaped as it rotates very fast.
Swirling galaxies, etc. must curve
space.
Geometry for curved space
Euclidean Geometry only held for flat
space.
Math for curved space is differential
geometry (tensor calculus), developed
by George Friedrich Riemann in the
1850s.
Einstein did not have these math
skills, so he asked his former
classmate Grossman for help.
Math of curved space is applied
to universe
Einstein and Grossmann
reworked Minkowski’s four
dimensional, linear space-time
into curved space-time.
The amount of mass and energy
determines curvature at that
location.
True nature of gravity
The gravitational field does not pull
objects, it simply curves space-time
as determined by the amount of mass
and energy.
Objects moving towards the earth are
simply following the shortest spacetime path as determined by the
curvature of space.
Newton had it backwards:
Objects in free-fall are not being acted
on by a force, which is why we feel no
force in free-fall.
Not following the natural space-time
path requires a force and is an
acceleration.
You are undergoing acceleration by
simply standing on the earth because
the earth is holding you back from the
path.
General Relativity’s Final Form
Einstein completed the final form
of this theory in 1915.
It explained the wobble in
Mercury’s orbit.
The 1919 solar eclipse also
supported the theory.
In it’s simplest form, Guv = 8πTuv
The left side defines the universe’s
shape.
The right side tells matter-energy (all
that the universe contains) how to
move.
Strengths of Relativity
It explains the constant speed of
light.
It preserves Newton’s equations
for everyday type situations while
also including extraordinary mass,
velocity, and energy situations.
Shows the equivalence of
(relationship between) mass and
energy, and time and space.