Rev. 16-Jan-05 GB
Y05-1
World Year of Physics 2005
Einstein’s Miraculous Year 1905
What was so miraculous about 1905?
A little-known Swiss patent clerk named Albert Einstein published three
seminal papers that changed the course of physics in the 20th Century.
1. The Special Theory of Relativity, which would be extended to the
General Theory of Relativity by 1915. (We’ll talk about this today.)
2. The idea of the Quantization of Energy in light, which was one of the
foundations of Quantum Mechanics. (A Physics II topic.)
3. Derivation of equations involving the random motions of particles in a
fluid that provided convincing evidence of the existence of molecules.
Y05-2
“Einstein Simplified”
Y05-3
Newton’s Laws of Motion
1. Newton’s First Law: No net force, no change in motion.


2. Newton’s Second Law: Fnet  m a
3. Newton’s Third Law: All forces come in pairs.
(equal magnitudes and opposite directions)
(We will study these laws in coming classes.)
Y05-4
Are Newton’s Laws True?
It’s been over 300 years since Newton published his laws in Principia
Mathematica (1687). How have his laws done since then?
The First Law is still doing fine. In modern times, many types of very
low-friction motion (space travel, magnetic bearings, air hockey tables,
etc.) make this notion more intuitively appealing than in the past.
The Third Law is also doing fine. All forces currently known to physics
obey this law. Any force not obeying this law would cause big problems
in physics, like getting free mechanical energy from nothing.
However, the Second Law in the form we learn it in Physics I is not
exactly correct. Where did Newton go wrong?
Y05-5
Where Did Newton Go Wrong?
Isaac Newton, 1642-1727
Newton defined time and space as follows:
“Absolute, true, and mathematical time, of itself and from its own nature,
flows equably without relation to anything external…”
“Absolute space, in its own nature, without relation to anything external,
remains always similar and immovable.”
As the 19th Century drew to a close, it became evident that there was
something wrong with these assumptions.
Y05-6
Maxwell’s Electromagnetic
Theory - 1873
Maxwell developed a theory of electromagnetism that
explained all the phenomena of electricity and
magnetism known then and predicted something new:
electromagnetic waves. This prediction was confirmed
by Hertz in 1886 and light was soon shown to be a type
of electromagnetic wave.


B
E  
t
James Clerk Maxwell
(1831-1879)

 D  

  D
H  J 
t

 B  0
But a question remained: If light is a wave, what is its
medium of propagation? Most physicists assumed that
there must be one and called it the ether. Ether was
assumed to define a fixed reference frame for the
universe (Newton’s “absolute space”) through which
electromagnetic waves travel at speed c.
Y05-7
The Michelson-Morley
Experiment - 1887
Michelson’s interferometer was designed to measure slight differences in phase
between two light beams that travel in orthogonal directions. By measuring the
phase differences at various places in earth’s orbit, Michelson and Morley hoped
to measure the absolute velocity of earth with respect to the ether.
However, no effect was found. The speed of light is constant for all observers.
Y05-8
Einstein’s Postulates of the
Special Theory of Relativity
Albert Einstein (1879–1955)
Studying Maxwell’s equations and noting a
remarkable symmetry in them between space and
time, Einstein replaced Newton’s definitions of
space and time with two new postulates that led
directly to the Special Theory of Relativity.
Einstein’s Two Postulates of Special Relativity (1905):
1. The laws of physics are the same in all inertial frames.
2. The speed of light, c, is constant in all inertial frames.
Y05-9
“Special Lorentz
Transformation”
From Einstein’s
1912 manuscript
on Special Relativity.
“We can now also formulate the relativity principle in the following way.
The theory of relativity requires that systems of equations in physics turn into systems
of equations of the same form if one transforms them by means of the Lorentz
transformation.
“Simple calculation shows that the fundamental equations of classical mechanics do
not have this property. Thus, they are incompatible with the theory of relativity.”
Y05-10
Consequences of the
Special Theory of Relativity
1. Time Dilation: All clocks in uniform motion relative to an
observer slow down compared to his clocks.
2. Length Contraction: Lengths of objects in uniform motion
relative to an observer contract in the direction of motion.
3. Events that are simultaneous for one observer may not be
simultaneous for another observer.
4. No object having mass can reach the speed of light.
5. No mass, energy, or information can travel faster than the speed
of light.
6. E = m c2 – Mass can covert into energy and vice versa.
Y05-11
Length Contraction
v=0
0.5 c
The length contraction effect
applies only in the direction of
relative motion of an object as
observed from another inertial
frame of reference.
To the equipment and people
0.8 c inside Enterprise, nothing
unusual is noticed. As far as
they are concerned, they are at
rest while everything around
0.95 c them is moving.
Y05-12
If “F = m a” isn’t true,
why do we still use it?
The original form of Newton’s Second Law is true to a very good
approximation when dealing with velocities much less than the speed of
light. For most calculations involving ordinary objects, it is close enough
for practical purposes. For some calculations, we need relativity.
“Disintegration of the Persistence of
Memory” by Salvador Dalí, 1931
Art inspired by the
Theory of Relativity?
Y05-13
What’s so “special” about
Special Relativity?
The “special” part means that it
deals only with non-accelerating
frames of reference for
measuring space and time.
Einstein worked another decade
to generalize his ideas to
accelerating frames of reference.
He added the Principle of
Equivalence as a third postulate.
Y05-14
General Theory of Relativity
By 1915, Einstein had worked through all the math (with some help)
to show that his postulates led to a new theory of gravity based on
the effect of mass and energy to curve the structure of space and
time. His theory has some startling implications, one being the
existence of “black holes” – regions of space where the gravity field
is so high that even light cannot escape. The predictions of General
Relativity, including the existence of black holes, have been
confirmed by all experiments to date.
Y05-15
Black Holes
Black holes are detected by the characteristic
x-rays given off by matter falling into them.
Y05-16
Images and illustration of a black hole (XTE J1550-564) pulling gas from a
nearby star and ejecting some of it in high-energy jets (right/left in image,
up/down in illustration). From the Chandra x-ray telescope (satellite),
named after Indian physicist Subrahmanyan Chandrasekhar (1910-1995).
Y05-17
Time-lapse animation of XTE J1550-564 images from Chandra.
Y05-18
Gravitational Waves
Computer
Simulation
The General Theory of Relativity predicts that accelerating masses should
generate gravitational waves – ripples in space and time traveling at the
speed of light. These are hard to detect because they are so small.
Y05-19
Detecting Gravitational Waves
LIGO – The Laser Interferometer Gravitational Wave Observatory – was
built to detect gravitational waves. A facility in Hanford, WA, (shown
above) and a sister facility in Livingston, LA, are basically giant
Michelson-Morley experiments. Ripples in space and time will cause slight
phase differences in laser beams traveling at right angles.
Y05-20
Detecting Gravitational Waves
How You Can Participate
Einstein@home –is a program that uses your computer’s idle time to
search for spinning neutron stars (pulsars) from data provided by LIGO and
GEO (another gravitational wave observatory). This software is currently
in its final testing stage and should be ready for downloading “soon”.
http://einstein.phys.uwm.edu/
Y05-21
Einstein’s Words (1943)
"Ladies and gentlemen, our age is proud of the progress it has made in
man's intellectual development. The search and striving for truth and
knowledge is one of the highest of man's qualities - though often, the
pride is most loudly voiced by those who strive the least. And certainly
we should take care not to make the intellect our god; it has, of course,
powerful muscles, but no personality. It cannot lead, it can only serve;
and it is not fastidious in its choice of a leader. This characteristic is
reflected in the qualities of its priests, the intellectuals. The intellect has
a sharp eye for methods and tools, but is blind to ends and values. So it
is no wonder that this fatal blindness is handed on from old to young
and today involves a whole generation."
Y05-22
http://www.amnh.org/exhibitions/einstein/?src=h_h
Y05-23