Download 01. State of Physics - University of Central Florida

The State of Physics at the Start of the 3rd Millenium
Michael Bass, Professor of Optics and Physics
School of Optics/CREOL
University of Central Florida
Orlando, FL 32816-2700
We live in a Newtonian world, in an Einsteinian universe, where quantum effects are
critically important and yet gravity, the weakest of all known forces, governs the ultimate fate of
all that there is. We also live in a world in which science and technology are integral parts of our
everyday lives. You turn on a light, use a cell phone, put on glasses or corrective lenses, use an
automobile, listen to radio, watch TV, travel on an airplane or benefit from some advance in
medicine and don’t think of the events in science which made these modern marvels possible. We
are concerned with how we came to understand the science that underlies our technological
society, who were the people who contributed to our knowledge, how were they affected by the
cultures in which they lived and how, in turn, they affected the culture in which we now live. This
review of the state of physics at the start of the millenium is a broad-brush approach to the general
underlying principles in physics, how they came about, who developed them, and how they
impacted our society. It should enable one to understand what has gone on in the past in the context
of where we are today so that we may understand where we are headed.
Physics is the science by which we understand the workings of the universe. It is the
science that underlies all other sciences and the thought processes developed in Physics are those
used in the other sciences. For these reasons we consider its development to understand science
in general.
To understand the universe – from sub nuclear quarks (or even smaller super strings) to the
entire universe – physicists have identified just four forces. Recent observations of the motions of
galaxies and the recession speeds of galaxies at great distances suggest the existence of a possible
5th force that repels masses from one another (sort of anti-gravity) or that over very large distances
Newton’s law of gravity may be a little bit off. These observations are so recent that they must be
checked and re-checked to be certain. One thing is clear though – the universe is even stranger
than it seems. The four forces themselves are not yet fully understood and yet they seem, thus far,
to govern the interactions taking place between all particles. In addition, there are certain
symmetries that result in the reality we perceive. The first force we ever knew about – we all sense
it – is gravity and yet it remains the most mysterious of all. Perhaps because it is the weakest of
all the forces gravity still defies complete explanation. However, since it is responsible for
everything from the fall of an apple to the fate of the universe, it has been a subject of continuing
study. While we all sort of know about gravity it was Isaac Newton, perhaps the greatest physicist
ever, who, in the mid-17th century, synthesized the data of Tycho Brahe, Nicolaus Copernicus,
Galileo Galilei, and Johannes Kepler into his remarkable, Universal Law of Gravity. Coupled with
his even more spectacular laws concerning the motion of bodies he showed the remarkable fact
that the gravitational force that holds us to the earth is exactly the same as that which controls the
movement of the planets, stars, galaxies, and the universe. (Of course Newton didn’t know about
© Michael Bass
galaxies and the universe - those are 20th century matters - so he didn’t do all of this, but his law
does.)
Newton’s Laws of Motion are simple statements about how the motion of bodies change
(or doesn’t) when acted on by external forces.1 They are:
(1) A body in motion tends to remain in motion, or to remain stopped if stopped, except
insofar as acted on by an outside force.
(2) The rate at which a body’s momentum changes is equal to the net force acting on the
body; mathematically this law is
dp
d (mv)

 F
dt
dt
where p is the momentum, m is the mass of the body, v is its velocity and F is the force
acting on it. Or, if m is a constant we have the more familiar
F  m
d ( v)
 ma
dt
where a is the acceleration resulting from the action of the force.
(3) If object A exerts a force on object B, then object B exerts an oppositely directed force
of equal magnitude on object A.
As accurately as we can measure in everyday life these laws work - we find no violations.
However, as we will discuss later, when the body’s speed becomes too large, the definition of
momentum in the second law must be modified. To do that properly we will need Einstein.
Before we go too much further I must say a word about mathematics. It is the language of
science and just as you need Chinese to get along in China you need mathematics to get along in
science. Mathematics is used to represent in a sort of short hand notation the relationships between
various quantities that constitute the body of knowledge called science. As a result we must use a
little math to talk about science. To enable us to do this math had to be invented. In fact, that was
one of the things that Newton did for science. He established the basis of differential calculus so
that he (we) could discuss his physics. Of course, DesCartes in France and Liebnitz in Germany
were not doing nothing. DesCartes invented graphing, an essential contribution and Liebnitz, in
parallel to Newton, invented the calculus. We needed all of their work in math to be able to do the
physics that we now consider.
Back to gravity: Newton proposed that the magnitude of the gravitational force between
two bodies of masses m1 and m2 and with centers separated by a distance r12 was
1
Sometimes in this review mathematical expressions are given. This review can be read by the non-scientist just by skipping the
math. In doing so the beauty that results from the elegance of the math will be lost but the main concepts can still be acquired.
© Michael Bass
F  G
m1m2
r122
The proportionality constant, called G, was introduced to take account of the units (if nothing else).
It is clear from correspondence between Newton and Robert Hooke that Hooke first proposed the
inverse square law and suggested that it might account for the motions of the planets. Hooke
however, did not have the mathematical tools or skills that he would have needed to prove his
point. As a result, he passed the suggestion to Newton and Newton, a generally nasty man, solved
the problem but nowhere credits Hooke’s suggestion. Nasty or not, Newton had the nerve to
declare the gravitational constant and the law universally applicable. Think of how bold this
statement was – Newton, able to measure things on the earth and read of others’ observations of
the motion of planets, was probing the entire universe and had the temerity to think he could
describe it, and to do so so simply. In a moment we will see how this law actually reflects a
symmetry of the world in which we live. Meanwhile, let’s look at the consequences of Newton’s
Law of Gravitation:
He said
F  G
m1m2
r122
and was always attractive – pointing along the line from one mass to the other and was the force
of body 1 on body 2 and of body 2 on body 1.
Then using his 2nd law of motion he set
F  m1a  G
m1m2
r122
and used it to calculate the position of m1 as a function of time. (For the future note that
a  G
m2
r122
is independent of the mass of the object, m1 whose motion we seek to determine. This is the one
case in physics of a force giving rise to an acceleration that is independent of the mass being
accelerated.)
It is easy to calculate (though I won’t do it for you) from this statement that the orbit of a
planet around the sun is an ellipse and that Kepler’s Laws of orbital motion are correct – they
come from Newton’s law. Newton’s Universal Law of Gravitation and his Laws of Motion were
more general and we could use them to serve other purposes. The demonstration that the proposed
system of mechanics and the law of gravitation could result in the observed motions of the planets
© Michael Bass
(Kepler’s Laws) was Newton’s crowning achievement. He did what Hooke was unable to do and
did so in a manner that showed how his methods could be used to solve any mechanics problem.
One early consequence of the success of Newton’s Laws of Motion and Gravity was that
the universe could not be static. It had to either expand or contract but, since gravity was always
attractive, the universe could not stand still. This produced a major conflict with then existing
theological models. If the universe had to satisfy the law of gravity how could it be that which
God established. That is, how could such a universe be established according to God’s ideas and
totally at his whim when here was evidence that it wasn’t. Curiously the scientific community
waffled over this issue until well into the 20th century when we now have clear evidence that the
universe is currently expanding and we have some notion of the laws that govern the expansion.
We will examine this issue in the course when we discuss cosmology.
Another major consequence of Newton’s Laws but of less religious significance was what
happens at the earth’s surface. We see that if m2 = Me, the mass of the earth, then
m1a  G
m1 Me
re2
but G, Me and re, the radius of the earth, are constants and so we can clean this up a little into the
much more familiar
F  m1a  mg
where g = GMe/re2 is the acceleration due to the force of gravity. This is what Galileo Galilei in
Pisa observed by dropping balls made of different material off the leaning tower. Actually, this is
just a good fairy tale. While Galileo did live in Pisa and he did observe that all objects accelerated
at the same rate no matter how heavy they were, he did so by rolling balls down planes. Balls
rolling down planes moved slowly enough for him to accurately measure their displacements,
velocities and accelerations. Objects dropped off the tower fell too fast for him to measure. By
performing these experiments, Galileo not only demonstrated a critical fact of nature he showed
us how to do experiments. He set up a system in which he was able to make reasonably correct
measurements and then examined his data for regularities that might reveal the principles
governing that which he studied.
Speaking of Galileo it is important to note that he was also the first to make a telescope,
confirm its performance on the ground and then turn it towards the skies. He was sponsored in
this by the merchants of Venice who wanted to use telescopes to detect when a ship was coming
into port before their competitors. In those days (as perhaps is still true) a few hours advanced
warning could mean fortune or failure. We might say that the commercial culture of Italy gave
rise to one of science’s most important discoveries. In today’s parlance we would say that Galileo
had industry sponsors for his research. When Galileo looked skywards, what he saw produced a
revolution in how we see ourselves in the universe. Galileo observed that Jupiter had moons. Prior
to his work, the European world believed that the sun, moon, planets and stars were held in
spherical celestial orbs rotating about the earth at their center. This was Aristotle’s universe and
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had been working pretty well, with certain modifications called epicycles, for nearly 2000 years.
There was no place in the celestial orbs for moons around Jupiter. Worse yet for Galileo, the
Catholic Church had, sometime before, accepted the Aristotelian view. It had become dogma.
Galileo was given the choice of death or recanting. At the time he was forced to recant in 1642 in
Italy, a Catholic country, the Royal Society for the Advancement of Science was being formed in
England, a Protestant country. The center of science moved out of the Mediterranean and to the
north. It is sad to say that it has remained that way until very recently when scientific inquiry in
some of the Mediterranean countries revived in the 20th century.
Today we live in a world where Newton’s laws of motion apply – from colliding billiard
balls and swinging pendulums to racecars and spacecraft. His law of gravitation explains the
motion of astronomical bodies with great precision and, with Einstein’s refinements, is used to
study the fate of the universe.
There is something very, very critical in the form of the Universal Law of Gravity giving
a force which falls off inversely as the square of the distance between the bodies, r12. Let’s examine
this question from a geometrical perspective. Consider a mass m as shown. No matter
m
m1
r12
how weirdly the body is shaped, when we are far enough from it, it appears as a point mass. It is
obvious therefore that its gravitational attractive force on mass m1 at a distance r12 away can only
be determined by the total quantity of mass inside the sphere drawn in the picture. Therefore, we
can consider the total flux (or flow) of gravitational force per unit mass across this surface (sort of
like water being pulled in through the sphere). Since the problem is spherically symmetric and the
total gravitational flux can only depend on m, we can write
 g   F  dA  m
where mathematically we have defined gravitational flux, g as the integral (or sum) of the dot
product of the force of gravity per unit mass, F, with the outward pointing surface area vector. The
force of gravity per unit mass can be thought of as the gravitational flux per unit area. When we
integrate over the whole surface of our spherical shell and when we realize that, since the problem
is spherically symmetric, F can only depend on r we find
F (r )4r 2  m
© Michael Bass
or
mm
F (r )  m1F (r )  1 2
4r
which, with G as the proportionality constant, is Newton’s Universal Law of Gravity. Notice that
we found the 1/r2, or the inverse square law, property of Newton’s Law of Gravitation from the
fact that the area of a sphere is 4r2. What we have just done is apply to gravity the same thinking
that led Carl Freidrich Gauss to what we now call Gauss’ Law in electromagnetics. We will see
the inverse square law again and it will emphasize how the symmetry of our three space
dimensioned world affects our everyday lives.
We have seen what Newton did. Through his laws of mechanics and his demonstration of
the validity of the inverse square law for gravitational attraction he gave us a means to evaluate
the motion and changes in the motion of everything. He taught us how to deal with the motions
of stars and galaxies as well as atoms and molecules of air (when considering them to be just
smaller than normal, billiard balls). The mechanics that results from Newton’s contributions is
one basis of our society’s technology.
The others are thermodynamics and electromagnetism. With these three aspects of physics
most of today’s technological world is comprehensible. It is intriguing to consider that the
fundamentals of all three were well understood before the 20th century started. When we examine
20th century science we will see what it added to the body of physics and how some of that has
permeated everyday life. Then we consider what the future of modern science might be.
First though we examine thermodynamics. Thermodynamics is actually the sum of several
conservation laws that are powerful tools for understanding things. Science invented conservation
laws because they provide valuable guidance to the inner workings of the universe. Newton’s 2nd
law
dp
d (mv)

 F
dt
dt
gives us our first conservation law. For a system in which no net force is exerted on a body or
bodies it says
dp
d (mv)

 0
dt
dt
This reads that the quantity p = mv, the momentum, for the system does not change with time. A
quantity which doesn’t change with time remains constant - we say it is conserved. Another way
of thinking about conservation laws is to consider them as prohibitions. They prohibit any process
in which the conserved quantity changes. This allows one to rule out such things as perpetual
motion machines or propelling oneself through space without propelling something else in the
opposite direction.
© Michael Bass
Two billiard balls of masses m1 and m2 which initially have velocities v1 and v2 collide and
bounce off each other. There is (ignoring friction) no external force on the system and so we know
that since momentum is conserved the final momentum of the system must equal its initial
momentum. Mathematically this means that
(m1 v 1  m2 v 2 ) before  (m1 v 1  m2 v 2 ) after
If you weren’t a pool shark you could compete by calculating the momentum of the system before
and after the collision when planning your shots. No violation of the conservation of momentum
law has yet to be found. It applies equally well to billiard balls, bumper cars and colliding
subnuclear particles in multi-billion dollar accelerators. From the prohibition point of view we
say that no event is allowed in which the total momentum changes when no external forces act on
the system.
With the advent of mechanical machines (water wheels for example) we knew we were
converting one kind of something into another. By falling from some height the water made the
wheel turn. In the process we converted a property that the water had when it was up high and
didn’t have when it was down low into a motion of the wheel, its rotational motion. Later, when
steam engines were invented - and science was forced to develop thermodynamics - the conversion
process got even more complicated. Now we converted something which seemed to be stored in
wood or coal (their property of burning and making things hot) into something in the steam (its
property of being hot) and then into something in the motion of a wheel. To explain all these
somethings science was forced to invent the energy concept - the something was energy and while
we could transform one kind into another, it soon developed that in a closed system the quantity
called Total Energy didn’t change - it was conserved.
Temperature was introduced as a property of a system which enables us to believe that two
objects are in thermal equilibrium - that is two bodies are in thermal equilibrium when both have
the same temperature and so no thermal energy flows between them. This concept of temperature
as defining thermal equilibrium gave us the zeroth Law of Thermodynamics.
The law of conservation of energy is the First Law of Thermodynamics. It states that in a
closed system you can only convert energy from one sort to another - you can’t create or destroy
energy. This means that our machines can only do some limited sorts of things and we must put
in energy (fuel) if we want to get something out (motion of our autos for example). The prohibition
was that no machine could produce useful output energy without providing it with an appropriate
input energy. James Watt’s steam engine could not turn a single spinner in a single textile mill
unless the energy stored in the coal were released by burning to heat the water to make the steam.
Once we had these concepts, and not wishing to let go of a good thing, we tried to figure
out how efficient one of our machines could be. It seemed reasonable to ask, “If I put in some
energy stored in the fuel, how much energy can I expect to get out in the form of useful work from
my machine?” Sadi Carnot, a French engineer, analyzed this question for a certain kind of engine
in the early 1800s and decided, an instinctive and gloriously correct conclusion, that it, now called
a Carnot Engine, would be the most efficient engine possible. He wasn’t vain; he was right. As a
© Michael Bass
result, all engines must be less efficient and this comprehensive statement drew much study since
many physicists wanted to have the most efficient engine. The result however was the
development of a mathematical understanding of why Carnot’s was most efficient and others not.
The mathematical statement of Carnot’s Efficiency Law is that there is a quantity called entropy
that, for a closed system, must increase or, in ideal circumstances at least remain the same,
whenever a thermodynamic process takes place. Entropy it turns out is a measure of disorder in a
system. Since, in the real world, entropy must increase it means that disorder must increase. That
means that events always happen from ordered (past) to disordered (future) states. In other words,
Time flows forward!
The statement that entropy must always increase or remain constant is the 2nd Law of
Thermodynamics. It is the only place in physics where a law is asymmetric in time. Other laws
are the same if you reverse time. For example, when two billiard balls collide you don’t know in
what direction the clock was running. You can only tell that momentum was conserved. However,
you can tell that when a broken cup rises up off the floor and re-assembles itself on the table top
that time is running in the wrong direction. This is because the broken cup is much more
disordered than the assembled cup and the second law says that events progress towards more and
more disorder. The prohibition is that the cup never spontaneously rises off the floor. Of all the
laws of physics, only the Second Law of Thermodynamics gives one a sense to the flow of time.
It is curious that a basic, fundamental property of the universe results from asking about the
efficiency of engines.
Using an analogy with gambling, the laws of thermodynamics are sometimes stated as:
0. You are allowed to play.
1. You can do no better than break even.
2. If you play long enough you must lose.
So science had already (before 1900) not only created new and wonderful things it had
upset some long held views - the static universe was not possible and time flowed from past to
future (time was not cyclic). It had also begun to permeate how people thought and what they did.
Think of such phrases as “they have the momentum” and “where does she get her energy” to get
a sense of how science had impacted everyday life. However, science’s most critical contribution
to our lives was the electromagnetic revolution. In the late 1700’s people were examining things
that had been known for long time but with a “new” view to trying to understand what was going
on. Luigi Galvani was looking at frogs legs and saw them twitch when connected to a body
charged by rubbing say cat’s fur on glass. Ben Franklin was risking his life to show that lighting
was electricity; just the same kinds of charges as produced by rubbing one thing on another. Then
in the early 1800’s August Coulomb- a civil engineer with the French Army - put forth a law that
the force between two charged bodies of charges q1 and q2 and separated by a distance r12 was
Fe  k
q1 q 2
r122
© Michael Bass
where k was a constant introduced to get the units straight (that is since you had a force on the left
and charge squared divided by distance square on the right, you needed a constant with the right
units to make the equation consistent). Later on in the study of electromagnetics physicists realized
that k was not some arbitrary constant but a fundamental property of the universe related to the
speed of light. Notice in Coulomb’s Law that once again a force law has the inverse square law
form. A German, Carl Freidrich Gauss, understood the implications of Coulomb’s law and turned
it into the mathematically elegant form, now called Gauss’s Law for Electricity, which shows how
electric fields are related to the symmetry of our three spatial dimensioned universe.
Meanwhile others were studying magnets and magnetic forces. Biot and Savart, again in
France, showed that moving charges - currents - gave rise to magnetic forces. However, no one
then or since could find a single north or south magnetic charge; magnetic charges always came
in pairs. No matter how finely you divided a magnet you still got a north-south magnet. You
never got just a north or just a south. It seemed that while electric and magnetic forces might be
related they were different.
Then Michael Faraday in England showed that when a magnetic field (a spatial distribution
of magnetic force) changed with time you could induce an electromotive force (a voltage) in a
circuit. This brilliant former bookbinder’s assistant had invented the concept of fields of force to
explain his observations since he had no formal training in mathematics. His conclusion,
Faraday’s Law of Induction, leads directly to all our electric generators and motors. It is, therefore,
the foundation on which our electronic world is built. It is what allows us to generate electricity.
Think of our world without it!
It is interesting to note that Faraday was supported by the Royal Society for the
Advancement of Science, an organization that was funded by the British government. The Prime
Minister of Great Britain, William Gladstone was not out of line when he asked Faraday what was
so important about his idea. Faraday’s answer was that while he was uncertain of the details, he
was certain that Gladstone would tax it.
By midcentury the stage was set for someone to see the implications of all of this. It fell
to James Clerk Maxwell in Scotland to see the symmetry. He realized that electric and magnetic
forces were different aspects of the same phenomenon now called electromagnetism. Maxwell
assembled 4 laws - Gauss’ Law for Electricity, Gauss’ law for Magnetism, Faraday’s Law of
Induction, and Ampere’s Law for the magnetic fields due to currents, modified them a little and
showed that electric and magnetic fields were related. They were not only related but were
interchangeable. With these four famous equations and some one or two others which describe
the way different materials react to electromagnetic fields we can solve any problem in
electromagnetism - from the force between two charged “pith” balls to the design of a modern
computer. Maxwell went further. He showed that his equations predicted electromagnetic waves
that propagated in space with the speed of light. In fact, he showed that light itself was an
electromagnetic wave phenomenon (contradicting Newton’s view that light was corpuscular) and
set the stage for the interpretation of light as a wave phenomenon. As a result the phenomena of
diffraction, interference, and ray propagation of light could be understood, and it seemed clear to
everyone that light was best interpreted as a wave of electromagnetic energy. We shall see how
this view was to be challenged in just about 50 years by the data that led to quantum mechanics.
© Michael Bass
Maxwell’s was the first unification of two forces, electric and magnetic, into one; it was
the first use of mathematical symmetry arguments in establishing scientific principals and it
worked! It explained many things, predicted many things and made possible our electronic world.
A physicist’s “tee” shirt is sometimes seen with the words:
“And God said,
E 
q
0
B  0
E  
B
t
  B   0 J   0 0
E
t
and there was light”
The equations are Maxwell’s Equations. The quote is a physics joke. In these equations E is the
electric field, B is the magnetic field, q is the total amount of free charge in the region, J is the
density of currents flowing in the region, 0 and 0 and are constants which were originally
introduced to compensate for the units in less general equations. What is remarkable and what
Maxwell showed is that 0 and 0 are fundamental constants of the universe related to the speed of
light through the relationship, c = 1/  0  0 . Further, notice that Maxwell’s Equations are
symmetric in E and B. For example, a time varying electric field gives rise to a magnetic field in
the fourth equation and a time varying magnetic field gives rise to an electric field in the third.
These equations help to explain how electric generators work or how energy in an electronic circuit
gets through a capacitor. Maxwell’s Equations enable the solution of all problems in
electromagnetics. With them only you can analyze an optics problem, design a starter motor for
your car, plan a computer or build a cable TV system.
While God may not have used Maxwell’s Equations as mathematically expressed above,
they must have been what he/she had in mind when our universe got started because they are
satisfied exactly in every experimental test yet conceived. In other words, they are how the world
works. No one knew this for sure in 1873 when Maxwell’s results were made known. In fact,
demonstrating that members of the British parliament were no more aware than any member of
our congress might be, when told of Maxwell’s achievements one MP scoffed and said “Of what
possible use can that be?” He was put down with the remark, “Sir, the same can be asked of a
newborn babe?” You may not think of Maxwell every time you turn on a radio or TV or use a
phone or a computer or play a CD or get checked out with a laser scanner, but his contribution to
science enables them all.
Thus, before 1900, science had produced the three underpinnings of our modern
technological society: mechanics, thermodynamics, and electromagnetics. In fact, it may be said,
© Michael Bass
and I say so here, that if no new science, only engineering, had been carried out since 1900 our
world would be quite similar to what it currently is today (not identical, not as comfortable, but
similar).
In the 20th century our view of the universe clarified and became more complete.
However, first it became more complex and less comprehensible. Science would have to turn over
some of its own “apple cart” to get a better understanding of how things worked.
At the turn of the century scientists were in a proverbial “pickle”. According to Newton,
whose insights had been remarkably right in most things, there could be an absolute reference
frame in the universe and all motion could be measured relative to it. Now in daily life we don’t
much care about such things. After all the earth or your room is a good enough reference frame
against which to measure motion. What was bothering scientists was that if there were such a
reference frame then we should be able to measure motion relative to it. So for example when it
was January the earth would be moving one way and when it was July the earth would be moving
the other way. If Newton were right, the speed of light measured on the earth would depend on
the earth’s motion relative to the so called rest frame or ether. That means that we should be able
to sense our motion with respect to the absolute reference frame. We could do this by measuring
the speed of light in the direction of the earth’s motion and finding that it was different from that
measured in a direction perpendicular to the earth’s motion. Now this sounds as though it would
be a simple experiment. However, the speed of light is very large (3 x 108 m/sec) and the earth’s
motion in its orbit around the sun is very much slower (~100’s of m/sec). The result is that any
differences in the measured speed of light due to the earth’s motion would be very small and
consequently, the measurement would be very difficult.
In Cleveland, Ohio an American physicist, Albert Michelson invented an interferometer
that would be capable of the measurement. Together with an assistant, E. W. Morley, he put his
interferometer on a concrete slab and floated it in a pool of mercury (it is fortunate that they didn’t
both go mad because breathing mercury vapor causes madness). When they looked at the
interference patterns they found, to their astonishment, that the speed of light was the same no
matter how the earth moved. By rotating the interferometer so that different arms pointed in the
direction of motion or perpendicular to it and observing that no change in the pattern of interference
took place they were forced to this conclusion. For his work on the speed of light Michelson
became the first American to be awarded the Nobel Prize in Physics. The year was 1907.
The result of the Michelson-Morley experiment was that there could be no ether, no
absolute reference frame, or else something very strange was happening to their instruments. In
fact, a Dutch scientist, Hendrik Lorentz (who won the 1902 Nobel Prize in Physics for unrelated
work on magnetism) and independently, William Fitzgerald in Dublin, suggested that the arm of
the Michelson interferometer oriented parallel to the direction of motion contracted a little.
Lorentz was saying the arm in the direction of the motion got shorter. Therefore, light traveled a
shorter distance in that arm compensating for the movement in that direction and thus, giving the
same value for the speed of light as obtained for light traveling perpendicular to the earth’s motion.
Since, in the Lorentz-Fitzgerald picture, a ruler laid in the direction of the earth’s motion would
also shrink by the same amount as the length of the arm, you couldn’t measure the contraction
directly. As often happens, a scientist had got it right but not complete. That was left to a German,
© Michael Bass
born into a Jewish family, and working as a clerk in the Swiss Patent Office in Bern. In this job
he had the time and freedom to think about the problem. Of course we are talking about Albert
Einstein.
While Einstein claims not to have known of the Michelson-Morley experiment in detail he
certainly read the journals and knew of the difficulties engendered by its results. Einstein in
proposing his Theory of Special Relativity was about to overthrow the central construct of the
Newtonian universe. In it, Einstein said that there was no absolute reference frame but instead he
proposed that all motion is relative. That is, any motion must be described with respect to some
reference frame which may be moving with respect to some other reference frame which itself
might be moving. In other words, Einstein was claiming that there was no absolute reference
frame. The consequences of this idea revolutionized physics. Since any non-accelerating or
inertial reference frame was likely to be moving with respect to any another, Einstein reasoned, it
was essential that the laws of physics be the same in all inertial reference frames. He was saying
that all observers, moving relative to each other without acceleration, must decide on the same
laws of physics. This meant that we might measure different time intervals or lengths but we
would always, no matter how we were moving, get c = 2.997924589 x 108 m/s for the speed of
light. The implications of this were staggering. If a body moved near the speed of light its length
in the direction of motion would contract, clocks on the body would run slower (since velocity is
length/time this had to be so in order to get c for the speed of light in all cases), the mass of the
body would increase, becoming infinite when the speed equaled c, and so the body could never
reach a speed of c. No material body could ever move at the speed of light since it would take an
infinite acceleration to ever move that fast. Einstein’s philosophic point of view that physics had
to be the same in all reference frames also led to his famous relationship between mass and energy
E = mc2
This relationship would make possible the nuclear science that led to nuclear weapons, nuclear
medicine and nuclear power systems.
What was amazing about Einstein’s initial relativity work, now called Special Relativity,
was that it was not only explanatory, it was predictive, and it worked. It has never failed any
experimental test. Strange as it seems from a common sense point of view the twin who travels in
a space ship at a speed near the speed of light ages more slowly than her sister who stayed on the
earth. You may ask, how can we be so sure? The answer is that we did the experiment. Ultra
high precision atomic clocks, not twins, were compared as follows. One remained at the starting
point and one was flown around the earth on a series of jet planes. The one that traveled came
back having counted off less time than the one that stayed home. Einstein is completely correct;
the twins age differently depending on their motion relative to one another.
Einstein published this and other critical papers in the “wonder year” of 1905 yet he
remained a clerk in the Swiss Patent Office and then a junior professor in Prague until 1914, when
he was appointed Professor of Physics at the University of Berlin. During this time he worked on
the principal of general relativity in which he examined the properties of physics in accelerating
reference frames and in the presence of gravity. He proposed another brilliant insight. He
suggested that being in an accelerating reference frame is indistinguishable from being in the
© Michael Bass
presence of a gravitational field. From this equivalence principle Einstein was able to show that
gravitational fields caused the shape of space-time (he proposed that we live in a 4 dimensional 3 space and 1 time - universe) to be curved. Light would follow the shortest path from one point
to another in this curved space-time and so light from a star would be bent by passing close to the
sun. The observed position of the star when viewed close to the sun would be displaced a little
from the position viewed from another place as sketched below.
True position of distant star
Sun
Apparent position of distant star
Light is bent as it passes through
the sun’s gravitational field
Observer on the earth
An expedition to test Einstein’s prediction that gravity bends light was planned to take
place in the Crimea in Russia in 1914 where a complete solar eclipse was to occur. To see a distant
star in the light of the sun would be impossible. However, during a total eclipse, when the moon
blocked the sun’s light, it might just work. Particularly, if you were careful and lucky. Luck was
needed because the weather had to cooperate. Unfortunately, while the weather may have been
all right, in 1914 luck ran out and World War I started. The test of Einstein’s prediction didn’t
occur until 1919 when a British expedition to the island of Principe, off the west coast of Africa,
under Sir Arthur Eddington confirmed the theory proposed by Albert Einstein, a German. Not
only was Einstein instantly more famous than ever but the British-German aspect of the scientific
endeavor was viewed as an aspect of rapprochement between the two former enemies. Many
hoped it would signify the start of an era of cooperation between these countries and between
others as well. As you know, that turned out to be wishful thinking.
If light were bent by a gravitational field then light leaving a star would follow a curved
path. If the star’s density became large enough the local gravitation would curve the light paths
back on themselves and the light would not escape the star’s gravity. Since no information would
ever get out of such a concentration of mass, it would, in effect vanish from the universe. Today
this vanished concentration of mass is called a black hole and is the subject of much research. It
is the fate of large stars when they have burned their nuclear fuel and can no longer avoid the pull
of gravity. They collapse and form black holes. Black holes also seem to be present at the centers
of galaxies and may have been present in the early universe. Such primordial black holes, some
speculate, may be the cause of the non-uniformities we call galactic clusters and galaxies
themselves. If so, they may be the reason be why we are here to wonder about black holes.
© Michael Bass
Meanwhile, Einstein in evaluating his theory realized that it required that the universe had
to either expand or contract or expand so that eventually it would exactly stop. Einstein couldn’t
accept the expansion or contraction - he believed the universe was static - and invented a term to
add to his equations called a cosmological constant which, like antigravity, just balanced the
universe so that it would be static. This was before an American using the Mount Wilson
Observatory in California, Edwin Hubble, showed that the galaxies were rushing apart. The
universe was indeed expanding. When he learned of these results Einstein admitted his error
calling the “cosmological constant” his biggest scientific mistake. Today, it seems Einstein had it
right after all as the “cosmological constant” may be the cause of the acceleration in the galactic
expansion. More on this later.
Einstein won the 1921 Nobel Prize for physics. He did not win it for his work on relativity
that restructured our view of the universe and opened up unimagined possibilities. While relativity
revolutionized our world the Nobel committees, knowing Einstein deserved the prize but not
understanding (or thinking of) relativity gave him the prize for his critically important contribution
to the understanding of the photo-electric effect. In this work Einstein made a major contribution
to the development of quantum mechanics, which along with relativity, is one of the two major
revolutions to affect physics in the 20th century. While relativity explained the universe as a whole
and the very large scale of things such as stars, black holes, galaxies, universes and so on, quantum
mechanics proved necessary to understand the very small. The workings of molecules, atoms,
electrons, nuclei, protons, neutrons, quarks and so on are only understandable using quantum
mechanics. Classical mechanics fails completely when applied to things that are very, very small.
Here small means having dimensions of a molecule or less than a micron or two. As quantum
mechanics developed it became clear that the very small was governed by a principle called, after
its originator, the Heisenberg Uncertainty Principle. In simple terms it states that if we measure
one property of a body, called A, with some degree of precision, A, then there is a conjugate
property, B, whose precision can only be determined within the limit set by the relation
A B  h
where h = 6.63 x 10-34 Js is Planck’s Constant.
This means that if we know position with exact precision we can’t know momentum at all.
Or if we know a particle’s energy precisely we can’t know when it was present. The Uncertainty
Principle in fact sets a boundary to the early universe when the whole universe was very, very,
very small. The Uncertainty Principle also set the stage for the Copenhagen interpretation of
Quantum Mechanics. Niels Bohr, a Dane, proposed that we could only know the time averaged
probability that a body be in a place. Einstein, while understanding quantum mechanics, couldn’t
accept this probabilistic view of the world and pontificated that it couldn’t be so since “God doesn’t
play dice with the universe”. In fact, all our evidence says that on a certain scale God (if there is
one) doesn’t care that the universe can only be described statistically. On that scale, the world of
the very small, things are not deterministic.
Now let’s consider why we had to have quantum mechanics in the first place. In the second
half of the 1800’s spectroscopists - people who measured the spectra of light emitted or absorbed
by various things - reported curious lines in the spectra of the sun and of hydrogen and other gas
© Michael Bass
discharges. Since classical theories of these systems, no matter what they might look like in detail,
could not give discrete sharp spectral lines, physics was in a quandary. Also, if one heated a body
to some temperature, classical theories predicted that the body would emit far more ultraviolet
light than was observed. Again there was a problem. In 1900, Max Planck, in Germany, proposed
that light could only appear with finite energies given by
E = h
where h was a constant now called Planck’s constant and  the frequency of the associate light
wave. Only now it was a quantum of light or a light particle with energy determined by the
frequency of the light wave. Already there was a problem. Planck introduced us to light quanta
but could not do so without retaining some of the wave nature of light. The problem was, and
remains to the present, the issue of the particle/wave duality of light. It was, and for many is still,
a very unsatisfying way to understand how things work. After only about half a century, the wave
theory of light which had been so successful was challenged by the notion that actually light was,
in some sense, particle like in nature. It seemed that Newton’s idea that light was made up of
corpuscles was in some respects correct.
Planck’s idea that light came in quanta enabled him to explain the spectra of black bodies
and overcome the deficiencies of earlier classical models. His idea was applied by Einstein in
1905 to explain the photo electric effect. By about this time electrons and nuclei had been
discovered and the planetary model of the atom had been proposed. However, the classical model
where an electron circled the nucleus like a planet circling the sun had a problem. The electrostatic
attraction between the negatively charged electron and the positively charge nucleus would
eventually cause the electron to collide with the nucleus producing no atoms at all. But there are
atoms and they are stable. Niels Bohr and the quantum theorists proposed that while in the classical
model electrons could occupy any orbit they wanted to, in the proper quantum mechanical model
the electrons were restricted to only a few, special, stable orbits. The orbits were quantized and
when an electron changed from one quantized orbit to another it changed its energy. In so doing,
to conserve total energy, the atom either absorbed or emitted a quantum of energy in the form of
one of Planck’s quanta. But think for a moment - since only certain transitions could occur, only
certain discrete quanta were possible and only certain specific spectral lines (wavelengths of light)
could be expected. These would be characteristic of the atoms and would explain the
spectroscopists results.
Bohr’s model was given mathematical rigor by Erwin Schrodinger, Werner Heisenberg,
Paul Dirac and others. The accuracy and utility of quantum mechanics was proven by numerous
experiments. Both theory and experiment were eventually demonstrated with very high precision.
Quantum mechanics now forms the basis of our understanding of all sorts of things. Today, the
combination of quantum mechanics with gravity, a relativistic but classical theory, is the goal of
physicists seeking to understand such things as black holes, star histories and the early universe.
They seek something called quantum gravity.
By mid-century physics had Newton’s mechanics which worked perfectly and quite
precisely for speeds much less than the speed of light; thermodynamics telling us how energy
changes types and why time flows from past to future; electromagnetics giving us electricity, radio,
© Michael Bass
TV and electronics; relativity explaining the structure of our universe; and quantum mechanics
explaining the structures of atoms and subatomic particles so that we have lasers and solid state
electronics and nuclear magnetic resonance. As all this developed researchers began to understand
that only four forces were needed to explain the interactions between the particles which we could
observe. The weakest force is gravity. It is always attractive and is the interaction between all
bodies having non zero mass. The range of gravity is unlimited. The next strongest force is
electromagnetism describing the interaction between charged bodies and which can be either
attractive or repulsive. It is many millions of time stronger than gravity and also has unlimited
range. Then comes the weak nuclear force that is responsible for holding nuclei composed of
protons and neutrons together. It is attractive, has a range of the order of the radius of a nucleus
(~10-13 m) and is much stronger than the electromagnetic force. Finally comes the strong nuclear
force that holds individual protons and neutrons together. It is always attractive, very short range
(it acts inside a proton), and very, very, very strong!
Modern physicists are trying to unify these forces. Maxwell had shown that electric and
magnetic forces were different manifestations of one force, electromagnetism. Today physicists
are trying to find out if all four forces are different manifestations of a single force. Their thinking
goes something like this: if the energy of the particles were sufficiently high, the interactions
caused by all these forces should look the same. The problem is when, if ever, could this have
been so? As far as anyone can tell, only once in the history of the universe could such conditions
have existed. Only at the instant of its beginning could all forces in the universe have been
indistinguishable. At that instant, when energies were extraordinarily large (temperatures many
trillions of times that of the sun’s interior), when the universe was pure energy, too hot to contain
particles, there was only one force. As the universe expanded and things cooled down it became
possible for particles to exist and the symmetry of having only a single force was broken. The
forces separated and our universe of particles and massless quanta of light came into being.
So far we know of Maxwell’s unification of electric and magnetic forces. Then between
1961 and 1972, Sheldon Glashow, Steven Weinberg and Abdus Salam showed how to unite the
electromagnetic and weak nuclear forces. Their electro-weak unification has been demonstrated
experimentally and led to their sharing the 1979 Nobel Prize. They and others have pursued grand
unified theories to try to unify the electro-weak and the strong nuclear forces. A number of models
have been proposed but there are problems. These models, called GUTs, predict that a proton will
decay in ~1031 years. Now the time since the big bang is only ~1010 years and we only live ~102
years so this isn’t easy to measure. However, if we take ~1031 protons we can try to see if 1 proton
per year decays. The experiment is conceptually very simple. Take a tank of very pure water, put
it underground where the cosmic ray background radiation is weak, surround it with detectors to
sense a decay and watch and wait and wait and wait. So far we have no evidence for a proton
decay and so its lifetime must be >1035 yrs. There is a problem here to be solved.
More disturbing and vastly more complex is the problem of unifying the quantized forces,
electromagnetism, weak and strong nuclear, with that classical force - gravity. Trying to do this
is the field of many researchers. However, time and space restrict this discussion to the work of
Stephen Hawking. He contributed significantly to our understanding of that ultimate gravitational
event, the black hole. From this work he realized the thermodynamic properties of black holes
and showed that they don’t, can’t, violate the second law of thermodynamics. Stated differently,
© Michael Bass
Hawking showed that no black hole is “naked.” They are all surrounded by an event horizon that
remains forever in our universe but which prevents any information from the interior from leaking
out and violating the 2nd law. Hawking then became interested in quantum gravity and now studies
it. He has done all this while suffering from amyotrophic lateral sclerosis (ALS) or “Lou Gehrig’s
disease”. He can’t speak understandably, use his hands to write or draw or use a conventional
computer. He must carry out his research entirely in his own mind and use a special computer to
communicate his results.
Given the fact that the universe is expanding and the body of knowledge we now have, it
is only reasonable that physicists are trying to construct a picture of how the universe came into
existence and what is its future. If we trace the expansion back to the beginning it seems as though
the universe started with a very hot “Big Bang” about 13.7 billion years ago. It then went through
an exponential inflation to a very large size accounting for the fact that the universe is essentially
the same on the large scale everywhere we look. The inflation also accounts for the small nonuniformities that grew into the galaxies and galactic clusters that we see in the universe. The
evidence for such a beginning is overwhelming. First there is Hubble’s evidence for the motion
of galaxies away from each other. Then there is the universal ~3 K black body radiation which is
a remnant of the radiation present at the moment of the Big Bang and which is seen virtually
uniformly throughout the sky. Arno Penzias and Robert W. Wilson of the former Bell Telephone
Laboratories won the 1978 Nobel Prize for discovering the presence of this cosmic background
radiation. Further evidence for the Big Bang model of the universe comes from the fact that the
measured ratio of helium to hydrogen in the universe is what the model predicts. Very recently,
though still to be verified by independent measurements, the polarization of the microwave
background that the inflation predicts has been detected.
There are issues to be resolved concerning the model such as how did the non-uniformities
we see form in so little time though confirmation of the inflationary universe may take care of this.
For example, as we look out into the universe we see galaxies, galactic clusters and super clusters
as well as immense regions void of any visible matter. The Big Bang model must allow for such
structures and it is being studied and revised to do so. In recent years it has become clear that in
addition to ordinary matter that makes up about 4% of the universe there is dark matter that is
about 26% of the universe and dark energy that is the rest. The model has to account for all three.
Another intriguing feature of the Big Bang, as alluded to earlier, is that at the beginning energies
were so high that the four forces were unified. Thus, the study of the very small is being united
with the exploration of the entire universe in efforts to understand how unification occurs.
Cosmologists are also concerned with the future of the universe. Humankind won’t likely
be there to see it but we would like to try to figure out what is the ultimate end of all things.
Consider the Big Bang to be analogous to firing a rocket off the earth. If it has too little speed,
gravity will cause it to fall back to the surface. If it has too much speed it will escape the earth’s
gravity and fly off into space, or it could have just exactly the right speed to slowly rise into a
permanent orbit around the earth. In the case of the universe the Big Bang is like firing the rocket.
The universe itself is like the rocket. Depending on how much mass is present (how much gravity
there is), the universe can expand for a while and then fall back in a “Big Crunch”, go on expanding
forever, or expand but ever more slowly until, after an infinite time, it comes to a halt with all
matter (if any remains) infinitely far from all other matter. We don’t know which of these scenarios
© Michael Bass
will play out. The problem is in determining how much matter there is in the universe. The visible
matter in the universe is barely a few percent of the critical mass needed to produce closure.
However, there is evidence from the motions of the galaxies that there is a great deal of matter that
we can’t detect. This so called dark matter interacts gravitationally with other matter and could
provide enough additional mass to cause the universe to either re-collapse (the Big Crunch) or
slowly stop expanding. One of the most interesting problems in modern physics is to try to identify
the “dark matter”. It may be in the form of huge numbers of Jupiter-like objects that do not emit
enough radiation to be detected or it may be black holes. Another possibility is that the
fundamental particle called the neutrino, thought to be massless, may actually have a very small
mass. Since there are immense numbers of neutrinos in the universe, a small mass could have
major consequences. In fact, experiments have shown that some neutrinos do have a finite amount
of mass. These experiments showed that one type of neutrino changed into another type and that
can only happen if they are traveling at less than the speed of light. In that case, they have mass.
Or dark matter may be more exotic and result from such things as weakly interacting massive
particles or WIMPs. No matter the source of the dark matter, we have to have dark matter to
explain the motion and distribution of galaxies in the universe and so our cosmology is incomplete.
In the next paragraph you will read how it is even more incomplete than we thought.
In the first years of the 21st century astronomers made a startling discovery. Since Hubble’s
work it was known that the galaxies were flying apart from one another. Further, it seemed that
the rate was constant and was a measure of the universe’s age. With better telescopes and light
detectors evidence began to come in that showed that galaxies that were more than a few billion
light years away were moving away faster than they should have been. The recessional speed was
accelerating. The explanation of this is a difficult problem for scientists. They have to determine
either that there is some, as yet, unknown force driving the acceleration or that Newton’s inverse
square law breaks down at very large distances. This acceleration is attributed to something called
dark energy and it makes up something close to 70% of the universe’s mass-energy content. At
the present time we don’t know enough to explain what it is. However, the observations won
Nobel prizes in 2011for Saul Perlmutter, Brian P. Schmidt and Adam G. Riess. Scientists around
the world, are working on finding an explanation for dark energy that works and satisfies our ideas
on what is good science.
The foundations of our technological world were established before the start of the 20th
Century. Since then, physics has continued to develop making it possible, for the first time, to
seek scientifically valid answers to such questions as how did the universe come into existence
and what is its fate. We may have asked those questions in the past but then the only possible
answers would have come from theologians. Today science may provide them. That is, it may
give answers based on a method allowing for testing and verification - answers not requiring belief
alone. We are a long way from complete answers but parts of them are in hand and with the effort
to finish the work comes a deeper, more complete, and more satisfying understanding of the
universe and our place in it.
© Michael Bass