I. General Introduction:
p1 "Physics, the most fundamental physical science, is concerned with the basic principles of the Universe. It is the foundation upon which the other physical sciences - astronomy, chemistry, and geology - are based.
The beauty of physics lies in the simplicity of the fundamental physical theories and in the manner in which just a small number of fundamental concepts, equations, and can alter and expand our view of the world around us.
The myriad physical phenomena in our world are a part of one or more of the following 5 areas of physics:
1. Classical mechanics, which is concerned with the motion of objects moving at speeds that are low compared to the speed of light.
2. Relativity, which is a theory describing objects moving at any speed, even those whose speeds approach the speed of light.
3. Thermodynamics, which deals with heat, work, temperature, and the statistical behavior of a large number of particles.
4. Electromagnetism, which involves the theory of electricity, magnetism, and electromagnetic fields.
5. Quantum mechanics, a theory dealing with the behavior of particles at the submicroscopic level as well as the macroscopic world."
p2 ... the laws of conservation and energy and momentum introduced in mechanics retain their importance in the fundamental theories that follow, including the theories of modern physics
p3 "Physics is a fundamental science concerned with understanding thenatural
phenomena
that occur in our Universe. Like all sciences,
physics is based on experimental
observations and quantitative measurements. The main objective
of physics is to use the limited number of fundamental laws that
govern natural phenomena to develop theories that can predict the
results of future experiments. The fundamental laws used in developing
theories are expressed in the language of mathematics, the tool
that provides a bridge between theory and experiment.
When a discrepancy
between theory and experiment arises, new theories and experiments
must be formulated to remove the discrepancy.
Many times a theory is satisfactory only under limited conditions; a more
general theory might be satisfactory without such limitations.
A classic example is Newton's laws of motion, which
accurately describe the motion of bodies at normal speeds but do not apply
to objects moving at speeds comparable to the speed of light. The
special theory of relativity developed by Einstein successfully predicts
the motion of objects at low speed and at speeds approaching the speed
of light and hence is a more general theory of motion.
Classical physics, which means all of the physics
developed prior to 1900, includes the theories, concepts, laws, and experiments
in classical mechanics, thermodynamics, and electromagnetism. Galileo
Galilei (1564-1642) made significant contributions to classical
mechanics through his work on the motion of objects having constant acceleration.
In the same era, Johannes Kepler (1571-1630) analyzed
astronomical data to develop empirical laws for the motion of planetary
bodies.
The most important contributions to classical mechanics
were provided by Isaac Newton (1642-1727), who developed
classical mechanics as a systematic theory and was one of the originators
of the calculus as a mathematical tool.
p108 [Isaac Newton, a British physicist and mathematician,
is regarded as one of the greatest
scientists in history. Before the age of 30 he formulated
the basic concepts and laws of motion, discovered the universal law of
gravitation, and invented the calculus. Newton was able to explain
the motions of the planets, the ebb and flow of the tides, and many special
features of the motion of the Moon and the Earth. He also made many
important discoveries in optics, showing, ... that white light is composed
of a spectrum of colors. His contributions to physical
theories dominated scientific thought for two centuries and remain important
today. ... Newton was a very private person who studied alone
and labored day and night in his laboratory, conducting experiments, performing
calculations, and immersing himself in theological
studies. His greatest single work, Mathematical Principles
of Natural Philosophy, was published in 1687. ... He was elected
president of the Royal Society in 1703, and he retained that office until
his death in 1727.]
Although major developments in classical physics
continued in the 18th century, thermodynamics and electricity and magnetism
were not developed until the latter part of the 19th century, principally
because the apparatus for controlled experiments was either too crude or
unavailable until then. ... the disciplines of mechanics and electromagnetism
are basic to all the branches of classical and modern physics.
A new era in physics, usually referred to as 'modern
physics', began near the end of the 19th century. Modern physics
developed mainly because of the discovery that many physical
phenomena could not be explained by classical physics. The two most
important developments in this modern era were the theories of relativity
and quantum mechanics. Einstein's theory
of reltivity completely revolutionized the traditional concepts
of space, time, and energy. Among other things, Einstein's theory corrected
Newton's laws of motion for describing the motion of objects moving at
speeds comparable to the speed of light. The theory of relativity also
assumes that the speed of light is the upper limit of the speed of an object
or signal and shows the relationship between mass and energy.
Quantum mechanics was formulated by a number of
distinguished scientists to provide descriptions of physical phenomena
at the atomic level.
Scientists are constantly working at improving our
understanding of fundamental laws, and new discoveries are being made every
day. In many research areas, there
is a great deal of overlap between physics, chemistry, and biology, as
well as engineering. Some of the most notable developments
are 1) numerous space missions and the landing of astronauts on the Moon,
2) microcircuitry and high-speed computers, and 3) sophisticated imaging
techniques used in scientific research and medicine. The impacts
of such developments and discoveries on our society have indeed been great,
and it is very likely that future discoveries and developments will be
just as exciting and challenging and of great benefit to humanity.
II. Basic Laws
of Physics
1. Newton's first Law (p 109): An object at rest remains at rest and an object in motion will continue in motion with a constant velocity unless it experiences a net external force.
2. Newton's Second Law (p 111): The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
3. Newton's Third Law (p 114): If two bodies interact, the force exerted on body 1 by body 2 is equal to and opposite the force exerted on body 2 by body 1. (F12 = - F21)
4. Conservation of Energy in General
(p 219): Energy can never be created
or destroyed. Energy may be transformed from one form to another,
but the total energy of an isolated system is always
constant.
From a universal point of view, we can say that
the total energy of the Universe is constant:
If one part of the Universe gains energy in some form, another part must
lose an equal amount of energy. No violation of this
principle has been found.
5. Conservation of mass (p 220): In any kind of physical or chemical process, mass is neither created nor destroyed.
6. Conservation
of Mass and Energy (p 220): (... in 1905 Einstein
made the incredible discovery that mass, or inertia, of any system is a
measure of the total energy of the system. Hence
) energy and mass are related concepts: E =
mc^2 or as a combined conservation law mass
and energy are neither created nor destroyed but may be transformed from
one form to another.
(p1177)
... the energy, and therefore the mass, of a system
of particles before interaction must equal the energy, and therefore the
mass, of the system after interaction, where the mass is defined as
m = E / c^2 or E = mc^2
7. Conservation of Momentum (p237): Whenever two isolated, uncharged particles interact with each other, their total momentum (mv) remains constant. ... the total momentum of an isolated system at all times equals its initial momentum.
8. Conservation of Angular Momentum
(p318): The total angular momentum
of a system is constant if the resultant external torque acting on the
system is zero. ... L = constant or L initial = L final = constant
...
the energy, linear momentum (mv), and angular
momentum of an isolated system all remain constant.
(p 312 The instantaneous angular momentum L
of the particle relative to the origin O is defined by the cross product
of the instantaneous vector position of the particle and its instantaneous
linear momentum p. L = r x p or L = r x
mv.
L involves a rotation motion of matter at a certain
velocity around a point of reference.)
9. Newton's Law of Gravity (p392):
Every particle in the Universe attracts every other
particle with a force that is directly proportional to the product of their
masses and inversely proportional to the square of the distance between
them
or F = G (M1)(M2) / R^2 (G
= 6.672E-11 N*m^2/kg^2)
10. Kepler's Laws (p396):
1. All planets move in elliptical orbits with the
Sun at one of the focal points.
2. The radius vector drawn from the Sun to a planet
sweeps out equal areas in equal time intervals.
3. The square of the orbital period of any planet
is proportional to the cube of the semimajor axis of the elliptical orbit.
11. THE LAWS OF THERMODYNAMICS &
ENTROPY
lst LAW:
(pg 552) - The first law of thermodynamics
is merely the law of conservation of energy.
It tells us only that an increase in one form of energy must be accompanied
by a decrease in some other form of energy.
(pg 563) - The first law of thermodynamics ... is a generalization known as the law of conservation of energy ... It is a universally valid law that can be applied to all kinds of processes. Furthermore, it provides us with a connection between the microscopic and macroscopic worlds.
(pg 575) - The first law of thermodynamics states that when a system undergoes a change from one state to another, the change in its internal energy is equal to the thermal energy transferred into (or out of) the system minus the work done by (or on) the system. (delta U = Q - W)
(pg 615) - The first law of thermodynamics ... is a statement of conservation of energy, generalized to include heat as a form of energy transfer. This law tells us only than an increase in one form of energy must be accompanied by a decrease in some other form of energy. It makes no restrictions on the types of energy conversions that can occur.
2nd LAW of Thermodynamics:
(pg 617) Kelvin-Planck form = It is impossible to construct a heat engine that, operating in a cycle, produces no other effect than the absorption of thermal energy from a reservoir & the performance of equal amount of work.
(pg 617) - The first law says that we cannot get more energy out of a cyclic process than the amount of thermal energy we put in, and the second law says that we cannot break even because we must put more thermal energy in, at the higher temperature, than the net amount of work output.
(pg 618) Clausius statement form = It is impossible to construct a machine operating in a cycle that produces no other effect than to transfer thermal energy continuously from one object to another object at a higher temperature. In simpler terms, thermal energy does not flow spontaneously from a cold object to a hot object.
ENTROPY:
(pg 628) ... Consider any infinitesimal process for a system between
two equilibrium states ... the change in entropy (S) ... is equal to the
amount of thermal energy transferred along the reversible path divided
by the absolute temperature of the system (dS = dQr / T).
(pg 629) ... Isolated systems tend toward disorder, and entropy
is a measure of this disorder.
(pg 629) ... The entropy of the Universe increases in all processes. This statement is yet another way of stating the second law of thermodynamics.
(pg 632) ... The second law of thermodynamics can be stated as follows:
The
total entropy of an isolated system that undergoes a change
CANNOT
DECREASE
Furthermore, the process is irreversible, the
total entropy of an isolated system always increases.
(pg 632) ... Ultimately, the entropy of the Universe should reach a maximum value. At this point the Universe will be in a state of uniform temperature and density. All physical, chemical, and biological processes will cease, since a state of perfect disorder implies that no energy is available for doing work .. = heat death of the Universe
12. Einstein's Special Theory of Relativity
(p1182):
1. The Principle of Relativity: All the laws
of physics are the same in all inertial reference frames.
2. The Constancy of the Speed of Light: The
speed of light in vacuum has the same value, c = 3.00E8 m/s, in all
inertial frames, regardless of the velocity of the obvserver or the velocity
of the source emitting the light.
Three Consequences
of Special Relativity (p 1182):
1. Events that are simultaneous for one observer are not simultaneous for
another observer who is in motiion relative to
the first.
2. Clocks in motion relative to an observer appear to be slowed down by
a factor gamma. This is known as time
dilation.
3. Lengths of objects in motion appear to be contracted in the direction
of motion.
13. Einstein's General Theory of Relativity
(p1181):
1. Postulate #1 = All the laws of nature have the
same form for observers in any frame of reference, whether
accelerated or not.
2. Postulate #2 = In the vicinity of any given point,
a gravitational field is equivalent to an accelerated frame of reference
in the absence of gravitational effects. (This is the principle
of equivalence.)
Consequences
of General Relativity (p1181):
1. The second postulate implies that gravitational mass and inertial mass
are completely equivalent ...
2. Time scales are altered by gravity. A clock in the presence of
gravity runs more slowly than one where gravity is
negligible.
3. The second postulate suggests that a gravitational field may be "transformed
away" at any point if we choose an appropriate accelerated frame of reference
- a freely falling one. Einstein .... specified a certain quantity,
the curvature of space-time, that describes the gravitational effect at
every point. In fact, the curvature of space-time completely replaces
Newton's gravitational theory. According to Einstein, there is no
such thing as a gravitational force. Rather, the presence of a mass
causes a curvature of space-time in the vicinity of the mass, and this
curvature dictates the space-time path that all freely moving objects must
follow.
If the concentration of mass becomes very great,
as is believed to occur when a large star exhausts its nuclear fuel and
collapses to a very small volume, a black hole may
form. Here the curvature of space-time is so extreme that, within
a certain distance from the center of the black hole, all matter and light
become trapped.
III. Radioactivity
p1346 In 1896, the year that marks the birth of nuclear physics, the French physicist Henri Becquerel (1852-1908) discovered radioactivity in uranium conpounds. ... alpha rays are helium nuclei, beta rays are electrons, and gamma rays are high-energy photons. ...
p1361 ... The half-life of a radioactive substance is the time it takes half of a given number of radioactive nuclei to decay.
... T1/2 = ln2/(dc) ... [dc = decay constant = lamda]
... N = No x e^(-dc*t) [No = # radioactive nuclei at t = 0]
p1367 Carbon Dating
The beta decay of Carbon 14 ... is commonly used to date organic samples. Cosmic rays in the upper atmosphere cause nuclear reactions that create C14. In fact, the ratio of C14 to C12 in the carbon dioxide molecules of our atmosphere has a constant value of approximately 1.3E-12. All living organisms have this same ratio of C14 to C12 because they continuously exchange carbon dioxide with their surroundings. When an organism dies, however, it no longer absorbs C14 from the atmosphere, and so the C14/C12 ratio decreses as the result of the beta decay of C14, which has a half-life of 5730 years. It is therefore possible to measure the age of a material by measuring its activity per unit mass caused by the decay of C14. Using this technique, scientists have been able to identify samples of wood, charcoal, bone, and shell as having lived from 1000 to 25,000 years ago. This knowledge has helped us reconstruct the history of living organisms - including humans - during this time sppan.
p1370 ... The existence of radioactive series in nature enables our
environment to be constantly replenished with radioactive elements that
would otherwise have disappeared long ago. For example, because the
Solar System is approximately 5E9 (5,000,000,000. = 5 Billion) years old,
the supply of Ra226 (whose half-life is only 1600 years) would have been
depleted by radioactive decay long ago if it were not for the decay series
that starts with U238. ...
IV. Particle Physics (p1413)
p1414 Quarks ... all particles
except electrons, photons, and a few related
particles are made of smaller
particles called
quarks. Thus, protons and neutrons, for example, are not truly elementary
but are systems of tightly bound quarks. ...
Fundamental Forces In Nature: (in order of decreasing
strength)
1. Strong force: represents the glue that holds nucleons
together. It is very short-range ...
2.Electromagnetic force: which binds atoms and molecules
together to form ordinary matter ... It is a
long-range force that decreases in strength as the inverse square of the
separation between interacting particles.
3. Weak force: is a short-range force that tends to
produce instability in certain nuclei. It is responsible for most
radioactive decay processes such as beta decay, and its strength is only
about E-5 of the strong force.
4. Gravitational force: is a long-range force that
has a strength of only about E-39 times that of the strong
force. Although this familiar interaction is the force that holds
the planets, stars, and galaxies together, its
effect on elementary particles is negligible.
p1415 ... for
every particle, there is an antiparticle.
The antiparticle has the same mass as the particle, but opposite charge.
...
... Perhaps the most common process for producing positrons is pair
production. In this process, a gamma-ray photon
with sufficiently high energy collides with a nucleus and an electron-positron
pair is created. ...The reverse process can also occur.
Under the proper conditions, an electron and positron can annihilate each
other to produce two gamma-ray photons ...
... Practically every known elementary particle has an antiparticle.
p1420 Conservation Laws
... conservation laws are important in understanding why
certain decay and reactions occur and others do not. In general, the
laws of conservation of energy, linear momentum, angular momentum, and
electric charge provide us with a set of rules that all processes must
follow ...
V. The Cosmic Connection
(p 1432) Big
Bang: ... one of the most fascinating theories
in all of science - the Big Bang theory of
the creation of the Universe. ... This theory of cosmology
states that the Universe had a beginning and, further, that
the beginning was so cataclysmic that it is impossible to look back beyond
it. According to this theory, the Universe erupted from
a point-like singularity about 15
to 20 billion years ago.
The first few minutes after the Big Bang saw such
extremes of energy that it is believed that all four interactions of physics
were unified and that all matter melted down into an undifferentiated "quark
soup."
The evolution of the four fundamental forces from
the Big Bang to the present ... During the first E-43 sec (the ultra-hot
epoch during which T = E32 K), it is presumed that the strong, electroweak,
and gravitational forces were joined to form a completely unified force.
In the first E-32 sec following the Big Bang (the hot epoch, T = E29 K),
gravity broke free of this unification while the strong and electroweak
forces remained as one, described by a grand unificatiion theory.
This was a period when particle energies were so great (> E16 GeV) that
very massive particles as well as quarks, leptons, and their antiparticles
existed.
Then, the Universe rapidly expanded and cooled during
the warm epoch when the temperatures ranged from E29 to E15 K, the strong
and electroweak forces parted company, and the grand unification scheme
was broken. As the Universe continued to cool, the electroweak force
split into the weak force and the electromagnetic force about E-10 sec
after the Big Bang.
Until about 700,000 years after the Big Ban, the
Universe was dominated by radiation: Ions absorbed and re-emitted
photons, thereby ensuring thermal equilibrium of radiatioin and matter.
Energetic radiatioin also prevented matter from forming clumps or even
single hydrogen atoms.
p1433 When the Universe was about 700,000 years old, it had expanded and colled to about 3000 K, and protons could bind to electrons to form neutral hydrogen atoms. Because neutral atoms do not appreciably scatter photons, the Universe suddenly became transparent to photons. Radiation no longer dominated the Universe and clumps of neutral matter steadily grew - first atoms, followed by molecules, gas clouds, stars, and finally galaxies.
Evidence for the Big Bang:
1.
Observation of Radiation from the Primordial Fireball
(p 1433): In 1965, Penzias and Wilson of Bell Labs ...
perceiving microwave background radiation (at a wavelength of 7.35 cm)
representing the leftover glow from the Big Bang. ... The intensity
of the detected signal remained unchanged as the antenna was pointed in
different directions. The fact that the radiatioin had equal strengths
in all directions suggested that the entire Universe was the source of
this radiation. ... Penzias and Wilson discovered that a group
at Princeton had predicted the residual radiation from the Big Bang and
were planning an experiment seeking to confirm the theory. ... Penzias
and Wilson announced that they had already observed an excess microwave
background compatible with a 3-K blackbody source.
p 1434 Subsequent experiments by other groups added
intensity data at different wavelengths ... The results confirm that
the radiatioin is that of a black body at 2.9 K. ... perhaps,
the most clearcut evidence for the Big Bang theory.
p1438 ... The background microwave radiatin discovered
by Penzias and Wilson strongly suggests that the Universe
started with a "Big Bang" about 15 billion years ago. ...
2. (p 1435) ... In the late 1920s, Edwin P. Hubble
made the bold assertion that the whole Universe is expanding. From
1928 to 1936, he and Milton Humason toiled at Mount Wilson to prove this
assertion until they reached the limits of the 100-inch telescope.
The results of this work and its continuation on a 200-inch telescope in
the 1940s showed that the speeds of galaxies increase
in direct proportion to their distance R from us. This linear
relationship, known as Hubble's law, may be written
v = HR where H, called the Hubble parameter, has the approximate
value H = 17 E-3 m/(s.lightyear).
[note: current values in 2000 are much higher with an average around
about 50 E-3. Further, as T = 1/H the age of the universe is estimated
to be anywhere from 10 Bil to 20 Bil years old depending on the value of
H used etc.]
[note: Vesto Slipher, an American astronomer, reported that most nebulae are receding from the Earth at speeds up to several million miles per hour. Slipher was one of the first to use the methods of Doppler shifts in spectral lines to measure velocities. It was this method that Hubble adopted and used to determine the velocities of distant galaxies and thus observing that most of them had red shifts in their spectra which he interpreted to mean that all the distant galaxies were moving away from the earth and thus that the whole Universe was expanding etc.]
Missing Mass in the Universe (?)
p 1437 The visible matter in galaxies averages out
to 5 E-33 g/cubic cm. The radiatiion in the Universe has a
mass equivalent of approximately 2% of the visible matter. Nonluminous
matter (such as interstellar gas or black holes) may be estimated from
the speeds of galaxies orbiting each other in the cluster. The higher
the galaxy speeds, the more mass in the cluster. Results from measurements
on the Coma cluster of galaxies, surprisingly, indicate that the amount
of invisible matter is 20 to 30 times the amount present in stars and luminous
gas clouds. Yet even this large invisible component, if applied to
the Universe as a whole, leaves the observed mass density a factor of 10
less than critical density. This so-call missing mass ( or dark matter)
has been the subject of intense theoretical and experimental work, with
exotic particles such as axions, photinos, and superstring particles suggested
as candidates for the missing mass. More mundane proposals have been
that the missing mass is present in certain galaxies as neutrinos.
In fact, neutrinos are so abundant that a tiny neutrino rest mass on the
order of 20 eV would furnish the missing mass and "close" the Universe.
p1437 ... Although we are a bit more sure about the beginning of the
Universe, we are uncertain about its end. Will the Universe expand forever?
Will it collapse and repeat its expansion in an endless series of oscillations?
Results and answers to these questions remain
inconclusive
and the exciting controversy
continues.