A collection of notes on physics compiled from various sources. See also philosophy of science.

# Physics - a compilation

Last updated 07 December 2013

### Index

stars and the universe

energy and mass

electromagnetism

gravitation

atoms and electrons

symmetry

mathematics

fundamental units

waves

particles

light and photons (quanta)

matter

mind and matter

fields

double slit experiment

Planck's constants

black body radiation

quantum

Bell's theorem

string theory

space and time

holography

chaos

chemical processes

references

### absolute zero

*At absolute zero, there is a minimum amount of vibration that the
atoms can have, but not zero ... Helium merely decreases the atomic
motions as much as it can, but even at absolute zero there is still
enough motion to keep it from freezing.*

### stars and the universe

Our known universe originated 13.7 billion years ago. It is estimated to contain over 100 billion galaxies, each containing several hundred billion stars.

Massive stars only forge elements up to Fe (the first 26) which constitute 99% of all elements on earth. Elements heavier than that are forged in the final death throes of stars 10 times larger than our sun, in supernova explosions - the most powerful explosions in the universe.

These supernovae form rich chemical clouds, the nebulae. The heart of the nebula now contains a little neutron star. Our sun was formed from a nebulae 5 million years ago.

New stars will be formed from the elements blown out by supernovae explosions. The Orion nebula contains molucules such as H2O, formaldehyde, Ether, Methanol, Sulfer Dioxide, Hydrogen Cyanide - complex carbon chemistry in deep space - the beginning of the chemistry of life.

Meteorites originating from the formation of the solar system and found in the Andez Atacama desert contain Amino Acids (the fundamental building blocks of proteins).

91.2% of our Sun is hydrogen. Every second, the sun converts 5 million tons
of its mass into energy, converting hydrogen into helium using a process called *fusion*.
The core of the sun comprises
half the star's mass though only 2% of its volume. At the core the temperature
builds up to 15 million degrees C. The surface temperature is only 5500 degrees C.

Due to the immense pressures, light escapes from the core at a rate of only 1mm/s. Since the distance to the surface is about 500,000 Km, it takes light 200,000 years to travel from the core to the surface, and only 8 minutes to eventually reach our earth!

The diagrams we see of our solar system give us a false impression.
All distances are scaled in order to be able to see all the planets.
Given some very basic information, it is easy to draw some comparisons,
the unit of measure I use here is the *smarties* chocolate sweet
which I'm sure most of us are familiar with. So here goes -

If the Earth were the size of a smarties (13 mm diameter), then

- The Sun would be 150 meters away and have a diameter of 1.4 meters.
- The Moon would be 0.5 meter away.
- Pluto would be 6 km away.

If the sun were the size of a smarties (14 mm diameter) then

- Earth would be 1.5 m away.
- Pluto would be 60 meters away.
- The next star would be 420 km away.

If our galaxy, the Milky Way were the size of a smarties, then

- The next galaxy - M31 - would be 13 cm away
- The entire observable universe would fit within a sphere just 1 km accross.

#### Other interesting measurements

- The universe is about 15 billion years old.
- There are about 100 billion galaxies in the universe.
- The Milky Way has about a 100 billion bright stars.
- The Milky Way is about 100,000 lightyears accross, 30,000 lightyears thick at the center, and 2600 lightyears thick on the outsides.
- The nearest star is 4.2 lightyears away.
- We can see about 3000 stars with the naked eye.
- The solar system orbits the center of our galaxy at 220 km per second.
- The Earth is 4.5 billion years old.
- The Earth's speed around the sun is 30 km/s.
- The Earth's biosphere is proportional in size to the skin of an apple.
- The Moon's size is 1/4 of the Earth, but 1/80th the Earth's mass.
- Only one five billionth of the sun's light strikes the earth.

#### Further comments

- Interesting how we say
*the*Earth,*the*Sun and*the*Moon, but not*the*Saturn. - The Big Bang theory is still in dispute by some eminent scientists,
such as John Dobson, the inventor of the Dobsonian telescope. In his
words ...

*The Big Bang cosmologists want to get the Universe out of nothing. It's like asking us to believe that nothing made everything out of nothing. But that's not what shows in our physics.* - Since more distant galaxies recede from us at a faster speed (one argument against a 'Big Bang' starting from an origin), we should maybe call this universe the 'observable universe'.
- There is proportionality in the distances within our galaxy,
expressed as Bode's Law: Given the distance Sun-Earth (149.6 x 10
^{6}km) as x, and a doubling sequence {3, 6, 12, 24, 48, ...}, then each successive distance can be calculated with ((2n + 4)/10)x, where n is each successive number from the series. Read more on this here.

* Through a variety of fusion processes, stars build hydrogen into
helium; helium into carbon; carbon into oxygen and magnesium, and so
forth. Indeed, given that the energy released amounts to but a tiny
fraction of the mass being shuffled about, we could say that element
making is the primary business of stars, and that their light and heat
is but a by-product of that process... *

*... the ultimate energy source in the stars which produces the
greatest amount of energy is gravity power.*

*Speculation about the origin of the universe is an old and
notorious human activity; notorious because the cosmogonic [pertaining
to the origin and evolution of the universe] speculations that resulted
told us more about ourselves than about the universe they claimed to
describe.*

*The recession velocity of any galaxy we observe is proportional to
the galaxy's distance. The more distant the galaxy, the faster it moves
away from us. At double the distance, the recession velocity will also
double. We observe the furthest galaxies approach the speed of light,
and the light from galaxies beyond that distance will never reach us.*

* So, in accordance with the second law, the orbital speed of each
planet is such that the radius "sweeps out" equal areas in equal times.
*

### energy and mass

* Under proper circumstances any substance can have its mass
exploded outwards as energy. A single sheet of paper harnasses an energy
that if erupted would cause an explosion greater than that of a large
power station. *

*To give an idea on how much stronger electricity is than
gravitation, consider 2 grains of sand, a milimeter accross, 30 meters
apart. If the force between them were not balanced, if everything
attracted everything else instead of likes repelling, so that there were
no cancellation, how much force would there be? There would be a force
of 3 million tons between the two! *

* The law of conservation of energy is a theorem concerning
quantities that have to be calculated and added together, with no
mention of the machinery, and likewise the great laws of mechanics are
quantitative mathematical laws for which no machinery is available. Why
can we use mathematics to describe nature without a mechanism behind it?
No one knows. We have to keep going because we find out more that way.*

* However, gravitation and other forces are very similar, and it is
interesting to note analogies. For example, the force of electricity
between 2 charged objects looks just like the law of gravitation: The
force of electricity is a constant, with a minus sing, times the product
of the charges, and varies inversely as the square of the distance. It
is in the opposite direction - likes repel. But is it still not very
remarkable that the 2 laws involve the same function of distance? *

* If we take, in some natural units, the repulsion of 2 electrons
(nature's universal charge) due to electricity, and the attraction of 2
electrons due to their masses, we can measure the ratio of electrical
repulsion to the gravitational attraction. The ratio is independent of
the distance and is a fundamental constant of nature ... The
gravitational attraction relative to the electrical repulsion between 2
electrons is 1 / (4.17 * 10^42). The question is, where does such a
large number come from? It is not accidental, like the ratio of the
volume of the earth to the volume of a flea. We have considered 2
natural aspects of the same thing, an electron. This fantastic number is
a natural constant, so it involves something deep in nature. *

### electromagnetism

Magnetism is the force you get when electrons are moving. In a permanent magnet, electricity is flowing all the time, each electron spinning in the same direction.

* As the light beam starts going forward, a little bit of
electricity is produced, and as this electricity moves forward it powers
up a little bit of magnetism, this in turn powers up another surge of
electricity, and so on. The electricity and magnetism keep on
leapfrogging over each other in tiny, fast jumps. Maxwell's equations
summarizing this insight became known as one of the greatest theoretical
achievements of all time. *

The faster a charge moves through a magnetic field, the stronger the force on this charge.

* So what would happen if our object was traveling close to the
speed of light and a great amount of energy would be added to it? If the
speed can't go over the limit, what happens to the extra energy?
Experiments with protons in huge powerful accelerators showed that their
mass was increasing! At speeds of 99.9997 percent of the speed of light,
the protons ended up 430 times bigger than their original size. *

* Maxwell found that the speed with which electromagnetic fields
are propagated is equal to the ratio between the electrical force
exerted between two electrical charges when at rest and the magnetic
force they exert when in motion. As this turned out to be nothing other
than the velocity of light, Maxwell concluded that light itself is an
electromagnetic field ... The velocity of light results from a
fundamental constant in the equations that describe the behaviour of
electromagnetic fields. *

* Electromagnetism is the force that holds electrons in their
orbits around nuclear particles to make atoms, binds atoms together to
form molecules, and ties molecules together to form objects. Every
tangible thing, from stars and planets to this page and the eyes that
reads it, carries electromagnetism in the fibre of its being. *

* Maxwell's equations show that electric fields and magnetic fields
cannot exist separately. There is indeed only a combined electromagnetic
field with an electric component and a magnetic component at right
angles to each other. *

* In electric phenomena, positive charges and negative charges can
exist independently of each other. An object can be either positively
charged or negatively charged. In magnetic phenomena, the magnetic poles
do not exist separately. *

* Maxwell showed that from his equations you can demonstrate that
an oscillating electric field will produce inevitably an oscillating
magnetic field, which will in turn produce another oscillating electric
field, and so on indefinitely. *

### gravitation

* I was sitting in a chair in the patent office at Bern, when all
of a sudden a thought occurred to me: "If a person falls freely he will
not feel his own weight". I was startled. This simple thought made a
deep impression on me. It impelled me toward a theory of gravitation. *

* What is this law of gravitation? It is that every object in the
universe attracts every other object with a force which for any two
bodies is proportional to the mass of each and varies inversely as the
square of the distance between them: F = G((m1.m2)/r^2) *

* An object released near the earth's surface will fall 16 feet in
the first second. An object shot out horizontally will also fall 16
feet; even though it is moving horizontally, it still falls the same 16
feet in the same time ... What happens if we shoot a bullet faster and
faster? Do not forget that the earth's surface is curved. If we shoot it
fast enough, then when it falls 16 feet it may be at just the same
height above the ground as it was before ... Thus we see that if the
bullet moves 5 miles a second, it will then continue to fall toward the
earth at the same rate of 16 feet each second, but it will never get any
closer because the earth keeps curving away from it.*

[From the first part of the section above, it is an interesting fact that when a ball is dropped while at the same time, and from the same height, a gun fires a bullet horizontally, both the bullet and the ball will reach the ground at the same time].

F = G (m1*m2)/r^{2}

G = 6.670 * 10^{-11} Newton * m^{2}/kg^{2}

* It is hard to exaggerate the importance of the effect on the
history of science produced by this great success of the theory of
gravitation. Compare the confusion, the lack of confidence, the
incomplete knowledge that prevailed in the earlier ages, when there were
endless debates and paradoxes, with the clarity and simplicity of this
law - this fact that all the moons and planets and stars have such a
simple rule to govern them, and further that man could understand it and
deduce how the planets should move! This is the reason for the success
of the sciences in following years, for it gave hope that the other
phenomena of the world might also have such beautifully simple laws. *

* It is a fact that the force of gravitation is proportional to the
mass, the quantity which is fundamentally a measure of inertia - of how
hard it is to hold something which is going around in a circle.
Therefore 2 objects, one heavy and one light, going around a larger
object in the same circle at the same speed because of gravity, will
stay together because to go in a cirle requires a force which is
stronger for a bigger mass. That is, the gravity is stronger for a given
mass in "just the right proportion" so that the 2 objects will go around
together. If one object were inside the other it would stay inside; it
is a perfect balance. *

* [The law of gravitation] was modified by Einstein to take into
account the theory of relativity. According to Newton, the gravitational
effect is instantaneous, that is, if we were to move a mass, we would at
once feel a new force because of the new position of that mass; by such
means we could send signals at infinite speed. Einstein advanced
arguments which suggest that we *cannot send signals faster than the
speed of light*, so the law of gravitation must be wrong. By correcting
it to take the delays into accout, we have a new law, called Einstein's
law of gravitation. One feature of this new law which is quite easy to
understand is this: In the Einstein relativity theory, anything which
has energy has mass - mass in the sense that it is attracted
gravitationally. *

### atoms and electrons

Refer also to The Atom: Filling the Gaps.

* The electron is a little bubble of wave energy. The electron wave
can set up paricularly stable standing vibrations (resonance) - this
leads to emmision or absorption of electro-magnetic radiation in atoms
and molecules. When an electron falls from an outer to an inner orbit it
emits a photon. The wavelength of that photon is determined by the
particular orbits between which the electron has made the transition.
And that is why a spectrum, which records the wavelengths of photons,
reveals the chemical elements that make up the stars or other object the
spectroscopist is studying. *

* The dot over a letter i has many more protons than there are
stars in our galaxy. (+100 billion) *

* The nucleus virtually ties up all the mass of the atom, electrons
determine its size. *

* What happens inside a nucleus is largely independent of what
happens to the electrons. *

* Atomic explosion works by 'rearranging' inside nuclei. Chemical
explosion rearranges electrons in their orbits. *

* In the outer regions of an atom, electrons emit visible light
when changing orbit. Inside the nucleus, a proton or neutron making a
similar change emits an x-ray with a million times more energy. *

* The diameter of an atom is approximately 4 . 10 ^{-10}
meters.
Roughly 1000 atoms span one wavelength of light.
One milimeter is around 2.5 million wavelengths.*

*All things are made of atoms - little particles that move around
in perpetual motion, attracting each other when they are a little
distance apart, but repelling upon being squeezed into one another.*

### symmetry

* Nothing in physics seems so hopeful to me as the idea that it is
possible for a theory to have a very high degree of symmetry which is
hidden from us in ordinary life. *

* Weinberg, Glashow, and Salam had been right; we live in a
universe of broken symmetries, where at least two of the fundamental
forces of nature, electromagnetism and the weak nuclear force, have
diverged from a single, more symmetrical parent. *

### mathematics

* We observe how the very geometry of our world often produces
squares... In fact, almost anything that steadily accumulates will turn
out to grow in terms of simple squared numbers. *

[Mathematics reveals underlying similarities in nature. For example the
equation for the attraction between 2 masses is
F = G * (m1 * m2)/r^{2} (Newton's law), while the equation for the attraction
between 2 charges is F = k * (q1 * q2)/r^{2} (Coulomb's law).
The reason why these 2 equations are the same is unknown.]

* Mathematical truth is independent of perception and it is a truth
of a very peculiar sort, and is concerned only with symbols. Numbers are
logical fictions. *

### fundamental units

**inertia**

* ... that is the principle of inertia - if something is moving,
with nothing touching it and completely undisturbed, it will go on
forever, coasting at a uniform speed in a straight line. (Why does it
keep on coasting? We do not know, but that's the way it is). *

**rules of thumb**

Here's a great general rule to remember the units of force, energy, and power. It builds on the alleged idea that Newton discovered the concept of gravity from observing an apple fall from a tree:

- 1
*Newton*is roughly equal to the force of Earth's gravity on a small apple. - 1
*Joule*is roughly equal to the energy required to lift that apple one meter off the ground. - 1
*Watt*is the power required when lifting this apple 1 meter off the ground in 1 second.

**Newton's laws of motion**

Newton's first 3 laws are so fundamental to physics that it is worthwhile to remember them:

- Objects move unless some force changes the motion
- F = m * a
- Every action produces an equal and opposite reaction

**force**

Aristotle described force as anything which causes an object to undergo
*unnatural motion*. Newton was able to describe force in more
mathematical terms.
From Newton's second law: F = m * a (kg * m/s^{2}). The unit of force is the *Newton*,
which is equal to the amount of net force required to accelerate a mass
of one kilogram at a rate of one meter per second squared.

**energy**

basic units

- The Joule (Newton*m), which roughly equates the energy required to lift an apple 1 meter off the ground.
- The Calorie (cal). One cal is the energy needed to increase the temperature of 1 gram of water by 1 °C. One cal equals 4.1858 Joules.
- The
*Dietary Calorie*= 1000 calories = 1 kilocalorie = 4185.8 Joules.

**power**

Rate of energy use. in cal/s or joule/s ( or Watt).

1 Horse Power is somewhat less than 1 kW (746 Watts).

Sunlight delivers power at a rate of 1kW/m^{2}. Current commercial solar cells have an efficiency
of around 10%, while NASA's solar cells have a 50% efficiency.

The amount of energy a substance contains per gram can be surprising:

- bullet: 0.01 cal/g
- computer battery: 0.1 cal/g
- TNT: 0.65 cal/g
- Choc cookie: 5 cal/g
- Coal: 6 cal/g
- Fuel: 10 cal/g
- Natural gas: 13 cal/g

Note that TNT is powerful not because the potential energy it contains but because
of the fact that it can release this energy in a very short time (Nitrogen reactions). Its *rate
of energy release* (power) is high.

We saw that the average human needs about 2000 dietary calories a day. This equates to 8,371,600 Joules per day, which is 8,371,600 Joules per 86400 seconds. Which is 96.9 Watt. That is the energy needed to keep the body alive. As a comparison, the average human in the developed world consumes about 11,000 W!

Half an hour of exhaustive exercise equates to one can of coke.

### waves

* Jean B.J.Fourier (Eighteenth century Frenchman) ... developed a
mathematical way of converting any pattern, no matter how complex, into
a language of simple waves. He also showed how these waveforms could be
converted into the original pattern. The equations he developed to
convert images into wave forms and back again are known as Fourier
transforms. *

* Particles moving in wave patterns do not exist in nature. In a
water wave, for example, the water particles do not move along with the
wave but move in circles as the wave passes by. Similarly, the air
particles in a sound wave merely oscillate back and forth, but do not
propagate along with the wave. What is transported along the wave is the
disturbance causing the wave phenomenon, but not any material particle.
*

* TRANSVERSE waves: Water waves spread outward,
and the particles of water move up and down in a direction perpendicular
to the direction in which the wave progresses.
LONGITUDINAL waves: Sound waves also spread outward,but
the particles of air move parallel with the direction in which the waves
progress. *

### particles

* Electrons and all other particles are no more substantive or
permanent than the form a geyser of water takes as it gushes out of a
fountain. They are sustained by a constant influx from the implicate
order, and when a particle appears to be destroyed, it is not lost. It
has merely enfolded back into the deeper order from which it sprang. *

* ... A particle can only be defined in terms of its connections to
the whole, and these connections are of a statistical nature -
probabilities rather than certainties. *

* The electromagnetic field can manifest itself as a free field
in the form of travelling waves / photons, or it can play the role of a
field of force between charged particles. In the latter case, the force
manifests itself as the exchange of photons between the interacting
particles. The electric repulsion between two electrons, for example, is
mediated through these photon exchanges. *

* Neither of the two electrons feels a force when they
approach each other. All they do is interact with the exchanged photons.
The repulsive force is nothing but the collective macroscopic effect of
these multiple photon exchanges. *

* ... According to quantum field theory, all interactions take
place through the exchange of particles. In the case of electromagnetic
interactions, the exchanged particles are photons; nucleons, on the
other hand, interact through the much stronger nuclear force which
manifests itself as the exchange of a new kind of particles called
"mesons". *

#### Bosons

In particle physics, bosons are particles which obey Bose-Einstein statistics; they are named after Satyendra Nath Bose and Albert Einstein. In contrast to fermions, which obey Fermi-Dirac statistics, several bosons can occupy the same quantum state. Thus, bosons with the same energy can occupy the same place in space. Therefore bosons are often force carrier particles while fermions are usually associated with matter, though the distinction between the two concepts is not clear cut in quantum physics.

All observed elementary particles are either fermions or bosons. The observed elementary bosons are all gauge bosons: photons, W and Z bosons and gluons.

- Photons are the force carriers of the electromagnetic field.
- W and Z bosons are the force carriers which mediate the weak nuclear force.
- Gluons are the fundamental force carriers underlying the strong nuclear force.

In addition, the standard model postulates the existence of Higgs bosons, which give other particles their mass via the Higgs mechanism.

Finally, many approaches to quantum gravity postulate a force carrier for gravity, the graviton, which is a boson of spin 2.

One boson in a state can stimulate or induce another boson into the same state, causing a quantum event (eg. an atomic transition).

*A splendid light has dawned on me about the absorption and
emission of radiation...*

What Einstein had realized is that light shined on an atom which is
in an excited state can induce the atom to make a downward transition
(emitting a photon) if the incoming light's frequency matches the atomic
transition energy. The incoming photon is a boson, and for this reason
it stimulates the emission of a second photon in the same state,
inducing an atomic transition. (Otherwise the "spontaneous emission"
would happen randomly.)

Thus, in stimulated emission we have an example of "quantum causality."
This process combined with reflection can yield many photons in the same
state: coherent light. Stimulated emission underlies the laser.

* Consciousness is in its essence relational and it can only arise
where at least 2 things come together. ... our human consciousness is
only different in degree and complexity with more elementary life forms
or with elementary matter. .. Bosons are particles of relationship.
Their wave functions can overlap to such degree that they merge totally.*

### light and photons (quanta)

* Light follows a path along which the time taken is a minimum. *

* C stands for CELERITAS which is latin for swiftness. *

* What's hard to comprehend about light is that an object traveling
close to the speed of light and emitting a light beam will observe this
light beam ahead still at the full speed of C. *

* The photon, having no charge, is its own antiparticle. Pairs of
electrons and positrons can be created spontaneously by photons, and can
be made to turn into photons in the reverse process of annihilation. *

* About 50 atoms can be placed end to end along a single wavelength
of light. *

[According to my calculations this should be more in the order of 1000 atoms. Also, it takes about 2.5 million wavelengths to traverse 1 mm of distance.]

* It takes only 5 or 6 photons to activate a nerve cell via the
human eye and pass a message to the brain. If we could see 10 times more
sensitively, then we would see very dim light of a particular colour as
a series of intermittent little flashes of equal intensity. *

* The energy of an atom is precisely related to its wavelength. An
atom absorbing a photon provides energy for an electron to move to an
orbit further away from the nucleus. When an electrom falls into the old
orbit, it emits a photon with the same energy - the energy corresponding
to the gap between the orbits. *

* Note that the light you see 'reflected' doesn't consist of the
same photons that reached the object in the first place. *

* Each element is capable of generating only photons of a few
specific frequencies (colours), hence it has a unique spectrum. *

* When we look at photons on a large scale, the rules are
approximated by Light travels in straight lines. But when the
space becomes small, such as the pinholes in the double slit experiment,
those rules fail. The same holds true for electrons; on a large scale
they travel like particles on definite paths, but on a small scale, such
as inside an atom, there is no main path - and interference reins. *

Space and time are not constants. Time slows down near the speed of light. Speed of light is the true constant.

* A body radiates energy not in a continuous stream, but in
discrete bundles called quanta. Each of these bundles of energy carries
the amount of energy that is a multiple of its frequency. The higher the
frequency, the higher the energy. The equation for calculating the
energy of a bundle of, say, light from its frequency is called Planck's
Law. The constant that accomplishes the conversion is Planck's
Constant. Einstein extended this idea for light, whose discrete
bundles could knock electrons out of a metal - calling the light quanta
photons. However the term photon is often extended to comprise
any quanta of the electro-magnetic spectrum. *

* A wavelength of light is around 4 . 10 ^{-7} meters. 1
milimeter contains roughly 2.5 million wavelengths. *

* If you are a photon, traveling at the speed of light, then it's
true that you sense no passage of time; everything becomes simultaneous.
*

* Photons carry energy in proportion to their frequency. *

* Photons came about, at the turn of the 19th century, as a
consequence of the German physicist Max Planck's solution to a difficult
puzzle presented by classical physics: the black body radiation. *

* Green light will expel electrons from a piece of sodium metal,
but to knock electrons out of more common metals, such as copper or
aluminium, you need to go to more energetic ultraviolet light. Moreover,
it was found that, once electron liberation has begun, turning up the
intensity of the light increases the number but not the energy of the
electrons that are popped out, while turning up the frequency of the
light brings out electrons of higher individual energy, but at the same
rate as before. These facts are hard to understand using a wave theory
of light, in which the energy carried by waves is a product of the
frequency and the intensity. *

*What is this *zero mass*? The masses given here are the masses of
the particles at *rest*. The fact that a particle has zero mass means,
in a way, that it cannot be at rest. A photon is never at rest, it is
always moving at 186,000 miles a second. *

* You may have heard that photons come out in blobs and that the
energy of a photon is Planck's constant times the frequency. That is
true, but since the frequency of light can be anything, there is no law
that says that energy has to be a certain definite amount. *

### matter

* Bohm's analogy to space / matter separation:
A crystal cooled to absolute zero will allow a stream of electrons to
pass through it without scattering them. If the temperature is raised,
various flaws in the crystal will lose their transparency, and
begin to scatter electrons. From an electron's point of view such flaws
would appear as pieces of matter floating in a sea of nothingness. But
this is not really the case, they are both part of the same fabric, the
deeper order of the crystal. *

* When two particles collide with high energies, they generally
break into pieces, but these pieces are not smaller than the original
particles. They are again particles of the same kind and are created out
of the energy of motion (kinetic energy) involved in the collision
process. The whole problem of dividing matter is thus resolved in an
unexpected sense...[because] this way we can divide matter again and
again. *

* The inertia of a material object - the object's resistance
against being accelerated - is not an intrinsic property of matter, but
a measure of its interaction with all the rest of the universe. *

* Momentum is conserved, so momentum rather than speed is the
important quantity. *

Plasma is the 4th manifestation of matter after solids, liquids, and gasses. It consists of super-heated gas which becomes ionized.

All the gold ever mined on earth would only fill 3 olympic size swimming pools.

### mind and matter

Mind and matter are different aspects of the same reality. What we
call "matter" is the aspect we apprehend when we look at a person, a
plant, or a molecule *from the outside*; "mind" is the aspect we
obtain when we look at the same thing *from the inside*.

### fields

* What is an electric field? We don't know. When we discover a new
kind of field it seems mysterious. Then we name it, get used to dealing
with it and describing its properties, and it no longer seems
mysterious. But we still do not know what an electric or a gravitational
field really is. *

* Faraday and Maxwell found it more appropriate to say that each
charge creates a disturbance, or a condition, in the space
around it so that the other charge, when it is present, feels a force.
This condition in space which has the potential of producing a force is
called a field. It is created by a single charge and it exists whether
or not another charge is brought in to feel its effect. *

* Electric fields are created by charged bodies and their effects
can only be felt by charged bodies. Magnetic fields are produced by
charges in motion, i.e., by electric currents, and the magnetic forces
resulting from them can be felt by other moving charges. *

* Since all motion is relative, every charge can also appear as a
current - in a frame of reference where it moves with respect to the
observer - and consequently, its electric field can also appear as a
magnetic field. In the relativistic formulation of electrodynamics, the
two fields are thus unified into a single electromagnetic field. *

*The existence of the positive charge, in some sense, distorts, or
creates a "condition" in space so that when we put the negative charge
in, it feels a force. This potentiality for producing a force is called
an electric field.
... If we were to charge a body, say a comb, electrically and then place
a charged piece of paper at a distance and move the comb back and forth,
the paper will respond by always pointing to the comb. If we shake it
faster, it will be discovered that the paper is a little behind, there
is a DELAY in the action
...Charges make a field and charges in fields have forces on them and
move.*

*Here is an analogy. If we are in a pool of water and there is a
floating cork very close by, we can move it directly by pushing the
water with another cork. If you looked only at the 2 corks, all you
would see would be that one moved immediately in response to the motion
of the other - there is some kind of interaction between them. Of course
what we really do is disturb the water, the water then disturbs the
other cork. We could make up a "law" that if you pushed the water a
little bit, an object close by in the water would move. If it were
farther away, of course, the second cork would scarcely move, for we
move the water *locally*. On the other hand, if we jiggle the cork, a
new phenomenon is involved, in which the motion of the water moves the
water there, etc ., and *waves* travel away, so that by jiggling, there
is an influence *very much farther out*, an oscillatory influence, that
cannot be understood from the direct interaction. Therefore the idea of
direct interaction must be replaced with the existence of the water, or
in the electrical case, with what we call the *electromagnetic field*.*

### double slit experiment

* Atoms, like electrons, can be scattered, and can create
interference patterns, Just recently a version of the two-split
expreriment was done with atoms instead of photons, and the appropriate
interference pattern emerged. *

* There is no interaction of any kind between the photons in the
two-split experiment. they are always alone. *

* Photons arrive at the screen of a two-split experiment, having
traveled through empty space, whith as much energy as they had in the
first place. *

### Planck's constants

Planck units are units of measurement named after the German physicist Max Planck, who first proposed them in 1899. They are an example of natural units, i.e. units of measurement designed so that certain fundamental physical constants are normalized to 1. In Planck units, the constants thus normalized are:

- the gravitational constant, G;
- The reduced Planck constant, h;
- the speed of light in a vacuum, c;
- the Coulomb force constant, k;
- Boltzmann's constant, kB (or simply k).

For a little mathematical tour on the relationship between Planck's constants and the Gravitational constant, see Relationship between Planck's Constants and the Gravitational Constant.

* The Planck length is the scale at which classical ideas about
gravity and space-time cease to be valid, and quantum effects dominate.
This is the 'Quantum of Length', the smallest measurement of length with
any meaning. It is roughly equal to 1.6 x 10 ^{-35} m or about 10^{-20}
times the size of a proton. *

* The Planck time is the time it would take a photon travelling at
the speed of light to across a distance equal to the Planck length. This
is the 'Quantum of Time', the smallest measurement of time that has any
meaning, and is equal to 10 ^{-43} seconds. No smaller division
of time has any meaning. *

* The energy E contained in a photon, which represents the smallest
possible 'packet' of energy in an electromagnetic wave, is directly
proportional to the frequency f according to the following equation:
E = hf
If E is given in joules and f is given in hertz (the unit measure of
frequency), then:
E = (6.626176 x 10*

^{-34}) f and conversely: f = E / (6.626176 x 10

^{-34})

### black body radiation

* Physicists could not find any way to figure out how a fixed
amount of energy would be shared among these infinite possibilities
(infinite harmonics) in such a way as to arrive at a meaningful average
energy per wave which could be thought of as the temperature.
Planck suggested that each electromagnetic wave could carry energy only
in multiples of a basic amount proportional to its frequency, so that
the energy in any individual wave was a whole number times the frequency
of that wave, multiplied by a conversion factor that came to be knowns
as Planck's constant.
For waves at very high frequency (the zillionth harmonic) the minimum
unit of energy became so large that it exceeded all the energy in the
heated box, which meant that very high frequency oscillations never
arose. Planck's quantization of energy meant that the available number
of oscillations in a box became finite.
This unit, this quantity of energy, this division into little packets,
was a new idea in physics. And so the photon was born. *

### quantum

* There are 2 aspects to quantum physics; in a sense it's a bit
like dice. There are 2 aspects to dice. There are the individual dice
events that occur, and then there are the statistical patterns - like a
lot of sevens will occur and not many twelves. Bell's theorem shows that
none of these patterns are ever connected faster than light; you will
never see a faster than light pattern. But the individual events, the
dice falls themselves, must be tight together faster than light. *

Here's a great analogy for getting a taste of the quantum world. It's
taken from *Where does the weirdness go?* from David Lindley -
ISBN 0-09-974751-0

Imagine a pair of gloves, each of which is packed in a sealed box. Each
box is then sent with a person to opposite sides of the globe, say
France and Australia. First consider the normal state of affairs in the
macro world we live in. Assuming you don't know which glove is in your
packet - you only can find out when you open it - then you also know the
other's glove.

Now consider the quantum gloves. The difference here is that the glove
in each packet is neither RH nor LH before someone actually opens a
packet. If person A opens it up in Australia, there's a 50/50 change
that it is either R or L - and it will also determine the state of the
other glove. Trouble is that you can't tell if the other one already had
opened it and finalised the state of your glove before you opened it. If
you wanted to find out, you would have to phone her - and there you are
limited by the speed of light. In other words, and this is crucial, when
one person opens up the parcel, the other one becomes realised as well
INSTANTANEOUSLY, but to actually find out what happened you're limited
by the speed of light.

* In quantum , measurement is an act by which the measurer and the
measured interact to produce a result. It's not simply the determination
of a preexisting property ... Rather, the system is indeterminate until
the measurement is made. *

* In classical applications, probabilities are a cover for
ignorance - acquiring more data can make steadily more accurate
predictions. Predictions in quantum mechanics are probabilistic not
because of insufficient information or understanding, but because the
theory itself has nothing more to say. *

* The raw material of quantum mechanics - the formulas and
equations, deviced throught the collective efforts of many physicists
and preserved within the pages of numerous textbooks - is not the topic
disagreement. The theory is rigorous and exact; physicists know how to
use it, and don't argue about the predictions it makes. ... but
physicists still cannot honestly say what the theory means. *

*No elementary phenomenon is a real phenomenon until it is a
measured phenomenon.*

### Bell's theorem

* No physical theory of local hidden variables can ever reproduce
all of the predictions of quantum mechanics. *

Bell's Theorem has been described as the 'most profound discovery of science' (not just physics) and many people seem to agree. This theory basically proves that reality is non-local and thus validates Schrodinger's notion of 'entanglement', i.e. when 2 quantum systems meet and then separate, they still remain connected somehow, even when they are lightyears apart.

A good starting point is Gary Felder's article Spooky Action at a Distance.

A more detailed description can be found at the University of Toronto - a particularly enlightening one.

Alain Aspect, of the university of Paris, was the first to provide an unambiguous practical test of Bell's theorem.

### wavefunction

* The wavefunction is a mathematical device that allows you to
figure out the correct probability for the photon hitting the screen at
any place you choose (Thomas Young's double split experiment (1801)). *

* Wavefunctions are what we use to predict the results of
measurements, and measurements are the way we build up knowledge of the
world ... A wavefunction describes a system - the thing being measured
and the measurement being made - rather than being an independent
description only of the thing being measured. *

* What was initially a half-up, half-down electron becomes simply
an up electron. After any such measurement, the wavefunction becomes
less expansive or capacious than it was. Hence the name "collapse" or
"reduction" of the wavefunction. *

### string theory

* String theory postulates that there exists and has existed only a
single variety of particle, but that this particle has an infinite
number of manifestations - as in the innumerable tunes that may be
composed on a single string of Pythagoras's lyre. Thus a single
supersymmetric variety of particle shows up in various harmonics as
gravitons and gravitini, quarks and squarks, photons and photinos, and
so forth. Since, as Gell-Mann noted, "these infinitely many particles
all obey a single very beautiful master equation," the theory suggests
how maximum complexity could have arisen from maximum simplicity. *

*
There are 10 dimensions of space...
There appear to be about 20 numbers that really describe our universe:
strength of gravity and emf, mass of particles like electrons and quarks, etc .
Any changes in these numbers makes the universe disappear.
The extra dimensions fold in on themselves.
The way the strings vibrate is affected by the geometry of these extra dimensions.
*

### space and time

We only perceive *instantaneously*, in the close space-time
vicinity around us.

* The fact that objects are events can only be understood when it
is realised that space and time are interpenetrating.*

*The sun, moon and stars, which we see, are cross-sections of
spirals which we do not see. These cross-sections do not fall out of
the spirals because of the same principle by reason of which the
cross-section of an apple cannot fall out of the apple. *

*In some strange sense this is a participatory universe *

* Whatever we call reality, it is revealed to us only through an
active construction in which we participate.*

* The most important thing to keep in mind about Einstein's
universe is the fantastic stiffness of space - of the rubber sheet if
you like...space is 1032 times stiffer than steel...In other words, the
enormous but not infinite stiffness of Einstein's space-time tells us
that, while space is not infinitely rigid, it is very, very rigid. In
fact, odd as it sounds, space is the most rigid stuff in the universe. *

* Space is merely a system of relations *

* Since Einstein, distance is between events, not between things,
and thus involves time as well as space. This modern view can not be
stated except in terms of differential equations. *

The direction of time is determined by the second law of thermodynamics which states that isolated macroscopic systems never change from low entropy (ordered state) to high entropy (disordered state). Even though there is no scientific reason that it shouldn't go the other way (high to low entropy), the probability of it occuring is so low that it is negligable.

A classic example that is often used to illustrate this principle is a sand pile on the beach that can exist in many states (high entropy, high probability that random physical forces can create similar piles) as opposed to a sand sculpture shaped with a child's beach bucket which has low entropy, there is a very low probability that a similar shape can be constructed by random physical forces.

This change from low to high entropy determines the direction of time.
If the somewhat depressing theory of a *Heat Death Universe* is correct,
all time should stop at the end of the universe's lifespan, since there
will be no more movement from low to high entropy.

### holography

* ... holograms also possess a fantastic capacity for information
storage. By changing the angle at which the two lasers strike a piece of
photographic film, it is possible to record many different images on the
same surface. Any image thus recorded can be retrieved simply by
illuminating the film with a laser beam possessing the same angle as the
original two beams. By employing this method researchers have calculated
that a one-inch-square of film can store the same amount of information
contained in 50 bibles. *

### chaos

* The dripping tap whose intervals are timed reveals a graph that
shows an infinite order. Successively zooming into the graph will
produce likewise pattens. *

* A curve can twist in such a complex way that it fills a plane.
The dimension is fractional between 1 (a line) and 2 (a surface). *

* An attractor is a region of space, called phase space, which
exerts a magnetic appeal for a system, seemingly pulling the system
towards it. *

I have dedicated a whole page on chaos in Literature on Chaos.

### chemical processes

**Burning**

Carbon attracts oxygen much more than oxygen
attracts oxygen or carbon attracts carbon. Therefore in this
process, the oxygen may arrive with only a little energy, but the
oxygen and carbon will snap together with a tremendous vengeance and
commotion, and anything near them will pick up the energy. A large
amount of motion energy (kinetic energy) is thus generated. This of
course is burning.

### references

These are some references to publications. Many other excerpt and ideas are from reputable web articels and radio/tv programs.

- David Bodanis: e = mc2, ISBN: 0-330-39165-8
- Fritjof Capra: The Tao of Physics, ISBN: 0-553-26379-x
- Michael Talbot: The Holographic Universe, ISBN: 0-246-13690-1
- Roger Penrose: The Emperor's new mind, ISBN: 0-19-286198-0
- Timothy Ferris: Coming of age in the Milky Way, ISBN: 0-09-980050-0
- D.Blair, G.McNamara: Ripples on a cosmic sea, ISBN: 1-86448-503-5
- Oliver Sacks: Musicophelia, ISBN: 978-0-330-44436-1
- Isaac Asimov: Atom, ISBN: 0-452-26834-6
- Ervin Laszlo: science and the Akashic field, ISBN: 978-1-59477-181-1
- David Lindley: Where does the weirdness go? ISBN 0-09-974751-0
- Kevin Frank: Stuart Hameroff's theories regarding microtubules as the seat of consciousness. Magazine: Rolf Lines
- Danah Zohar: The Quantum Self. ISBN 0-00-654426-6
- Richard P. Feynman: Six easy pieces

To my knowledge, the fact that mass increases at high velocity is regularly observed in the CERN particle accellerators.

I wouldn't know the exact amount by which this mass increases, but it should satisfy the e=mc^2 equation.