Dirk Bertels

The greatest malfunction of spirit
is to believe things (Louis Pasteur)

Physics - a compilation

Last updated 07 December 2013

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


absolute zero
stars and the universe
energy and mass
atoms and electrons
fundamental units
light and photons (quanta)
mind and matter
double slit experiment
Planck's constants
black body radiation
Bell's theorem
string theory
space and time
chemical processes

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.

R.Feynman: Six easy pieces, pp10

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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 106 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...

T. Ferris: Coming of age in the Milky Way, pp272

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

T. Ferris: Coming of age in the Milky Way, pp280

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.

T. Ferris: Coming of age in the Milky Way, pp349

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.

F. Capra: The Tao of Physics, pp181

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.

R. Feynman: Six easy pieces, pp91

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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.

D. Bodanis: e = mc2

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!

R.Feynman: Six easy pieces, pp4

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.

R.Feynman: Six easy pieces, pp107

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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.

Berkeley Letters and Science course

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.

D. Bodanis: e = mc2

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.

D. Bodanis: e = mc2

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.

T. Ferris: Coming of age in the Milky Way, pp187

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.

T. Ferris: Coming of age in the Milky Way, pp193

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.

Isaac Asimov: Atom

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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)

R. Feynman: Six easy pieces, pp89

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.

R. Feynman: Six easy pieces, pp95

[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)/r2

G = 6.670 * 10-11 Newton * m2/kg2

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.

R. Feynman: Six easy pieces, pp106

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.

R. Feynman: Six easy pieces, pp111

[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.

R. Feynman: Six easy pieces, pp112

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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.

T. Ferris: Coming of age in the Milky Way, pp258

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.

R.Feynman: Six easy pieces, pp4

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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 1977

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.

T. Ferris: Coming of age in the Milky Way, pp326

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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.

D. Bodanis: e = mc2

[Mathematics reveals underlying similarities in nature. For example the equation for the attraction between 2 masses is F = G * (m1 * m2)/r2 (Newton's law), while the equation for the attraction between 2 charges is F = k * (q1 * q2)/r2 (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.


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fundamental units


... 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).

R. Feynman: Six easy pieces, pp93

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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:

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


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/s2). 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.


basic units

  1. The Joule (Newton*m), which roughly equates the energy required to lift an apple 1 meter off the ground.
  2. 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.
  3. The Dietary Calorie = 1000 calories = 1 kilocalorie = 4185.8 Joules.


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/m2. 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.


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.

M. Talbot: The Holographic Universe, 27

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.

F. Capra: The Tao of Physics, p137

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.

Isaac Asimov: Atom

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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.

M. Talbot: The Holographic Universe, pp43

... 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.

F. Capra: The Tao of Physics, p144

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".

F. Capra: The Tao of Physics, p202


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...

Albert Einstein, letter to Michele Angelo Besso November 1916

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.

Danah Zohar: The Quantum Self (pp86)

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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.

F. Capra: The Tao of Physics, p168

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

Isaac Asimov: Atom

[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.

R. Feynman

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.

David Lindley: Where does the weirdness go?

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.

David Lindley: Where does the weirdness go?

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.

David Lindley: Where does the weirdness go?

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.

R.Feynman: Six easy pieces, pp43

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.

R.Feynman: Six easy pieces, pp84

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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.

F. Capra: The Tao of Physics, pp67

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.

Ernest Mach

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

David Lindley: Where does the weirdness go?

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.

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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.

Ervin Laszlo: Science and the Akashic field

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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.

F. Capra: The Tao of Physics, pp47

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.

F. Capra: The Tao of Physics, pp193

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.

F. Capra: The Tao of Physics, pp194

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.

R.Feynman: Six easy pieces, pp30

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*.

R.Feynman: Six easy pieces, pp31

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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.

David Lindley: Where does the weirdness go?

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

David Lindley: Where does the weirdness go?

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.

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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)

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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.

David Lindley: Where does the weirdness go?

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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.

Nick Herbert: Consciousness and Quantum Reality (interview - Thinking Allowed Productions)

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.

David Lindley: Where does the weirdness go?

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.

David Lindley: Where does the weirdness go?

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.

David Lindley: Where does the weirdness go?

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

John Wheeler

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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.

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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)).

David Lindley: Where does the weirdness go?

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.

David Lindley: Where does the weirdness go?

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.

David Lindley: Where does the weirdness go?

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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.

T. Ferris: Coming of age in the Milky Way, pp347

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.

Brian Green on TED Talks

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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

John Weeler

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

Ilya Prigogine

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.

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... 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.

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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.

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chemical processes

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.

R.Feynman: Six easy pieces, pp16

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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

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  • From: Douglas Hinckfuss
  • Date: 2012-06-02 23:22:45
On page 52 of Bodanis'book "E=mc2", he says " The protons first "swell" to become two units of mass ........... At speeds of 99.9997 percent of "c", the protons end up 430 times bigger than their original size." Do you know if these claims are just calculations or did the CERN people actually observe such increases in experiment? Please advise.

  • From: Dirk
  • Date: 2012-06-03 03:00:50
Hi Douglas,
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.

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