Appendix

Written by Bernd Schneider

Coming soon.

7.2 Fundamental Constants

Constants, Notations, and Their Values
Name Symbol Value Unit
Speed of light in vacuum $c$ $299792458$ $m s −1$
Permeability of vacuum $μ 0$ $1.25663706143592 e −6$ $N A −2$
Permittivity of vacuum $ε 0$ $8.854187817 e −12$ $F m −1$
Newtonian constant of gravitation $G$ $6.67259 e −11 ±8.5 e −15$ $m 3 kg −1 s −2$
Planck constant $h$ $6.6260755 e −34 ±4.0 e −40$ $Js$
Planck constant in eV $4.1356692 e −15 ±1.2 e −21$ $eVs$
Planck mass $m p$ $2.17671 e −8 ±1.4 e −12$ $kg$
Planck length $l p$ $1.61605 e −35 ±1.0 e −39$ $m$
Planck time $t p$ $5.39056 e −44 ±3.4 e −48$ $s$
Elementary charge $e$ $1.60217733 e −19 ±4.9 e −26$ $C$
Electron mass $m e$ $9.1093897 e −31 ±5.4 e −37$ $kg$
Electron mass in u $0.000548579903±1.3 e −11$ $u$
Electron mass in eV $510999.06±0.15$ $eV$
Proton mass $m p$ $1.6726231 e −27 ±1.0 e −33$ $kg$
Proton mass in u $1.00727647±1.2 e −08$ $u$
Proton mass in eV $938272310±280$ $eV$
Proton-electron mass ratio $1836.152701±3.7 e −5$
Proton specific charge $95788309±29$ $C kg −1$
Neutron mass $m n$ $1.6749286 e −27 ±1.0 e −33$ $kg$
Neutron mass in u $1.008664904±1.4 e −8$ $u$
Neutron mass in eV $939565630±280$ $eV$
Neutron-electron mass ratio $1838.683662±4.0 e −5$
Neutron-proton mass ratio $1.001378404±9 e −9$
Avagadro constant $N A$ $6.0221367 e 23 ±3.6 e 17$ $mol −1$
Boltzmann constant $k$ $1.380658 e −23 ±1.2 e −28$ $J K −1$
Boltzmann constant in eV $8.617385 e −5 ±7.3 e −10$ $eV K −1$
Molar volume ideal gas, STP $V m$ $0.0224141±1.9 e −7$ $m 3 mol −1$
Electron volt $eV$ $1.60217733 e −19 ±4.9 e −26$ $J$
Atomic mass unit $u$ $1.6605402 e −27 ±1.0 e −33$ $kg$
Standard acceleration of gravity $g n$ $9.80665$ $m s −2$

This data is derived from the 1986 CODATA recommended values of the fundamental physical constants. Complete list of constants: NIST Reference.

Coming soon.

Coming soon.

7.5 Glossary

Acceleration (a)
Change of velocity $v$ per time $t$ . $a= dv dt$
Accelerator
Machine used to accelerate particles to high speeds (and thus high energy compared to their rest mass-energy).
Amplitude
In any periodic motion, the maximum displacement from equilibrium.
Antimatter
Complementary form of matter in which the single particle has the same mass but reversed charge.
Axiom
Rule without proof, nonetheless valid.
Bohr, Niels Henrik David
1885-1962, established a new understanding of the atomic structure, Nobel Prize 1922.
Center of mass
A point of an object in which its whole mass may be assumed concentrated with respect to outer forces.
Coordinate system
Diagram which consists of two or more, mostly perpendicular axes (e.g. x and y), in which a function can be illustrated.
Constant
Quantity which doesn’t change and must not change within an equation.
Factor of ten.
Derivative
Rate of change (steepness) of a function $f(x)$ , given as the quotient of two differentials $df(x) dx$ .
Differential
Very small (infinitesimal) difference between two values of a quantity.
Differential equation
Equation which includes one or more derivatives of a variable, and which has to be solved with special methods.
Diffraction
Bending of a wave passing through slits which are about the size of its wavelength.
Dispersion
Variation of speed of light with wavelength in a material, resulting in separation of light into its spectrum.
Doppler shift
Change in wavelength due to relative motion between source and detector.
Duc de Broglie, Louis Victor Pierre Raymond
1892-1987, demonstrated that a (small) particle may be represented by a wave, Nobel Prize 1929.
Efficiency
Mostly the ratio of useful power to total power, also applicable to other quantities.
Einstein, Albert
1879-1955, conceived the Special and General Theories of Relativity, Nobel Prize 1921.
Electromagnetic force
One of the four fundamental forces due to electric charges, both static and moving.
Electromagnetic wave
Wave consisting of oscillating electric and magnetic fields that move through space at the speed of light.
Electron ($e −$ )
Elementary particle of small mass and negative charge found in every atom.
Electron-volt (eV)
Energy gained by an electron which accelerates through a potential difference of one volt, used as an alternative unit of energy.
Energy (E)
Work stored in matter, for instance as kinetic energy or potential energy.
Equilibrium
Condition in which the net force on an object is zero.
Force (F)
Agent that results in accelerating or deforming an object.
Frequency (f)
Number of oscillations per unit time $t$ . $f=1/t$
FTL
Acronym for Faster Than Light.
Function
Mathematical relationship between two quantities y and x , given as an equation. $y=f(x)$
Gravitational field
Distortion of space due to the presence of a mass.
Gravitational force
One of the four fundamental forces, attraction between two objects due to their mass.
Heisenberg, Werner
1901-1976, discovered the Uncertainty Principle, Nobel Prize 1932.
Hertz (Hz)
Unit of frequency. $1Hz=1/s$
Imaginary number
Multiple of the square root of -1, a number which may be an aid in certain calculations, but which cannot represent a measurable (real) value.
Inertia
Tendency of an object to remain in its current state of motion.
Infinitesimal
Very small quantity, approaching zero.
Electromagnetic radiation with a longer wavelength and lower energy content than visible light.
Integral
Mathematically, the area under a curve $f(x)$, inverse operation to derivation.
Interference
Superposition of two or more waves, locally producing either larger or smaller amplitudes.
Ion
Any electrically charged particle, in particular atom nuclei lacking one or more electrons of their nominal complement.
Joule (J)
Unit of energy (or work or heat). $1J=1Nm$
Kinetic energy
Energy of a mass $m$ due to its motion with a speed $v$ . $E kin =(m v 2 )/2$
Laser
Acronym for Light Amplification by Stimulated Emission of Radiation, a light source that produces large amounts of narrow-band light, taking advantage of resonance effects.
Light
Visible electromagnetic radiation with wavelengths between 400nm and 700nm.
Lorentz, Hendrik Antoon
1853-1928, developed, among other work, the Lorentz transformation as a basis for Special Relativity, Nobel Prize 1902.
Mass (m)
Property inherent to any matter, representing its resistance to gravity and acceleration.
Model
Mathematical description of physical behavior in the form of a set of (mostly simplified) equations.
Momentum (p)
Product of mass and velocity of an object. $p=ma$
Monochromatic light
Light of a single wavelength.
Neutral
Having a net (electric) charge equal to zero.
Neutron (n)
Elementary particle with no charge and mass slightly greater than that of a proton.
Newton (N)
Unit of force. $1N=1kgm s −2$
Nucleon
Proton or a neutron, one of the particles that makes up a nucleus.
Nucleus
Core of an atom, consisting of protons and neutrons (plural: nuclei).
Origin
The zero point of a coordinate system.
Particle
Subatomic object with a definite mass and charge (among other properties).
Period
Time cycle in which the shape of an oscillation or wave repeats.
Phase
Fixed shift to a wave, given as an angle
Photon
Elementary particle which is equivalent to the energy of an electromagnetic wave.
Planck, Max
1858-1947, introduced the Quantum Theory, Nobel Prize 1918.
Planck’s constant (h)
Constant determining the relation between the energy $E$ of a photon and its wavelength $f$ . $E=hf$
Plasma
Ionized gas.
Postulate
Assumption necessary to further pursue a theory
Potential energy
Energy of an object with a mass $m$ due to its position or height $h$ , specifically in a gravitational field with an acceleration $g$ . $E pot =mgh$
Power
Release or consumption of energy $E$ per time $t$ . $P= dE dt$
Principle of superposition
Displacement due to two or more forces is equal to vector sum of forces.
Proportional
Changing with the same factor as another quantity.
Proton (p)
Elementary particle with a positive charge that is nucleus of hydrogen atom.
Qualitative
Giving a tendency instead of numbers, e.g. “Starship A is faster than starship B”.
Quantitative
Using numbers, e.g. “Starship A travels at $0.38752c$”.
Quantum
Smallest discrete amount of any quantity (plural: quanta).
Quantum mechanics
Study of properties of matter using its wave properties, at very small scales.
Refraction
Change in direction of light ray when passing from one medium to another.
Resonance
Effect that occurs when an object is excited with its natural frequency, resulting in a dramatic increase of the amplitude.
Scalar
Mathematical description of a physical quantity, consisting only of a value, as opposed to a vector.
Spectrum
Collection of waves with different wavelengths and amplitudes.
Standing wave
Wave with stationary nodes.
STL
Acronym for Slower Than Light.
Theorem
General scientific rule.
Thermodynamics
Science of the conversion of one form of energy into another.
Traveling wave
A moving, periodic disturbance in a medium or field.
Electromagnetic radiation with a shorter wavelength and higher energy content than visible light.
Uncertainty principle
Quantum principle that states that it is not possible to know exactly both the position $x$ and the momentum $p$ of an object at the same time.
Variable
Quantity which is subject to change and supposed to change within an equation.
Vector
Mathematical description of a physical quantity, consisting of an absolute value (scalar) and a direction.
Velocity (v)
Change of displacement $S$ per time $t$ . $v= ds dt$ .
Watt (W)
Unit of power. $1W=1J/s$
Wavelength (λ)
Distance between corresponding points on two successive waves.
Weight
Force $F$ of gravity $g$ on an object with a mass $m$ . $F=mg$
Work (W)
Product of force $F$ and displacement $s$ in the direction of the force. $W=Fs$