Appendix

Written by Bernd Schneider

6.0.1 Timeline

Coming soon.

6.0.2 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	$G$	$6.67259 e^{- 11} \pm 8.5 e^{- 15}$	$m^{3} {kg}^{- 1} s^{- 2}$
Planck constant	$h$	$6.6260755 e^{- 34} \pm 4.0 e^{- 40}$	$J s$
Planck constant in eV		$4.1356692 e^{- 15} \pm 1.2 e^{- 21}$	$eV s$
Planck mass	$m_{p}$	$2.17671 e^{- 8} \pm 1.4 e^{- 12}$	$kg$
Planck length	$l_{p}$	$1.61605 e^{- 35} \pm 1.0 e^{- 39}$	$m$
Planck time	$t_{p}$	$5.39056 e^{- 44} \pm 3.4 e^{- 48}$	$s$
Elementary charge	$e$	$1 .60217733 e^{- 19} \pm 4.9 e^{- 26}$	$C$
Electron mass	$m_{e}$	$9.1093897 e^{- 31} \pm 5.4 e^{- 37}$	$kg$
Electron mass in u		$0 .000548579903 \pm 1 .3 e^{- 11}$	$u$
Electron mass in eV		$510999 .06 \pm 0 .15$	$eV$
Proton mass	$m_{p}$	$1 .6726231 e^{- 27} \pm 1.0 e^{- 33}$	$kg$
Proton mass in u		$1 .00727647 \pm 1 .2 e^{- 08}$	$u$
Proton mass in eV		$938272310 \pm 280$	$eV$
Proton-electron mass ratio		$1836 .152701 \pm 3 .7 e^{- 5}$
Proton specific charge		$95788309 \pm 29$	$C {kg}^{- 1}$
Neutron mass	$m_{n}$	$1 .6749286 e^{- 27} \pm 1.0 e^{- 33}$	$kg$
Neutron mass in u		$1 .008664904 \pm 1 .4 e^{- 8}$	$u$
Neutron mass in eV		$939565630 \pm 280$	$eV$
Neutron-electron mass ratio		$1838 .683662 \pm 4 .0 e^{- 5}$
Neutron-proton mass ratio		$1 .001378404 \pm 9 e^{- 9}$
Avagadro constant	$N_{A}$	$6 .0221367 e^{23} \pm 3.6 e^{17}$	${mol}^{- 1}$
Boltzmann constant	$k$	$1 .380658 e^{- 23} \pm 1.2 e^{- 28}$	$J K^{- 1}$
Boltzmann constant in eV		$8 .617385 e^{- 5} \pm 7.3 e^{- 10}$	$eV K^{- 1}$
Molar volume ideal gas, STP	$V_{m}$	$0 .0224141 \pm 1 .9 e^{- 7}$	$m^{3} {mol}^{- 1}$
Electron volt	$eV$	$1 .60217733 e^{- 19} \pm 4.9 e^{- 26}$	$J$
Atomic mass unit	$u$	$1.6605402 e^{- 27} \pm 1.0 e^{- 33}$	$kg$
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.

6.0.3 Other Useful Values

Coming soon.

6.0.4 Units

Coming soon.

6.0.5 Glossary

Acceleration (a): Change of velocity $v$ per time $t$ . $a = \frac{d v}{d t}$
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.
Decade: Factor of ten.
Derivative: Rate of change (steepness) of a function $f (x)$ , given as the quotient of two differentials $\frac{d f (x)}{d x}$ .
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. $1 Hz = 1 / s$
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.
Infrared (IR) radiation: 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). $1 J = 1 Nm$
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. $p = m a$
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. $1 N = 1 kg m s^{- 2}$
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 $f$ . $E = h f$
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 $g$ . $E_{p o t} = m g h$
Power: Release or consumption of energy $E$ per time $t$ . $P = \frac{d E}{d t}$
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 $0.38752 c$ ".
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.
Ultraviolet (UV) radiation: 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 $t$ . $v = \frac{d s}{d t}$ .
Watt ( $W$ ): Unit of power. $1 W = 1 J / s$
Wavelength ( $λ$ ): Distance between corresponding points on two successive waves.
Weight: Force $F$ of gravity $g$ on an object with a mass $m$ . $F = m g$
Work ( $W$ ): Product of force $F$ and displacement $s$ in the direction of the force. $W = F s$

6.0.6 References

Usenet Relativity FAQ, Alternate Version, Alternate Version
Astronomy FAQ, http://sciastro.astronomy.net/, http://www.faqs.org/faqs/astronomy/faq/
B. Scent, S. Davis, L. Scheinbeim, Black Holes - Portals into the Unknown
M. G. Millis, Warp Drive When?
J. Hinson, Relativity and FTL Travel
J. Hinson, Subspace Physics
J. Bell, Star Trek Technology: Frequently Asked Questions Lists
R. Mercer, The Star Trek Technical Reference
G. Kennedy, Daystrom Institute Technical Library
C. Rühl, Star Trek Dimension - Subspace Manual
[Alc94] M. Alcubierre, The warp drive: hyper-fast travel within general relativity, Classical and Quantum Gravity, Vol. 11, L73-77, May 1994
http://www.lysator.liu.se/~nisse/doc/alcubierre/
[Ein92] A. Einstein, Über die spezielle und die allgemeine Relativitätstheorie, reprint, Vieweg, 1992
[Fey63] R. P. Feynman, R. B. Leighton, M. Sands, The Feynman Lectures on Physics, Vol. I, Addison-Wesley, 1963
[Ger89] C. Gerthsen, H. Kneser, H. Vogel, Physik, 16. Auflage, Springer Verlag, 1989
[Haw98] S. W. Hawking, Eine kurze Geschichte der Zeit, reprint, Rowohlt, 1998
[Kra96] L. M. Krauss, Die Physik von Star Trek, Heyne Verlag, 1996
[Oku99] M. Okuda, D. Okuda, D. Drexler, The Star Trek Encyclopedia, 3. Edition Pocket Books, 1999
[Sex87] R. and H. Sexl, Weiße Zwerge - Schwarze Löcher, 2. Auflage, Vieweg, 1987
[Ste91] R. Sternbach, M. Okuda, Star Trek: The Next Generation Technical Manual, Pocket Books, 1991
[Zim98] H. Zimmerman, R. Sternbach, D. Drexler, I. S. Behr, Star Trek: Deep Space Nine Technical Manual, Pocket Books, 1998

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Appendix

6.0.1 Timeline

6.0.2 Fundamental Constants

6.0.3 Other Useful Values

6.0.4 Units

6.0.5 Glossary

6.0.6 References