Appendix

Timeline
Fundamental Constants
Other Useful Values
Units
Glossary
References

7.1 Timeline

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	$G$	$6.67259 e^{- 11} \pm 8.5 e^{- 15}$	$m^{3} {kg}^{- 1} s^{- 2}$
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.

7.3 Other Useful Values

Coming soon.

7.4 Units

Coming soon.

7.5 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. $W = F s$

7.6 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

7.1 Timeline

7.2 Fundamental Constants

7.3 Other Useful Values

7.4 Units

7.5 Glossary

7.6 References