# Appendix

### Written by Bernd Schneider

## 7.1 Timeline

Coming soon.

## 7.2 Fundamental Constants

Name | Symbol | Value | Unit |
---|---|---|---|

Speed of light in vacuum | $c$ | $299792458$ | $m{s}^{-1}$ |

Permeability of vacuum | ${\mu}_{0}$ | $1.25663706143592{e}^{-6}$ | $N{A}^{-2}$ |

Permittivity of vacuum | ${\epsilon}_{0}$ | $8.854187817{e}^{-12}$ | $F{m}^{-1}$ |

Newtonian constant of gravitation | $G$ | $6.67259{e}^{-11}\pm 8.5{e}^{-15}$ | ${m}^{3}{\mathrm{kg}}^{-1}{s}^{-2}$ |

Planck constant | $h$ | $6.6260755{e}^{-34}\pm 4.0{e}^{-40}$ | $Js$ |

Planck constant in eV | $4.1356692{e}^{-15}\pm 1.2{e}^{-21}$ | $\mathrm{eV}s$ | |

Planck mass | ${m}_{p}$ | $2.17671{e}^{-8}\pm 1.4{e}^{-12}$ | $\mathrm{kg}$ |

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 | $\mathrm{e}$ | $1.60217733{e}^{-19}\pm 4.9{e}^{-26}$ | $C$ |

Electron mass | ${m}_{e}$ | $9.1093897{e}^{-31}\pm 5.4{e}^{-37}$ | $\mathrm{kg}$ |

Electron mass in u |
$0.000548579903\pm 1.3{e}^{-11}$ | $u$ | |

Electron mass in eV |
$510999.06\pm 0.15$ | $\mathrm{eV}$ | |

Proton mass | ${m}_{p}$ | $1.6726231{e}^{-27}\pm 1.0{e}^{-33}$ | $\mathrm{kg}$ |

Proton mass in u | $1.00727647\pm 1.2{e}^{-08}$ | $u$ | |

Proton mass in eV | $938272310\pm 280$ | $\mathrm{eV}$ | |

Proton-electron mass ratio | $1836.152701\pm 3.7{e}^{-5}$ | ||

Proton specific charge | $95788309\pm 29$ | $C{\mathrm{kg}}^{-1}$ | |

Neutron mass | ${m}_{n}$ | $1.6749286{e}^{-27}\pm 1.0{e}^{-33}$ | $\mathrm{kg}$ |

Neutron mass in u | $1.008664904\pm 1.4{e}^{-8}$ | $u$ | |

Neutron mass in eV | $939565630\pm 280$ | $\mathrm{eV}$ | |

Neutron-electron mass ratio | $1838.683662\pm 4.0{e}^{-5}$ | ||

Neutron-proton mass ratio | $1.001378404\pm 9{e}^{-9}$ | ||

Avagadro constant | ${N}_{A}$ | $6.0221367{e}^{23}\pm 3.6{e}^{17}$ | ${\mathrm{mol}}^{-1}$ |

Boltzmann constant | $k$ | $1.380658{e}^{-23}\pm 1.2{e}^{-28}$ | $J{K}^{-1}$ |

Boltzmann constant in eV | $8.617385{e}^{-5}\pm 7.3{e}^{-10}$ | $\mathrm{eV}{K}^{-1}$ | |

Molar volume ideal gas, STP | ${V}_{m}$ | $0.0224141\pm 1.9{e}^{-7}$ | ${m}^{3}{\mathrm{mol}}^{-1}$ |

Electron volt | $\mathrm{eV}$ | $1.60217733{e}^{-19}\pm 4.9{e}^{-26}$ | $J$ |

Atomic mass unit | $u$ | $1.6605402{e}^{-27}\pm 1.0{e}^{-33}$ | $\mathrm{kg}$ |

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 $t$ . $a=\frac{dv}{dt}$
- 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.
- Decade
- Factor of ten.
- Derivative
- Rate of change (steepness) of a function $f(x)$ , given as the quotient of two differentials $\frac{df(x)}{dx}$ .
- 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. $1\mathrm{Hz}=1/s$
- 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). $1J=1\mathrm{Nm}$
- Kinetic energy
- Energy of a mass $m$ due to its motion with a speed $v$ . ${E}_{\mathrm{kin}}=(m{v}^{2})/2$
- 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. $1N=1\mathrm{kg}m{s}^{-2}$
- 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 $f$ . $E=hf$
- 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 $t$ . $P=\frac{dE}{dt}$
- 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.
- 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 $t$ . $v=\frac{ds}{dt}$ .
- 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. $W=Fs$

## 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