# 7 Appendix

The Physics and Technology of Warp Propulsion

## 7.1 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.

Coherence Property of a bundle of waves whose relative phases are spatially or temporally equal or constant (example: laser), as opposed to incoherent waves.

Coordinate system Diagram which consists of two or more, mostly perpendicular axes (e.g. x and y), in which a function can be illustrated.

Complex number Sum of a real part x and an imaginary part x which, since the real axis and the imaginary axis are perpendicular to each other, defines a point (x,y) in the complex plane. s=x+iy

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 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 a hole, creating a characteristic diffraction pattern in the image plane.

Dispersion Variation of the speed of light and therefore the refractive index with wavelength in the same 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, arising from 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. i=sqrt (-1)

Incoherence Property of a bundle of waves whose relative phases are varying statistically (examples: sunlight, light bulb), as opposed to coherent waves .

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.

Ionized State in which one or more of the usual complement of electrons have left the atom, thereby leaving an ion.

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=0.5mv^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.

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 (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=1kg*m*s^-2

Newton, Sir Isaac 1642-1727, conceived, among other important work, the theory of gravitation, thereby explaining the motion of celestial bodies as well as falling objects.

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.

Statistical Property of any quantity which is not exactly predictable.

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=ds/dt.

Visible light Electromagnetic radiation with a wavelength between 380nm (violet) and 780nm (red).

Watt (W) Unit of power. 1W=1J/S

Wavelength (lambda) 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

## 7.2 Fundamental Constants

 Name Symbol Value Unit Speed of light in vacuum c 299792458 m s-1 Permeability of vacuum mu_0 1.25663706143592e-06 N A-2 Permittivity of vacuum epsilon_0 8.854187817e-12 F m-1 Newtonian constant of gravitation G 6.67259e-11 ± 8.5e-15 m3 kg-1 s-2 Planck constant h 6.6260755e-34 ± 4.0e-40 J s Planck constant in eV 4.1356692e-15 ± 1.2e-21 eV s Planck mass m_p 2.17671e-08 ± 1.4e-12 kg Planck length l_p 1.61605e-35 ± 1.0e-39 m Planck time t_p 5.39056e-44 ± 3.4e-48 s Elementary charge e 1.60217733e-19 ± 4.9e-26 C Electron mass m_e 9.1093897e-31 ± 5.4e-37 kg Electron mass in u 0.000548579903 ± 1.3e-11 u Electron mass in eV 510999.06 ± 0.15 eV Proton mass m_p 1.6726231e-27 ± 1.0e-33 kg Proton mass in u 1.00727647 ± 1.2e-08 u Proton mass in eV 938272310 ± 280 eV Proton-electron mass ratio 1836.152701 ± 3.7e-05 Proton specific charge 95788309 ± 29 C kg-1 Neutron mass m_n 1.6749286e-27 ± 1.0e-33 kg Neutron mass in u 1.008664904 ± 1.4e-08 u Neutron mass in eV 939565630 ± 280 eV Neutron-electron mass ratio 1838.683662 ± 4.0e-05 Neutron-proton mass ratio 1.001378404 ± 9e-09 Avogadro constant N_A 6.0221367e+23 ± 3.6e+17 mol-1 Boltzmann constant k 1.380658e-23 ± 1.2e-28 J K-1 Boltzmann constant in eV 8.617385e-05 ± 7.3e-10 eV K-1 Molar volume ideal gas, STP V_m 0.0224141 ± 1.9e-07 m3 mol-1 Electron volt eV 1.60217733e-19 ± 4.9e-26 J Atomic mass unit u 1.6605402e-27 ± 1.0e-33 kg Standard acceleration of gravity g_n 9.80665 m s-2

Tab. 7.1 Fundamental physical constants

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

## 7.3 References

[Use] Usenet Relativity FAQ, Desy mirror

[Ast] Astronomy FAQ, http://www.faqs.org/faqs/astronomy/faq/

[Sce] B. Scent, S. Davis, L. Scheinbeim, Black Holes - Portals into the Unknown

[Mil] M. G. Millis, Warp Drive When?

[Hin1] J. Hinson, Relativity and FTL Travel

[Hin2] J. Hinson, Subspace Physics

[Bel] J. Bell, Star Trek Technology: Frequently Asked Questions Lists

[STTR] R. Mercer, The Star Trek Technical Reference

[DITL] G. Kennedy, Daystrom Institute Technical Library

[STD] 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, link to article

[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, 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

[Whi68] Stephen E. Whitfield, Gene Roddenberry, The Making of Star Trek, Del Rey Books, 1968

[Zim98] H. Zimmerman, R. Sternbach, D. Drexler, I. S. Behr, Star Trek: Deep Space Nine Technical Manual, Pocket Books, 1998

## 7.4 Credits

Some screen caps from TrekCore. Thanks to Jörg, to Tobias Heintz and to Jan for suggestions and corrections.