Light Speed

The Speed of Light, or Light Speed, is the maximum possible speed in the N-space universe, and is a constant speed of 299,792.458 km/s (often expressed as 3×10⁸ m/s) in vacuum at which any particle of zero rest-mass (such as the photon) will automatically propagate.

This value is commonly abbreviated as "c".

Description (Specifications)

The Speed of light is an upper-limiting speed for all particles or physical objects in the Universe under the conventional laws of physics as defined by Einsteinian geometrodynamical spacetime.

Exceeding Light Speed (FTL) requires a way to circumvent or modify the conventional physical laws of the universe.

Background: Special Relativity

The Special Theory of Relativity, is a subset of the more comprehensive General Theory of Relativity attributed to the ancient Solomani physicist Albert Einstein that deals strictly with the special case of the motion of objects in a flat spacetime environment independent of the influence of gravitational fields. The two principles that underlie the theory from which its consequences derive are:

The laws of physics are invariant in all frames of reference.
The speed of light in a vacuum is the same for all observers, regardless of the motion of the light source.

The latter principle is a consequence of the fact that electromagnetic radiation (i.e. "light") is a sinusoidal oscillation of the magnitude and direction of electric and magnetic fields in vacuum. It is not an oscillating wave within a physical material medium against which the velocity of the wave can be gauged (i.e. there is no absolute reference frame relative to which all independent observers can measure the speed of light - it is always measured relative to the observer because one cannot measure velocity relative to the "emptiness" of the vacuum).

Lorentz equations: Length-contraction and Time-dilation

In classical Newtonian physics, length/distance and time are independent invariant quantities that are the same relative to all observers. The basic relationship between distance, motion, and time is given by the equation:

d = vt

where:

d = distance
v = velocity
t = time

In classical mechanics when an object is in motion, the distance (d) between two points and the time (t) experienced are the same for all observers, regardless of their state of motion. The velocity (v), however, is different depending on the state of motion for any given observer. Consider two air/rafts moving at 30 kph and 50 kph, respectively, relative to an observer on a world surface. The distance that the air/rafts traverse and the time it takes them to do so are the same for someone on the ground or on either of the air/rafts. However, the velocities observed by these observers are relative. If the two air/rafts are moving in the same direction, the person on the ground will say they are moving at 30 kph and 50 kph, respectively, but to the person on the first air/raft moving at 30 kph relative to the ground, the other air/raft is only moving at 20 kph relative to him, and the ground is moving at 30 kph in the opposite direction of the other air/raft relative to him. In classical physics this is known as the Galilean transformation.

However, as noted above, the speed of light is the same for all observers, independent of any relative motion. The implication of this simple observation has far-reaching consequences. In order for light to have both a constant velocity of propagation and exhibit that same constant velocity relative to any observer regardless of the observer's relative state of motion (i.e. you are not catching up to or receding from the light as you move), then for any two given observer's velocities the spatial distance through which the light is moving and the time it takes to do so must change in order for the laws of physics to remain constant in both reference frames. Put mathematically, if the speed of light (c) is observed to be the same for either of two observers moving at different velocities relative to one another, then in order for c to have the same value for either observer, d and t must change based on the relative velocities of the observers. By logical extension, therefore, when any two objects are moving relative to one another, the spatial distance through which they are moving and the time they take to do so are different depending on the relative velocities of one observer relative to another.

The degree of change of length/distance or dilation of the passage of time experienced by any given observer is given by the Lorentz transformation equations:

Time dilation: t = t_o / (1 - v²/c²)^½
Length-contraction: l = l_o × (1 - v²/c²)^½

Note that at the speed of light when v=c, the radical (1 - v²/c²)^½ = 0, meaning that time for the moving reference frame relative to an independent observer has dilated to infinity (i.e. it has ground to a halt) and distance/length has shrunk to zero along the direction of motion.

The effects of time dilation and length/distance contraction become a meaningful consideration for an alternate reference frame moving at speeds greater than ~ 0.10c relative to a given observer, whereas the effects of time dilation and length/distance contraction become significant for an alternate reference frame moving at speeds greater than ~ 0.90c relative to a given observer.

Simultaneity and Local Time

TBD: Simultaneity of events is a local, not absolute phenomenon.

Mass-Energy Equivalency Principle

According to the mass-energy equivalency principle arising from the Special Theory of Relativity, the energy of any particle may be described by the equation:

E = mc²

where:

m = mass

c = speed of light

Thus, any particle has an intrinsic "rest-energy" (E₀) as defined by its mass while motionless (its "rest-mass", m₀), independent of any internal thermal properties or kinetic energy it may acquire due to motion, as described by the equation:

E₀ = m₀c².

By extension, an object has a "kinetic mass" (m_k) due to its kinetic energy (E_k) while in motion relative to an independent observer that is in addition to its rest mass (m₀):

E_k = m_kc²

or

m_k = E_k / c²

Thus, as an object accelerates relative to an independent observer, its total mass (m_tot), also known as "relativistic mass", relative to that observer increases:

m_tot = m₀ + m_k = (E₀ / c²) + (E_k / c²)

The "total energy" (E_tot) of a particle is described as the sum of its rest energy (E₀) and its kinetic energy (E_k) by the following equation:

E_tot = E₀ + E_k = m_oc² / (1 - v²/c²)^½

And is dependent upon its velocity relative to the one observing.

As a consequence, a constant force applied to a particle will produce a continually decreasing acceleration as its mass increases as a function of velocity, implying that in fact F ≠ m₀a, but rather F ≈ m₀a for small enough values of velocity. Thus, due to the equivalency principle of mass and energy, as m → ∞ with increasing velocity, a → 0, asymptotically approaching a maximum velocity. This limiting velocity is the maximum speed of the universe, and is also the constant speed at which zero-rest mass particles (such as photons and gravitons) propagate, and is colloquially known as the speed of light as a result. It is thus impossible to accelerate an object with non-zero rest mass to the speed of light in a finite amount of time (or alternatively, it would require an infinite force (and/or an infinite amount of energy) to produce the acceleration necessary to accelerate a non-zero rest mass particle to the speed of light).

Lightspeed as a distance metric

Due to the vast distances involved in interstellar measurements, it is often convenient to use the very large constant value of the speed of light in vacuum as the basis for a distance metric. As light travels at a constant speed of ~ 3×10⁵ km/s in vacuum, the distance that light will travel in one year can be calculated to be approximately 9.47×10¹² km. This distance is used as a common metric for interstellar distances, and is known as a lightyear. Shorter distances are also often defined in a similar manner, and include such distance metrics as the light-week, light-day, light-hour, light-minute, and light-second.

A related metric for measuring interstellar distances is the parsec, an abbreviation of "parallax second". A parsec is defined as the distance at which a shift in the position of an observer of 1.0 astronomical unit, or AU, will produce a shift in the observed position of a distant object of one second of arc. A parsec is calculated to be roughly 3.26 lightyears in distance, multiples of which also happen to be close to the maximum Jumpspace traverse distances of the standard Jump Drive.

History & Background (Dossier)

The lightspeed limit has proved a troublesome barrier to many sophont-cultures attempting to colonize outside their home star systems throughout the history of the galaxy. The vast majority of known sophonts both current and extinct have historically relied on various methods of slower-than-light (STL) propulsion to explore and colonize on an interstellar scale, utilizing technologies such as "sleeper ships", generation ships, and high-velocity relativistic time-dilation to bridge the gap between the stars. Such propulsion systems have included various types of fusion rocket (such as the Bussard ramjet or Nuclear pulse propulsion similar to the proposed ancient Solomani projects named Project Daedalus or Project Longshot). However, many interstellar STL drives both modern and ancient have relied on the principles of the gravitic-based NAFAL drive.

A very few sophont-species have discovered a method of circumventing the normal restrictions of classical Einsteinian spacetime over the history of Charted Space, each having independently discovered the drive system known as the jump drive. The jump drive opens a bridge into an alternate dimension of spacetime that is related to normal Einsteinian space (or "N-space") in a non-linear fashion. As such, both velocity and positional information take on imaginary values during the operation of the drive, resulting in a transition from point-to-point in N-space that takes about 168 (±10%) hours, the N-space distance of the jump limited only by the performance characteristics of the drive. While in jumpspace (or "J-space") the positional and velocity values of objects in the N-space universe have corresponding imaginary values relative to the vessel. Thus, the only interaction the vessel in jump has with the N-space universe is the jumpspace "shadow" of gravitational sources in N-space that project into jumpspace via a complex non-linear (and not well understood) interaction.

Those races known to have independently discovered the jump drive are known in Imperial culture as the "Major Races", and number only seven throughout the known history of Charted Space (though only six are extant today): Humaniti (specifically the Vilani, Solomani, and Zhodani branches), the Vargr, the Aslan, the K'kree, the Hivers, the Droyne, and the extinct Ancients.

Relations or implications to the OTU.
TBD

References & Contributors (Sources)

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TBD
Author & Contributor: Wayne
Author & Contributor: Lord (Marquis) and Master of Sophontology Maksim-Smelchak of the Ministry of Science