Editing Light Speed

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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 '''3×10<sup>8</sup> 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"'''. 
* [[Starship]]s commonly travel at effective velocities measured in multiples of 170.0c (±20.0c jump variance).

== Description ([[Specifications]]) ==
The [[Light_Speed|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 [[Wikipedia: Albert Einstein|Einsteinian]] [[Wikipedia: Geometrodynamics|geometrodynamical]] [[Wikipedia: Spacetime|spacetime]]. 
* Exceeding [[Light Speed]] ([[FTL]]) requires a way to circumvent or modify the conventional physical laws of the universe. 

=== Background: Special Relativity ===
The ''[[Wikipedia: Special relativity|Special Theory of Relativity]]'', is a subset of the more comprehensive ''[[Wikipedia: General relativity|General Theory of Relativity]]'' attributed to the ancient [[Solomani]] physicist [[Wikipedia: Albert Einstein|Albert Einstein]] that deals strictly with the special case of the motion of objects in a flat [[Wikipedia: Spacetime|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 & 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/raft]]s moving at 30 kph and 50 kph, respectively, relative to an observer on a world surface.  The distance that the [[air/raft]]s traverse and the time it takes them to do so are the same for someone on the ground or on either of the [[air/raft]]s.  However, the velocities observed by these observers are relative.  If the two [[air/raft]]s 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 ''[[Wikipedia: Galilean transformation|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 ''[[Wikipedia: Lorentz transformation|Lorentz transformation equations]]'': 

* ''Time dilation'':  '''''t''' = '''t<sub>o</sub> / (1 - R<sup>2</sup>)<sup>½</sup>''''', where '''''R = v/c'''''
* ''Length-contraction'':  '''''l''' = '''l<sub>o</sub> × (1 - R<sup>2</sup>)<sup>½</sup>''''', where '''''R = v/c'''''

Note that at the [[speed of light]] when '''v=c''', the term '''(1 - R<sup>2</sup>)<sup>½</sup>''' = 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 & Local Time ====
Another consequence of the invariance of the [[Light Speed|velocity of light]] in all reference frames is that the ''[[Wikipedia: Relativity of simultaneity|simultaneity]]'' of two or more events occurring within a given inertial reference frame is not preserved from the perspective of an alternate inertial reference frame.  In other words, [[Wikipedia: Relativity of simultaneity|simultaneity]] of events is an entirely ''local'' phenomenon, not an absolute one. 

By way of illustration, suppose a [[G-Carrier]] is moving with respect to an observer on the ground.  If a passenger in the center of the [[G-Carrier]] payload compartment fires a dual laser, each beam propagating in opposite directions toward the fore and aft of the compartment, respectively, then from the perspective of the observer within the [[G-Carrier]], both beams strike the fore and aft walls at the same time.  However, to an external observer on the ground, he will also see the beams from the two ends of the laser-device travel at he same speed ('''c''') in opposite directions, but the [[G-Carrier]] will be moving in the same direction as the forward-propagating beam and the light will be "catching-up" to the front compartment wall, and at the same time the light from the aft-propagating beam will be receding from the laser and propagating into the forward-approaching rear-wall of the compartment .  The net result is that from the perspective of the ground observer, the aft-propagating beam of the laser will strike the rear of the compartment ''before'' the forward propagating beam strikes the forward wall of the [[G-Carrier]] compartment.  What happens [[Wikipedia: Relativity of simultaneity|simultaneously]] in one reference frame does not occur [[Wikipedia: Relativity of simultaneity|simultaneously]] from the perspective of the other reference frame. 

This has important consequences for relativistic vessels traveling between [[star]] systems at [[STL|sublight velocities]] that are significant fractions of [[lightspeed]].  If a vessel is traveling between two star systems separated by 5.0 [[light-year]]s at a velocity just under [[lightspeed]], an observer on the origin or destination world would say it took them almost 5.0 years to complete the journey, but that the vessel was "compressed" in length along its direction of motion and that the space-farers aboard were moving very slowly, and experienced only 3.5 years (for example) of subjective time aboard the ship. On the other hand, aboard the ship time would be experienced normally, 3.5 years passing from the beginning to the end of the journey, but as they moved between the origin and destination world, the distance between their start and endpoint will have contracted, so that the distance they needed to travel was shorter, requiring only 3.5 years of flight time instead of 5.0 years.  But at the same time, the origin and destination worlds were moving relative to the ship at just under [[lightspeed]], meaning that though 3.5 years passed for them aboard ship, only about 2.45 years has passed on the destination or origin worlds by the time they arrive.  

The end result is that from the perspective of the originating world, the journey took about 5.0 years, but the space-farers were only about 3.5 years older.  From the perspective of the space-farers, the journey only took 3.5 years, but on the originating and destination worlds, only 2.45 years had passed.  Thus, the vessel has moved from one location in ''[[Wikipedia: Spacetime|spacetime]]'', to another location in ''[[Wikipedia: Spacetime|spacetime]]'', with temporal coordinates out of synchronization with one another.  Thus, time and [[Wikipedia: Relativity of simultaneity|simultaneity]] are ''local'' phenomena, not absolute or universal ones.

==== Mass-Energy Equivalency Principle ====
According to the ''[[Wikipedia: Mass–energy equivalence|mass-energy equivalency principle]]'' arising from the ''[[Wikipedia: Special relativity|Special Theory of Relativity]]'', the energy of any particle may be described by the equation:

* '''E = mc<sup>2</sup>'''
: where:
::'''m''' = mass
:: '''c''' = speed of light

Thus, any particle has an intrinsic "'''rest-energy'''" ('''E<sub>0</sub>''') as defined by its mass while motionless (its "'''rest-mass'''", '''m<sub>0</sub>'''), independent of any internal thermal properties or kinetic energy it may acquire due to motion, as described by the equation: 
* '''E<sub>0</sub> = m<sub>0</sub>c<sup>2</sup>'''.  
By extension, an object has a "'''kinetic mass'''" '''(m<sub>k</sub>)''' due to its '''kinetic energy''' ('''E<sub>k</sub>''') while in motion relative to an independent observer that is in addition to its '''rest mass''' ('''m<sub>0</sub>'''):  
* '''E<sub>k</sub> = m<sub>k</sub>c<sup>2</sup>'''
: or
* '''m<sub>k</sub> = E<sub>k</sub> / c<sup>2</sup>'''

Thus, as an object accelerates relative to an independent observer, its '''total mass''' ('''m<sub>tot</sub>'''), also known as "'''relativistic mass'''", relative to that observer ''increases'':

* '''m<sub>tot</sub>''' = '''m<sub>0</sub>''' + '''m<sub>k</sub>''' = '''(E<sub>0</sub> / c<sup>2</sup>)''' + '''(E<sub>k</sub> / c<sup>2</sup>)'''

The "'''total energy'''" ('''E<sub>tot</sub>''') of a particle is described as the sum of its rest energy ('''E<sub>0</sub>''') and its kinetic energy ('''E<sub>k</sub>''') by the following equation:
* '''E<sub>tot</sub>''' = '''E<sub>0</sub>''' + '''E<sub>k</sub>''' = '''m<sub>o</sub>c<sup>2</sup> / (1 - R<sup>2</sup>)<sup>½</sup>''', where '''''R = v/c'''''

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 ≠ m<sub>0</sub>a''', but rather '''F ≈ m<sub>0</sub>a''' for small enough values of velocity. Thus, due to the equivalency principle of mass and energy, as '''m → <big>∞</big>''' 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|speed of light]] in vacuum as the basis for a distance metric.  As light travels at a constant speed of ~ 3×10<sup>5</sup> km/s in vacuum, the distance that light will travel in one year can be calculated to be approximately 9.47×10<sup>12</sup> 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|parsec]], an abbreviation of "'''par'''allax '''sec'''ond".  A [[Parsec|parsec]] is defined as the distance at which a shift in the position of an observer of 1.0 [[Astronomical unit|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 [[lightyear]]s 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 [[Light Speed|lightspeed]] limit has proved a troublesome barrier to many [[sophont]]-cultures attempting to colonize outside their home [[star]] systems throughout the history of the [[Galaxias|galaxy]].  

=== Interstellar STL Exploration ===
The vast majority of known [[sophont]]s 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 Ship|sleeper ship]]s", [[generation ship]]s, and high-velocity relativistic time-dilation to bridge the gap between the [[star]]s. {{Page cite|name= Referee's Manual|page= 9 (sidebar)|citeName= MegaTraveller Referee's Manual}} {{Page cite|name= T5 Core Rules|page= TBD|citeName= T5-1}} Such propulsion systems have included various types of fusion rocket (such as the [[Bussard Ramjet|Bussard ramjet]] or [[Wikipedia: Nuclear pulse propulsion|Nuclear pulse propulsion]] similar to the proposed ancient [[Solomani]] projects named [[Wikipedia: Project Daedalus|Project Daedalus]] or [[Wikipedia: Project Longshot|Project Longshot]]).  However, many interstellar [[STL]] drives both modern and ancient have relied on the principles of the [[Gravity control technology|gravitic]]-based [[NAFAL]] drive. {{Page cite|name= T5 Core Rules|page= TBD|citeName= T5-1}}

=== Interstellar FTL Exploration ===
A very few [[sophont]]-species have discovered a method of circumventing the normal restrictions of classical [[Wikipedia: Albert Einstein|Einsteinian]] [[Wikipedia: spacetime|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 [[Wikipedia: spacetime|spacetime]] that is related to normal [[Wikipedia: Albert Einstein|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 "[[Jumpspace|J-space]]") the positional and velocity values of objects in the [[N-space]] universe have corresponding imaginary values relative to the vessel.  Since t = d/v, the imaginary components of position and velocity cancel each other, yielding a common real-valued time coordinate in both the N-space and J-space environments.  Thus, since gravity is uniquely a curvature of both temporal as well as spatial coordinates in Einsteinian-spacetime, the only interaction a vessel in jump has with the [[N-space]] universe is the complex-valued [[jumpspace]] "shadow" of gravitational sources in [[N-space]] that project into [[jumpspace]] via a complex non-linear (and not well understood) interaction.  

=== Major Races & FTL === 
Those races known to have independently discovered the [[jump drive]] are known in [[Imperium|Imperial]] culture as the "[[Major Race]]s", 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 [[Hiver]]s, the [[Droyne]], and the extinct [[Ancients]].

== See also ==
{{:Referral-Tree-Speed-of-Travel}}

== References & Contributors ([[Sources]]) ==
{{Advanced}}
{{Wikipedia|Speed_of_light}}
{{Wikipedia|Special_relativity}}
{{Sources
|S1= {{Ludography cite|name= Referee's Manual |page= }}
|S2= {{Ludography cite|name= T5 Core Rules |page= }}
|S3= [[Traveller Wiki Editorial Team]]
|S4= Author & Contributor: [[User:WHULorigan|WHULorigan]]
|S5= Author & Contributor: Lord (Marquis) and Master of Sophontology [[Maksim-Smelchak]] of the [[Ministry of Science]]
}}
{{LE|Metric|Science}}