Anti-de Sitter Drive - Revision history

Tesinormed at 22:55, August 18, 2025

2025-08-18T22:55:58Z

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	<math>\large \tau</math>: Proper time elapsed in the AdS subspace.		<math>\large \tau</math>: Proper time elapsed in the AdS subspace.

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	<math>\large \tau</math>: Proper time elapsed in the AdS subspace.		<math>\large \tau</math>: Proper time elapsed in the AdS subspace.

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MMONTAGEe at 10:11, June 11, 2025

2025-06-11T10:11:26Z

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	!<center>[[File:Anti-de-sitter-visible-distortions.png\|450px\|center]]</center>		!<center>[[File:Anti-de-sitter-visible-distortions.png\|450px\|center]]</center>
	!<center>[[File:~~Anti-de-sitter~~ ~~first~~ ~~interpretation~~.png\|450px\|center]]</center>		!<center>[[File:AdS jump from side.png\|450px\|center]]</center>
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	!<center>Visible Anti-de Sitter distortion accompanied by bright Flash caused by the shift into subspace (@retrovisor)</center>		!<center>Visible Anti-de Sitter distortion accompanied by bright Flash caused by the shift into subspace (@retrovisor)</center>
	!<center>~~Early~~ Anti-de Sitter ~~drive~~ ~~travel~~ ~~visualisation~~ in ~~SpaceEngine~~</center>		!<center>Anti-de Sitter Jump happening inside Lagrangian Cloud captured from side perspective</center>
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			!<center>[[File:Anti-de-sitter first interpretation.png\|450px\|center]]</center>
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			!<center>Early Anti-de Sitter drive travel visualisation in SpaceEngine</center>
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MMONTAGEe at 15:32, June 9, 2025

2025-06-09T15:32:00Z

← Older revision		Revision as of 15:32, June 9, 2025
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	<blockquote> "So, check this out: this thing is totally wild—it goes 'boosh kaboosh' and makes these eerie humming noises. Then, everything around you starts stretching and wobbling like you're on the craziest rollercoaster ride ever, and suddenly, you're in this scary, dark place that's like being squished between two totally different worlds." </blockquote> - Ford Dastarian, Nemesis Galaxy recovered logs		<blockquote> "So, check this out: this thing is totally wild—it goes 'boosh kaboosh' and makes these eerie humming noises. Then, everything around you starts stretching and wobbling like you're on the craziest rollercoaster ride ever, and suddenly, you're in this scary, dark place that's like being squished between two totally different worlds." </blockquote> - Ford Dastarian, Nemesis Galaxy recovered logs

	The '''Anti-de Sitter Drive''', or more commonly referred to as the '''AdS Drive''', is a revolutionary interstellar propulsion system enabling faster-than-light travel. This device allows this because of its abilities to navigate through a three-dimensional Anti-de Sitter subspace embedded within four-dimensional geometry. Its principles are derived from the laws outlined in the M ~~Model~~ of the universe, developed through the groundbreaking works of Marcus Hector Cüpernik. Initially, AdS Drives were mass-produced by the [[United LunaTerra]], followed by the Martian Technate and [[Ceres ShipYards\|Ceres Shipyards]]. By the mid-24th century, engineering advancements had miniaturized and optimized the AdS Drive, making it standard equipment on privately-owned spacecraft due to its efficiency and reduced energy requirements.		The '''Anti-de Sitter Drive''', or more commonly referred to as the '''AdS Drive''', is a revolutionary interstellar propulsion system enabling faster-than-light travel. This device allows this because of its abilities to navigate through a three-dimensional Anti-de Sitter horse saddle shaped hyperbolic subspace embedded within four-dimensional geometry. Its principles are derived from the laws outlined in the M Cosmology of the universe, developed through the groundbreaking works of Marcus Hector Cüpernik. Initially, AdS Drives were mass-produced by the [[United LunaTerra]], followed by the Martian Technate and [[Ceres ShipYards\|Ceres Shipyards]]. By the mid-24th century, engineering advancements had miniaturized and optimized the AdS Drive, making it standard equipment on privately-owned spacecraft due to its efficiency and reduced energy requirements.

	== [[Harrison Wells (Distant Worlds)\|Professor Wells]] Explains the AdS Drive ==		== [[Harrison Wells (Distant Worlds)\|Professor Wells]] Explains the AdS Drive ==

MMONTAGEe at 19:46, May 31, 2025

2025-05-31T19:46:32Z

← Older revision		Revision as of 19:46, May 31, 2025
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	====LAGRANGIAN FOR ADS DRIVE DYNAMICS====		====LAGRANGIAN FOR ADS DRIVE DYNAMICS====

	<math mode="display" fleqn> \mathcal{L}_{\text{~~AdS~~}} = \frac{1}{2} m \left( g_{\mu\nu} \dot{x}^\mu \dot{x}^\nu - 1 \right) - \epsilon \, g_{\mu\nu} \, \phi \, F(\dot{x}^\mu, \partial_\mu \phi) + \frac{\alpha}{2} \dot{x}^\mu \frac{d}{d\tau} \dot{x}_\mu - \frac{\beta}{r^2 + \gamma} + \mathcal{L}_{\text{~~AdS~~ Transition}}</math>		<math mode="display" fleqn> \mathcal{L}_{\text{Ⲝ}} = \frac{1}{2} m \left( g_{\mu\nu} \dot{x}^\mu \dot{x}^\nu - 1 \right) - \epsilon \, g_{\mu\nu} \, \phi \, F(\dot{x}^\mu, \partial_\mu \phi) + \frac{\alpha}{2} \dot{x}^\mu \frac{d}{d\tau} \dot{x}_\mu - \frac{\beta}{r^2 + \gamma} + \mathcal{L}_{\text{Ⲝ Transition}}</math>

	'''Where:'''		'''Where:'''
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	<math>\large \frac{\beta}{r^2 + \gamma} </math>: Models <strong>gravity-like forces</strong> within AdS, where <math>\large \ r </math> is the distance traveled within the AdS space.		<math>\large \frac{\beta}{r^2 + \gamma} </math>: Models <strong>gravity-like forces</strong> within AdS, where <math>\large \ r </math> is the distance traveled within the AdS space.

	<math>\large \mathcal{L}_{\text{~~AdS~~ Transition}} </math>: Accounts for the <strong>transition phases</strong> (entry and exit) of the ship into and out of AdS space, describing the forces and energies involved in shifting dimensions.		<math>\large \mathcal{L}_{\text{Ⲝ Transition}} </math>: Accounts for the <strong>transition phases</strong> (entry and exit) of the ship into and out of AdS space, describing the forces and energies involved in shifting dimensions.

	----		----
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	====EQUATION OF MOTION====		====EQUATION OF MOTION====

	<math mode="display" fleqn> \frac{d}{d\tau} \left( \frac{\partial \mathcal{L}_{\text{~~AdS~~}}}{\partial \dot{x}^\mu} \right) - \frac{\partial \mathcal{L}_{\text{~~AdS~~}}}{\partial x^\mu} = 0 </math>		<math mode="display" fleqn> \frac{d}{d\tau} \left( \frac{\partial \mathcal{L}_{\text{Ⲝ}}}{\partial \dot{x}^\mu} \right) - \frac{\partial \mathcal{L}_{\text{Ⲝ}}}{\partial x^\mu} = 0 </math>

	'''Where:'''		'''Where:'''

	<strong>Entering AdS (Warp Transition):</strong> The energy <math>\large \epsilon </math> from the ship’s reactor powers a <strong>cyclotron ring</strong>, creating a "lift" into AdS. The term <math>\large \epsilon \, g_{\mu\nu} \, \phi </math> ensures the curvature interacts with the energy and mass, facilitating the ship's entry.		<strong>Entering AdS (Ⲝ) (Warp Transition):</strong> The energy <math>\large \epsilon </math> from the ship’s reactor powers a <strong>cyclotron ring</strong>, creating a "lift" into AdS. The term <math>\large \epsilon \, g_{\mu\nu} \, \phi </math> ensures the curvature interacts with the energy and mass, facilitating the ship's entry.

	<strong>Travel Through AdS:</strong> The <strong>contracted distances</strong> effectively shorten the travel path. The metric <math>\large g_{\mu\nu} </math> describes the <strong>shortened distance</strong>, allowing rapid transit.		<strong>Travel Through AdS:</strong> The <strong>contracted distances</strong> effectively shorten the travel path. The metric <math>\large g_{\mu\nu} </math> describes the <strong>shortened distance</strong>, allowing rapid transit.

MMONTAGEe at 19:44, May 31, 2025

2025-05-31T19:44:52Z

← Older revision		Revision as of 19:44, May 31, 2025
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	====GENERAL ACTION OF ADS DRIVE DYNAMICS====		====GENERAL ACTION OF ADS DRIVE DYNAMICS====

	<math mode="display" fleqn> S = \int d\tau \, \mathcal{L}_{\text{~~AdS~~}}(x^\mu, \dot{x}^\mu, \phi, g_{\mu\nu}, \epsilon, E) </math>		<math mode="display" fleqn> S = \int d\tau \, \mathcal{L}_{\text{Ⲝ}}(x^\mu, \dot{x}^\mu, \phi, g_{\mu\nu}, \epsilon, E) </math>

	'''Where:'''		'''Where:'''

MMONTAGEe at 10:57, May 28, 2025

2025-05-28T10:57:20Z

← Older revision		Revision as of 10:57, May 28, 2025
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	{{DSTheme}}		{{DSTheme}}
	{{DSLogo}} {{DSTimeline24to26}}		{{DSLogo}} {{DSTimeline24to26}}{{DiegeticDS}}
	[[Category:Technology]]		[[Category:Technology]]

MMONTAGEe at 07:05, May 21, 2025

2025-05-21T07:05:48Z

MMONTAGEe at 11:15, May 17, 2025

2025-05-17T11:15:54Z

← Older revision		Revision as of 11:15, May 17, 2025
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MMONTAGEe at 11:15, May 17, 2025

2025-05-17T11:15:26Z

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	!<center>[[File:Anti-de-sitter-visible-distortions.png\|450px\|center]]</center>		!<center>[[File:Anti-de-sitter-visible-distortions.png\|450px\|center]]</center>
	!<center>[[File:\|450px\|center]]</center>		!<center>[[File:Anti-de-sitter first interpretation.png\|450px\|center]]</center>
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	!<center>Visible Anti-de Sitter distortion accompanied by bright Flash caused by the shift into subspace (@retrovisor)</center>		!<center>Visible Anti-de Sitter distortion accompanied by bright Flash caused by the shift into subspace (@retrovisor)</center>
	!<center></center>		!<center>Early Anti-de Sitter drive travel visualisation in SpaceEngine</center>
	\|}		\|}
	----		----

MMONTAGEe at 10:57, May 17, 2025

2025-05-17T10:57:45Z

← Older revision		Revision as of 10:57, May 17, 2025
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	{{Infobox Device		{{Infobox Device
	\| title1 = Anti-de Sitter Drive		\| title1 = Anti-de Sitter Drive
	\| image1 = ~~Anti-de-sitter-visible-distortions~~.png		\| image1 = Ads branes.png
		⚫	\| caption-image1 = Anti-de Sitter warping inbetween dimensional Branes
	\| caption1 = Anti-de Sitter Jump Distortions, Warping between Dimensional Warping accompanied by bright flash during shift
	\| inventor = Marcus Hector Cüpernik		\| inventor = Marcus Hector Cüpernik
	\| invention_date = 2278		\| invention_date = 2278
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	\| average_price = 10000 ExoCredits		\| average_price = 10000 ExoCredits
	\| function_description = Interstellar Travel		\| function_description = Interstellar Travel
	\| image2 = Ads branes.png
⚫	\| caption-~~image2~~ = Anti-de Sitter warping inbetween dimensional Branes
	\| caption-image1 = Visible Anti-de Sitter distortion accompanied by bright Flash caused by the shift into subspace (@retrovisor)		\| caption-image1 = Visible Anti-de Sitter distortion accompanied by bright Flash caused by the shift into subspace (@retrovisor)
	}}		}}
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	{\| class="article-tabled"		{\| class="article-tabled"
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	!<center>[[File:\|450px\|center]]</center>		!<center>[[File:Anti-de-sitter-visible-distortions.png\|450px\|center]]</center>
	!<center>[[File:\|450px\|center]]</center>		!<center>[[File:\|450px\|center]]</center>
	\|-		\|-
	\|		\|
			!<center>Visible Anti-de Sitter distortion accompanied by bright Flash caused by the shift into subspace (@retrovisor)</center>
	!<center></center>
	!<center></center>		!<center></center>
	\|}		\|}

← Older revision		Revision as of 07:05, May 21, 2025
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	'''Where:'''		'''Where:'''

	<math> \tau </math>: is the <strong>proper time</strong> experienced by the ship.		<math>\large \tau </math>: is the <strong>proper time</strong> experienced by the ship.

	<math> x^\mu </math>: represents the <strong>position coordinates</strong> in 4D space (including the 3D + 1 extra dimension).		<math>\large x^\mu </math>: represents the <strong>position coordinates</strong> in 4D space (including the 3D + 1 extra dimension).

	<math> \dot{x}^\mu </math>: is the <strong>velocity</strong> of the ship in this extended space.		<math>\large \dot{x}^\mu </math>: is the <strong>velocity</strong> of the ship in this extended space.

	<math> \phi </math>: is the <strong>field</strong> that describes the AdS space curvature and connection between the branes.		<math>\large \phi </math>: is the <strong>field</strong> that describes the AdS space curvature and connection between the branes.

	<math> g_{\mu\nu} </math>: is the <strong>metric tensor</strong> that describes the curvature of the AdS space.		<math>\large g_{\mu\nu} </math>: is the <strong>metric tensor</strong> that describes the curvature of the AdS space.

	<math> \epsilon </math>: is a <strong>coupling constant</strong> related to the energy provided by the ship’s reactor.		<math>\large \epsilon </math>: is a <strong>coupling constant</strong> related to the energy provided by the ship’s reactor.

	<math> E </math> is the <strong>total energy</strong> used by the drive.		<math>\large E </math> is the <strong>total energy</strong> used by the drive.


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	'''Where:'''		'''Where:'''

	<math> \frac{1}{2} m \left( g_{\mu\nu} \dot{x}^\mu \dot{x}^\nu - 1 \right) </math>: Represents the <strong>kinetic energy</strong> of the ship’s mass <math> \ m </math> traveling through the 4D curved AdS space.		<math>\large \frac{1}{2} m \left( g_{\mu\nu} \dot{x}^\mu \dot{x}^\nu - 1 \right) </math>: Represents the <strong>kinetic energy</strong> of the ship’s mass <math>\large \ m </math> traveling through the 4D curved AdS space.

	<math> \epsilon \, g_{\mu\nu} \, \phi \, F(\dot{x}^\mu, \partial_\mu \phi) </math>: Accounts for the <strong>interaction between the ship’s energy field</strong> and the AdS space. It includes how energy from the reactor <math> \epsilon </math> interacts with the field <math> \phi </math> governing the AdS curvature.		<math>\large \epsilon \, g_{\mu\nu} \, \phi \, F(\dot{x}^\mu, \partial_\mu \phi) </math>: Accounts for the <strong>interaction between the ship’s energy field</strong> and the AdS space. It includes how energy from the reactor <math>\large \epsilon </math> interacts with the field <math>\large \phi </math> governing the AdS curvature.

	<math> \frac{\alpha}{2} \dot{x}^\mu \frac{d}{d\tau} \dot{x}_\mu </math>: Captures the <strong>acceleration and deceleration</strong> processes.		<math>\large \frac{\alpha}{2} \dot{x}^\mu \frac{d}{d\tau} \dot{x}_\mu </math>: Captures the <strong>acceleration and deceleration</strong> processes.

	<math> \frac{\beta}{r^2 + \gamma} </math>: Models <strong>gravity-like forces</strong> within AdS, where <math> \ r </math> is the distance traveled within the AdS space.		<math>\large \frac{\beta}{r^2 + \gamma} </math>: Models <strong>gravity-like forces</strong> within AdS, where <math>\large \ r </math> is the distance traveled within the AdS space.

	<math> \mathcal{L}_{\text{AdS Transition}} </math>: Accounts for the <strong>transition phases</strong> (entry and exit) of the ship into and out of AdS space, describing the forces and energies involved in shifting dimensions.		<math>\large \mathcal{L}_{\text{AdS Transition}} </math>: Accounts for the <strong>transition phases</strong> (entry and exit) of the ship into and out of AdS space, describing the forces and energies involved in shifting dimensions.

	----		----
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	'''Where:'''		'''Where:'''

	<strong>Entering AdS (Warp Transition):</strong> The energy <math> \epsilon </math> from the ship’s reactor powers a <strong>cyclotron ring</strong>, creating a "lift" into AdS. The term <math> \epsilon \, g_{\mu\nu} \, \phi </math> ensures the curvature interacts with the energy and mass, facilitating the ship's entry.		<strong>Entering AdS (Warp Transition):</strong> The energy <math>\large \epsilon </math> from the ship’s reactor powers a <strong>cyclotron ring</strong>, creating a "lift" into AdS. The term <math>\large \epsilon \, g_{\mu\nu} \, \phi </math> ensures the curvature interacts with the energy and mass, facilitating the ship's entry.

	<strong>Travel Through AdS:</strong> The <strong>contracted distances</strong> effectively shorten the travel path. The metric <math> g_{\mu\nu} </math> describes the <strong>shortened distance</strong>, allowing rapid transit.		<strong>Travel Through AdS:</strong> The <strong>contracted distances</strong> effectively shorten the travel path. The metric <math>\large g_{\mu\nu} </math> describes the <strong>shortened distance</strong>, allowing rapid transit.

	<strong>Acceleration/Deceleration Dynamics:</strong> The term <math> \frac{\alpha}{2} \dot{x}^\mu \frac{d}{d\tau} \dot{x}_\mu </math> regulates momentum change, smooth acceleration and deceleration within the warped space.		<strong>Acceleration/Deceleration Dynamics:</strong> The term <math>\large \frac{\alpha}{2} \dot{x}^\mu \frac{d}{d\tau} \dot{x}_\mu </math> regulates momentum change, smooth acceleration and deceleration within the warped space.

	<strong>Exit Phase:</strong> The term <math> \mathcal{L}_{\text{AdS Transition}} </math> represents the energy changes and interactions needed to revert to 3D space.		<strong>Exit Phase:</strong> The term <math>\large \mathcal{L}_{\text{AdS Transition}} </math> represents the energy changes and interactions needed to revert to 3D space.

	====EQUATION OF TRANSITION====		====EQUATION OF TRANSITION====
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	'''Where:'''		'''Where:'''

	<math> d </math> Effective warped distance, perceived distance traveled in shorter AdS subspace than normal space		<math>\large d </math> Effective warped distance, perceived distance traveled in shorter AdS subspace than normal space

	<math> p </math> Momentum during the acceleration phase. This value is dependent on the initial thrust and acceleration of the spacecraft in subspace.		<math>\large p </math> Momentum during the acceleration phase. This value is dependent on the initial thrust and acceleration of the spacecraft in subspace.

	<math> Q </math> Momentum during the deceleration phase. This reflects the energy needed to slow the ship down as it approaches its destination.		<math>\large Q </math> Momentum during the deceleration phase. This reflects the energy needed to slow the ship down as it approaches its destination.

	<math> m </math> Total mass of the ship, including the details (Mass, crew, cargo) which affects energy requirement		<math>\large m </math> Total mass of the ship, including the details (Mass, crew, cargo) which affects energy requirement

	====STRESS BUILD-UP====		====STRESS BUILD-UP====
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	Where:		Where:

	<math>S_0</math>: Baseline structural stress at <math>\tau = 0</math>		<math>\large S_0</math>: Baseline structural stress at <math>\large \tau = 0</math>

	<math>\epsilon</math>: Drive energy coupling constant (from the reactor).		<math>\large \epsilon</math>: Drive energy coupling constant (from the reactor).

	<math>\kappa_1</math>: Linear stress‐growth coefficient <math>(\kappa_1 \ll \kappa_2\)</math>.		<math>\large \kappa_1</math>: Linear stress‐growth coefficient <math>\large (\kappa_1 \ll \kappa_2\)</math>.

	<math>\kappa_2</math>: Quadratic fatigue coefficient (models field fatigue over time).		<math>\large \kappa_2</math>: Quadratic fatigue coefficient (models field fatigue over time).

	<math>\delta</math>: Cooling/recovery amplitude (how much stress is relieved).		<math>\large \delta</math>: Cooling/recovery amplitude (how much stress is relieved).

	<math>\lambda</math>: Cooling rate constant (how quickly the reactor/system recovers).		<math>\large \lambda</math>: Cooling rate constant (how quickly the reactor/system recovers).

	<math>\tau</math>: Proper time elapsed in the AdS subspace.		<math>\large \tau</math>: Proper time elapsed in the AdS subspace.

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	<math mode="display" fleqn> E(\tau) = E_0 + \eta\,\epsilon\,\tau + \zeta\,\epsilon^2\,\tau^2 </math>		<math mode="display" fleqn> E(\tau) = E_0 + \eta\,\epsilon\,\tau + \zeta\,\epsilon^2\,\tau^2 </math>

	<math>E_0</math>: Baseline energy already spent at <math>\tau = 0</math>.		<math>\large E_0</math>: Baseline energy already spent at <math>\large \tau = 0</math>.

	<math>\epsilon</math>: Drive energy coupling constant.		<math>\large \epsilon</math>: Drive energy coupling constant.

	<math>\eta</math>: Linear consumption coefficient.		<math>\large \eta</math>: Linear consumption coefficient.

	<math>\zeta</math>: Quadratic “efficiency loss” coefficient.		<math>\large \zeta</math>: Quadratic “efficiency loss” coefficient.

	<math>\tau</math>: Proper time elapsed in the AdS subspace.		<math>\large \tau</math>: Proper time elapsed in the AdS subspace.

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