Anti-de Sitter Drive

"ACROSS SPACE & TIME TOWARDS DISTANT WORLDS"

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This article takes place in the 24 & 26 centuries of Distant Worlds.

OVERVIEW

The Anti-De-Sitter Drive, or more commonly referred to as the AdS Drive, is a revolutionary interstellar propulsion system that enables faster-than-light travel by navigating 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 the 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.

Professor Wells Explains the AdS Drive

The following is an excerpt from an educational session with Professor Wells, answering a question posed by students:

"Thank you, Professor Wells, for taking the time to answer our students' questions. One burning question is: How do ships reach other stars? What exactly is the AdS Drive?"

"Alright, you’ve likely heard the term ‘hyperspace’ in old books or movies for years. But what does it really mean? As per our current understanding, we live in an eleven-dimensional universe. Humans exist in three spatial dimensions, along with the temporal time dimension that we’re affected by. A more accurate term for this concept is ‘subspace.’ Specifically, the AdS Drive exploits a three-dimensional subspace within a four-dimensional Anti-De-Sitter geometry.

"The Anti-De-Sitter space acts as a 'shortcut' between dimensions by warping the distances within. Essentially, several million light-years in our normal space become only a few hundred within the AdS subspace. This phenomenon enables travel that appears to exceed the speed of light, but technically, it does not violate relativity or the laws of physics. Instead of exceeding light speed, we take a shorter path through this warped geometry. Of course, the mathematics behind the drive are classified by the Assembly. I’m not sure I fully understand it myself—it’s quite complex"

Understanding Subspace

"What exactly is subspace? How can we imagine it?"

"Let’s use a simple analogy with a cube. Imagine a cube in three dimensions, with a diagonal vector extending from one corner to the opposite corner at coordinates (1,1,1). Now, imagine projecting the entire cube onto a plane perpendicular to that vector. The result is a two-dimensional hexagonic subspace within the cube. If we apply the same concept to a four-dimensional cube, we get a three-dimensional subspace. This specific subspace has a name: the Rhombic Dodecahedron. Interestingly, you can reconstruct the original cube from this subspace, showing how the dimensions are interconnected."

"This concept forms the foundation of my work on mythical new particles, which I’ve named Fractons. These are five-dimensional particles that I theorize as key to understanding even higher-dimensional interactions. But that’s a topic for another day"

AdS Travel Dynamics

"Do ships drop out of subspace normally when they reach their target?"

"Not exactly. No one cancels the laws of conservation of momentum. The standard protocol of acceleration-deceleration flight still applies. For the first fifty percent of the journey, the ship accelerates, and for the second half, it decelerates. This ensures that when you exit subspace into normal space, you don’t overshoot your target by traveling at near-light speeds. It’s a careful balance to achieve precision without forgetting safety."

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GENERAL ACTION OF ADS DRIVE DYNAMICS

S = \int d\tau \, \mathcal{L}_{\text{AdS}}(x^\mu, \dot{x}^\mu, \phi, g_{\mu\nu}, \epsilon, E)

Where:

\tau\: is the proper time experienced by the ship.

x^\mu: represents the position coordinates in 4D space (including the 3D + 1 extra dimension).

\dot{x}^\mu: is the velocity of the ship in this extended space.

\phi\: is the field that describes the AdS space curvature and connection between the branes.

g_{\mu\nu}\: is the metric tensor that describes the curvature of the AdS space.

\epsilon\: is a coupling constant related to the energy provided by the ship’s reactor.

E\ is the total energy used by the drive.

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LAGRANGIAN FOR ADS DRIVE DYNAMICS

\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}}

Where:

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

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

\frac{\alpha}{2} \dot{x}^\mu \frac{d}{d\tau} \dot{x}_\mu: Captures the acceleration and deceleration processes.

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

\mathcal{L}_{\text{AdS Transition}}\: Accounts for the transition phases (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

\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

Where:

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

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

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

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