Editing Nexus World (section)

== Spacetime Dynamics in Nexus Worlds ==

=== Space-Time Fabric and Nexus Points ===
Nexus Worlds are regions where the fabric of [[space-time]] is significantly more complex and malleable than in ordinary universes. This is due to the concentration of cosmic energies and the deep links binding these worlds across the multiverse.

'''''Curvature of Space-Time:'''''
The presence of multiple Nexus Worlds in proximity causes a unique curvature in space-time, described mathematically by the modified [[Einstein Field Equations]]:
<math>G_{\mu\nu} + \Lambda g_{\mu\nu} = 8 \pi G T_{\mu\nu} + \beta N_{\mu\nu}</math>
Where:
* <math>G_{\mu\nu}</math> represents the curvature of space-time,
* <math>\Lambda g_{\mu\nu}</math> is the cosmological constant,
* <math>T_{\mu\nu}</math> denotes the energy-momentum tensor,
* <math>\beta N_{\mu\nu}</math> introduces a new term specific to Nexus Worlds, where <math>\beta</math> represents the influence of Nexus World connections on space-time curvature.

'''''Nexus Points as Gravitational Wells:'''''
Nexus Points can be understood as gravitational wells within the fabric of space-time, where the gravitational pull is not just a function of mass but also of the interdimensional energy flow. The mathematical representation of this gravitational anomaly can be expressed as:
<math>\Phi(r) = -\frac{GM}{r} \left(1 + \frac{\gamma}{r^2} \right)</math>
Where <math>\Phi(r)</math> is the potential at a distance <math>r</math> from the Nexus Point, <math>G</math> is the gravitational constant, <math>M</math> is the mass, and <math>\gamma</math> is a parameter related to the interdimensional energy influence.

=== Temporal Mechanics and Multiversal Time ===
Time within Nexus Worlds operates differently than in ordinary realms, leading to phenomena such as time dilation, time loops, and cross-temporal interactions.

'''''Time Dilation and Nexus Energy:'''''
The flow of time can be heavily influenced by the presence of Nexus energy. This can be modeled using the [[general relativity]] framework, where time dilation is described by:
<math>\Delta t = \frac{\Delta t_0}{\sqrt{1 - \frac{2\Phi(r)}{c^2}}}</math>
Here, <math>\Delta t_0</math> is the proper time, <math>\Phi(r)</math> is the gravitational potential influenced by Nexus energy, and <math>c</math> is the speed of light.

'''''Multiversal Time Continuum:'''''
Nexus Worlds are theorized to be aligned on a [[Multiversal Time Continuum]], where different realities can have asynchronous time flows but maintain a relative synchronization at Nexus Points. The time evolution of such a system can be represented by a modified [[Schrödinger equation]]:
<math>i\hbar \frac{\partial \Psi(t)}{\partial t} = \left[ H_0 + \alpha H_{\text{Nexus}} \right] \Psi(t)</math>
Where:
* <math>\Psi(t)</math> is the time-dependent wave function of the multiversal state,
* <math>H_0</math> is the Hamiltonian of the isolated universe,
* <math>H_{\text{Nexus}}</math> represents the Nexus interaction term, and <math>\alpha</math> is a coupling constant specific to the Nexus effect.