Many have sought a StarTrek-like warp drive that would allow for the exploration of our vast Universe at speeds much greater than the speed of light that Einstein's Special Theory of Relativity seems to confine us to. For the most part, such warp drives have only been a flight of the imagination to only be found within the confines of science fiction. But in 1994, Miguel Alcubierre proposed a warp drive capable of faster-than-light travel, consistent with the General Theory of Relativity, by creating a bubble around a spacecraft that warps spacetime itself. The Alcubierre warp drive would compress spacetime in front of a spacecraft and expand spacetime behind it, allowing it to “surf” a warped wave of spacetime at faster-than-light speeds while the spacecraft serenely sat inside a bubble of flat spacetime. Instead of accelerating to the speed of light within normal spacetime, the Alcubierre warp drive shifts spacetime around the spacecraft. This allows the spacecraft to arrive at its destination much faster than light would in normal spacetime, all without breaking any physical laws. Below is the original 1994 paper by Miguel Alcubierre. It is surprisingly short and somewhat accessible for most.
The warp drive: hyper-fast travel within general relativity
https://arxiv.org/abs/gr-qc/0009013
Abstract
It is shown how, within the framework of general relativity and without the introduction
of wormholes, it is possible to modify a spacetime in a way that allows a
spaceship to travel with an arbitrarily large speed. By a purely local expansion of
spacetime behind the spaceship and an opposite contraction in front of it, motion
faster than the speed of light as seen by observers outside the disturbed region is
possible. The resulting distortion is reminiscent of the “warp drive” of science fiction.
However, just as it happens with wormholes, exotic matter will be needed in
order to generate a distortion of spacetime like the one discussed here.
Figure 1 – From the above paper showing Miguel Alcubierre's warp drive consisting of a bubble of distorted spacetime rapidly moving much faster than the speed of light.
For more on the Alcubierre warp drive see:
Wikipedia - Alcubierre drive
https://en.wikipedia.org/wiki/Alcubierre_drive
Simulating an Alcubierre Warp Drive in SpaceEngine
In SpaceEngine - the Very Finest Available in 3-D Astronomical Simulation Software, I explained how an Alcubierre warp drive could be simulated in SpaceEngine.
Figure 2 – First, create an interstellar spacecraft in SpaceEngine and switch on its conventional drive.
Figure 3 – Then, turn on the Alcubierre warp drive. Observe now that the spacecraft resides within a bubble of flat spacetime that is surrounded by distorted spacetime. The Alcubierre warp drive bubble now compresses spacetime in front of the spacecraft and expands spacetime behind the spacecraft allowing the spacecraft to surf along much faster than the speed of light.
Figure 4 – From within the Alcubierre warp drive bubble the Universe looks highly deformed because of relativistic lensing.
The Warp Factory Software
Over the past 30 years, several other similar warp drive metrics have been proposed. These other metrics were all developed by solving the equations of Einstein's General Theory of Relativity analytically in a brute-force manner which required some simplifying assumptions in order for the equations to be solved. The developers of the Warp Factory software wish to overcome these analytical simplifications by developing a numerical toolkit for modeling warp drive spacetimes. The Warp Factory developers explain the theory behind Warp Factory in their recent paper below:
Analyzing Warp Drive Spacetimes with Warp Factory
Christopher Helmerich, Jared Fuchs, Alexey Bobrick, Luke Sellers, Brandon Melcher, Gianni Martire
https://arxiv.org/abs/2404.03095
Abstract
The field of warp research has been dominated by analytical methods to investigate
potential solutions. However, these approaches often favor simple metric forms that
facilitate analysis but ultimately limit the range of exploration of novel solutions. So far
the proposed solutions have been unphysical, requiring energy condition violations and
large energy requirements. To overcome the analytical limitations in warp research,
we introduce Warp Factory: a numerical toolkit designed for modeling warp drive
spacetimes. By leveraging numerical analysis, Warp Factory enables the examination of
general warp drive geometries by evaluating the Einstein field equations and computing
energy conditions. Furthermore, this comprehensive toolkit provides the determination
of metric scalars and insightful visualizations in both 2D and 3D, offering a deeper
understanding of metrics and their corresponding stress-energy tensors. The paper
delves into the methodology employed by Warp Factory in evaluating the physicality
of warp drive spacetimes and highlights its application in assessing commonly modeled
warp drive metrics. By leveraging the capabilities of Warp Factory, we aim to further
warp drive research and hopefully bring us closer to realizing physically achievable
warp drives.
The above paper explains that to build physically realizable warp drives they must not violate the following restrictions:
The physicality of warp metrics is established through a set of conditions, known as
energy conditions, which are imposed on the stress-energy tensor components [10].
Among these conditions, the most frequently used and implemented within Warp
Factory are:
(i) The Point-wise Null Energy Condition (NEC) is the null (light-ray) frame’s energy
density observation, at all points in spacetime. For this condition to be physical,
the density should be non-negative for any null observer at every point in spacetime.
(ii) The Point-wise Weak Energy Condition (WEC) is a timelike frame’s energy density
observation, at all points in spacetime. For this condition to be physical, the density
should be non-negative for any timelike observer at every point in spacetime.
(iii) The Point-wise Strong Energy Condition (SEC) is a measure of the experienced
tidal effect from the matter present acting on timelike observers. For this condition
to be physical, tidal effects must be non-negative, meaning that matter should
gravitate together at every point in spacetime.
(iv) The Point-wise Dominant Energy Condition (DEC) is an observation of the matter
flow rate at all points in spacetime. For this condition to be physical, the velocity
must be observed to be less than the speed of light.
So far, none of the warp drives proposed by solving the equations of General Relativity in an analytical manner have been able to do so:
Figure 5 – All the warp drive spacetime metrics calculated by solving analytic equations seem to be non-physical theoretical constructs.
The developers of Warp Factory hope that it will allow users to numerically explore other metrics that might be more in tune with the known physics of our Universe.
Installing the Warp Factory Software
Warp Factory uses MATLAB software to perform numerical calculations on the tensor matrices of General Relativity. Here is its location in GitHub:
GitHub Warp Factory
Developed by Christopher Helmerich and Jared Fuchs
https://github.com/NerdsWithAttitudes/WarpFactory
Here is the documentation on how to install and use Warp Factory:
Warp Factory Documentation
https://applied-physics.gitbook.io/warp-factory
This is how the developers of Warp Factory describe its use:
Workflow
How users work within Warp Factory
The goal of Warp Factory is to construct spacetimes and evaluate them for physicality and then visualize their structure. The design of Warp Factory is for building spacetimes in the following general sequence:
The first thing a user will do is define the spacetime in which they will perform analysis, this step is the creation of the metric tensor. The metric tensor in Warp Factory is a .struct object which requires several fields that are used to make the stress-energy tensor and other analysis products. The most important of these is the value of metric components defined in the 4D grid. Users can also construct using standard metric components or using 3+1 formalism. Additionally, Warp Factory includes a standard library of warp metrics defined in the literature.
See the Metrics examples for details on how users can construct spacetimes in Warp Factory.
After the metric is defined, the stress-energy tensor can be computed. This is a simple call of a function that takes in the metric object and returns the stress-energy tensor. The stress-energy tensor is a .struct object, just like the metric, which has several fields associated, including each of the tensor component values defined in the 4D grid.
See the Energy Tensor examples for details on how users evaluate the field equation in Warp Factory.
With either the metric or stress-energy tensor different analysis products can be generated by Warp Factory. These include finding metric scalars and energy conditions.
See Analysis for examples of how to evaluate the energy conditions, scalars, and momentum flow.
Having created metrics, found the stress-energy tensor, and made any desired analysis products, all of these can be visualized using MATLAB inbuilt functions and several special extensions developed for Warp Factory. These include creating flow lines for understanding momentum flow and helpful plot functions to handle the tensor and 4D array object data used.
Plotting examples can be found throughout the different example modules, showing different ways of plotting metric and stress-energy tensors.
Figure 6 – Animation of the stress-energy tensor. Lighter regions in the cross-section correspond to higher energy densities. The blue lines demonstrate the direction of momentum flow within the warp drive.
Comments are welcome at
scj333@sbcglobal.net
To see all posts on softwarephysics in reverse order go to:
https://softwarephysics.blogspot.com/
Regards,
Steve Johnston
