Warp drives may swim through spacetime
I recently wrote about how viscoelastic fluids can be used in liquid body armor to stop bullets. While spacetime isn’t a fluid in the…
I recently wrote about how viscoelastic fluids can be used in liquid body armor to stop bullets. While spacetime isn’t a fluid in the traditional sense, it has many of the same properties. In particular, it deforms when a massive body or any energy at all passes through it. The spacetime manifold resists deformation and seeks to return to flatness whenever a massive body passes on. This property is elasticity.
In addition, the more quickly the object deforms spacetime, the more resistance one encounters. This is because spacetime deformations contain energy which itself gravitates and affects other massive bodies, so the deformation of spacetime by a massive body causes additional deformations between the deformed spacetime and the spacetime nearby. These are in the form of high frequency gravitational waves that quickly dissipate. Essentially, like a viscous fluid, spacetime damps disturbances nonlinearly. The shorter wavelength those are the faster they get damped.
This becomes a problem when you want to build a warp drive, which is all about deforming spacetime. A non-viscous spacetime would allow a warp drive to generate a standing wave which would travel faster than light forever, carrying a ship with it at a cost of no additional energy. A non-elastic spacetime would not resist deformation.
Spacetime is not perfectly elastic of course since gravitational waves leave an indelible mark when they pass by, called the memory effect.
Both of these properties take away energy. Currently warp drives need far more energy than is feasible, and many need exotic negative mass energy to even be possible.
One exception is a solution to the Einstein equations provided by Erik Lentz in 2021 which only needs positive energy even while traveling faster than light. How one would actually produce his solution physically has not yet been solved but likely would involve some kind of powerful charged plasma that can generate magnetic and electric fields with energies larger than the equivalent mass of a planet using Einstein’s famous equation, ee equals em cee squared.
Understanding that spacetime is viscoelastic is important because methods of propulsion that don’t work in Newtonian fluids can work in viscoelastic fluids, a type of non-Newtonian fluid.
Sperm cells, for example, must using their whip tails to navigate the viscoelastic fluid of the female reproductive system, requiring very different propulsion mechanisms than they would in, say, water.
Artificial swimmers, meanwhile, can exploit the properties of these fluids to enhance or even create new methods of propulsion. Rigid helices rotated externally, for example, can propel in non-Newtonian fluids but cannot in water. Propulsion can also result from what are called secondary flows in non-Newtonian fluids. These are flows near a boundary such as a river bed or the wall of a cup or bowl. Secondary flows explain the so-called tea leaf paradox where tea leaves tend to gather at the center of the bottom of a tea cup instead of the edges when stirred.
A good example of a method of propulsion that works in a non-Newtonian, viscoelastic fluid but not in a Newtonian fluid is the spinning of a snowman shaped object around its axis. Normally, this spinning would generate no motion at all but in a non-Newtonian fluid the differences in viscosity generated by the different rates of velocity of the smaller vs. the larger ball creates a net force that propels it through the fluid.
This analogy can be made more concrete by looking at studies that have been done on fluid analogs to warped spacetime. In these studies, a rigid object is places in a fluid flow. The object “warps” the path objects and waves have to take from point A to point B making it longer or shorter. Units of sound energy called phonons are then propagated through the fluid as analogs to light. These “quasiparticles” help us to establish the causal structure in the warped spacetime analog, since that is defined, in real spacetime, by the speed of light particles.
The reason this is important is because when you warp spacetime you are effectively changing both the speed of light and the causal structure of that spacetime. Locally, the speed of light is always the same but light may take longer to go from A to B depending on which path it takes.
The sound particle propagation speed through different parts of the fluid tells us whether we are traveling at supersonic speeds in analogy to the superluminal speeds in warped spacetime in one part of the fluid when compared to another. Locally, of course, our sound particles cannot travel supersonically because they are sound, but globally when we compare one part of the fluid to another they can. This is what is meant by superluminal warp speed. Warp drives never goes faster than light in the part of spacetime where they are. They only go faster when compared to some other part of spacetime.
One of the problems, however, with these analogs is that they use non-viscous fluids, so they essentially ignore the viscous and elastic properties of spacetime.
What does this mean for warp drives?
The research on this question hasn’t really been done yet but it seems as if the way we propagate through spacetime using warp drives will be difference if we take the viscoelastic properties of spacetime into account than if we just assume spacetime is a perfect fluid. If we take the analogy of the snowman shaped spinning ball which moves in a viscoelastic fluid but not in an ordinary fluid, there may be ways to exploit the way spacetime reacts differently to asymmetric magnetic fields, for example, to enable warping of spacetime.
Gamble, Ronald, and K. Flurchick. “Viscoelastic Representation of Gravitational Strain Fields and the Massive Longitudinal Wave Equation.” APS April Meeting Abstracts. Vol. 2018. 2018.
Gamble, Ronald. On Gravitational Radiation: A Nonlinear Wave Theory in a Viscoelastic Kerr-Lambda Spacetime. Diss. North Carolina Agricultural and Technical State University, 2017.
Lentz, Erik W. “Breaking the warp barrier: hyper-fast solitons in Einstein–Maxwell-plasma theory.” Classical and Quantum Gravity 38.7 (2021): 075015.
Puente-Velázquez, J., et al. “Viscoelastic propulsion of a rotating dumbbell.” Microfluidics and Nanofluidics 23.9 (2019): 1–7.
Lobo, Francisco SN, and Matt Visser. “Fundamental limitations on ‘warp drive’spacetimes.” Classical and Quantum Gravity 21.24 (2004): 5871.
Fischer, Uwe R., and Matt Visser. “Warped space-time for phonons moving in a perfect nonrelativistic fluid.” EPL (Europhysics Letters) 62.1 (2003): 1.
Baggioli, Matteo, Sebastian Grieninger, and Hesam Soltanpanahi. “Nonlinear oscillatory shear tests in viscoelastic holography.” Physical Review Letters 124.8 (2020): 081601.