Physical Warp Drives: Time Travel and Quantum Solutions PDF

Introducing Physical Warp Drives

Alexey Bobrick, Gianni Martire

Advanced Propulsion Laboratory at Applied Physics, 477 Madison Avenue, New

York, 10022, U.S.

E-mail: [email protected]

September 2020

Abstract. The Alcubierre warp drive is an exotic solution in general relativity.

It allows for superluminal travel at the cost of enormous amounts of matter

with negative mass density. For this reason, the Alcubierre warp drive has been

widely considered unphysical. In this study, we develop a model of a general

warp drive spacetime in classical relativity that encloses all existing warp drive

definitions and allows for new metrics without the most serious issues present

in the Alcubierre solution. We present the first general model for subluminal

positive-energy, spherically symmetric warp drives; construct superluminal warp-

drive solutions which satisfy quantum inequalities; provide optimizations for the

Alcubierre metric that decrease the negative energy requirements by two orders of

magnitude; and introduce a warp drive spacetime in which space capacity and the

rate of time can be chosen in a controlled manner. Conceptually, we demonstrate

that any warp drive, including the Alcubierre drive, is a shell of regular or exotic

material moving inertially with a certain velocity. Therefore, any warp drive

requires propulsion. We show that a class of subluminal, spherically symmetric

warp drive spacetimes, at least in principle, can be constructed based on the

physical principles known to humanity today.

Submitted to: Class. Quantum Grav.

1. Introduction

The classical-relativistic Alcubierre drive solution allows timelike observers to travel

superluminally, although at the expense of using material with negative rest-mass

energy (Alcubierre 1994); for recent reviews see also (Lobo 2007, Alcubierre &

Lobo 2017). This solution is given by the following asymptotically-flat metric:

= −c

+ (dx − f(r

dt)

+ dy

+ dz

, (1)

where r

(x − v

+ y

+ z

. The metric describes a spherical warp bubble

(a region deviating from the flat metric) moving along the x-axis with an arbitrary

velocity v

, which may be larger or smaller than the speed of light c.

The shape function f(r

), present in the metric, defines the size and profile of the

warp bubble. For large distances r

from the bubble, f(r

) = 0 and the spacetime is

flat. For small distances, r

≈ 0, the shape function f(r

) = 1, and the metric describes

the flat internal region of the bubble. In a coordinate system with x → x

= x−v

t, this

internal region is described explicitly by the Minkowski flat metric. The intermediate

arXiv:2102.06824v2 [gr-qc] 17 Feb 2021

Introducing Physical Warp Drives 2

region, for which f (r

) & 0, corresponds to the spherical boundary of the warp. In

the original study, (Alcubierre 1994) chose function f(r

), somewhat arbitrarily, as:

Alc

) =

tanh(σ(r

+ R)) − tanh(σ(r

− R))

2 tanh(σR)

, (2)

where parameters R and σ

−1

define the radius and the thickness of the transition from

the internal to the external region, correspondingly.

In the case of superluminal motion, the metric possesses a black hole-like event

horizon behind the bubble and a white hole-like event horizon in front of it (Finazzi

et al. 2009). These event horizons arise because timelike observers cannot exit the

superluminal ship in the direction ahead of it, and cannot enter it from behind. In

both cases, the timelike observers would have to move superluminally when outside

of the ship.

The energy density for the Alcubierre drive, as measured by Eulerian observers

= (1, 0, 0, 0)), is given by:

= −

8π





, (3)

where ρ

≡ y

+ z

is the cylindrical coordinate.

Despite its interesting properties which allow timelike observers to travel at

arbitrary velocities, the Alcubierre drive solution possesses several drawbacks. As

noted earlier, it requires negative energy densities, Equation (3), and thus violates the

weak energy condition. Although negative energy densities are a general property

of any superluminal drive (Olum 1998, Visser et al. 2000), the energy density is

also negative at subluminal speeds for the Alcubierre drive, even in the weak-field

approximation (Lobo & Visser 2004). Additionally, superluminal motion allows for

closed timelike loops, e.g. leading to grandfather paradox, and violates the null energy

condition and causality, e.g. (Everett 1996), although the latter may be recovered at

the expense of Lorentz invariance (Liberati et al. 2002). When moving superluminally,

the drive has an additional problem. It leads to quantum instabilities related to pair

production near the horizon behind the warp as well as accumulation of particles at

the horizon in the front part of the warp (Finazzi et al. 2009).

The Alcubierre drive is also problematic at sub-relativistic speeds. Firstly, it

requires unphysically large amounts of (negative) energy. For instance, it would require

an amount of negative energy comparable to the mass of the Sun to produce relativistic

bubbles of ≈ meter sizes (Alcubierre 1994). Furthermore, such high negative energy

densities do not appear even theoretically feasible. There are no known materials

which would allow for gathering large amounts of negative energy in a controlled

way. While zero-point vacuum fluctuations may produce negative energies in curved

spacetimes, for Alcubierre drives this situation is only possible if the walls of the

bubble had thicknesses comparable to Planck scales. Such thin walls, however, require

extreme amounts of energy – comparable to the rest-mass energy of the Universe –

as may be seen from Equation (3). Therefore, there is no physical way to create an

Alcubierre drive (Pfenning & Ford 1997, Ford & Roman 1997).

Finally, there is no proposed way of creating an Alcubierre drive, even if negative

energy were available. In the original study, (Alcubierre 1994) suggested that the

velocity may be time-dependent, v

= v

(t). Indeed, Equation (3) retains its form even

for time-dependent velocities. And, since v

= 0 corresponds to flat spacetime, it was

assumed that the Alcubierre drive might be generated through acceleration. However,

Introducing Physical Warp Drives 3

the metric in Equation (1) with time-variable v

= v

(t) corresponds to a time-variable

stress-energy tensor which does not satisfy continuity equations. Alternatively, such

solutions may be said to require an implicit dynamical field to effectively provide

propulsion for the object, e.g. (Bassett et al. 2000). Generally, there are no self-

consistent warp drive solutions proposed in the literature which can self-accelerate at

all from zero velocities, not to mention gain superluminal speeds.

Despite the rather extensive work on the properties of the Alcubierre drive

solution, it remains unclear which of the above issues are features of the Alcubierre

solution specifically or more fundamental properties of warp drives as such. New warp

drive solutions have been introduced only in very few studies. (Van Den Broeck 1999)

reduced the energy requirements of the Alcubierre drive to about the mass of the

Sun while satisfying the vacuum energy inequalities. The reduction was realized

by decreasing the externally measured size of the warp bubble down to 10

−15

while keeping the internal volume constant. This solution satisfies the weak energy

conditions, although it requires that classical gravity remains applicable down to such

small scales, at which it was never tested. However, as we show in Appendix A through

a coordinate transformation, this solution is equivalent to the Alcubierre solution.

(Nat´ario 2002) constructed a warp drive solution without space contraction or

expansion, contrary to the earlier assumption that it facilitated the movement of

warp drives. (Nat´ario 2006) constructed a new subluminal warp drive solution in the

weak-field regime, which required negative energies. (Loup et al. 2001) had previously

introduced a modified version of the Alcubierre drive intended to alter the rate of

time for the observers inside the bubble. However, their modification reduces to the

original Alcubierre metric, as we also show in Appendix A. Finally, (Lentz 2020)

has recently proposed a warp drive metric claiming to have purely positive energy

everywhere in both subluminal and superluminal regimes, although without providing

means to reproduce the study.

The works above, to our knowledge, summarize all the modifications of the

Alcubierre drive available in the literature. Superluminal travel had also been studied

by (Krasnikov 1998) and (Everett & Roman 1997). In these studies, the authors

introduced Krasnikov tubes. Krasnikov tubes are ‘spacetime tunnels’ which allow for

superluminal travel without violating causality, but only for round trips and with

much larger energy requirements than the Alcubierre drive. Superluminal travel has

also been discussed in the context of wormholes, e.g. (Garattini & Lobo 2007), and

time-machine metrics, e.g. (Fermi & Pizzocchero 2018), in all cases requiring negative

energies. Finally, modified gravity theories may provide some desirable properties

for the Alcubierre drive. For instance, conformal gravity allows for construction of

Alcubierre solutions with positive energy only (Varieschi & Burstein 2013), while

extra-dimensional theories of gravity may reduce the energy requirements of the drive

(White 2013).

In this study, we show that the properties of the Alcubierre metric – in particular,

its negative energy density and the accompanying immense energy requirements – are

not a necessary feature of warp drive spacetimes. In Section 2, we discuss that any

general warp drive, including the Alcubierre metric, may be thought of as a shell of

positive- or negative-energy density material which modifies the state of spacetime in

the flat vacuum region inside it. In Section 3, we introduce, for the first time, the most

general spherically symmetric warp drives. We show that the reason for the negative

energy requirements of the Alcubierre metric and all the warp drives introduced in

the literature is, likely, the truncation of the gravitational field outside of the metric,

Overview

Physical Warp Drives: Time Travel and Quantum Solutions

Physical warp drives explore the concept of time travel through closed timelike curves, which are legitimate solutions to Einstein's equations. This research highlights how quantum mechanics can resolve associated paradoxes while maintaining consistent physics. The study includes a photonic experiment simulating a qubit interacting with an earlier version of itself, demonstrating practical applications of these theories. Ideal for physicists and students interested in advanced concepts of relativity and quantum mechanics, this work delves into the implications of warp drives on our understanding of time and space. Key Points Explores closed timelike curves as solutions to Einstein's equations Demonstrates quantum resolution of time travel paradoxes Includes a photonic experiment sim…

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FAQs

what is the concept of physical warp drives

The concept of physical warp drives refers to theoretical constructs in physics that allow for faster-than-light travel by manipulating spacetime.

These drives are based on solutions to Einstein's equations of general relativity.
They often involve the use of exotic matter with negative energy density.
The most well-known model is the Alcubierre drive, which creates a 'warp bubble' around a spacecraft.

how do physical warp drives work

Physical warp drives work by contracting space in front of the spacecraft and expanding it behind, effectively allowing for superluminal travel.

This manipulation of spacetime enables the ship to move faster than light without violating the laws of physics.
Warp drives rely on specific metrics that define the geometry of spacetime.
Recent studies have proposed models that reduce the negative energy requirements significantly.

what are the findings in physical warp drives research

Research on physical warp drives has revealed several important findings regarding their feasibility and underlying physics.

New models suggest warp drives can be constructed using positive energy densities.
Optimizations have been proposed that decrease the negative energy requirements by two orders of magnitude.
Some warp drive solutions allow for controlled manipulation of time and space within the drive.

can physical warp drives enable time travel

Physical warp drives theoretically enable time travel by creating conditions that allow for closed timelike curves.

These conditions arise from the manipulation of spacetime geometry.
However, practical implementation remains speculative and fraught with challenges.
Research continues to explore the implications of warp drives on causality and time travel.

what is the Alcubierre warp drive

The Alcubierre warp drive is a theoretical model that allows for superluminal travel by creating a 'warp bubble' in spacetime.

It requires negative energy density to function, which has not been physically realized.
The drive moves the bubble through spacetime while the contents inside remain stationary relative to their local environment.
Recent research has aimed to optimize this model to reduce its energy requirements.

what are the challenges of physical warp drives

There are several significant challenges associated with physical warp drives that hinder their practical application.

The requirement for negative energy density is a major barrier, as no known materials can provide this.
Quantum instabilities and causality violations pose additional theoretical concerns.
Finally, the immense energy requirements for even small warp bubbles make practical implementation currently unfeasible.

how do physical warp drives relate to quantum physics

Physical warp drives are closely related to quantum physics, particularly in their implications for energy conditions.

Quantum inequalities suggest limits on the distribution of energy, which warp drives must navigate.
Some recent models propose that warp drives could be constructed while satisfying these quantum constraints.
This intersection of quantum mechanics and general relativity is a key area of ongoing research.

what is the significance of negative energy in warp drives

Negative energy plays a crucial role in the theoretical framework of physical warp drives.

It is essential for creating the spacetime distortions necessary for superluminal travel.
Negative energy densities can lead to paradoxes and challenges in maintaining stability.
Research aims to find ways to minimize or eliminate the need for negative energy in warp drive models.

what are new models of physical warp drives

New models of physical warp drives have emerged that explore alternative metrics and energy requirements.

These models aim to construct warp drives using only positive energy densities.
They also propose methods to optimize the shape and energy distribution of the warp bubble.
Such advancements could potentially make warp drives more feasible and less reliant on exotic matter.

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