Warp Drives - Revision history

Lwcamp: /* Challenges and possible resolutions */

2026-08-11T16:48:21Z

Challenges and possible resolutions

← Older revision		Revision as of 08:48, 11 August 2026
Line 83:		Line 83:
	<li>In the same work, Pfenning and Ford also found that for a bubble a hundred meters in radius, a warp speed of around the speed of light, and the required thickness of about 100 Planck lengths the energy in the bubble shell would be <i>E</i> ≈ -10<sup>63</sup> kg <i>c</i><sup>2</sup>. The magnitude of this latter value is ten orders of magnitude larger than the energy of the entire visible universe. They do note, however, that if quantum energy inequalities can be ignored then a warp drive with a hundred meters radius but a shell thickness of one meter would "only" have an energy magnitude of about a quarter solar mass.		<li>In the same work, Pfenning and Ford also found that for a bubble a hundred meters in radius, a warp speed of around the speed of light, and the required thickness of about 100 Planck lengths the energy in the bubble shell would be <i>E</i> ≈ -10<sup>63</sup> kg <i>c</i><sup>2</sup>. The magnitude of this latter value is ten orders of magnitude larger than the energy of the entire visible universe. They do note, however, that if quantum energy inequalities can be ignored then a warp drive with a hundred meters radius but a shell thickness of one meter would "only" have an energy magnitude of about a quarter solar mass.
	<li>As with any method of faster than light travel, the warp drive could be used to make a time machine.		<li>As with any method of faster than light travel, the warp drive could be used to make a time machine.
	<li>Perhaps most seriously, if the warp drive is going faster than light speed, the ~~negative~~ energy ~~regions~~ on the outside of the shell won't be in the warp parts of the bubble. They will have to be moving through space at faster than light speed if the bubble is to maintain its integrity, which is the very problem that the warp drive was designed to avoid. The outside of the warp bubble shell that maintains the warp bubble would fall away and the warp bubble would quickly erode to sub-luminal speeds.<ref name="Van Den Broeck 2000">Chris Van Den Broeck, "On the (im)possibility of warp bubbles", arXiv:gr-qc/9906050 https://doi.org/10.48550/arXiv.gr-qc/9906050</ref>		<li>Perhaps most seriously, if the warp drive is going faster than light speed, the matter and energy that create the warp bubble that are on the outside of the shell won't be in the warp parts of the bubble. They will have to be moving through space at faster than light speed if the bubble is to maintain its integrity, which is the very problem that the warp drive was designed to avoid. The outside of the warp bubble shell that maintains the warp bubble would fall away and the warp bubble would quickly erode to sub-luminal speeds.<ref name="Van Den Broeck 2000">Chris Van Den Broeck, "On the (im)possibility of warp bubbles", arXiv:gr-qc/9906050 https://doi.org/10.48550/arXiv.gr-qc/9906050</ref>
	<li>A more general problem that includes the previous one is that the geometry of the warp drive determines the distribution of energy, momentum, and stress (pressure, shear, and tension) by Einstein's field equation, which states that the stress energy tensor is directly proportional to a reduced order curvature tensor of space-time. However, the stress-energy tensor must also obey the continuity equation – basically, for the energy to change in a given volume of space that energy must come in or go out of the boundary of that volume and similarly for the momentum. So a warp drive can have the warp condition for one moment in time. But after that, the stress-energy that maintains the warp will start to move according to the forces on it and according to the natural paths that it takes through the warped space-time. There is no guarantee that the configuration of the stress-energy at later times will be sufficient to maintain the warp.		<li>A more general problem that includes the previous one is that the geometry of the warp drive determines the distribution of energy, momentum, and stress (pressure, shear, and tension) by Einstein's field equation, which states that the stress energy tensor is directly proportional to a reduced order curvature tensor of space-time. However, the stress-energy tensor must also obey the continuity equation – basically, for the energy to change in a given volume of space that energy must come in or go out of the boundary of that volume and similarly for the momentum. So a warp drive can have the warp condition for one moment in time. But after that, the stress-energy that maintains the warp will start to move according to the forces on it and according to the natural paths that it takes through the warped space-time. There is no guarantee that the configuration of the stress-energy at later times will be sufficient to maintain the warp.
	<blockquote>		<blockquote>

Lwcamp: /* So what is going on? */

2026-08-11T16:43:53Z

So what is going on?

← Older revision		Revision as of 08:43, 11 August 2026
Line 58:		Line 58:
	</table>		</table>

	In most formulations, warp drives are restricted to spacetime geometries with a constant lapse function - all observers go forward by the same time coordinate after experiencing the same amount of proper time. Thus, ~~all~~ warp drives have no time dilation.		In most formulations, warp drives are restricted to spacetime geometries with a constant lapse function - all observers go forward by the same time coordinate after experiencing the same amount of proper time. Thus, these warp drives have no time dilation.
	Far from the warp bubble, the shift vector vanishes – each spatial coordinate is mapped to the same spatial coordinate after any amount of proper time so long as the warp drive is not near. But the inside of the warp bubble is an extended region where the shift vector field is non-zero and constant. In this bubble, all spatial coordinates are mapped to a coordinate that shifts linearly in time with the proper time of the observer. Astute readers will see that this linear change in position with time is very similar to a velocity. This region of constant shift vector then moves with the shift vector velocity to keep stuff originally in the bubble so that it stays in the bubble. In between the inside of the bubble and the far away regions with zero shift vector, the shift vector field falls away to match one region to the other.		Far from the warp bubble, the shift vector vanishes – each spatial coordinate is mapped to the same spatial coordinate after any amount of proper time so long as the warp drive is not near. But the inside of the warp bubble is an extended region where the shift vector field is non-zero and constant. In this bubble, all spatial coordinates are mapped to a coordinate that shifts linearly in time with the proper time of the observer. Astute readers will see that this linear change in position with time is very similar to a velocity. This region of constant shift vector then moves with the shift vector velocity to keep stuff originally in the bubble so that it stays in the bubble. In between the inside of the bubble and the far away regions with zero shift vector, the shift vector field falls away to match one region to the other.

Lwcamp: /* So what is going on? */

2026-08-11T16:43:39Z

So what is going on?

← Older revision		Revision as of 08:43, 11 August 2026
Line 58:		Line 58:
	</table>		</table>

	In most formulations, warp drives are ~~generally~~ restricted to spacetime geometries with a constant lapse function - all observers go forward by the same time coordinate after experiencing the same amount of proper time. Thus, all warp drives have no time dilation.		In most formulations, warp drives are restricted to spacetime geometries with a constant lapse function - all observers go forward by the same time coordinate after experiencing the same amount of proper time. Thus, all warp drives have no time dilation.
	Far from the warp bubble, the shift vector vanishes – each spatial coordinate is mapped to the same spatial coordinate after any amount of proper time so long as the warp drive is not near. But the inside of the warp bubble is an extended region where the shift vector field is non-zero and constant. In this bubble, all spatial coordinates are mapped to a coordinate that shifts linearly in time with the proper time of the observer. Astute readers will see that this linear change in position with time is very similar to a velocity. This region of constant shift vector then moves with the shift vector velocity to keep stuff originally in the bubble so that it stays in the bubble. In between the inside of the bubble and the far away regions with zero shift vector, the shift vector field falls away to match one region to the other.		Far from the warp bubble, the shift vector vanishes – each spatial coordinate is mapped to the same spatial coordinate after any amount of proper time so long as the warp drive is not near. But the inside of the warp bubble is an extended region where the shift vector field is non-zero and constant. In this bubble, all spatial coordinates are mapped to a coordinate that shifts linearly in time with the proper time of the observer. Astute readers will see that this linear change in position with time is very similar to a velocity. This region of constant shift vector then moves with the shift vector velocity to keep stuff originally in the bubble so that it stays in the bubble. In between the inside of the bubble and the far away regions with zero shift vector, the shift vector field falls away to match one region to the other.

Lwcamp: /* So what is going on? */

2026-08-11T16:43:13Z

So what is going on?

← Older revision		Revision as of 08:43, 11 August 2026
Line 58:		Line 58:
	</table>		</table>

	~~Warp~~ drives are generally restricted to spacetime geometries with a constant lapse function - all observers go forward by the same time coordinate after experiencing the same amount of proper time. Thus, all warp drives have no time dilation.		In most formulations, warp drives are generally restricted to spacetime geometries with a constant lapse function - all observers go forward by the same time coordinate after experiencing the same amount of proper time. Thus, all warp drives have no time dilation.
	Far from the warp bubble, the shift vector vanishes – each spatial coordinate is mapped to the same spatial coordinate after any amount of proper time so long as the warp drive is not near. But the inside of the warp bubble is an extended region where the shift vector field is non-zero and constant. In this bubble, all spatial coordinates are mapped to a coordinate that shifts linearly in time with the proper time of the observer. Astute readers will see that this linear change in position with time is very similar to a velocity. This region of constant shift vector then moves with the shift vector velocity to keep stuff originally in the bubble so that it stays in the bubble. In between the inside of the bubble and the far away regions with zero shift vector, the shift vector field falls away to match one region to the other.		Far from the warp bubble, the shift vector vanishes – each spatial coordinate is mapped to the same spatial coordinate after any amount of proper time so long as the warp drive is not near. But the inside of the warp bubble is an extended region where the shift vector field is non-zero and constant. In this bubble, all spatial coordinates are mapped to a coordinate that shifts linearly in time with the proper time of the observer. Astute readers will see that this linear change in position with time is very similar to a velocity. This region of constant shift vector then moves with the shift vector velocity to keep stuff originally in the bubble so that it stays in the bubble. In between the inside of the bubble and the far away regions with zero shift vector, the shift vector field falls away to match one region to the other.

Lwcamp: /* So what is going on? */

2026-08-11T16:39:41Z

So what is going on?

← Older revision		Revision as of 08:39, 11 August 2026
Line 45:		Line 45:
	Unfortunately, by convention, both the symbols <i>G</i> and <i>R</i> get used for a lot of different things. Here, symbols in bold are second rank tensors – constructs of arrays of 4×4 numbers where 4 is necessary because that is the number of dimensions of spacetime. Conventionally, these numbers are indexed by a value going from 0 to 3, with 0 being the part corresponding to the coordinate of time and 1 to 3 being the spatial Cartesian coordinates that you might know as <i>x</i>, <i>y</i>, and <i>z</i>.		Unfortunately, by convention, both the symbols <i>G</i> and <i>R</i> get used for a lot of different things. Here, symbols in bold are second rank tensors – constructs of arrays of 4×4 numbers where 4 is necessary because that is the number of dimensions of spacetime. Conventionally, these numbers are indexed by a value going from 0 to 3, with 0 being the part corresponding to the coordinate of time and 1 to 3 being the spatial Cartesian coordinates that you might know as <i>x</i>, <i>y</i>, and <i>z</i>.

	<i><b>T</b></i> is the stress-energy tensor: the (0,0) component represents the energy density at a given point; the (0,<i~~>i</i>~~) and (~~<i>i</~~i>, 0) components (with ~~<i>i</~~i> going from 1 to 3) represent the momentum density; and the (i,j) components represent the stresses present, such as pressure or tension or shear.		<i><b>T</b></i> is the stress-energy tensor: the (0,0) component represents the energy density at a given point; the (0,i) and (i, 0) components (with i going from 1 to 3) represent the momentum density; and the (i,j) components represent the stresses present, such as pressure or tension or shear.

	The other term, <i><b>R</b> - R <b>g</b>/2</i>, involves a partial description of the curvature. A full description of the curvature requires a construct of 4×4×4×4 components; too much for the stress energy tensor to fully constrain. Which is okay, because this allows curvature to exist away from where matter is, allowing gravity to have long range effects across empty space as well as for phenomena like gravitational waves. But it is enough that a given distribution of matter <i><b>T</b></i> gives enough constraints (along with specifying how the geometry behaves far away) that you can generally figure out what the actual gravity is.		The other term, <i><b>R</b> - R <b>g</b>/2</i>, involves a partial description of the curvature. A full description of the curvature requires a construct of 4×4×4×4 components; too much for the stress energy tensor to fully constrain. Which is okay, because this allows curvature to exist away from where matter is, allowing gravity to have long range effects across empty space as well as for phenomena like gravitational waves. But it is enough that a given distribution of matter <i><b>T</b></i> gives enough constraints (along with specifying how the geometry behaves far away) that you can generally figure out what the actual gravity is.

Lwcamp: /* So what is going on? */

2026-08-11T16:38:43Z

So what is going on?

← Older revision		Revision as of 08:38, 11 August 2026
Line 43:		Line 43:
	</table>		</table>
	</div>		</div>
	Unfortunately, by convention, both the symbols <i>G</i> and <i>R</i> get used for a lot of different things. Here, symbols in bold are second rank tensors – constructs of arrays of 4×4 numbers where 4 is necessary because that is the number of dimensions of spacetime. Conventionally, these numbers are indexed by a value going from 0 to 3, with 0 being the part corresponding to the coordinate of time and 1 to 3 being the Cartesian coordinates that you might know as <i>x</i>, <i>y</i>, and <i>z</i>.		Unfortunately, by convention, both the symbols <i>G</i> and <i>R</i> get used for a lot of different things. Here, symbols in bold are second rank tensors – constructs of arrays of 4×4 numbers where 4 is necessary because that is the number of dimensions of spacetime. Conventionally, these numbers are indexed by a value going from 0 to 3, with 0 being the part corresponding to the coordinate of time and 1 to 3 being the spatial Cartesian coordinates that you might know as <i>x</i>, <i>y</i>, and <i>z</i>.

	<i><b>T</b></i> is the stress-energy tensor: the (0,0) component represents the energy density at a given point; the (0,<i>i</i>) and (<i>i</i>, 0) components (with <i>i</i> going from 1 to 3) represent the momentum density; and the (i,j) components represent the stresses present, such as pressure or tension or shear.		<i><b>T</b></i> is the stress-energy tensor: the (0,0) component represents the energy density at a given point; the (0,<i>i</i>) and (<i>i</i>, 0) components (with <i>i</i> going from 1 to 3) represent the momentum density; and the (i,j) components represent the stresses present, such as pressure or tension or shear.

Lwcamp: /* The Alcubierre warp drive */

2026-08-11T16:37:03Z

The Alcubierre warp drive

← Older revision		Revision as of 08:37, 11 August 2026
Line 7:		Line 7:
	== The Alcubierre warp drive ==		== The Alcubierre warp drive ==

	The first warp drive that actually used relativity was proposed by Miguel Alcubierre<ref>M. Alcubierre, "The warp drive: hyper-fast travel within general relativity." Classical and Quantum Gravity. 11 (5): L73–L77 (1994). [https://arxiv.org/abs/gr-qc/0009013 arXiv:gr-qc/0009013]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1994CQGra..11L..73A 1994CQGra..11L..73A]. doi:[https://doi.org/10.1088%2F0264-9381%2F11%2F5%2F001 10.1088/0264-9381/11/5/001]. S2CID [https://api.semanticscholar.org/CorpusID:4797900 4797900].</ref>. In this geometry, a sphere of space-time moves at an arbitrary speed (potentially but not necessarily a speed much faster than light). Objects within the sphere are moved along with the sphere; an object at rest within the sphere would be moved along with the sphere indefinitely. Space is expanding at the rear boundary and contracting at the front boundary in order to keep the sphere moving. In order to ~~satisfy~~ the ~~Einstein field equations,~~ the boundary of the sphere ~~must~~ have a negative energy density. The challenges of space-time geometries with negative energy densities are described in our page on [[Wormholes#Exotic_energy_conditions\|wormholes]], for our purposes it is enough to note that negative energy densities can pose problems if not handled carefully, there may be limits on how much negative energy you can have without nearby positive energy density, and it may not be possible to get enough negative energy to support a warp drive; although none of this is ruled out by physics – yet!		The first warp drive that actually used relativity was proposed by Miguel Alcubierre<ref>M. Alcubierre, "The warp drive: hyper-fast travel within general relativity." Classical and Quantum Gravity. 11 (5): L73–L77 (1994). [https://arxiv.org/abs/gr-qc/0009013 arXiv:gr-qc/0009013]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1994CQGra..11L..73A 1994CQGra..11L..73A]. doi:[https://doi.org/10.1088%2F0264-9381%2F11%2F5%2F001 10.1088/0264-9381/11/5/001]. S2CID [https://api.semanticscholar.org/CorpusID:4797900 4797900].</ref>. In this geometry, a sphere of space-time moves at an arbitrary speed (potentially but not necessarily a speed much faster than light). Objects within the sphere are moved along with the sphere; an object at rest within the sphere would be moved along with the sphere indefinitely. Space is expanding at the rear boundary and contracting at the front boundary in order to keep the sphere moving. Spacetime is curved by matter, energy, and their flows; in order to generate the necessary geometry you need the matter-energy at the boundary of the sphere to have a negative energy density. The challenges of space-time geometries with negative energy densities are described in our page on [[Wormholes#Exotic_energy_conditions\|wormholes]], for our purposes it is enough to note that negative energy densities can pose problems if not handled carefully, there may be limits on how much negative energy you can have without nearby positive energy density, and it may not be possible to get enough negative energy to support a warp drive; although none of this is ruled out by physics – yet!

	<table align=center>		<table align=center>

Lwcamp: /* The Alcubierre warp drive */

2026-08-11T16:35:15Z

The Alcubierre warp drive

← Older revision		Revision as of 08:35, 11 August 2026
Line 7:		Line 7:
	== The Alcubierre warp drive ==		== The Alcubierre warp drive ==

	The first warp drive ~~geometry~~ that ~~satisfied the Einstein field equations of~~ relativity was proposed by Miguel Alcubierre<ref>M. Alcubierre, "The warp drive: hyper-fast travel within general relativity." Classical and Quantum Gravity. 11 (5): L73–L77 (1994). [https://arxiv.org/abs/gr-qc/0009013 arXiv:gr-qc/0009013]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1994CQGra..11L..73A 1994CQGra..11L..73A]. doi:[https://doi.org/10.1088%2F0264-9381%2F11%2F5%2F001 10.1088/0264-9381/11/5/001]. S2CID [https://api.semanticscholar.org/CorpusID:4797900 4797900].</ref>. In this geometry, a sphere of space-time moves at an arbitrary speed (potentially but not necessarily a speed much faster than light). Objects within the sphere are moved along with the sphere; an object at rest within the sphere would be moved along with the sphere indefinitely. Space is expanding at the rear boundary and contracting at the front boundary in order to keep the sphere moving. In order to satisfy the Einstein field equations, the boundary of the sphere must have a negative energy density. The challenges of space-time geometries with negative energy densities are described in our page on [[Wormholes#Exotic_energy_conditions\|wormholes]], for our purposes it is enough to note that negative energy densities can pose problems if not handled carefully, there may be limits on how much negative energy you can have without nearby positive energy density, and it may not be possible to get enough negative energy to support a warp drive; although none of this is ruled out by physics – yet!		The first warp drive that actually used relativity was proposed by Miguel Alcubierre<ref>M. Alcubierre, "The warp drive: hyper-fast travel within general relativity." Classical and Quantum Gravity. 11 (5): L73–L77 (1994). [https://arxiv.org/abs/gr-qc/0009013 arXiv:gr-qc/0009013]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1994CQGra..11L..73A 1994CQGra..11L..73A]. doi:[https://doi.org/10.1088%2F0264-9381%2F11%2F5%2F001 10.1088/0264-9381/11/5/001]. S2CID [https://api.semanticscholar.org/CorpusID:4797900 4797900].</ref>. In this geometry, a sphere of space-time moves at an arbitrary speed (potentially but not necessarily a speed much faster than light). Objects within the sphere are moved along with the sphere; an object at rest within the sphere would be moved along with the sphere indefinitely. Space is expanding at the rear boundary and contracting at the front boundary in order to keep the sphere moving. In order to satisfy the Einstein field equations, the boundary of the sphere must have a negative energy density. The challenges of space-time geometries with negative energy densities are described in our page on [[Wormholes#Exotic_energy_conditions\|wormholes]], for our purposes it is enough to note that negative energy densities can pose problems if not handled carefully, there may be limits on how much negative energy you can have without nearby positive energy density, and it may not be possible to get enough negative energy to support a warp drive; although none of this is ruled out by physics – yet!

	<table align=center>		<table align=center>

Lwcamp: /* But what if I don't want all the science? */

2026-08-10T00:15:02Z

But what if I don't want all the science?

← Older revision		Revision as of 16:15, 9 August 2026
Line 244:		Line 244:
	Incidentally, this can let you get places without actually warping there – just build up enough velocity in the right direction, warp to where your resulting trajectory can get you to your destination, and turn off your warp drive. It also lets you match your velocity with any planet you happen to be going to. If you're coming from a star system that is moving with respect to your destination with a speed of 100 km/s, you can warp to your destination planet and hover there for long enough to bleed off your velocity and allow you to land.		Incidentally, this can let you get places without actually warping there – just build up enough velocity in the right direction, warp to where your resulting trajectory can get you to your destination, and turn off your warp drive. It also lets you match your velocity with any planet you happen to be going to. If you're coming from a star system that is moving with respect to your destination with a speed of 100 km/s, you can warp to your destination planet and hover there for long enough to bleed off your velocity and allow you to land.

	Other forces will behave the same, such as if your spacecraft has a net electric charge and is affected by ~~electron~~ and/or magnetic fields in space.		Other forces will behave the same, such as if your spacecraft has a net electric charge and is affected by electric and/or magnetic fields in space.

	== Warp Railroads ==		== Warp Railroads ==

Lwcamp: /* But what if I don't want all the science? */

2026-08-10T00:14:44Z

But what if I don't want all the science?

← Older revision		Revision as of 16:14, 9 August 2026
Line 241:		Line 241:

	Where does that energy come from? Your spacecraft. It has a reactor that produces energy that you use to do work. The power required to accelerate at a vector <i><b>a</b></i> when your velocity vector is <i><b>v</b></i> is <i>P</i> = -<i>m</i> <i><b>v</b></i> · <i><b>a</b></i>. Here, the symbol · means to take the dot product or inner product. If your speed is 10 km/s (1×10<sup>4</sup> m/s), gravity is pulling you at 1 g, and your spacecraft masses 200,000 tons (2×10<sup>8</sup> kg) you would need nearly 20 TW of power to keep up! So you can see that your reactor power might not be able to make all that kinetic energy fast enough. But you can still reach arbitrarily high speeds – you just need to move away from the planet where gravity is less and so the acceleration while hovering doesn't take as much power. This will take longer; you'll be adding kinetic energy at the rate limited by your reactor rather than just raw acceleration.		Where does that energy come from? Your spacecraft. It has a reactor that produces energy that you use to do work. The power required to accelerate at a vector <i><b>a</b></i> when your velocity vector is <i><b>v</b></i> is <i>P</i> = -<i>m</i> <i><b>v</b></i> · <i><b>a</b></i>. Here, the symbol · means to take the dot product or inner product. If your speed is 10 km/s (1×10<sup>4</sup> m/s), gravity is pulling you at 1 g, and your spacecraft masses 200,000 tons (2×10<sup>8</sup> kg) you would need nearly 20 TW of power to keep up! So you can see that your reactor power might not be able to make all that kinetic energy fast enough. But you can still reach arbitrarily high speeds – you just need to move away from the planet where gravity is less and so the acceleration while hovering doesn't take as much power. This will take longer; you'll be adding kinetic energy at the rate limited by your reactor rather than just raw acceleration.

			Incidentally, this can let you get places without actually warping there – just build up enough velocity in the right direction, warp to where your resulting trajectory can get you to your destination, and turn off your warp drive. It also lets you match your velocity with any planet you happen to be going to. If you're coming from a star system that is moving with respect to your destination with a speed of 100 km/s, you can warp to your destination planet and hover there for long enough to bleed off your velocity and allow you to land.

	Other forces will behave the same, such as if your spacecraft has a net electric charge and is affected by electron and/or magnetic fields in space.		Other forces will behave the same, such as if your spacecraft has a net electric charge and is affected by electron and/or magnetic fields in space.