Wormholes - Revision history

Lwcamp: /* Space-time: three space dimensions and one time dimension */

2026-08-18T19:12:44Z

Space-time: three space dimensions and one time dimension

← Older revision		Revision as of 11:12, 18 August 2026
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	</table>		</table>

	There is one distinction between space-time manifolds that will become important later. Some manifolds have an isolated region of high curvature (corresponding to a concentration of mass, or at least of stress-energy) but as you go farther away from the strongly curved region the space-time becomes increasingly flat. If you can always go out far enough away from a curved region that space-time becomes flatter than whatever flatness criterion you choose, no matter what direction you choose to leave the curved region, the manifold is called <i>asymptotically flat</i>. For our purposes, if you can go far enough away that the Newtonian approximation to general relativity is accurate, and gravity can be described as a force rather than requiring a geometric description, then the geometry can be considered asymptotically flat. You can also allow gravitational waves in your asymptotically flat space-time – their very small space-time curvature is not enough to cause problems and they can still be described by a linearized version of gravity; linear deviations from Newtonian gravity such as gravito-magnetic effects can also fall into ~~asymptitcally~~ flat region of space-time. Both the Schwarzschild and the Minkowski geometries are asymptotically flat. Spherical or hyperbolic geometries are not asymptotically flat. Planets, stars, galaxies, neutron stars, black holes, and galactic clusters are all approximately asymptotically flat; but the universe as a whole is <i>not</i>. As long as we confine our attention to merely galactic clusters, we can make the approximation of asymptotic flatness.		There is one distinction between space-time manifolds that will become important later. Some manifolds have an isolated region of high curvature (corresponding to a concentration of mass, or at least of stress-energy) but as you go farther away from the strongly curved region the space-time becomes increasingly flat. If you can always go out far enough away from a curved region that space-time becomes flatter than whatever flatness criterion you choose, no matter what direction you choose to leave the curved region, the manifold is called <i>asymptotically flat</i>. For our purposes, if you can go far enough away that the Newtonian approximation to general relativity is accurate, and gravity can be described as a force rather than requiring a geometric description, then the geometry can be considered asymptotically flat. You can also allow gravitational waves in your asymptotically flat space-time – their very small space-time curvature is not enough to cause problems and they can still be described by a linearized version of gravity; linear deviations from Newtonian gravity such as gravito-magnetic effects can also fall into asymptotically flat region of space-time. Both the Schwarzschild and the Minkowski geometries are asymptotically flat. Spherical or hyperbolic geometries are not asymptotically flat. Planets, stars, galaxies, neutron stars, black holes, and galactic clusters are all approximately asymptotically flat; but the universe as a whole is <i>not</i>. As long as we confine our attention to merely galactic clusters, we can make the approximation of asymptotic flatness.

	===Making a wormhole===		===Making a wormhole===

Lwcamp: /* So just how do I get the ANEC-violating stuff I need? */

2026-08-11T17:28:30Z

So just how do I get the ANEC-violating stuff I need?

← Older revision		Revision as of 09:28, 11 August 2026
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	<ref name="gravitationally_squeezed_vacuum">David Hochberg and Thomas W. Kephart, "Lorentzian wormholes from the gravitationally squeezed vacuum", Physics Letters B 268, 377-383 (1991)</ref>		<ref name="gravitationally_squeezed_vacuum">David Hochberg and Thomas W. Kephart, "Lorentzian wormholes from the gravitationally squeezed vacuum", Physics Letters B 268, 377-383 (1991)</ref>
	. If you have the curved space-time of gravity, all of the modes of oscillation in it become squeezed states. So it might be possible that the curved space-time of a wormhole can squeeze the vacuum enough to support itself. Or a combination of gravitational vacuum squeezing and the topological Casimir vacuum from the wormhole's geometry constraints might be all that is needed. At least one proposal has suggested a class of wormholes that can be self supporting in such a way		. If you have the curved space-time of gravity, all of the modes of oscillation in it become squeezed states. So it might be possible that the curved space-time of a wormhole can squeeze the vacuum enough to support itself. Or a combination of gravitational vacuum squeezing and the topological Casimir vacuum from the wormhole's geometry constraints might be all that is needed. At least one proposal has suggested a class of wormholes that can be self supporting in such a way
	<ref>S. V. Krasnikov, "Toward a Traversable Wormhole", arXiv:gr-qc/0003092v1 22 Mar 2000</ref>		<ref>S. V. Krasnikov, "Toward a Traversable Wormhole", arXiv:gr-qc/0003092v1 22 Mar 2000 https://doi.org/10.48550/arXiv.gr-qc/0003092</ref>
	<ref>S. Krasnikov, "Traversible Wormhole", Physical Review D, volume 62, article 084028 (2000) DOI: https://doi.org/10.1103/PhysRevD.62.084028</ref>,		<ref>S. Krasnikov, "Traversible Wormhole", Physical Review D, volume 62, article 084028 (2000) DOI: https://doi.org/10.1103/PhysRevD.62.084028</ref>,
	although the throat of these wormholes is very "wrinkly" or "crumpled up" and it is unclear what the effects of that would be on anyone passing through. Unfortunately, this proposal contained an error that invalidated its main result<ref>S. V. Krasnikov, "Erratum: Traversable wormhole [Phys. Rev. D 62, 084028 (2000)]", Physical Review D 76, article 109902 (14 November 2007) DOI: https://doi.org/10.1103/PhysRevD.76.109902</ref>.		although the throat of these wormholes is very "wrinkly" or "crumpled up" and it is unclear what the effects of that would be on anyone passing through. Unfortunately, this proposal contained an error that invalidated its main result<ref>S. V. Krasnikov, "Erratum: Traversable wormhole [Phys. Rev. D 62, 084028 (2000)]", Physical Review D 76, article 109902 (14 November 2007) DOI: https://doi.org/10.1103/PhysRevD.76.109902</ref>.

Lwcamp: /* So just how do I get the ANEC-violating stuff I need? */

2026-08-11T17:26:55Z

So just how do I get the ANEC-violating stuff I need?

← Older revision		Revision as of 09:26, 11 August 2026
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	<ref>S. V. Krasnikov, "Toward a Traversable Wormhole", arXiv:gr-qc/0003092v1 22 Mar 2000</ref>		<ref>S. V. Krasnikov, "Toward a Traversable Wormhole", arXiv:gr-qc/0003092v1 22 Mar 2000</ref>
	<ref>S. Krasnikov, "Traversible Wormhole", Physical Review D, volume 62, article 084028 (2000) DOI: https://doi.org/10.1103/PhysRevD.62.084028</ref>,		<ref>S. Krasnikov, "Traversible Wormhole", Physical Review D, volume 62, article 084028 (2000) DOI: https://doi.org/10.1103/PhysRevD.62.084028</ref>,
	although the throat of these wormholes is very "wrinkly" or "crumpled up" and it is unclear what the effects of that would be on anyone passing through. Unfortunately, this proposal contained an error that invalidated its main result<ref>S. V. Krasnikov, "Erratum: Traversable wormhole [Phys. Rev. D 62, 084028 (2000)]", Physical Review D 76, article 109902 (14 November 2007) DOI: https://doi.org/10.1103/PhysRevD.76.109902</ref>		although the throat of these wormholes is very "wrinkly" or "crumpled up" and it is unclear what the effects of that would be on anyone passing through. Unfortunately, this proposal contained an error that invalidated its main result<ref>S. V. Krasnikov, "Erratum: Traversable wormhole [Phys. Rev. D 62, 084028 (2000)]", Physical Review D 76, article 109902 (14 November 2007) DOI: https://doi.org/10.1103/PhysRevD.76.109902</ref>.

	====Quantum energy inequalities====		====Quantum energy inequalities====

Lwcamp: /* So just how do I get the ANEC-violating stuff I need? */

2026-08-11T17:26:41Z

So just how do I get the ANEC-violating stuff I need?

← Older revision		Revision as of 09:26, 11 August 2026
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	. If you have the curved space-time of gravity, all of the modes of oscillation in it become squeezed states. So it might be possible that the curved space-time of a wormhole can squeeze the vacuum enough to support itself. Or a combination of gravitational vacuum squeezing and the topological Casimir vacuum from the wormhole's geometry constraints might be all that is needed. At least one proposal has suggested a class of wormholes that can be self supporting in such a way		. If you have the curved space-time of gravity, all of the modes of oscillation in it become squeezed states. So it might be possible that the curved space-time of a wormhole can squeeze the vacuum enough to support itself. Or a combination of gravitational vacuum squeezing and the topological Casimir vacuum from the wormhole's geometry constraints might be all that is needed. At least one proposal has suggested a class of wormholes that can be self supporting in such a way
	<ref>S. V. Krasnikov, "Toward a Traversable Wormhole", arXiv:gr-qc/0003092v1 22 Mar 2000</ref>		<ref>S. V. Krasnikov, "Toward a Traversable Wormhole", arXiv:gr-qc/0003092v1 22 Mar 2000</ref>
	<ref>S. Krasnikov, "Traversible Wormhole", Physical Review D, volume 62, article 084028 (2000)</ref>,		<ref>S. Krasnikov, "Traversible Wormhole", Physical Review D, volume 62, article 084028 (2000) DOI: https://doi.org/10.1103/PhysRevD.62.084028</ref>,
	although the throat of these wormholes is very "wrinkly" or "crumpled up" and it is unclear what the effects of that would be on anyone passing through.		although the throat of these wormholes is very "wrinkly" or "crumpled up" and it is unclear what the effects of that would be on anyone passing through. Unfortunately, this proposal contained an error that invalidated its main result<ref>S. V. Krasnikov, "Erratum: Traversable wormhole [Phys. Rev. D 62, 084028 (2000)]", Physical Review D 76, article 109902 (14 November 2007) DOI: https://doi.org/10.1103/PhysRevD.76.109902</ref>

	====Quantum energy inequalities====		====Quantum energy inequalities====

Lwcamp: /* Exotic energy conditions */

2026-07-28T04:04:51Z

Exotic energy conditions

← Older revision		Revision as of 20:04, 27 July 2026
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	==Exotic energy conditions==		==Exotic energy conditions==

	It is fairly easy to see ~~than~~ any wormhole requires negative energy densities (or more generally, regions where the tension is higher than the energy in natural units) to exist. Take a look at any of the wormhole diagrams above – the spherically symmetric ones will probably make it the most clear. If you send a parallel ray of stuff – maybe particles or light or golf balls – through the wormhole, and trace out the straightest possible path of all of those parallel lines, you will see that after they go through the wormhole all those initially parallel trajectories will now be diverging. Positive energy (such as mass) causes attractive forces, drawing trajectories toward it and making the paths converging. To get diverging paths you need the opposite – repulsive gravity – which you can get from negative energy densities or very high tensions. Having the tension be higher than the energy density turns out to be equivalent to a negative energy density – in some frames of reference observers will measure a negative energy density there.		It is fairly easy to see that any wormhole requires negative energy densities (or more generally, regions where the tension is higher than the energy in natural units) to exist. Take a look at any of the wormhole diagrams above – the spherically symmetric ones will probably make it the most clear. If you send a parallel ray of stuff – maybe particles or light or golf balls – through the wormhole, and trace out the straightest possible path of all of those parallel lines, you will see that after they go through the wormhole all those initially parallel trajectories will now be diverging. Positive energy (such as mass) causes attractive forces, drawing trajectories toward it and making the paths converging. To get diverging paths you need the opposite – repulsive gravity – which you can get from negative energy densities or very high tensions. Having the tension be higher than the energy density turns out to be equivalent to a negative energy density – in some frames of reference observers will measure a negative energy density there.

	A lot of physicists used to be reflexively dismissive of negative energy densities. After all, they can't really exist; all energy in the real world is positive.		A lot of physicists used to be reflexively dismissive of negative energy densities. After all, they can't really exist; all energy in the real world is positive.

Lwcamp at 19:07, 7 March 2026

2026-03-07T19:07:52Z

← Older revision		Revision as of 11:07, 7 March 2026
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	==References==		==References==

	[[Category:Physics]][[Category:Infrastructure]][[Category:Physics & Engineering‏‎]][[Category:Transportation & Infrastructure‏‎]][[Category:Metric Engineering]]		[[Category:Physics]][[Category:Infrastructure]][[Category:Physics & Engineering‏‎]][[Category:Physics & Math & Engineering]][[Category:Transportation & Infrastructure‏‎]][[Category:Metric Engineering]]

Lwcamp: /* Space-time: three space dimensions and one time dimension */

2026-03-07T18:51:10Z

Space-time: three space dimensions and one time dimension

← Older revision		Revision as of 10:51, 7 March 2026
Line 144:		Line 144:
	</table>		</table>

	There is one distinction between space-time manifolds that will become important later. Some manifolds have an isolated region of high curvature (corresponding to a concentration of mass, or at least of stress-energy) but as you go farther away from the strongly curved region the space-time becomes increasingly flat. If you can always go out far enough away from a curved region that space-time becomes flatter than whatever flatness criterion you choose, no matter what direction you choose to leave the curved region, the manifold is called <i>asymptotically flat</i>. For our purposes, if you can go far enough away that the Newtonian approximation to general relativity is accurate, and gravity can be described as a force rather than requiring a geometric description, then the geometry can be considered asymptotically flat. You can also allow gravitational waves in your asymptotically flat space-time – their very small space-time curvature is not enough to cause problems and they can still be described by a linearized version of gravity. Both the Schwarzschild and the Minkowski geometries are asymptotically flat. Spherical or hyperbolic geometries are not asymptotically flat. Planets, stars, galaxies, neutron stars, black holes, and galactic clusters are all approximately asymptotically flat; but the universe as a whole is <i>not</i>. As long as we confine our attention to merely galactic clusters, we can make the approximation of asymptotic flatness.		There is one distinction between space-time manifolds that will become important later. Some manifolds have an isolated region of high curvature (corresponding to a concentration of mass, or at least of stress-energy) but as you go farther away from the strongly curved region the space-time becomes increasingly flat. If you can always go out far enough away from a curved region that space-time becomes flatter than whatever flatness criterion you choose, no matter what direction you choose to leave the curved region, the manifold is called <i>asymptotically flat</i>. For our purposes, if you can go far enough away that the Newtonian approximation to general relativity is accurate, and gravity can be described as a force rather than requiring a geometric description, then the geometry can be considered asymptotically flat. You can also allow gravitational waves in your asymptotically flat space-time – their very small space-time curvature is not enough to cause problems and they can still be described by a linearized version of gravity; linear deviations from Newtonian gravity such as gravito-magnetic effects can also fall into asymptitcally flat region of space-time. Both the Schwarzschild and the Minkowski geometries are asymptotically flat. Spherical or hyperbolic geometries are not asymptotically flat. Planets, stars, galaxies, neutron stars, black holes, and galactic clusters are all approximately asymptotically flat; but the universe as a whole is <i>not</i>. As long as we confine our attention to merely galactic clusters, we can make the approximation of asymptotic flatness.

	===Making a wormhole===		===Making a wormhole===

Oddturnip: /* Space-time: three space dimensions and one time dimension */

2026-02-18T03:14:21Z

Space-time: three space dimensions and one time dimension

← Older revision		Revision as of 19:14, 17 February 2026
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	</table>		</table>

	There is one distinction between space-time manifolds that will become important later. Some manifolds have an isolated region of high curvature (corresponding to a concentration of mass, or at least of stress-energy) but as you go farther away from the strongly curved region the space-time becomes increasingly flat. If you can always go out far enough away from a curved region that space-time becomes flatter ~~that~~ whatever flatness criterion you choose, no matter what direction you choose to leave the curved region, the manifold is called <i>asymptotically flat</i>. For our purposes, if you can go far enough away that the Newtonian approximation to general relativity is accurate, and gravity can be described as a force rather than requiring a geometric description, then the geometry can be considered asymptotically flat. You can also allow gravitational waves in your asymptotically flat space-time – their very small space-time curvature is not enough to cause problems and they can still be described by a linearized version of gravity. Both the Schwarzschild and the Minkowski geometries are asymptotically flat. Spherical or hyperbolic geometries are not asymptotically flat. Planets, stars, galaxies, neutron stars, black holes, and galactic clusters are all approximately asymptotically flat; but the universe as a whole is <i>not</i>. As long as we confine our attention to merely galactic clusters, we can make the approximation of asymptotic flatness.		There is one distinction between space-time manifolds that will become important later. Some manifolds have an isolated region of high curvature (corresponding to a concentration of mass, or at least of stress-energy) but as you go farther away from the strongly curved region the space-time becomes increasingly flat. If you can always go out far enough away from a curved region that space-time becomes flatter than whatever flatness criterion you choose, no matter what direction you choose to leave the curved region, the manifold is called <i>asymptotically flat</i>. For our purposes, if you can go far enough away that the Newtonian approximation to general relativity is accurate, and gravity can be described as a force rather than requiring a geometric description, then the geometry can be considered asymptotically flat. You can also allow gravitational waves in your asymptotically flat space-time – their very small space-time curvature is not enough to cause problems and they can still be described by a linearized version of gravity. Both the Schwarzschild and the Minkowski geometries are asymptotically flat. Spherical or hyperbolic geometries are not asymptotically flat. Planets, stars, galaxies, neutron stars, black holes, and galactic clusters are all approximately asymptotically flat; but the universe as a whole is <i>not</i>. As long as we confine our attention to merely galactic clusters, we can make the approximation of asymptotic flatness.

	===Making a wormhole===		===Making a wormhole===

Lwcamp: /* Reducing or eliminating ANEC violating stuff */

2026-02-02T14:52:02Z

Reducing or eliminating ANEC violating stuff

← Older revision		Revision as of 06:52, 2 February 2026
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	<ref name="Blazquez-Salcedo_Knoll_Radu">Jose Luis Blázquez-Salcedo, Christian Knoll, and Eugen Radu, “Transversable wormholes in Einstein-Dirac-Maxwell theory”, Physical Review Letters <b>126</b>, 101102 (2021); ArXiv: 2010.07317v2 [gr-qc].</ref>		<ref name="Blazquez-Salcedo_Knoll_Radu">Jose Luis Blázquez-Salcedo, Christian Knoll, and Eugen Radu, “Transversable wormholes in Einstein-Dirac-Maxwell theory”, Physical Review Letters <b>126</b>, 101102 (2021); ArXiv: 2010.07317v2 [gr-qc].</ref>
	.		.
	However, an analysis<ref>Ben Kain, "Are Einstein-Dirac-Maxwell wormholes traversable", [https://arxiv.org/abs/2305.11217 arXiv:2305.11217 [gr-qc]], Phys. Rev. D 108, 044019 (2023) [https://doi.org/10.1103/PhysRevD.108.044019]</ref> was unable to find any solutions ~~of this class of wormholes~~ which did not collapse into a black hole before any signal could propagate through them and concluded that they were not traversable.		However, an analysis<ref>Ben Kain, "Are Einstein-Dirac-Maxwell wormholes traversable", [https://arxiv.org/abs/2305.11217 arXiv:2305.11217 [gr-qc]], Phys. Rev. D 108, 044019 (2023) https://doi.org/10.1103/PhysRevD.108.044019</ref> of this class of wormholes was unable to find any solutions which did not collapse into a black hole before any signal could propagate through them and concluded that they were not traversable.

	==Fields and conserved properties==		==Fields and conserved properties==

Lwcamp: /* Reducing or eliminating ANEC violating stuff */

2026-02-02T14:50:14Z

Reducing or eliminating ANEC violating stuff

← Older revision		Revision as of 06:50, 2 February 2026
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	Thin shell wormholes have also been the subject of investigation. One study <ref name="Mazharimousavi_Halilsoy">S. Habib Mazharimousavi, M. Halilsoy, "3 + 1-dimensional thin shell wormhole with deformed throat can be supported by normal matter", Eur. Phys. J. C (2015) 75:271 DOI 10.1140/epjc/s10052-015-3506-6</ref> found a number of thin shell wormholes with sharp-edged shapes could be supported entirely without any exotic energy. However, this only applies if the edges are infinitely sharp. A finite radius of curvature at the edges would require negative energy at those edges.		Thin shell wormholes have also been the subject of investigation. One study <ref name="Mazharimousavi_Halilsoy">S. Habib Mazharimousavi, M. Halilsoy, "3 + 1-dimensional thin shell wormhole with deformed throat can be supported by normal matter", Eur. Phys. J. C (2015) 75:271 DOI 10.1140/epjc/s10052-015-3506-6</ref> found a number of thin shell wormholes with sharp-edged shapes could be supported entirely without any exotic energy. However, this only applies if the edges are infinitely sharp. A finite radius of curvature at the edges would require negative energy at those edges.

	If the wormhole is taken to have the properties of a class of subatomic particles called a fermion, then if the ratio of the electric charge to the mass is sufficiently large you can get a wormhole that can remain open without any negative energy regions at all		If the wormhole is taken to have the properties of a class of subatomic particles called a fermion, then if the ratio of the electric charge to the mass is sufficiently large you can get a wormhole that can remain open without any additional negative energy regions at all
	<ref name="Blazquez-Salcedo_Knoll_Radu">Jose Luis Blázquez-Salcedo, Christian Knoll, and Eugen Radu, “Transversable wormholes in Einstein-Dirac-Maxwell theory”, Physical Review Letters <b>126</b>, 101102 (2021); ArXiv: 2010.07317v2 [gr-qc].</ref>		<ref name="Blazquez-Salcedo_Knoll_Radu">Jose Luis Blázquez-Salcedo, Christian Knoll, and Eugen Radu, “Transversable wormholes in Einstein-Dirac-Maxwell theory”, Physical Review Letters <b>126</b>, 101102 (2021); ArXiv: 2010.07317v2 [gr-qc].</ref>
	.		.
			However, an analysis<ref>Ben Kain, "Are Einstein-Dirac-Maxwell wormholes traversable", [https://arxiv.org/abs/2305.11217 arXiv:2305.11217 [gr-qc]], Phys. Rev. D 108, 044019 (2023) [https://doi.org/10.1103/PhysRevD.108.044019]</ref> was unable to find any solutions of this class of wormholes which did not collapse into a black hole before any signal could propagate through them and concluded that they were not traversable.

	==Fields and conserved properties==		==Fields and conserved properties==