The warp drive: hyper-fast travel within general relativity
Open accessAbstract
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 happens with wormholes, exotic matter will be needed in order to generate a distortion of spacetime like the one discussed here.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the Alcubierre warp bubble, the NEC, SEC, WEC, and DEC are all explicitly violated.
“In this situation explicit computation shows that the NEC, and so the SEC, WEC and DEC, are all explicitly violated.See specifically the original discussion in [1], and the subsequent follow-up discussions in [12][13][14][15][16][17], and [20,21].”
From ADM mass in warp drive spacetimes (2023) · cites this paper as [1]
In L77 (p. 77), Alcubierre explicitly says the metric violates the weak, dominant, and strong energy conditions. Our copy does not explicitly discuss or demonstrate violation of the null energy condition, so it does not support the claim that all four are explicitly violated. (LLM, conf=0.88)
Experimental — accuracy not yet measuredFor the Alcubierre warp bubble, the flow field is auto-parallel.
“For the Alcubierre warp bubble the flow field v(t, x) is auto-parallel. That is v(t, x) = v(t, x) v;v = (constant).”
From ADM mass in warp drive spacetimes (2023) · cites this paper as [1]
In the passage labelled U 5, Alcubierre says the timelike curves of the Eulerian observers are geodesics. The L76 passage also says the spaceship follows a geodesic. Those statements support geodesic motion in the warp-bubble spacetime, but our copy does not state that the spatial flow field v(t, x) itself is auto-parallel or satisfies the citing sentence’s equation. (LLM, conf=0.79)
Experimental — accuracy not yet measuredThe transport logistics of the presented positive-energy solitons are similar to the solitons of the Alcubierre solution.
“The transport logistics of the presented positive-energy solitons are similar to the solitons of the Alcubierre solution.”
From Breaking the warp barrier: hyper-fast solitons in Einstein–Maxwell-plasma theory (2021) · cites this paper as [1]
The passages labeled L74 and L77 describe Alcubierre’s transport mechanism: a spaceship is carried by a local spacetime distortion, with expansion behind it and contraction ahead. They do not discuss the citing paper’s positive-energy solitons or establish the claimed similarity. L77 also says Alcubierre’s metric requires negative energy density. (LLM, conf=0.82)
Experimental — accuracy not yet measuredThe solution of [1] possesses only one negative expansion lobe at the leading edge of its soliton and one positive expansion lobe at the trailing edge.
“The solution of [1] possesses only one negative expansion lobe at the leading edge of its soliton and one positive expansion lobe at the trailing edge.”
From Breaking the warp barrier: hyper-fast solitons in Einstein–Maxwell-plasma theory (2021) · cites this paper as [1]
The introduction (L74) describes expansion behind the spaceship and contraction ahead of it; the discussion of Figure 1 (section (11)) repeats that pattern. These passages support the locations and signs of the expansion regions, but the available text does not establish the claim that there is only one lobe of each sign. (LLM, conf=0.82)
Experimental — accuracy not yet measuredThe largest values of θ for the positive-energy soliton coincide with the sources of stress-energy density, in contrast to the solution of Ref. [1] where the energy density and expansion factor are maximally separated on the soliton boundary.
“The largest values of θ for the positive-energy soliton coincide with the sources of stress-energy density, in contrast to the solution of Ref. [1] where the energy density and expansion factor are maximally separated on the soliton boundary.”
From Breaking the warp barrier: hyper-fast solitons in Einstein–Maxwell-plasma theory (2021) · cites this paper as [1]
Split into 2 atoms — 0 confirmed, 1 partially supported, 0 disputed, 0 misattributed, 1 unverifiable. Expand the claim to see per-atom verdicts.
Experimental — accuracy not yet measured
Alcubierre warp drives have long been known to violate the WEC.
“Alcubierre warp drives have long been known to violate the WEC [9]”
From Generic warp drives violate the null energy condition (2022) · cites this paper as [9]
The argument applies to Alcubierre, Natario zero-expansion, Lentz/Fell-Heisenberg zero-vorticity warp drives, and also to the model warp drives considered by Bobrick-Martire.
“This argument applies, in particular, to all three of the Alcubierre [9], Nat´ ario zeroexpansion [10], and Lentz/Fell-Heisenberg zero-vorticity [1, 3] warp drives, and also (for slightly different reasons) to the model warp drives considered by Bobrick-Martire [2].”
From Generic warp drives violate the null energy condition (2022) · cites this paper as [9]
Alcubierre's original shape function uses tanh functions and does not have compact support; he sets r_inner=0 and r_outer=∞, which is not a truncation.
“Specifically, in Alcubierre's original article [9, equation (6)] the concrete realization of the shape function f ( r s ) he chooses, see equation (A.8), uses tanh functions and so does not have compact support. In this terminology, Alcubierre sets r inner = 0 and r outer = ∞ , which is certainly not a truncation.”
From Generic warp drives violate the null energy condition (2022) · cites this paper as [9]
Alcubierre's solution allows for acceleration using a time-varying v_s(t).
“Alcubierre's solution allows for acceleration using a time-varying v s ( t ).”
From Constant velocity physical warp drive solution (2024) · cites this paper as [1]
Alcubierre's solution is a shift vector addition to an otherwise Minkowski spacetime.
“Alcubierre's solution is a shift vector addition to an otherwise Minkowski spacetime.”
From Constant velocity physical warp drive solution (2024) · cites this paper as [1]
All characteristic warp drive features of the Alcubierre spacetime are sourced purely by the shift vector.
“Thus, it is clear that all the characteristic warp drive features of this spacetime are sourced purely by the shift vector.”
From Constant velocity physical warp drive solution (2024) · cites this paper as [1]
The Alcubierre warp metric implies violation of the energy conditions because a negative energy density appears to be required for creation of the warp bubble.
“In a seminal paper, Alcubierre also concluded that the warp metric would imply the violation of the energy conditions since it appeared that a negative energy density would be required for the creation of the warp bubble.”
From Fluid dynamics in the warp drive spacetime geometry (2021) · cites this paper as [1]
The field equations of general relativity permit inertial observers to be transported at superluminal rates relative to distant observers.
“The field equations of general relativity (GR) permit inertial observers to be transported at superluminal rates relative to distance observers.”
From Positive energy warp drive from hidden geometric structures (2021) · cites this paper as [6]
The multi-compartment structure is a distinct departure from the single top-hat soliton found in [1] and [11].
“The multi-compartment structure is a distinct departure from the single top-hat soliton fond in [1] and [11].”
From Breaking the warp barrier: hyper-fast solitons in Einstein–Maxwell-plasma theory (2021) · cites this paper as [1]
The Einstein tensor components for the Alcubierre warp drive metric imply that negative energy density would be required to create the warp bubble, violating the weak and dominant energy conditions.
“The Einstein tensor components were calculated and it was noticed that negative energy density would be required to create the warp bubble, thus violating the weak and dominant energy conditions.”
From Perfect fluid warp drive solutions with the cosmological constant (2021) · cites this paper as [1]
The original Alcubierre warp drive metric was established without solving the Einstein equations.
“In the original paper by M. Alcubierre the warp drive metric was established without solving the Einstein equations [1].”
From Perfect fluid warp drive solutions with the cosmological constant (2021) · cites this paper as [1]
The Alcubierre metric describes a spacetime geometry that allows a massive particle inside a warp bubble to travel with superluminal global velocities.
“The Alcubierre metric describes a spacetime geometry that allows a massive particle inside a spacetime distortion, called warp bubble, to travel with superluminal global velocities.”
From Perfect fluid warp drive solutions with the cosmological constant (2021) · cites this paper as [1]
Neither the original Alcubierre paper nor the subsequent cited papers solved the Einstein equations using the warp drive metric.
“Motivated by the fact that neither the original paper by Alcubierre, nor the subsequent ones cited above, did actually solve the Einstein equations using the warp drive metric, we proceed to investigate possible solutions for a dust particle energy momentum tensor [26].”
From Perfect fluid warp drive solutions with the cosmological constant (2021) · cites this paper as [1]
In Ref. [1], the Einstein equations were not solved, since the metric was merely guessed with a form function that rules the warp bubble shape.
“In Ref. [1] the Einstein equations were not solved, since the metric was merely guessed with a form function (see Eq. 2.8) that rules the warp bubble shape.”
From Perfect fluid warp drive solutions with the cosmological constant (2021) · cites this paper as [1]
Proposed warp drive solutions have been unphysical, requiring energy condition violations and large energy requirements.
“So far the proposed solutions have been unphysical, requiring energy condition violations and large energy requirements.”
From Analyzing warp drive spacetimes with warp factory (2024) · cites this paper as [1]
The first warp drive solutions by Alcubierre and Van Den Broeck enabled passengers to move at arbitrary speeds but required enormous energy density and unphysical stress-energy tensors using negative energy.
“The first warp drive solutions developed by Alcubierre [1] and then further developed by Van Den Broeck [16] enabled passengers inside the warp bubble to move at arbitrary speeds but at the cost of both enormous energy density and unphysical stress-energy tensors using negative energy.”
From Analyzing warp drive spacetimes with warp factory (2024) · cites this paper as [1]
The Alcubierre metric violates all energy conditions within the bubble region.
“The Alcubierre metric violates all energy conditions within the bubble region, as it necessitates negative energy density, as Alcubierre demonstrated. This fact is confirmed through the analysis conducted using Warp Factory.”
From Analyzing warp drive spacetimes with warp factory (2024) · cites this paper as [1]
Alcubierre's first warp solution was constructed so that passengers and external observers experience the same passage of time.
“In line with the Star Trek conception of warp drives, the first warp solution from Alcubierre was constructed such that the passengers and external observers both experience the same passage of time (proper time).”
From Analyzing warp drive spacetimes with warp factory (2024) · cites this paper as [1]
Alcubierre's warp solution has a flat passenger volume and a warp bubble whose spatial extent is determined by a shape parameter.
“For example, Alcubierre has a flat passenger volume and a warp bubble whose spatial extent is determined by a shape parameter 9 .”
From Analyzing warp drive spacetimes with warp factory (2024) · cites this paper as [1]
Alcubierre introduced the first general relativistic warp drive in 1994.
“Alcubierre introduced the first general relativistic warp drive in 1994 [1].”
From Analyzing warp drive spacetimes with warp factory (2024) · cites this paper as [1]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
General Relativity – An Einstein Centenary Survey
Irvine, J. M. (1980) · Physics Bulletin · doi:10.1088/0031-9112/31/4/029 · Cited by 2,871 · see citing works
The Large Scale Structure of Space–Time
Woodhouse, N. M. J. (1974) · Physics Bulletin · doi:10.1088/0031-9112/25/6/029 · Cited by 2,565 · see citing works
Kinematics and dynamics of general relativity
York, J. W. (1979) · Cited by 241 · see citing works
Flagged first, then by citations
Research works printed but not linked: 2
- [2]2. Hawking S W and Ellis G F R 1973 7'ke Large Scale Srrucrure ofSpncerime (Cambridge: Cambridge Univesily
- [3]3. DeWin B S 1979 General Relariviry: An &insrein Cenlemwy Sumey ed S W Hawking and W Israel (Cambridge: Smarr (Cambridge: Cambridge University Press) pp 8>126 PES) Cambridge Univeniiy Press)
Cited by
Sorted by citations
A generic foresight process framework
Voros, J. (2003) · foresight · doi:10.1108/14636680310698379 · Cited by 562 · see citing works
Averaged energy conditions and quantum inequalities
Ford, L. H., & Roman, T. A. (1995) · Physical Review D · doi:10.1103/physrevd.51.4277 · Cited by 284 · see citing works
Energy conditions in general relativity and quantum field theory
Kontou, E.-A., & Sanders, K. (2020) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ab8fcf · Cited by 223 · see citing works
“Similarly, for an Alcubierre bubble the thickness is constrained to be of the order of only a few hundred Planck lengths, while the negative energy required for a macroscopic bubble is greater than the total mass of the entire visible universe.”
InfluentialCuriel, E. (2017) · Einstein Studies · doi:10.1007/978-1-4939-3210-8_3 · Cited by 226 · see citing works
““hyper-fast” travel84 [necessarily] [2, 127, 144]”
Quantum field theory constrains traversable wormhole geometries
Ford, L. H., & Roman, T. A. (1996) · Physical Review D · doi:10.1103/physrevd.53.5496 · Cited by 192 · see citing works
Wormholes, Warp Drives and Energy Conditions
(2017) · Fundamental Theories of Physics · doi:10.1007/978-3-319-55182-1 · Cited by 189 · see citing works
“Shortly after the discovery of the Alcubierre warp drive solution [3], an interesting feature of the spacetime was found.”
InfluentialSelf-citationRestrictions on negative energy density in flat spacetime
Ford, L. H., & Roman, T. A. (1997) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.55.2082 · Cited by 168 · see citing works
The river model of black holes
Hamilton, A. J. S., & Lisle, J. P. (2008) · American Journal of Physics · doi:10.1119/1.2830526 · Cited by 153 · see citing works
“R ( 28 ) again with � = �/R for black hole ergospheres, and � = �/R for white hole ergospheres.”
BackgroundQUANTUM ENERGY INEQUALITIES IN TWO-DIMENSIONAL CONFORMAL FIELD THEORY
Fewster, C. J., & Hollands, S. (2005) · Reviews in Mathematical Physics · doi:10.1142/s0129055x05002406 · Cited by 144 · see citing works
Hyperfast travel in general relativity
Krasnikov, S. V. (1998) · Physical Review D · doi:10.1103/physrevd.57.4760 · Cited by 138 · see citing works
Surface stresses on a thin shell surrounding a traversable wormhole
Lobo, F. S. N. (2004) · Classical and Quantum Gravity · doi:10.1088/0264-9381/21/21/005 · Cited by 130 · see citing works
Superluminal Travel Requires Negative Energies
Olum, K. D. (1998) · Physical Review Letters · doi:10.1103/physrevlett.81.3567 · Cited by 126 · see citing works
Fundamental limitations on ‘warp drive’ spacetimes
Lobo, F. S. N., & Visser, M. (2004) · Classical and Quantum Gravity · doi:10.1088/0264-9381/21/24/011 · Cited by 117 · see citing works
“Alcubierre demonstrated that it is theoretically possible, within the framework of general relativity, to attain arbitrarily large velocities [1].”
Superluminal subway: The Krasnikov tube
Everett, A. E., & Roman, T. A. (1997) · Physical Review D · doi:10.1103/physrevd.56.2100 · Cited by 117 · see citing works
The unphysical nature of `warp drive'
Pfenning, M. J., & Ford, L. H. (1997) · Classical and Quantum Gravity · doi:10.1088/0264-9381/14/7/011 · Cited by 117 · see citing works
The quantum interest conjecture
Ford, L. H., & Roman, T. A. (1999) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.60.104018 · Cited by 113 · see citing works
Brane surgery: energy conditions, traversable wormholes, and voids
Barceló, C., & Visser, M. (2000) · Nuclear Physics B · doi:10.1016/s0550-3213(00)00379-5 · Cited by 107 · see citing works
The generalized second law implies a quantum singularity theorem
Wall, A. C. (2013) · Classical and Quantum Gravity · doi:10.1088/0264-9381/30/16/165003 · Cited by 106 · see citing works
Everett, A. E. (1996) · Physical Review D · doi:10.1103/physrevd.53.7365 · Cited by 105 · see citing works
A Class of Time-Machine Solutions with a Compact Vacuum Core
Ori, A. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.021101 · Cited by 101 · see citing works
The Unphysical Nature of ‘Warp DrivePreprint
Pfenning, M. J., & Ford, L. H. (1997) · Cited by 97 · see citing works
Classical and Semi-classical Energy Conditions
Martín–Moruno, P., & Visser, M. (2017) · Fundamental theories of physics · doi:10.1007/978-3-319-55182-1_9 · Cited by 96 · see citing works
“Moreover, stress-energy tensors violating the NEC can support hypothetical configurations as wormholes [9] and warp drives [25] in the framework of general relativity(6), which may lead to pathological situations.”
Visser, M., Bassett, B. A., & Liberati, S. (2000) · Nuclear Physics B - Proceedings Supplements · doi:10.1016/s0920-5632(00)00782-9 · Cited by 92 · see citing works
A quantum weak energy inequality for spin-one fields in curved space–time
Fewster, C. J., & Pfenning, M. J. (2003) · Journal of Mathematical Physics · doi:10.1063/1.1602554 · Cited by 83 · see citing works
Quantum effects in the Alcubierre warp-drive spacetime
Hiscock, W. A. (1997) · Classical and Quantum Gravity · doi:10.1088/0264-9381/14/11/002 · Cited by 82 · see citing works
Exotic solutions in General Relativity: Traversable wormholes and 'warp drive' spacetimesPreprint
Lobo, F. S. N. (2007) · arXiv (Cornell University) · doi:10.48550/arxiv.0710.4474 · Cited by 172 · see citing works
“However, it moves along a spacetime temporal trajectory, contained within it’s light cone, as light suffers the same distortion of spacetime [176].”
InfluentialA `warp drive' with more reasonable total energy requirements
Broeck, C. V. D. (1999) · Classical and Quantum Gravity · doi:10.1088/0264-9381/16/12/314 · Cited by 99 · see citing works
Null geodesics in the Alcubierre warp-drive spacetime: the view from the bridge
Clark, C., Hiscock, W. A., & Larson, S. L. (1999) · Classical and Quantum Gravity · doi:10.1088/0264-9381/16/12/313 · Cited by 74 · see citing works
Challenge to Create the Space Drive
Millis, M. G. (1997) · Journal of Propulsion and Power · doi:10.2514/2.5215 · Cited by 73 · see citing works
The quantum physics of chronology protectionPreprint
Visser, M. (2002) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/0204022 · Cited by 71 · see citing works
Absolute Quantum Energy Inequalities in Curved Spacetime
Fewster, C. J., & Smith, C. J. (2008) · Annales Henri Poincaré · doi:10.1007/s00023-008-0361-0 · Cited by 68 · see citing works
“Since their inception QEIs have been applied to a variety of physical problems; they form the basis of the arguments constraining exotic spacetimes such as the warp drive [2, 27] and traversable wormholes [26, 19].”
BackgroundScalar field quantum inequalities in static spacetimes
Pfenning, M. J., & Ford, L. H. (1998) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.57.3489 · Cited by 70 · see citing works
Warp drive with zero expansion
Natário, J. (2002) · Classical and Quantum Gravity · doi:10.1088/0264-9381/19/6/308 · Cited by 70 · see citing works
Holographic proof of the averaged null energy condition
Kelly, W. R., & Wall, A. C. (2014) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.90.106003 · Cited by 61 · see citing works
A Quantum Weak Energy Inequality for Spin-One Fields in Curved Spacetime
Fewster, C. J., & Pfenning, M. J. (2003) · CERN Document Server (European Organization for Nuclear Research) · Cited by 61 · see citing works
Classical scalar fields and the generalized second law
Ford, L. H., & Roman, T. A. (2001) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.64.024023 · Cited by 57 · see citing works
On wormholes with arbitrarily small quantities of exotic matter
Fewster, C. J., & Roman, T. A. (2005) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.72.044023 · Cited by 56 · see citing works
Bounds on negative energy densities in static space-times
Fewster, C. J., & Teo, E. (1999) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.59.104016 · Cited by 56 · see citing works
Explanatory and illustrative visualization of special and general relativity
Weiskopf, D., Borchers, M. P., Ertl, T., Falk, M., Fechtig, O., Frank, R., Grave, F., King, A. P., Kraus, U., Müller, T., et al. (2006) · IEEE Transactions on Visualization and Computer Graphics · doi:10.1109/tvcg.2006.69 · Cited by 53 · see citing works
“which allows for faster-than-light travel [27].”
Breaking the warp barrier: hyper-fast solitons in Einstein–Maxwell-plasma theory
Lentz, E. W. (2021) · Classical and Quantum Gravity · doi:10.1088/1361-6382/abe692 · Cited by 50 · see citing works
Integration in action: four international case studies
Bethge, S. (2012) · International Journal of Integrated Care · doi:10.5334/ijic.981 · Cited by 51 · see citing works
Weak Energy Condition Violation and Superluminal Travel
Lobo, F., & Crawford, P. (2003) · Lecture Notes in Physics · doi:10.1007/3-540-36973-2_15 · Cited by 48 · see citing works
“However, it moves along a spacetime temporal trajectory, contained within it’s light cone, for light suffers the same distortion of spacetime [3].”
Quantum inequalities do not forbid spacetime shortcuts
Krasnikov, S. (2003) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.67.104013 · Cited by 48 · see citing works
From the Flamm–Einstein–Rosen bridge to the modern renaissance of traversable wormholes
Lobo, F. S. N. (2016) · International Journal of Modern Physics D · doi:10.1142/s0218271816300172 · Cited by 48 · see citing works
Special Relativity and Motions Faster than Light
Fayngold, M., & Cramer, J. G. (2002) · Wiley eBooks · doi:10.1002/3527602763 · Cited by 47 · see citing works
Constraints on spatial distributions of negative energy
Borde, A., Ford, L. H., & Roman, T. A. (2002) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.65.084002 · Cited by 47 · see citing works
Semiclassical instability of dynamical warp drives
Finazzi, S., Liberati, S., & Barceló, C. (2009) · Physical Review D · doi:10.1103/physrevd.79.124017 · Cited by 46 · see citing works
Introducing physical warp drives
Bobrick, A., & Martire, G. (2021) · Classical and Quantum Gravity · doi:10.1088/1361-6382/abdf6e · Cited by 45 · see citing works
“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).”
BackgroundMethodInfluentialQuantum inequalities and singular negative energy densities
Ford, L. H., Pfenning, M. J., & Roman, T. A. (1998) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.57.4839 · Cited by 45 · see citing works
Generic warp drives violate the null energy condition
Santiago, J., Schuster, S., & Visser, M. (2022) · Physical Review D · doi:10.1103/physrevd.105.064038 · Cited by 42 · see citing works
Comments on Jacobson’s “entanglement equilibrium and the Einstein equation”
Casini, H., Galante, D. A., & Myers, R. C. (2016) · Journal of High Energy Physics · doi:10.1007/jhep03(2016)194 · Cited by 37 · see citing works
“In particular, they may have important consequences for our understanding of the cosmological constant problem, early universe cosmology and perhaps warp drive engineering [51].”
Quantum inequalities in curved two-dimensional spacetimes
Vollick, D. N. (2000) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.61.084022 · Cited by 40 · see citing works
Time travel paradoxes, path integrals, and the many worlds interpretation of quantum mechanics
Everett, A. E. (2004) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.69.124023 · Cited by 40 · see citing works
NEGATIVE ENERGY DENSITIES IN QUANTUM FIELD THEORY
Ford, L. H. (2010) · International Journal of Modern Physics A · doi:10.1142/s0217751x10049633 · Cited by 39 · see citing works
Topological censorship and chronology protection
Friedman, J., & Higuchi, A. (2005) · Annalen der Physik · doi:10.1002/andp.200510172 · Cited by 38 · see citing works
Spatially averaged quantum inequalities do not exist in four-dimensional spacetime
Ford, L. H., Helfer, A. D., & Roman, T. A. (2002) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.66.124012 · Cited by 38 · see citing works
NASA breakthrough propulsion physics program
Millis, M. G. (1999) · Acta Astronautica · doi:10.1016/s0094-5765(99)00045-4 · Cited by 38 · see citing works
Local Thermal Equilibrium States and Quantum Energy Inequalities
Schlemmer, J., & Verch, R. (2008) · Annales Henri Poincaré · doi:10.1007/s00023-008-0380-x · Cited by 37 · see citing works
“This could, a priori, lead to solutions of Einstein’s equations exhibiting very strange spacetime geometries, such as spacetimes with closed timelike curves, wormholes or “warpdrive scenarios” [30, 1].”
Engineering the Zero-Point Field and Polarizable Vacuum For Interstellar FlightPreprint
Puthoff, H. E., Little, S. R., & Ibison, M. (2001) · arXiv (Cornell University) · doi:10.48550/arxiv.astro-ph/0107316 · Cited by 37 · see citing works
Warp drive with zero expansionPreprint
Natário, J. (2001) · Cited by 37 · see citing works
Can a negative-mass cosmology explain dark matter and dark energy?
Socas‐Navarro, H. (2019) · Astronomy and Astrophysics · doi:10.1051/0004-6361/201935317 · Cited by 35 · see citing works
“If negative masses exist then it would be possible to build an Alcubierre drive (Alcubierre 1994).”
BackgroundGödel-type universes and chronology protection in Hořava–Lifshitz gravity
Fonseca–Neto, J. B., Petrov, A. Y., & REBOUÇAS, M. J. (2013) · Physics Letters B · doi:10.1016/j.physletb.2013.07.018 · Cited by 35 · see citing works
Dynamics of false vacuum bubbles: beyond the thin shell approximation
Hansen, J., Hwang, D.-I., & Yeom, D.-H. (2009) · Journal of High Energy Physics · doi:10.1088/1126-6708/2009/11/016 · Cited by 37 · see citing works
Time, Closed Timelike Curves and Causality
Lobo, F. S. N., & Crawford, P. (2003) · Springer eBooks · doi:10.1007/978-94-010-0155-7_30 · Cited by 34 · see citing works
“Within the framework of general relativity, it is possible to warp spacetime in a small bubblelike region [11], in such a way that the bubble may attain arbitrarily large velocities, v(t).”
Visualization of Four-Dimensional Spacetimes
Weiskopf, D. (2001) · Cited by 34 · see citing works
Long, K. F. (2011) · Springer eBooks · doi:10.1007/978-1-4614-0607-5 · Cited by 33 · see citing works
González-Dı́az, P. F. (2000) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.62.044005 · Cited by 34 · see citing works
Construction of a 3D wormhole supported by phantom energy
Farook Rahaman, A., Kalam, M., Bhui, B., & Chakraborty, S. (2007) · Physica Scripta · doi:10.1088/0031-8949/76/1/010 · Cited by 32 · see citing works
Speed limits in general relativity
Low, R. J. (1999) · Classical and Quantum Gravity · doi:10.1088/0264-9381/16/2/016 · Cited by 32 · see citing works
“It therefore follows that a warp drive can only be constructed in the presence of exotic matter, confirming the suspicion voiced in Alcubierre (1994).”
InfluentialEngineering negative stress-energy densities with quantum energy teleportation
Funai, N., & Martín-Martínez, E. (2017) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.96.025014 · Cited by 31 · see citing works
Traversable acausal retrograde domains in spacetime
Tippett, B. K., & Tsang, D. (2017) · Classical and Quantum Gravity · doi:10.1088/1361-6382/aa6549 · Cited by 30 · see citing works
“The Alcubierre warp drive [1] can be used to generate CTCs [9, 15]; as can the Krasnikov tube [10, 23].”
ABC of multi-fractal spacetimes and fractional sea turtles
Calcagni, G. (2016) · The European Physical Journal C · doi:10.1140/epjc/s10052-016-4021-0 · Cited by 30 · see citing works
“characteristic time . t∗, i.e., below the scales of Standard-Model interactions. Therefore, even if the multi-fractional theory with q-derivatives can avoid the side effects that super-luminal travel [43] entails in Einstein gravity (existence of exotic matter [43–45] and quantum instability due to a thermal flux of Haw…”
BackgroundEnergy conditions and classical scalar fields
Stefano Bellucci, A., & Faraoni, V. (2002) · Nuclear Physics B · doi:10.1016/s0550-3213(02)00437-6 · Cited by 30 · see citing works
Quantum Inequality Restrictions on Negative Energy Densities in Curved SpacetimesPreprint
Pfenning, M. J., & Ford, L. H. (1998) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/9805037 · Cited by 30 · see citing works
Stress Tensor Fluctuations and Stochastic Spacetimes
Ford, L. H. (2000) · International Journal of Theoretical Physics · doi:10.1023/a:1003637613913 · Cited by 28 · see citing works
Simple and double walled Krasnikov tubes: I. Tubes with low masses
Gravel, P., & Plante, J.-L. (2004) · Classical and Quantum Gravity · doi:10.1088/0264-9381/21/4/l01 · Cited by 28 · see citing works
Closed timelike curves in asymmetrically warped brane universes
Päs, H., Pakvasa, S., Dent, J. B., & Weiler, T. J. (2009) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.80.044008 · Cited by 28 · see citing works
“These include Gödel’s rotating universe [2], van Stockum’s and Tipler’s rotating cylinders [3, 4], Gott’s pair of moving cosmic strings [5], Wheeler’s space-time foam [6], regions inside the horizon of Kerr- and Kerr-Newman geometries [7], Alcubierre’s warp drive [8], and Ori’s vacuum torus [9].”
Wormhole geometries in fourth-order conformal Weyl gravity
Varieschi, G. U., & AultONeal, K. (2016) · International Journal of Modern Physics D · doi:10.1142/s0218271816500644 · Cited by 28 · see citing works
Wesley, D. (2009) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2009/01/041 · Cited by 28 · see citing works
Quantum tunneling and quasinormal modes in the spacetime of the Alcubierre warp drive
Jusufi, K., Sakallı, İ., & Övgün, A. (2017) · General Relativity and Gravitation · doi:10.1007/s10714-017-2330-8 · Cited by 27 · see citing works
Alcubierre, M., & Lobo, F. S. N. (2017) · Fundamental Theories of Physics · doi:10.1007/978-3-319-55182-1_11 · Cited by 27 · see citing works
Self-citationRelativistic Bohmian trajectories of photons via weak measurements
Foo, J., Asmodelle, E., Lund, A. P., & Ralph, T. C. (2022) · Nature Communications · doi:10.1038/s41467-022-31608-6 · Cited by 26 · see citing works
“We finally draw a connection between the relativistic wavefunction and the Alcubierre metric [31], proposing this as a relativistic generalisation to the quantum potential [5] which is usually understood as guiding the particle in the nonrelativistic limit.”
BackgroundMethodBlack holes in a swirling universe
Astorino, M., Martelli, R., & Viganò, A. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.106.064014 · Cited by 26 · see citing works
Simple and double walled Krasnikov tubes: II. Primordial microtubes and homogenization
Gravel, P. (2004) · Classical and Quantum Gravity · doi:10.1088/0264-9381/21/4/001 · Cited by 25 · see citing works
Effingham, N. (2020) · doi:10.1093/oso/9780198842507.001.0001 · Cited by 28 · see citing works
Fluid dynamics in the warp drive spacetime geometry
Santos-Pereira, O. L., Abreu, E. M. C., & Ribeiro, M. B. (2021) · The European Physical Journal C · doi:10.1140/epjc/s10052-021-08921-3 · Cited by 29 · see citing works
A Discussion of Space-Time Metric Engineering
White, H. G. (2003) · General Relativity and Gravitation · doi:10.1023/a:1026247026218 · Cited by 24 · see citing works
Quantum inequalities for the free Rarita-Schwinger fields in flat spacetime
Yu, H., & Wu, P. (2004) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.69.064008 · Cited by 24 · see citing works
QUASIPARTICLE UNIVERSES IN BOSE–EINSTEIN CONDENSATES
Fischer, U. R. (2004) · Modern Physics Letters A · doi:10.1142/s0217732304015099 · Cited by 23 · see citing works
Assessing Potential Propulsion Breakthroughs
Millis, M. G. (2005) · Annals of the New York Academy of Sciences · doi:10.1196/annals.1370.023 · Cited by 23 · see citing works
“The warp drive concept involves moving a bubble of spacetime that carries a vehicle within [Alcubierre 1994].”
InfluentialCausality-violating Higgs singlets at the LHC
Ho, C. M., & Weiler, T. J. (2013) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.87.045004 · Cited by 22 · see citing works
“In chronological order (perhaps not the best listing scheme for CTC proposals), proposals include van Stockum and Tipler’s rotating cylinder [1, 2], Gödel’s rotating universe [3], Wheeler’s spacetime foam [4], Kerr and Kerr-Newman’s black hole event horizon interior [5], Morris, Throne and Yurtsever’s traversable worm…”
A Type D Non-Vacuum Spacetime with Causality Violating Curves, and Its Physical Interpretation
Ahmed, F. (2017) · Communications in Theoretical Physics · doi:10.1088/0253-6102/68/6/735 · Cited by 22 · see citing works
Alcubierre warp drive: On the matter of matter
McMonigal, B., Lewis, G. F., & O’Byrne, P. (2012) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.85.064024 · Cited by 22 · see citing works
Dust content solutions for the Alcubierre warp drive spacetime
Santos-Pereira, O. L., Abreu, E. M. C., & Ribeiro, M. B. (2020) · The European Physical Journal C · doi:10.1140/epjc/s10052-020-8355-2 · Cited by 25 · see citing works
“Alcubierre also stated [1] that the warp drive is possible without the use of non trivial topologies, such as wormholes.”
BackgroundMethodInfluentialMars, M., Mena, F. C., & Vera, R. (2013) · General Relativity and Gravitation · doi:10.1007/s10714-013-1574-1 · Cited by 21 · see citing works
“This is of course reminiscent to the superluminal warp drive discovered by Alcubierre [1].”
Four-dimensional non-linear ray tracing as a visualization tool for gravitational physics
Weiskopf, D. (2002) · Visualization · doi:10.1109/visual.2000.885728 · Cited by 21 · see citing works
Making the universe safe for historians: Time travel and the laws of physics
Woodward, J. F. (1995) · Foundations of Physics Letters · doi:10.1007/bf02187529 · Cited by 20 · see citing works
Hyopthetical Gravity Control and Possible Influence on Space Propulsion
Tajmar, M., & Orfeu Bertolami, A. (2005) · Journal of Propulsion and Power · doi:10.2514/1.15240 · Cited by 21 · see citing works
Effingham, N. (2020) · Oxford University Press eBooks · doi:10.1093/oso/9780198842507.003.0005 · Cited by 19 · see citing works
Pure radiation metric with stable closed timelike curves
Sarma, D., Patgiri, M., & Ahmed, F. (2013) · General Relativity and Gravitation · doi:10.1007/s10714-013-1633-7 · Cited by 20 · see citing works
- Authors
- Alcubierre, M.
- Affiliations
- University of Wales (GB)
- Corresponding author
- Alcubierre, Miguel
- ORCID
- Alcubierre, Miguel
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 1994-05-01
- Volume
- 11
- Issue
- 5
- Pages
- L73-L77
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2118757814
- Semantic Scholar
- 0e1f6aaae0fc62e638e46804c418ad71d27b6533
- Cited by
- 569
- References
- 3
- Citations by year
- 2026: 25 · 2025: 41 · 2024: 30 · 2023: 24 · 2022: 30 · 2021: 22 · 2020: 42 · 2019: 18 · 2018: 12 · 2017: 24 · 2016: 16 · 2015: 8 · 2014: 8 · 2013: 22 · 2012: 21
- FWCI
- 8.84
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- warp drive, faster-than-light travel, general relativity, spacetime distortion, exotic matter, wormholes, superluminal motion
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
