STM-D-0760Paper1988Published and peer-reviewed

Wormholes, Time Machines, and the Weak Energy Condition

Michael S. Morris · Kip S. Thorne · Ulvi Yurtsever

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In one page

Michael Morris, Kip Thorne and Ulvi Yurtsever open this famous four-page Letter by changing the question. Physicists usually ask what the laws of physics are, or what they predict about the universe. These three ask instead what constraints the laws place on the activities of an arbitrarily advanced civilisation — and that turns out to be a sharper question than it sounds. If such a civilisation can build and hold open a wormhole for interstellar travel, they show, it can then turn that wormhole into a time machine: leave one mouth at rest, take the other on a near-light-speed round trip so it ages less, and afterwards a traveller crossing from one mouth to the other arrives in the past. Holding the throat open at all requires stress-energy that dips below the ambient vacuum level along a light ray, and the authors build an explicit model out of two charged, perfectly conducting plates with the Casimir vacuum between them.

Why it matters hereChapter 4 treats wormholes and warp geometries as engineering problems in the metric, and this is the Letter that fixed the engineering requirement everyone has argued about since: the throat needs stress-energy that violates the averaged weak energy condition, and the Casimir vacuum is the first candidate anyone reached for. Chapter 2 owns that candidate, and chapter 13 owns the open question the authors leave standing — whether quantum field theory enforces the averaged condition at all.

What it claims

01The central argument, stated in the abstract: if the laws of physics permit an advanced civilisation to create and maintain a wormhole in space for interstellar travel, then that wormhole can be converted into a time machine with which causality might be violatable.Abstract, Physical Review Letters 61, page 1446
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02A Schwarzschild wormhole is useless for travel — its horizon prevents two-way passage and its throat pinches off too fast to cross even once — so preventing pinch-off and horizons requires threading the throat with nonzero stress and energy. That is the whole origin of the exotic-matter requirement.Page 1446, opening argument, Physical Review Letters 61
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03The requirement is then made precise and unavoidable: for any traversable wormhole, a two-sphere surrounding one mouth as seen through the wormhole from the other mouth is an outer trapped surface, which implies the stress-energy tensor must violate the averaged weak energy condition along null geodesics passing through the wormhole.Page 1446, section Wormhole maintenance, Physical Review Letters 61
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04The authors then build an explicit model from the Casimir vacuum: two identical, perfectly conducting spherical plates carrying equal electric charge, placed either side of the throat with a separation much smaller than the throat radius, with the electromagnetic field between them in the Casimir state. The Einstein equations can be satisfied throughout, with the wormhole’s charge and mass as measured by distant observers both equal to the throat radius.Page 1447, the Casimir-vacuum model, Physical Review Letters 61
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05The violation of the averaged condition is compatible with a total nonnegative energy for the plates plus the Casimir field taken together — the accounting stays ordinary — but whether the required plate energy per unit area is allowed depends on quantum-field-theory models of the plates the authors did not attempt, or on a general theorem that does not yet exist.Page 1447, following the force-balance conditions, Physical Review Letters 61
What to watch
06The time-machine construction is mechanical, not exotic: leave the left mouth at rest, accelerate the right mouth to near light speed and bring it back, which the advanced beings can do by pulling on it gravitationally or electrically. The right mouth ages less as seen from outside, so at late times crossing from right to left carries a traveller backward in time. The authors further argue the resulting Cauchy horizon may be fully stable — because the throat’s energy-condition violation makes it act as a diverging lens that damps the waves faster than they blueshift — which would be a counterexample to strong cosmic censorship.Pages 1447 to 1448, section Conversion of wormhole into time machine, with Figure 2, Physical Review Letters 61
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The way in

https://doi.org/10.1103/PhysRevLett.61.1446PUBLICATION. Physical Review Letters volume 61, number 13, pages 1446 to 1449, 26 September 1988; received 21 June 1988. All three authors were at Theoretical Astrophysics, California Institute of Technology, Pasadena. The work was supported in part by National Science Foundation grant AST85-14911. LICENCE, CHECKED 2026-09-08. Crossref registers only the APS default licence for the version of record, and Unpaywall returns is_oa false, oa_status closed and an empty location list; no Creative Commons statement exists, so this page reproduces no text of the article. SOURCE READ. The complete four-page article was retrieved on 2026-09-08 from the APS similarity-checking endpoint listed in the Crossref record, harvest.aps.org, and read in full; the locators below cite the article’s own printed pages and its named sections. The scan is an optical-character reading of the 1988 typesetting, so equations are described in words here rather than transcribed. COMPANION PAPER. Reference 4 of this Letter is the authors’ own longer treatment, Morris and Thorne, American Journal of Physics — at the time still ‘to be published’ — which is on this site at /library/stm-b8b6ab9b94. RELATED PAGES. The energy-condition and quantum-inequality literature this Letter set in motion: energy conditions in general relativity and quantum field theory at /library/stm-1bcd336342, averaged energy conditions and quantum inequalities at /library/stm-5e822858ce, restrictions on negative energy density in flat spacetime at /library/stm-09a7d97555, traversable wormholes supported by Casimir energy at /library/stm-87af684cc9, and the Defense Intelligence Reference Document on traversable wormholes, stargates and negative energy at /library/stm-359019548f.

How to cite it

Michael S. Morris, Kip S. Thorne, Ulvi Yurtsever (1988) Wormholes, Time Machines, and the Weak Energy Condition. doi:10.1103/PhysRevLett.61.1446

Where it sits in the curriculum

The metric, warp drives and wormholes What the vacuum is The unified picture