An Example of a New Type of Cosmological Solution to Einstein's Field Equations
Gödel's 1949 rotating-universe solution — a mathematically consistent cosmology with closed timelike curves
Tradition: General relativity / philosophy of time
A mathematically consistent rotating universe in which closed timelike curves exist — time-travel into the past is permitted by Einstein's equations
Gödel's 1949 contribution to the Einstein 70th-birthday Festschrift exhibits a cosmological solution to Einstein's field equations in which the matter content is a pressure-free perfect fluid rotating about every point and a non-zero cosmological constant. The solution is mathematically consistent but physically pathological in one striking respect: every point lies on a closed timelike curve, so "time-travel into the past" — and hence violation of any global temporal ordering — is permitted by general relativity itself. In the companion philosophical paper "A Remark about the Relationship between Relativity Theory and Idealistic Philosophy" (also 1949), Gödel argued that this shows the ordinary intuitive concept of time must be illusory: if a universe with no global time is physically possible, then global time is not metaphysically essential to physical reality, and the lived "now" must be an artefact of consciousness rather than a feature of the world. The Gödel universe became a touchstone in twentieth-century philosophy of time (Earman, Stein, Savitt) and in the philosophy of general relativity.
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Editions cited
- "An Example of a New Type of Cosmological Solution to Einstein's Field Equations of Gravitation," Reviews of Modern Physics 21 (1949); collected in Kurt Gödel: Collected Works, vol. II (Oxford UP, 1990)
School Embodiments
The Gödel universe is the strongest twentieth-century argument from physics for a block-universe / eternalist conception of time: if intuitive temporal becoming is incompatible with possible solutions to the field equations, becoming cannot be objective.
"It seems that one obtains an unequivocal proof for the view of those philosophers who deny the objectivity of change and consider change as an illusion." (Gödel, "A Remark...", 1949)
Gödel was a lifelong platonist about mathematical and (he thought) physical reality; the use of a mathematical possibility to draw a metaphysical conclusion about the actual world is paradigmatically platonist.
"The mere compatibility with the laws of nature of worlds in which there is no distinguished absolute time, and in which, therefore, no objective lapse of time can exist, throws some light on the meaning of time also in those worlds in which an absolute time can be defined." (Gödel, "A Remark...")
Scientific realism about general relativity: if the field equations have a rotating-universe solution, then the question whether the actual universe is such is a substantive empirical question, not a conceptual one.
"In all cosmological solutions of the gravitational equations a unique world-time exists, but this is not implied by general relativity itself." (Gödel, 1949 paper, §3)
The paper is the source-text for the analytic-metaphysical literature on the reality of tense, time-travel, and the block universe (Lewis, Mellor, Earman).
"The existence of an objective lapse of time, however, means (or, at least, is equivalent to the fact) that reality consists of an infinity of layers of 'now' which come into existence successively. But, if simultaneity is something relative... reality cannot be split up into such layers in an objectively determined way." (Gödel, "A Remark...")
The use of a possible (rotating) universe as evidence about the actual universe presupposes a kind of modal cosmology — taking other solutions as more than mathematical artefacts.
"If the experience of the lapse of time can exist without an objective lapse of time, no reason can be given why an objective lapse of time should be assumed at all." (Gödel, "A Remark...")
Gödel's reasoning is a paradigm rationalist move: from a mathematical possibility to a substantive conclusion about the nature of time, without empirical mediation.
"In our world, ... a temporal succession of layers can be defined; but the very fact that such a definition is possible only in our world shows that the temporal ordering is not an essential feature of physical reality." (Gödel, "A Remark...")
Internal Tensions
The Gödel universe is not (and was not expected by Gödel to be) the actual cosmology — the observed universe shows no global rotation. The philosophical argument depends on the modal move from "physically possible" to "metaphysically informative," which presentists and growing-block theorists resist (Tooley, Markosian, Sider). Whether the existence of pathological solutions teaches anything about the actual structure of time remains contested.
I. Time
The decisive dimension — the paper exhibits a relativistic universe with no global time function; closed timelike curves through every point mean past, present, and future cannot be globally distinguished.
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II. Space
Curved Lorentzian spacetime; the rotating matter induces a non-trivial global geometry.
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III. Matter
Pressure-free dust with non-zero density and angular velocity; Einstein's equations are satisfied with a negative cosmological constant.
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IV. Observer
The observer is "local" — a worldline in the spacetime — and the paper denies that any privileged global "now" picks out the observer's present.
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V. Energy
Energy-momentum tensor of the rotating dust; the cosmological-constant term contributes a constant background.
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VI. Information
The mathematical content of the solution and the philosophical lesson Gödel draws — that the lived "now" is not in the physics itself.
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Personas with the nearest attribute fingerprint
Historical figures whose own classification on the same six-dimensional grid lands closest to this work's. Computed by attribute-agreement on coordinates both address.
Computed school proximity
The work's attribute fingerprint scored against all schools using the same quiz scorer. Useful as a sanity check on the hand-curated embodiments above.
How An Example of a New Type of Cosmological Solution to Einstein's Field Equations resolves each dilemma
51 resolved positions across 4 dimensions, including 23 distinctive where the majority of schools go the other way · 6 unaligned.
Each dimension is sorted so minority positions come first. Mainstream positions are folded into an expandable list.
Time · 9 dilemmas · 5 distinctive
Persistence, the future, and the direction of becoming.
4 mainstream positions
Matter · 7 dilemmas, all mainstream
Observer · 37 dilemmas · 5 distinctive
Mind, agency, and the knower's relation to the known.