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On the dimensionality of spacetime
Open accessAbstract
Some superstring theories have more than one effective low-energy limit corresponding to classical spacetimes with different dimensionalities. We argue that all but the (3 + 1)-dimensional one might correspond to `dead worlds', devoid of observers, in which case all such ensemble theories would actually predict that we should find ourselves inhabiting a (3 + 1)-dimensional spacetime. With more or less than one time dimension, the partial differential equations of nature would lack the hyperbolicity property that enables observers to make predictions. In a space with more than three dimensions, there can be no traditional atoms and perhaps no stable structures. A space with less than three dimensions allows no gravitational force and may be too simple and barren to contain observers.
Overview
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Written from the paper’s full text.
TL;DR
Tegmark argues that only a (3+1)-dimensional spacetime is plausibly compatible with observers, because other numbers of time or space dimensions undermine predictability, stability, or complexity. This turns the multiple-dimensionality prediction of some superstring/ensemble theories from a weakness into a possible selection-effect strength.
Key findings
- With more or less than one time dimension, the partial differential equations of nature would lack hyperbolicity and well-posed initial-value problems, so observers could not make predictions with finite error bars; only \(m=1\) permits the required predictability.
- With more than three space dimensions, there are no stable classical atoms or planetary orbits, and the hydrogen atom has no bound states; the two-body problem has no stable orbits and a finite annihilation cross section.
- With fewer than three space dimensions, general relativity has no gravitational force for \(n<3\), and \(n=2\) faces topological problems such as two nerves being unable to cross; such worlds are conjectured to be too simple and barren for observers.
- The paper concludes that all other dimensionalities might be “dead worlds,” so ensemble theories may predict that we should find ourselves in (3+1) dimensions with 100% certainty.
Methods
- Conceptual/analytical letter; no empirical data or sample. It reviews known results on spatial dimensions and presents new arguments about time dimensions.
- Uses the classification of second-order linear PDEs by eigenvalue signs—elliptic, hyperbolic, ultrahyperbolic—and their causal/well-posedness properties, including Asgeirsson’s theorem.
- Applies selection-effect/anthropic reasoning: a probability distribution over spacetime dimensionality should be weighted by whether observers can exist in each case.
Limitations
- The paper explicitly states it has not rigorously demonstrated that observers are impossible for other dimensionalities; it only argues that it is far from obvious that any other \((n,m)\) permits observers, placing the burden of proof on critics.
- It suggests possible future exploration of stable structures in \((4,1)\) via short-distance quantum corrections or string-like particles.
- Evident from the text: the argument is qualitative and plausibility-based, with no empirical tests; it focuses mainly on linear PDEs and only briefly asserts that nonlinear terms cannot rescue locally ill-posed problems.
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Claims the paper makes
21 Own interpretation · 11 No full text of the sources · 6 No basis given · 2 Sources not found · 1 Supported · 1 Partly supported · 1 Not checked yet · accuracy not yet measured
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In the paper
“To compute the theoretically predicted probability distribution for the dimensionality of our spacetime ‡, we clearly need to take into account the selection effect arising from the fact that some of these states are more likely to contain self-aware observers such as us than others.”
§ On the dimensionality of spacetime > Abstract
What the sources say
- Partly supportedcites [3] sourceExperimental — accuracy not yet measured
In “Predictions from Quantum Cosmology” (page not supplied), Vilenkin weights a probability distribution over varying constants of nature by the average number of civilizations in each universe. This supports accounting for observer-selection effects, but the paper does not apply that calculation to a probability distribution for the dimensionality of spacetime. (LLM, conf=0.87)
boostedstates a cause- Asserted: passes — The authors put it forward as true.
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- Partly supported
Every source the paper cites for this claim was checked and supports it.
In the paper
“When n > 3, the two-body problem no longer has any stable orbits as solutions [6].”
§ On the dimensionality of spacetime > L70
What the sources say
- Supportedcites [6] Büchel W, 1963, Physikalische Blätter source
The section on planetary orbits for n > 3 says a planet can follow an exact circular orbit, but that orbit cannot remain stable under small disturbances; otherwise the planet spirals away or falls inward. The paper also rules out orbits whose radius oscillates between a minimum and maximum. Thus it supports the claim about stable orbits, not a claim that no orbit of any kind exists. (LLM, conf=0.93)
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In the paper
“and that the Bayesian prior probabilities of quantum-mechanical origin are completely irrelevant.”
§ On the dimensionality of spacetime > Abstract
plain- Asserted: passes — The authors put it forward as true.
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- Rests on an assumption: Observers can only exist in a world exhibiting a certain minimum complexity, predictability and stability.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“that if observers can only exist in a world exhibiting a certain minimum complexity, predictability and stability, then all such ensemble theories may actually predict that we should find ourselves inhabiting a (3 + 1)-dimensional spacetime with 100% certainty, as illustrated in figure 1, and that the Bayesian prior probabilities of quantum-mechanical origin are completely irrelevant.”
§ On the dimensionality of spacetime > Abstract
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- Rests on an assumption: Observers can only exist in a world exhibiting a certain minimum complexity, predictability and stability.
In the paper
“and traditional quantum atoms cannot be stable either [5].”
§ On the dimensionality of spacetime > L70
What the sources say
- Not checked — no full text of the sourcecites [5] Tangherlini F R, 1963, Nuovo Cimento source
plainstates a cause- Asserted: passes — The authors put it forward as true.
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In the paper
“With more or less than one time dimension, the partial differential equations of nature would lack the hyperbolicity property that enables observers to make predictions.”
§ On the dimensionality of spacetime > Abstract
hedgedstates a cause- Asserted: passes — The authors put it forward as true.
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In the paper
“On the other hand, giving 'initial' data for an elliptic PDE on a non-closed hypersurface, say a plane, is an ill-posed problem.”
§ On the dimensionality of spacetime > Elliptic equations allow well-posed boundary value problems.
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In the paper
“A localized observer can therefore make predictions about its future.”
§ On the dimensionality of spacetime > Elliptic equations allow well-posed boundary value problems.
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In the paper
“The situation in general relativity is analogous [5].”
§ On the dimensionality of spacetime > L70
What the sources say
- Not checked — no full text of the sourcecites [5] Tangherlini F R, 1963, Nuovo Cimento source
plain- Asserted: passes — The authors put it forward as true.
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In the paper
“Elliptic equations allow well-posed boundary value problems.”
§ On the dimensionality of spacetime > Elliptic equations allow well-posed boundary value problems.
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In the paper
“worlds with n < 3 are just too simple and barren to contain observers.”
§ On the dimensionality of spacetime > L70
plainstates a cause- Asserted: passes — The authors put it forward as true.
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In the paper
“Here, we will present an argument for why a world with the same laws of physics as ours and with an (n+m)-dimensional spacetime can only contain observers if the number of time dimensions m = 1, regardless of the number of space dimensions, n.”
§ On the dimensionality of spacetime > L70
plainstates a cause- Asserted: passes — The authors put it forward as true.
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- Rests on an assumption: Observers can only exist in a world exhibiting a certain minimum complexity, predictability and stability.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“If an observer is to be able to make any use of its self-awareness and information-processing abilities, the laws of physics must be such that it can make at least some predictions.”
§ On the dimensionality of spacetime > L72
plainstates a possible cause- Asserted: passes — The authors put it forward as true.
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In the paper
“This means that an observer in a world with no time dimensions (m = 0) would not be able do make any inferences at all about the situation in other parts of space based on what it observes locally.”
§ On the dimensionality of spacetime > Elliptic equations allow well-posed boundary value problems.
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In the paper
“a study of the Schrödinger equation shows that the hydrogen atom has no bound states for n > 3 [5].”
§ On the dimensionality of spacetime > L70
What the sources say
- Not checked — no full text of the sourcecites [5] Tangherlini F R, 1963, Nuovo Cimento source
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In the paper
“A corollary of a remarkable theorem by Asgeirsson [13] is that if we specify u in the cylinder in figure 3, then this determines u throughout the region made up of the truncated double cones.”
§ On the dimensionality of spacetime > Elliptic equations allow well-posed boundary value problems.
What the sources say
- Not checked — no full text of the sourcecites [13] Courant R, 1962 source
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In the paper
“Asgeirsson's theorem also applies to the ultrahyperbolic case as well, showing that initial data on a hypersurface containing both space-like and time-like directions leads to an ill-posed problem.”
§ On the dimensionality of spacetime > L74
What the sources say
- Not checked — no full text of the sourcecites [13] Courant R, 1962 source
plainstates a cause- Asserted: passes — The authors put it forward as true.
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In the paper
“Although this predictability requirement may sound modest, it is in fact only met by a small class of PDEs, essentially those which are hyperbolic.”
§ On the dimensionality of spacetime > L72
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In the paper
“the fundamental Green's function of the Poisson equation ∇ 2 φ = ρ, which gives the electrostatic/gravitational potential of a point particle, is r 2-n for n > 2.”
§ On the dimensionality of spacetime > L70
plain- Asserted: passes — The authors put it forward as true.
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In the paper
“In contrast, if the initial data for a hyperbolic PDE is specified on a hypersurface that is not space-like, the problem becomes ill-posed.”
§ On the dimensionality of spacetime > Elliptic equations allow well-posed boundary value problems.
plainstates a cause- Asserted: passes — The authors put it forward as true.
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In the paper
“Specifically, within the framework of a field theory, it should, by measuring various nearby field values, be able to compute field values at some more distant spacetime points (ones lying along its future world line being particularly useful) with noninfinite error bars.”
§ On the dimensionality of spacetime > L72
plain- Asserted: passes — The authors put it forward as true.
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In the paper
“Hyperbolic equations, on the other hand, allow well-posed initial-value problems.”
§ On the dimensionality of spacetime > Elliptic equations allow well-posed boundary value problems.
plainstates a cause- Asserted: passes — The authors put it forward as true.
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In the paper
“• More or less than one time dimension: insufficient predictability.”
§ On the dimensionality of spacetime > L74
plainstates a cause- Asserted: passes — The authors put it forward as true.
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- Rests on an assumption: Observers can only exist in a world exhibiting a certain minimum complexity, predictability and stability.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“• More than three space dimensions: insufficient stability.”
§ On the dimensionality of spacetime > L74
plainstates a cause- Asserted: passes — The authors put it forward as true.
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- Rests on an assumption: Observers can only exist in a world exhibiting a certain minimum complexity, predictability and stability.
In the paper
“Since a mere minus sign distinguishes space from time, the remaining case (n, m) = (1, 3) is mathematically equivalent to the case where (n, m) = (3, 1) and all particles are tachyons [14] with imaginary rest mass.”
§ On the dimensionality of spacetime > L74
What the sources say
- Not checked — no full text of the sourcecites [14] Asgeirsson L, 1936, Math Ann. source
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In the paper
“Our conclusions are graphically illustrated in figure 1: given the other laws of physics, it is not implausible that only a (3+1)-dimensional spacetime can contain observers that are complex and stable enough to be able to understand and predict their world to any extent at all, for the following reasons.”
§ On the dimensionality of spacetime > L74
hedgedstates a possible cause- Asserted: passes — The authors put it forward as true.
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- Rests on an assumption: Observers can only exist in a world exhibiting a certain minimum complexity, predictability and stability.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Viewed in this light, the multiple dimensionality prediction of some superstring theories is a strength rather than a weakness, since it eliminates the otherwise embarrassing discrete fine-tuning problem of having to explain the 'lucky coincidence' that the compactification mechanism itself happened to single out only a (3 + 1)-dimensional spacetime.”
§ On the dimensionality of spacetime > Additional information
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In the paper
“Also in this case, an observer would be unable to make any predictions since, as described in more detail in [15], well-posed problems require data to be specified in the non-local region outside the lightcones.”
§ On the dimensionality of spacetime > L74
What the sources say
- Not checked — no full text of the sourcecites [15] source
hedgedstates a cause- Asserted: passes — The authors put it forward as true.
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In the paper
“When PDEs give ill-posed problems even locally, in a small neighbourhood of a hypersurface (where we can generically approximate the nonlinear PDEs with linear ones), it is obvious that no nonlinear terms can make them well-posed in a larger neighbourhood.”
§ On the dimensionality of spacetime > L74
boosted- Asserted: passes — The authors put it forward as true.
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None of the sources cited for this claim could be matched to a paper in Crossref, so there is nothing to check it against.
In the paper
“Thus, although application of the so-called weak anthropic principle [16] does in general not appear to give very strong predictions for physical constants [17], its dimensionality predictions may indeed turn out to give the narrowest probability distribution possible.”
§ On the dimensionality of spacetime > Additional information
What the sources say
- Not matchedcites [16] Tegmark M, 1996
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not matchedcites [17] Carter B, 1974
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
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- Not matched
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- It may state two separate claims as one. 8
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In a space with more than three dimensions, there can be no traditional atoms and perhaps no stable structures.”
§ On the dimensionality of spacetime > Abstract
hedgedstates a possible cause- Asserted: passes — The authors put it forward as true.
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In the paper
“A space with less than three dimensions allows no gravitational force and may be too simple and barren to contain observers.”
§ On the dimensionality of spacetime > Abstract
hedgedstates a possible cause- Asserted: passes — The authors put it forward as true.
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In the paper
“Since the tunnelling probabilities between these states are negligible, such a theory for all practical purposes predicts an ensemble of classical (n+m)dimensional spacetimes, and the prediction for the dimensionality takes the form of a probability distribution over n and m [1].”
§ On the dimensionality of spacetime > Abstract
What the sources say
- Not matchedcites [1] Albrecht A, 1994
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plainstates a cause- Asserted: passes — The authors put it forward as true.
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- Rests on an assumption: Many superstring theories have several stable (or extremely long-lived) states that constitute different effective low-energy theories with different spacetime dimensionalities.
- Rests on an assumption: The tunnelling probabilities between different superstring states are negligible.
- Not matched
In the paper
“As was pointed out by Ehrenfest back in 1917 [4], neither classical atoms nor planetary orbits can be stable in a space with n > 3”
§ On the dimensionality of spacetime > L70
What the sources say
- Not checked yetcites [4] Ehrenfest P, 1917, Proc. Amsterdam Acad.
plainstates a cause- Asserted: passes — The authors put it forward as true.
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In the paper
“There are also inflationary models predicting a universe consisting of parts of exponentially large size having different dimensionality [2].”
§ On the dimensionality of spacetime > Abstract
What the sources say
- Not checked — no full text of the sourcecites [2] source
plainstates a cause- Asserted: passes — The authors put it forward as true.
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In the paper
“Another interesting difference, which can be shown by an elegant geometrical argument [10], is that particles become less stable when m > 1.”
- Also stated in: § L72 · plain
“When m > 1, this constraint vanishes [10].”
§ On the dimensionality of spacetime > L72
What the sources say
- Not checked — no full text of the sourcecites [10] Deser S, 1984, Ann. Phys. source
plainstates a cause- Asserted: passes — The authors put it forward as true.
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- Also stated in: § L72 · plain
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In the paper
“For instance, they will be hyperbolic in a metric of the signature (+ ---), corresponding to (n, m) = (3, 1), elliptic in a metric of the signature (+ + + + +), and ultrahyperbolic in a metric of the signature (+ + --).”
§ On the dimensionality of spacetime > Letter to the Editor L73
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In the paper
“there is no gravitational force in general relativity with n < 3.”
§ On the dimensionality of spacetime > L70
What the sources say
boosted- Asserted: passes — The authors put it forward as true.
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In the paper
“Even when m > 1, there is no obvious reason why an observer could not, none the less, perceive time as being one-dimensional, thereby maintaining the pattern of having 'thoughts' in a one-dimensional succession that characterizes our own reality perception.”
§ On the dimensionality of spacetime > L70
hedged- Asserted: passes — The authors put it forward as true.
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In the paper
“Modulo the important caveats in the discussion section, this means that such a world cannot contain any objects that are stable over time, and thus probably cannot contain stable observers.”
§ On the dimensionality of spacetime > L70
hedgedstates a cause- Asserted: passes — The authors put it forward as true.
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In the paper
“It has been argued [7] that organisms would face insurmountable topological problems if n = 2: for instance, two nerves cannot cross.”
§ On the dimensionality of spacetime > L70
What the sources say
- Not checked — no full text of the sourcecites [7] Freeman I M, 1969, Am. J. Phys. source
hedgedstates a cause- Asserted: fails — The authors may not put it forward as true.
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Probably not a substantial claim. The authors may not put it forward as true. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“there are no space-like or time-like hypersurfaces in the ultrahyperbolic case, and hence no well-posed problems †.”
§ On the dimensionality of spacetime > L74
plainstates a cause- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“• Less than three space dimensions: insufficient complexity.”
§ On the dimensionality of spacetime > Additional information
plainstates a cause- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper may give no reason why it holds.
- Rests on an assumption: Observers can only exist in a world exhibiting a certain minimum complexity, predictability and stability.
The paper relies on this without support.
Many superstring theories have several stable (or extremely long-lived) states that constitute different effective low-energy theories with different spacetime dimensionalities.
“Many superstring theories have several stable (or extremely long-lived) states that constitute different effective low-energy theories with different spacetime dimensionalities, corresponding to different compactifications of the many (e.g.11 or 26) dimensions of the fundamental manifold.”
The paper relies on this without support.
The tunnelling probabilities between different superstring states are negligible.
“Since the tunnelling probabilities between these states are negligible”
The paper relies on this without support.
Observers can only exist in a world exhibiting a certain minimum complexity, predictability and stability.
“if observers can only exist in a world exhibiting a certain minimum complexity, predictability and stability”
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ On the dimensionality of spacetime > L70
“Another problem, emphasized by Wheeler et al [8], is the well known fact (see e.g.[9]) that there is no gravitational force in general relativity with n < 3.”
§ On the dimensionality of spacetime > References
“8. Whitrow C J 1955 Brit. J. Phil. 6 13”
Citations
Cites
Methods of Mathematical Physics
Courant, R., & Hilbert, D. R. (1989) · Wiley eBooks · doi:10.1002/9783527617210 · Cited by 8,151
Particle Physics and Inflationary Cosmology
Linde, A. D. (1987) · Physics Today · doi:10.1063/1.881088 · Cited by 1,805
Methods of Mathematical Physics
Courant, R., Hilbert, D., & Teichmann, T. (1962) · Physics Today · doi:10.1063/1.3057861 · Cited by 1,419
The Anthropic Cosmological Principle
Barrow, J. D., Tipler, F. J., & Anderson, J. L. (1987) · Physics Today · doi:10.1063/1.2820190 · Cited by 1,359
Three-dimensional Einstein gravity: Dynamics of flat space
Deser, S., Jackiw, R., & 't Hooft, G. (1984) · Annals of Physics · doi:10.1016/0003-4916(84)90085-x · Cited by 1,222
Schwarzschild field inn dimensions and the dimensionality of space problem
Tangherlini, F. R. (1963) · Il Nuovo Cimento · doi:10.1007/bf02784569 · Cited by 1,003
The Anthropic Cosmological Principle
Campbell, I. C. G. (1987) · Physics Bulletin · doi:10.1088/0031-9112/38/2/028 · Cited by 805
Possibility of Faster-Than-Light Particles
Feinberg, G. (1967) · Physical Review · doi:10.1103/physrev.159.1089 · Cited by 650
Particle Physics and Inflationary Cosmology
Linde, A. (1990) · doi:10.1201/9780367807788 · Cited by 647
Predictions from Quantum Cosmology
Vilenkin, A. (1995) · Physical Review Letters · doi:10.1103/physrevlett.74.846 · Cited by 368
Research works printed but not linked: 1
- Ehrenfest P, 1917, Proc. Amsterdam Acad., 20, 200
Cited by
Sorted by citations
Is "the theory of everything" merely the ultimate ensemble theory?
Tegmark, M. (1998) · CERN Document Server (European Organization for Nuclear Research) · Cited by 222
Self-citationGibbons, G. W. (2003) · Classical and Quantum Gravity · doi:10.1088/0264-9381/20/12/301 · Cited by 216
Is “the Theory of Everything” Merely the Ultimate Ensemble Theory?
Tegmark, M. (1998) · Annals of Physics · doi:10.1006/aphy.1998.5855 · Cited by 264
Self-citationThe Fine-Tuning of the Universe for Intelligent Life
Barnes, L. A. (2012) · Publications of the Astronomical Society of Australia · doi:10.1071/as12015 · Cited by 156
“A number of authors have emphasised the life-permitting properties of the particular combination of one time- and three space-dimensions, going back to Ehrenfest (1917) and Whitrow (1955), summarised in Barrow & Tipler (1986) and Tegmark (1997)32.”
BackgroundLineweaver, C. H. (1998) · The Astrophysical Journal · doi:10.1086/311613 · Cited by 135
Metadata
- Authors
- Tegmark, M.
- Affiliations
- Institute for Advanced Study (US)
- Corresponding author
- Tegmark, Max
- ORCID
- Tegmark, Max
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 1997-04-01
- Volume
- 14
- Issue
- 4
- Pages
- L69-L75
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2098169780
- Semantic Scholar
- 080c1e8b41755c3bce3675fc605c5f3f05a2801e
- Cited by
- 135
- References
- 17
- Citations by year
- 2026: 8 · 2025: 7 · 2024: 3 · 2023: 9 · 2022: 4 · 2021: 7 · 2020: 4 · 2019: 10 · 2018: 1 · 2017: 10 · 2016: 8 · 2015: 8 · 2014: 6 · 2013: 6 · 2012: 3
- FWCI
- 3.60
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Keywords
- spacetime dimensionality, superstring theory, observer problem, hyperbolicity, temporal dimension, extra dimensions, gravitational force, ensemble theory
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.
A language model drew the claims from the paper on 2026-10-31, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-10-31 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
Cited sources are checked with a language model’s help (gpt-6-sol).
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 ›
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