Eternalism (philosophy of time): Difference between revisions
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==The present== |
==The present== |
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In classical philosophy, time is divided into three distinct regions: the "[[past]]", the "[[present]]", and the "[[future]]". Using that representational model, the past is generally seen as being immutably fixed, and the future as at least partly undefined. As time passes, the moment that was once the present becomes part of the past |
In classical philosophy, time is divided into three distinct regions: the "[[past]]", the "[[present]]", and the "[[future]]". Using that representational model, the past is generally seen as being immutably fixed, and the future as at least partly undefined. As time passes, the moment that was once the present becomes part of the past, and part of the future, in turn, becomes the new present. In this way time is said to pass, with a distinct present moment moving forward into the future and leaving the past behind. One view of this type, [[Presentism (philosophy of time)|presentism]], argues that only the present exists. The present does not travel forward through an environment of time, moving from a real point in the past and toward a real point in the future. Instead, is merely changes. The past and future do not exist and are only concepts used to describe the real, isolated, and changing present. This conventional model presents a number of difficult philosophical problems and may be difficult to reconcile with currently accepted scientific theories such as the [[theory of relativity]].<ref name="SEP-time">{{citation|last1=Markosian |first1=Ned |author-link=Ned Markosian |title=Time |year=2014 |encyclopedia=The Stanford Encyclopedia of Philosophy |edition=Fall 2016 |editor=Edward N. Zalta |url=https://plato.stanford.edu/archives/fall2016/entries/time/ |access-date=November 18, 2017}}</ref> |
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[[File:BarAndRing.svg|thumb|right|180px|The [[Ladder paradox#Bar and ring paradox|bar and ring paradox]] is an example of the [[relativity of simultaneity]]. Both ends of the bar pass through the ring simultaneously in the rest frame of the ring (left), but the ends of the bar pass one after the other in the rest frame of the bar (right).]] |
[[File:BarAndRing.svg|thumb|right|180px|The [[Ladder paradox#Bar and ring paradox|bar and ring paradox]] is an example of the [[relativity of simultaneity]]. Both ends of the bar pass through the ring simultaneously in the rest frame of the ring (left), but the ends of the bar pass one after the other in the rest frame of the bar (right).]] |
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It can be argued that [[special relativity]] eliminates the concept of absolute simultaneity and a universal present: according to the [[relativity of simultaneity]], observers in different [[Frame of reference|frames of reference]] can have different measurements of whether a given pair of events happened at the same time or at different times, with there being no physical basis for preferring one frame's judgments over another's. However, there are events that may be non-simultaneous in all frames of reference: when one event is within the [[light cone]] of another—its causal past or causal future—then observers in all frames of reference show that one event preceded the other. The causal past and causal future are consistent within all frames of reference, but any other time is "elsewhere", and within it there is no present, past, or future. There is no physical basis for a set of events that represents the present.<ref name="Savitt">{{citation|last1=Savitt|first1=Steven F.|title=There's No Time Like the Present (in Minkowski Spacetime)|doi=10.1086/392846|journal=Philosophy of Science|volume=67|issue=S1|date=September 2000|pages=S563–S574|citeseerx=10.1.1.14.6140|s2cid=121275903}}</ref> |
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Many philosophers have argued that relativity implies eternalism.<ref>{{citation|author=Thomas M. Crisp|url=http://people.biola.edu/thomasc/thomasmcrisp/Vita_files/Presentism,%20Eternalism%20and%20Relativity%20Physics.pdf|title=Presentism, Eternalism, and Relativity Physics|work=Einstein, Relativity and Absolute Simultaneity|year=2007|editor1=William Lane Craig|editor2=Quentin Smith|at=footnote 1|access-date=2012-08-07|archive-url=https://web.archive.org/web/20110428024231/http://people.biola.edu/thomasc/thomasmcrisp/Vita_files/Presentism,%20Eternalism%20and%20Relativity%20Physics.pdf|archive-date=2011-04-28|url-status=dead}}</ref> Philosopher of science Dean Rickles |
Many philosophers have argued that relativity implies eternalism.<ref>{{citation|author=Thomas M. Crisp|url=http://people.biola.edu/thomasc/thomasmcrisp/Vita_files/Presentism,%20Eternalism%20and%20Relativity%20Physics.pdf|title=Presentism, Eternalism, and Relativity Physics|work=Einstein, Relativity and Absolute Simultaneity|year=2007|editor1=William Lane Craig|editor2=Quentin Smith|at=footnote 1|access-date=2012-08-07|archive-url=https://web.archive.org/web/20110428024231/http://people.biola.edu/thomasc/thomasmcrisp/Vita_files/Presentism,%20Eternalism%20and%20Relativity%20Physics.pdf|archive-date=2011-04-28|url-status=dead}}</ref> Philosopher of science Dean Rickles says that, "the consensus among philosophers seems to be that special and general relativity are incompatible with presentism."<ref>{{citation|author=Dean Rickles|year=2008|title=Symmetry, Structure, and Spacetime|page=158|isbn=9780444531162|publisher=[[Elsevier]]}}</ref> Christian Wüthrich argues that supporters of presentism can only salvage absolute simultaneity if they reject either [[empiricism]] or relativity.<ref name="Wuthrich2010">{{cite book |first=Christian |last=Wüthrich |year=2010 |chapter=No Presentism in Quantum Gravity |title=Space, Time, and Spacetime: Physical and Philosophical Implications of Minkowski's Unification of Space and Time |editor= Vesselin Petkov|series=Fundamental Theories of Physics |publisher=Springer |isbn=9783642135378 |lccn=2010935080 |url= http://philsci-archive.pitt.edu/5363/|pages=[https://books.google.com/books?id=t35AR6–F5QQC&pg=PA262 262–264]}}</ref> [[Dean Zimmerman (philosopher)|Dean Zimmerman]] and others argue for [[Absolute space and time|a single privileged frame]] whose judgments about length, time and simultaneity are the ''true'' ones, even if there is no empirical way to distinguish this frame.<ref name="Zimmerman2011">{{cite book |first=Dean |last=Zimmerman |editor= C. Callender |year=2011 |title=The Oxford Handbook of Philosophy of Time |chapter=Presentism and the Space-Time Manifold |series=Oxford Handbooks in Philosophy |publisher=OUP Oxford |isbn=9780199298204 |lccn=2011283684 |url=http://fas-philosophy.rutgers.edu/zimmerman/Presentism%20and%20Rel.for.Web.2.pdf |at=pp.163-244 (PDF p.119)}}</ref><ref>{{citation|author=Yuri Balashov|title=Persistence and Spacetime|year=2010|publisher=Oxford University Press|page=222}}</ref> |
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== The flow of time == |
== The flow of time == |
Revision as of 00:44, 28 May 2023
![](http://upload.wikimedia.org/wikipedia/commons/thumb/3/3d/Illustration_of_block_universe.svg/220px-Illustration_of_block_universe.svg.png)
In the philosophy of space and time, eternalism[1] is an approach to the ontological nature of time, which takes the view that all existence in time is equally real, as opposed to presentism or the growing block universe theory of time, in which at least the future is not the same as any other time.[2] Some forms of eternalism give time a similar ontology to that of space, as a dimension, with different times being as real as different places, and future events are "already there" in the same sense other places are already there, and that there is no objective flow of time.[3]
It is sometimes referred to as the "block time" or "block universe" theory due to its description of space-time as an unchanging four-dimensional "block", as opposed to the view of the world as a three-dimensional space modulated by the passage of time.
The present
In classical philosophy, time is divided into three distinct regions: the "past", the "present", and the "future". Using that representational model, the past is generally seen as being immutably fixed, and the future as at least partly undefined. As time passes, the moment that was once the present becomes part of the past, and part of the future, in turn, becomes the new present. In this way time is said to pass, with a distinct present moment moving forward into the future and leaving the past behind. One view of this type, presentism, argues that only the present exists. The present does not travel forward through an environment of time, moving from a real point in the past and toward a real point in the future. Instead, is merely changes. The past and future do not exist and are only concepts used to describe the real, isolated, and changing present. This conventional model presents a number of difficult philosophical problems and may be difficult to reconcile with currently accepted scientific theories such as the theory of relativity.[4]
![](http://upload.wikimedia.org/wikipedia/commons/thumb/d/da/BarAndRing.svg/180px-BarAndRing.svg.png)
It can be argued that special relativity eliminates the concept of absolute simultaneity and a universal present: according to the relativity of simultaneity, observers in different frames of reference can have different measurements of whether a given pair of events happened at the same time or at different times, with there being no physical basis for preferring one frame's judgments over another's. However, there are events that may be non-simultaneous in all frames of reference: when one event is within the light cone of another—its causal past or causal future—then observers in all frames of reference show that one event preceded the other. The causal past and causal future are consistent within all frames of reference, but any other time is "elsewhere", and within it there is no present, past, or future. There is no physical basis for a set of events that represents the present.[5]
Many philosophers have argued that relativity implies eternalism.[6] Philosopher of science Dean Rickles says that, "the consensus among philosophers seems to be that special and general relativity are incompatible with presentism."[7] Christian Wüthrich argues that supporters of presentism can only salvage absolute simultaneity if they reject either empiricism or relativity.[8] Dean Zimmerman and others argue for a single privileged frame whose judgments about length, time and simultaneity are the true ones, even if there is no empirical way to distinguish this frame.[9][10]
The flow of time
Antiquity
Arguments for and against an independent flow of time have been raised since antiquity, represented by fatalism, reductionism, and Platonism: Classical fatalism argues that every proposition about the future exists, and it is either true or false, hence there is a set of every true proposition about the future, which means these propositions describe the future exactly as it is, and this future is true and unavoidable. Fatalism is challenged by positing that there are propositions that are neither true nor false, for example they may be indeterminate. Reductionism questions whether time can exist independently of the relation between events, and Platonism argues that time is absolute, and it exists independently of the events that occupy it.[4]
Earlier, pre-Socratic Greek philosopher Parmenides of Elea had posited that existence is timeless and change is impossible (an idea popularized by his disciple Zeno of Elea and his paradoxes about motion).
Middle ages
The philosopher Katherin A. Rogers argued that Anselm of Canterbury took an eternalist view of time,[11] although the philosopher Brian Leftow argued against this interpretation,[12] suggesting that Anselm instead advocated a type of presentism. Rogers responded to this paper, defending her original interpretation.[13] Rogers also discusses this issue in her book Anselm on Freedom, using the term "four-dimensionalism" rather than "eternalism" for the view that "the present moment is not ontologically privileged", and commenting that "Boethius and Augustine do sometimes sound rather four-dimensionalist, but Anselm is apparently the first consistently and explicitly to embrace the position."[14] Taneli Kukkonen argues in the Oxford Handbook of Medieval Philosophy that "what Augustine's and Anselm's mix of eternalist and presentist, tenseless and tensed language tells is that medieval philosophers saw no need to choose sides" the way modern philosophers do.[15]
Augustine of Hippo wrote that God is outside of time—that time exists only within the created universe. Thomas Aquinas took the same view, and many theologians agree. On this view, God would perceive something like a block universe, while time might appear differently to the finite beings contained within it.[16]
Modern period
One of the most famous arguments about the nature of time in modern philosophy is presented in The Unreality of Time by J. M. E. McTaggart.[17] It argues that time is an illusion. McTaggart argued that the description of events as existing in absolute time is self-contradictory, because the events have to have properties about being in the past and in the future, which are incompatible with each other. McTaggart viewed this as a contradiction in the concept of time itself, and concluded that reality is non-temporal. He called this concept the B-theory of time.[4]
Dirck Vorenkamp, a professor of religious studies, argued in his paper "B-Series Temporal Order in Dogen's Theory of Time"[18] that the Zen Buddhist teacher Dōgen presented views on time that contained all the main elements of McTaggart's B-series view of time (which denies any objective present), although he noted that some of Dōgen's reasoning also contained A-Series notions, which Vorenkamp argued may indicate some inconsistency in Dōgen's thinking.
A. Halliday has attempted to rationalise time by arguing that it is finite.[citation needed] This was founded on the thought that, if an entity has, or is assigned, parts then those parts must be finite. Assembling finite parts must result in a finite whole. Therefore, it follows that past, present and future are finite. It then follows that, as they also form a whole, then the whole of time is finite.
In the simplest case, if time is finite then it is limited. Time is thought of as existing inside of space. If there cannot be a gap between the edge of time and the limits of space, then time fills all of space, ensuring change everywhere. Therefore, time cannot flow if flow demands movement from one point to another?
Quantum physics
Some philosophers appeal to a specific theory that is "timeless" in a more radical sense than the rest of physics, the theory of quantum gravity. This theory is used, for instance, in Julian Barbour's theory of timelessness.[19] On the other hand, George Ellis argues that time is absent in cosmological theories because of the details they leave out.[20]
Recently, Hrvoje Nikolić has argued that a block time model solves the black hole information paradox.[21]
Objections
Philosophers such as John Lucas argue that "The Block universe gives a deeply inadequate view of time. It fails to account for the passage of time, the pre-eminence of the present, the directedness of time and the difference between the future and the past."[22] Similarly, Karl Popper argued in his discussion with Albert Einstein against determinism and eternalism from a common-sense standpoint.[23]
A flow-of-time theory with a strictly deterministic future, which nonetheless does not exist in the same sense as the present, would not satisfy common-sense intuitions about time. Some have argued that common-sense flow-of-time theories can be compatible with eternalism, for example John G. Cramer’s transactional interpretation. Kastner (2010) "proposed that in order to preserve the elegance and economy of the interpretation, it may be necessary to consider offer and confirmation waves as propagating in a “higher space” of possibilities.[24]
In Time Reborn, Lee Smolin argues that time is physically fundamental, in contrast to Einstein's view that time is an illusion. Smolin hypothesizes that the laws of physics are not fixed, but rather evolve over time via a form of cosmological natural selection.[25][26] In The Singular Universe and the Reality of Time, co-authored with philosopher Roberto Mangabeira Unger, Smolin goes into more detail on his views on the physical passage of time. In contrast to the orthodox block universe view, Smolin argues that what instead exists is a "thick present"[27][28] in which two events in the present can be causally related to each other. Marina Cortês and Lee Smolin also argue that certain classes of discrete dynamical systems demonstrate time asymmetry and irreversibility, which is inconsistent with the block universe interpretation of time.[29]
Avshalom Elitzur vehemently rejects the block universe interpretation of time. At the Time in Cosmology conference, held at the Perimeter Institute for Theoretical Physics in 2016, Elitzur said: "I’m sick and tired of this block universe, ... I don’t think that next Thursday has the same footing as this Thursday. The future does not exist. It does not! Ontologically, it’s not there."[30] Elitzur and Shahar Dolev argue that quantum mechanical experiments such as the Quantum Liar[31] and the evaporation of black holes[32] challenge the mainstream block universe model, and support the existence of an objective passage of time. Elitzur and Dolev believe that an objective passage of time and relativity can be reconciled, and that it would resolve many of the issues with the block universe and the conflict between relativity and quantum mechanics.[33] Additionally, Elitzur and Dolev believe that certain quantum mechanical experiments provide evidence of apparently inconsistent histories, and that spacetime itself may therefore be subject to change affecting entire histories.[34]
In popular culture
In fiction
Ideas related to Eternalism are described in Kurt Vonnegut’s novel, Slaughterhouse-Five. In the context of the novel, the Tralfamadorians are an alien species, members of which experience every point in time simultaneously. A character at one point argues that since all moments exist simultaneously, everyone is always alive-- a claim which implies Eternalism. The protagonist of the story, Billy Pilgrim, additionally lives his life out of sequence. It is stated that each moment of his life exists independent of the others, which is a clause of Eternalism.
Eternalism is also indirectly referenced in the comic book series Watchmen by Alan Moore. At one point, the character Dr. Manhattan describes how he perceives time in a manner which is consistent with Eternalism. He states that, from his perspective, the past, present, and future occur simultaneously. This is evidenced when he speaks about past or future events in the present tense, which is a frequent occurrence. His last line in the series is, "Nothing ends, Adrian. Nothing ever ends."
The science fiction novel The Number of the Beast , by Robert A. Heinlein, explores concepts related to Block Time. One protagonist, the mathematician Dr. Jacob Burroughs, invents a device which navigates through time as one scalar dimension in a six-dimensional universe. The novel unfolds across a variety of parallel worlds. Along with block time, it is implied that there exists a block plenum of innumerable alternate universes, with each being separated by one quantum step along an axis of space-time.[35]
The game Warframe introduces eternalism in the story quest "The New War." The example provided in the game describes a situation in which a girl's parents are trapped in separate cells, but the girl can only save one of them, as the other parent will be killed in response. According to the rules of eternalism, as explained by one of the characters, there will be different versions of reality regarding which parent is saved. The reason provided is that though the girl is assigned to one future, the other is no less real.
See also
- A series and B series
- Arrow of time
- Eternity of the world
- Introduction to special relativity
- Philosophical presentism
- Philosophy of space and time
- Problem of time
- Static interpretation of time
- Strata-cut animation
References
- ^ Le Bihan, Baptiste (2020). "String theory, loop quantum gravity and eternalism". European Journal for Philosophy of Science. 10 (2): 17. arXiv:2005.09335. doi:10.1007/s13194-020-0275-3. S2CID 210958803.
- ^ Kuipers, Theo A.F. (2007). General Philosophy of Science: Focal Issues. North Holland. p. 326. ISBN 978-0-444-51548-3.
- ^ Tim Maudlin (2010), "On the Passing of Time", The Metaphysics Within Physics, ISBN 9780199575374
- ^ a b c Markosian, Ned (2014), "Time", in Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy (Fall 2016 ed.), retrieved November 18, 2017
- ^ Savitt, Steven F. (September 2000), "There's No Time Like the Present (in Minkowski Spacetime)", Philosophy of Science, 67 (S1): S563–S574, CiteSeerX 10.1.1.14.6140, doi:10.1086/392846, S2CID 121275903
- ^ Thomas M. Crisp (2007), William Lane Craig; Quentin Smith (eds.), "Presentism, Eternalism, and Relativity Physics" (PDF), Einstein, Relativity and Absolute Simultaneity, footnote 1, archived from the original (PDF) on 2011-04-28, retrieved 2012-08-07
- ^ Dean Rickles (2008), Symmetry, Structure, and Spacetime, Elsevier, p. 158, ISBN 9780444531162
- ^ Wüthrich, Christian (2010). "No Presentism in Quantum Gravity". In Vesselin Petkov (ed.). Space, Time, and Spacetime: Physical and Philosophical Implications of Minkowski's Unification of Space and Time. Fundamental Theories of Physics. Springer. pp. 262–264. ISBN 9783642135378. LCCN 2010935080.
- ^ Zimmerman, Dean (2011). "Presentism and the Space-Time Manifold". In C. Callender (ed.). The Oxford Handbook of Philosophy of Time (PDF). Oxford Handbooks in Philosophy. OUP Oxford. pp.163-244 (PDF p.119). ISBN 9780199298204. LCCN 2011283684.
- ^ Yuri Balashov (2010), Persistence and Spacetime, Oxford University Press, p. 222
- ^ Katherin A. Rogers (2007). "Anselmian Eternalism". Faith and Philosophy 24 (1):3-27.
- ^ Brian Leftow (2009). "Anselmian Presentism. Faith and Philosophy" 26 (3):297-319.
- ^ Katherin Rogers (2009). "Back to Eternalism". Faith and Philosophy 26 (3):320-338.
- ^ Rogers, Katherin (2008). Anselm on Freedom. Oxford University Press. p. 159. ISBN 9780199231676.
- ^ From Kukkonen's chapter on "Eternity" in The Oxford Handbook of Medieval Philosophy edited by John Marenbon (2012), p. 529.
- ^ John Polkinghorne (2011). Science and Religion in Quest of Truth, p. 64.
- ^ J. M. E. McTaggart, "The Unreality of Time", Mind 17: 457–73; reprinted in J. M. E. McTaggart, The Nature of Existence, Vol. 2, 1927, Cambridge: Cambridge University Press: Book 5, Chapter 33.
- ^ Vorenkamp, Dirck (1995). "B-Series Temporal Order in Dogen's Theory of Time". Philosophy East and West, Volume 45, Number 3, 1995 July, P.387-408.
- ^ [Barbour, Julian, The End of Time, 1999 Oxford University Press ]
- ^ Ellis (2006). "Physics in the Real Universe: Time and Spacetime". Gen. Rel. Grav. 38 (12): 1797–1824. arXiv:gr-qc/0605049. Bibcode:2006GReGr..38.1797E. doi:10.1007/s10714-006-0332-z. S2CID 119540219.
- ^ Nikolic H. (2009). "Resolving the black-hole information paradox by treating time on an equal footing with space". Phys. Lett. B. 678 (2): 218–221. arXiv:0905.0538. Bibcode:2009PhLB..678..218N. doi:10.1016/j.physletb.2009.06.029. S2CID 15074164.
- ^ John LucasThe Future p8
- ^ Popper, K.R. (2002). Unended Quest: An Intellectual Autobiography. Routledge Classics. Routledge. pp. 148–150. ISBN 9780415285896. LCCN 2002067996.
- ^ "The Quantum Liar Experiment Kastner". Studies in History and Philosophy of Modern Physics. 41 (2).
- ^ "Time Reborn: a new theory of time - a new view of the world". Royal Society of Arts. May 21, 2013. Archived from the original on July 28, 2013.
- ^ Cortês, Marina; Smolin, Lee (6 October 2014). "The universe as a process of unique events". Physical Review D. 90 (8): 084007. arXiv:1307.6167. Bibcode:2014PhRvD..90h4007C. doi:10.1103/PhysRevD.90.084007. S2CID 118557476.
- ^ Smolin, Lee (2015). "Temporal naturalism". Studies in History and Philosophy of Science Part B. 52: 86–102. arXiv:1310.8539. Bibcode:2015SHPMP..52...86S. doi:10.1016/j.shpsb.2015.03.005. S2CID 8344858.
- ^ Smolin, Lee (30 April 2020). "Temporal Relationalism". In Nick Huggett; Keizo Matsubara; Christian Wuthrich (eds.). Beyond Spacetime. pp. 143–175. arXiv:1805.12468. doi:10.1017/9781108655705.010. ISBN 9781108655705. S2CID 118936279.
- ^ Cortês, Marina; Smolin, Lee (10 January 2018). "Reversing the irreversible: From limit cycles to emergent time symmetry". Physical Review D. 97 (2): 026004. arXiv:1703.09696. Bibcode:2018PhRvD..97b6004C. doi:10.1103/PhysRevD.97.026004. S2CID 119067096.
- ^ Falk, D. (2016, July 19). A Debate Over the Physics of Time. Retrieved February 14, 2019, from https://www.quantamagazine.org/a-debate-over-the-physics-of-time-20160719/
- ^ Elitzur, Avshalom C.; Dolev, Shahar (2005). "Quantum Phenomena Within a New Theory of Time". Quo Vadis Quantum Mechanics?. The Frontiers Collection. pp. 325–349. doi:10.1007/3-540-26669-0_17. ISBN 3-540-22188-3.
- ^ Elitzur, Avshalom C.; Dolev, Shahar (1999). "Black Hole Evaporation Entails an Objective Passage of Time". Foundations of Physics Letters. 12 (4): 309–323. arXiv:quant-ph/0012081. Bibcode:1999FoPhL..12..309E. doi:10.1023/A:1021644319368. S2CID 15532826.
- ^ Elitzur, Avshalom C.; Dolev, Shahar (2005). "Becoming as a bridge between quantum mechanics and relativity". Endophysics, Time, Quantum and the Subjective. pp. 589–606. doi:10.1142/9789812701596_0031. ISBN 978-981-256-509-9.
- ^ Elitzur, A. C.; Dolev, S. (2003). "Is there more to T". The Nature of Time: Geometry, Physics and Perception. Dordrecht: Springer. pp. 297–306. arXiv:quant-ph/0207029.
- ^ "Eternalism (Philosophy of time) - the Art and Popular Culture Encyclopedia".
Bibliography
- Smart, Jack. "River of Time". In Anthony Kenny. Essays in Conceptual Analysis. pp. 214–215.
- van Inwagen, Peter (2008). "Metaphysics." Stanford Encyclopedia of Philosophy.
External links
- Biswas; Shaw; Modak (1999). "Time in Quantum Gravity". International Journal of Modern Physics D. 10 (4): 595–606. arXiv:gr-qc/9906010. Bibcode:2001IJMPD..10..595B. doi:10.1142/S0218271801001384. S2CID 119472003.
- Davies, Paul (September 2002). "That Mysterious Flow". Scientific American. 287 (3): 40–45. Bibcode:2002SciAm.287c..40D. doi:10.1038/scientificamerican0902-40. PMID 12197100.
- Markosian, Ned (2002). "Time: 8. The 3D/4D Controversy". Stanford Encyclopedia of Philosophy. Retrieved 2006-12-20.
- Nikolic, Hrvoje. "Block time: Why many physicists still don't accept it?" (PDF).
- Barbour, Julian (1999). The End of Time. Oxford University Press. ISBN 0195145925.