Abstract
It is often claimed that the special theory of relativity (STR) necessitates the block universe view, according to which all the events spread out in space-time are determinate, ‘fixed’ once and for all. After having briefly recalled the basic notions of STR (principle of relativity, constancy of the speed of light, relativity of simultaneity) (Sect. 6.2), I will distinguish and discuss the different arguments taken from STR in favor of the block universe view: the ‘geometric argument’ (the spatialization of time) (Sect. 6.3), the ‘becoming-argument’ (the loss of the becoming) (Sect. 6.4), and the ‘determinateness-argument’ (the determinateness of the future) (Sect. 6.5). Among these, I will focus in particular on the last argument, which can be summarized as follows: STR entails this puzzling consequence that any future event in a given inertial reference frame is already present or past in another inertial reference frame. Any future event is therefore already determinate. I will show that this argument contains a fallacy, and present several replies to it. My conclusion is that the notion of time in STR does not necessarily imply the block universe view; rather, it gives rise to a new ontology that is more complex but nevertheless consistent.
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Notes
- 1.
But Eddington does not exclude the existence of indeterminate events within space-time . In the next page, he gives the example of an “ultimatum,” for which “it was possible to happen or not, consistently with the law of nature. Since physics does not attempt to cover indeterminate events of this kind, the distinction of absolute past and future is not directly important for physics” (1990, p. 52).
- 2.
- 3.
In this volume, Ismael (Chap. 2) provides an interesting solution to this conflict between the psychological time of everyday experience and the static time of the Block Universe .
- 4.
See Sect. 6.5.1 of this chapter for an explanation of this relativistic notion.
- 5.
See Popper (2000, pp. 57–61).
- 6.
On the different meanings of ‘eternalism ’, see Baron and Miller (2013).
- 7.
Dieks (2014, pp. 104–105) stressed that the “block determinism ” is completely different from the “physical determinism ”, which deals with the question whether “the equations of motion have unique solutions once boundary and initial conditions have been specified”.
- 8.
See also Petkov (2009, p. 172): “In the Minkowski four-dimensional world, however, there is no free will, since the entire history of every object is realized and given once and for all as the object’s worldtube.” On the issue of fatalism raised by eternalism , see Miller (2013, pp. 356–358). In this volume (Chap. 8, Sect. 8.5) Berkovitz argues that the block universe view implies the impossibility to change the future but not the impossibility to “influence the actual future to be what it is going to be.” I will come back to this issue at the end of this chapter.
- 9.
Even the “strongest arguments”, according to Smolin (2013, p. 55), who challenges the block universe view in his last book, by reintroducing the notion of “preferred observer ” and “preferred global time” in the framework of the general relativity. See Smolin (2013, chap. 14: “Time Reborn from Relativity”, pp. 164–171).
- 10.
I am summarizing Einstein’s demonstration. See Einstein (1955, appendixes I and II) for the details.
- 11.
See Eddington (1990, p. 48): “It is not very profitable to speculate on the implication of the mysterious \( \sqrt{-1} \), which seems to have the property of turning time into space. It can scarcely be regarded as more than an analytical device.”
- 12.
- 13.
A hyperplane of an n-dimentional space is a n-1 dimentional space.
- 14.
This text comes from the Appendix V, added in the second edition of 1952 (first edition : 1917).
- 15.
For an object with three spatial dimensions, the appropriate notion is a ‘world tube’.
- 16.
See Arthur (2006, p. 141) : “the quantity of time elapsed for a given process (such as a clock keeping time) is measured by the proper time, a quantity that is calculated by taking the integral along the world line of that process of the quantity: τ = ∫ dτ, where dτ = √ (c 2dt 2− dx 2 − dy 2 – dz 2)/c, where x, y, z and t are the co-ordinates in some given inertial frame, and are considered as functions of the proper time τ. The proper time so calculated is invariant to change of frame: it will come out the same no matter what inertial frame (with co-ordinate values x, y, z and t) is chosen”. τ is invariant because dτ = ds/c and ds (the space-time interval) is invariant (see section 6.3.2, where the square of the space-time interval Δs 2 = c 2Δt 2-Δx 2-Δy 2-Δz 2). If the clock is at rest, its space coordinates don’t change: dx = dy = dz = 0, so that: dτ = √ (c 2dt 2)/c = dt. In this case, the coordinate time t indicated by the clock is numerically equal to the proper time τ of the particle (Arthur 2008, p. 219).
- 17.
This can be illustrated by the famous Twin Paradox : the proper time of the twin who stayed on the Earth is greater than the proper time of the twin who travelled on the rocket. But in both cases, the reunion of the twins is located after their departure. On this paradox, see Proietti (Chap. 3 in this volume).
- 18.
- 19.
In the second part of his paper, Gödel points out that general theory of relativity allows possible worlds in which closed world lines exist without exceeding the limit of the speed of the light (Gödel , 1949, pp. 559–560). In these worlds, it is possible to travel in any region of the past, and the ‘earlier-later’ relationship is therefore never objective. But it raises lots of logical and metaphysical paradoxes, like the famous grandfather paradox (see Smeenk and Wüthrich 2011). Commenting Gödel ’s paper, Einstein concluded: “it will be interesting to weigh whether these [Gödel ’s cosmological solutions of the gravitation-equations with causal loops ] are not to be excluded on physical grounds.” (1949, p. 688)
- 20.
From this point of view, the coming into being of an event (becoming present) is “mind-dependent”, it is just “the coming into the present awareness of a sentient organism” (Grünbaum 1963, p. 328).
- 21.
Absolute means here “frame independent .”
- 22.
By convention, the time coordinate is given by ct where c is the speed of light.
- 23.
If a and b are simultaneous for O in the inertial frame of reference K, and if b and c are simultaneous for O′ in K′ in uniform linear motion in relation to K, then a and c are not simultaneous for O′ in K′ (since a and b are not simultaneous for O′ in K′). Strictly speaking, the relation “being simultaneous to” is not to be said intransitive: it is transitive only inside a specified frame of reference.
- 24.
See Sklar (1977, p. 272) : “Whereas the present and past, having occurred or currently occurring, can be said to have determinate reality, the events of the future, whatever they will be, cannot be said to have any kind of ‘determinate’ reality”.
- 25.
See Einstein (1955, p. 32): “Relative to K′, the same event would be fixed in respect of space and time by corresponding values x’, y’, z’, t’, which of course are not identical with x, y, z, t” (my emphasis).
- 26.
See Maxwell (1985, p. 23) : “Probabilism, as understood here, is the thesis that the universe is such that, at any instant, there is only one past but many alternative possible futures-the fundamental laws of the universe being probabilistic and not deterministic ”.
- 27.
Contrary to Laplace ’s determinism , that only has meaning in a Newtonian time, Rietdijk’s pre-determinism is defined without reference to natural laws or causation. Strictly speaking, we should say that for Rietdijk, the event P is not determined but determinate, according to Williams ’ distinction mentioned earlier in the introduction of this chapter. The word “determined” refers to causal law, which is not the case here.
- 28.
Note that we can use the same argument with another reference frame s relative to which P is past. See Rietdijk (1976, p. 599).
- 29.
See Sklar (1985, p. 291) who rejects Putnam’s claim that the principle of ‘No Privileged Observer ’ leads to affirm the transitivity of ‘reality for’ beyond the frames of reference.
- 30.
This point is made by Hofweber and Lange (2016).
- 31.
If existence is reduced to determinateness, it is relative to the different reference frame s and we face Gödel’s objection (1949, p. 558, note 5) that “existence is by its nature something absolute”. See also Mozersky (2000, p. 232), who argues that all events are determinate, because he identifies, like many others, existence and determinateness.
- 32.
Stein ’s argument has been further developed by Clifton and Hogarth (1995), who show that Stein’s proof can be extended to cover a more general kind of objective becoming that is understood to occur from the standpoint of events on the particular worldlines followed by observers .
- 33.
See above note 27.
- 34.
I follow the interpretation of Stein by Pooley (2013, p. 353): “So, to say that all and only events in the past light cone have become, as of some space-time point p, is to say that, while there is a unique matter of fact concerning what has occurred in all regions to the past of p, there is (as of p) a plurality of possibilities open for regions of space-time to p’s absolute future and in its elsewhere. This suggests that a first step towards a relativistic version of the open-future view of passage should be a relativistic generalization of branching-time models to structures that encodes this pattern of relational indeterminacy”. In the rest of his paper, Pooley studies the theories of ‘branching space-time ’ of McCall (1994) and more specifically of Benalp (1992). On branching space-time, see also Proietti (Chap. 3 in this volume).
- 35.
On the question (which I can’t address in this paper), whether simultaneity in STR is a mere convention or a physical fact, see Dieks’s presentation (2014, pp. 107–112).
- 36.
See Callender (2000, pp. 593–594).
- 37.
This is Callender’s conclusion (2000, pp. 592–593).
- 38.
Since A and P are time-like separated, the relation of succession between them (the fact that P is after A) is absolute (see above Sect. 6.4.2).
- 39.
See Clifton and Hogarth (1995, pp. 383–384) : “this situation is hardly more problematic than the corresponding assertion in Newtonian spacetime – that what is real for an observer depends upon where she is located in time. Indeed, location in spacetime would seem to be the most appropriate relativistic generalization of that Newtonian idea.”
- 40.
See Weingard (1972) who uses this reasoning to claim “that all events in special relativistic space-time are real” (p. 121).
- 41.
That is, if P is in the hyperplane of present of the observer .
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Acknowledgments
I wish to thank audiences in Paris (« Philosophie & Physique » seminar, University of Paris Diderot), Sydney (Centre for time, University of Sydney) and Bordeaux (Centre SPH, University Bordeaux Montaigne) for helpful comments and discussions. In particular, I wish to thank Elie During, Philippe Huneman, Kristie Miller, Huw Price , Carlo Rovelli and Blai Pié i Valls for their critical remarks, which helped improving the final version of the paper. An earlier draft was written while I was visiting scholar at the University of Sydney with a grant of the Institut Universitaire de France (IUF). I thank all the members of the philosophy department for their marvelous hospitality.
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Bouton, C. (2017). Is the Future already Present? The Special Theory of Relativity and the Block Universe View. In: Bouton, C., Huneman, P. (eds) Time of Nature and the Nature of Time. Boston Studies in the Philosophy and History of Science, vol 326. Springer, Cham. https://doi.org/10.1007/978-3-319-53725-2_6
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