Abstract
Presentism is, roughly, the metaphysical doctrine that maintains that whatever exists, exists in the present. The compatibility of presentism with the theories of special and general relativity was much debated in recent years. It has been argued that at least some versions of presentism are consistent with time-orientable models of general relativity. In this paper we confront the thesis of presentism with relativistic physics, in the strong gravitational limit where black holes are formed. We conclude that the presentist position is at odds with the existence of black holes and other compact objects in the universe. A revision of the thesis is necessary, if it is intended to be consistent with the current scientific view of the universe.
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Notes
See also the recent review by Mozersky (2011).
Probabilism is the thesis that the universe is such that, at any instant, there is only one past but many alternative futures (Maxwell 1985).
The controversy between Putman and Stein is reviewed by Saunders (2002).
Asymptotic flatness is a property of the geometry of space-time which means that in appropriate coordinates, the limit of the metric at infinity approaches the metric of the flat (Minkowskian) space-time.
These coordinates are usually referred as ‘Schwarzschild coordinates’.
Notice that this can never occur in Minkowski space-time, since there only photons can exist on a null surface. The black hole horizon, a null surface, can be crossed, conversely, by massive particles. The fact that the event horizon is a null surface is demonstrated in most textbook on relativity, see, e.g. Hartle (2003, p. 273) and d’Inverno (2002, p. 215).
ds = cdτ = 0 → dτ = 0, where dτ is the proper temporal separation.
An interesting case is Schwarzschild space-time in the so-called Painlevé-Gullstrand coordinates. In these coordinates the interval reads:
$$ ds^{2}=dT^{2}-\left(dr + \sqrt{\frac{2M}{r}} dT\right)^{2} - r^{2}d\Omega^{2},$$(11)with
$$ T=t + 4M \left(\sqrt{\frac{2M}{r}} + \frac{1}{2} \ln \left| \frac{\sqrt{\frac{2M}{r}}-1}{\sqrt{\frac{2M}{r}}+1} \right|\right).$$(12)If a presentist makes the choice of identifying the present with the surfaces of T = constant, from Eq. 11: ds 2 = −dr 2−r 2 dΩ2. Notice that for r = 2M this is the event horizon, which in turn, is a null surface. Hence, with such a choice, the presentist is considering that the event horizon is the hypersurface of the present, for all values of T. This choice of coordinates makes particularly clear that the usual presentist approach to define the present in general relativity self-defeats her position if space-time allows for black holes.
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Romero, G.E., Pérez, D. Presentism meets black holes. Euro Jnl Phil Sci 4, 293–308 (2014). https://doi.org/10.1007/s13194-014-0085-6
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DOI: https://doi.org/10.1007/s13194-014-0085-6