Čapek’s costly route to relativistic presentism by Hayden Wilkinson

It may be claimed that elements of the special theory of relativity, which has extensive empirical and theoretical support[1], directly contradict the central claims of presentism. Despite other unsuccessful attempts to overcome the relativistic objection[2], Milič Čapek (1975) responds to the apparent conflict by attempting to establish an absolute temporal order which, despite relativity, is invariant. His argument appears successful in establishing this absolute order in a localised setting, however the resulting restrictions on the present do pose serious problems, such as the non-existence of any spatially-extended objects in any such present. While relativity does not completely eliminate presentism, I argue that the limitations which it introduces are sufficient to justify an abandonment of the view.

For the purposes of this paper, presentism will refer both to: the ontological claim (i) it is precisely that which is present which exists; and the Heraclitean notion (ii) that there occurs a genuine change as so-called ‘future’ events become present. That is, future and past objects do not genuinely exist but become existent by way of this absolute change, or absolute becoming. Eternalism, or the block theory, will then refer to the view that all past and future events and objects do exist even if they are not present and that there is no becoming or genuine change in events, merely differences in temporal position for observers and the ensuing impression of change. There do, of course, exist other views[3] which accept a set of existent events smaller than that of eternalism and greater than that of the above presentism, or which take a different stance in regards to becoming, but here I will focus on presentism as the view specifically endorsing claims (i) and (ii).

Special relativity, used here[4], will refer to the theory that spatial and temporal distances are relative to the frame of reference in which they are measured. Duration, length and mass dilate or contract in accordance with the relative velocity of the observer and of whatever is under observation (Ives and Stilwell, 1938). Simultaneity of spatially-separated events is not absolute but instead dependent on reference frame. On a Minkowskian spacetime diagram, this is represented as a rotation of the axes – axes which correspond to the present time-slice of simultaneous points across space and to the extensions of stationary points over time (Minkowski, 1910). The theory also postulates that the maximum magnitude of velocity of a particle and of the propogation of any physical process is that of light in a vacuum. Thus, causal interaction cannot occur at a distance in a time any less than that required for light to propogate across the distance. Based on the considerable empirical evidence supporting the theory, particularly in observing a constant speed of light in a vacuum in different reference frames (relative to the frames themselves), it will be treated here as sufficiently well-justified such that a metaphysical view must either be consistent with the theory, or at least with the extensive empirical evidence for it.

The majority of work preceding Čapek considers special relativity to support an eternalist view. Putnam, for instance, begins by accepting that all things present are real. Then, for Observer A in a given reference frame, A themself is real in that present and, for some observer B moving relative to A, B is also real. In B’s reference frame, the ‘present’ is shifted so the future state of A, say A’, occurs in the present of B – that is, A’, who is at the spatial position[5] of A but at a later time, is real for B. If transitivity is allowed, then A’ being real for B and B being real for A gives us the result that A’ is real for A. This may be repeated with increasing speeds of B and additional observers C, D and so on. With no bound on the distance of these observers from A and only the bound of lightspeed on their relative velocity, this establishes the reality of points further into the future of A – indeed, indefinitely far into that future. Conversely, points in the past of all such A’ are also real for them. Putnam claims that, in this way, the reality of future and past entities is ensured by special relativity and hence we are left with the entire eternalist manifold of real events and objects (Putnam, 1967).

Gödel argues that the change and objective lapses in time which occur in the presentist conception require that it is possible that spacetime be foliated into time-slices. The time-slice which the presentist takes as exclusively existent cannot be defined objectively and independently of the observers in those frames, as relativity provides that differences in reference frames shift what is identified as present – the same spacetime points may be past, present or future, depending on the frame (Gödel, 2006). Like Putnam, Gödel takes this as confirming the eternalist proposition that, instead, all events and objects throughout spacetime are real regardless of an observer’s position. Events do not become but rather are encountered by the observer at different positions in time.

One slight problem for this eternalist view which results, which won’t addressed in detail here, is that the reality of those future events may entail that it is logical impossible for them to occur in any way other than that in which they already will. Such a change would lead to contradiction, much like Aristotle’s sea battle, between earlier claims that “x occurs at point Y” and “z occurs at point Y but x does not” which would typically be seen as having a fixed truth value for real future events. Future events may hence be universally determinate and free will a questionable phenomenon, according to an eternalist view accepting bivalence. The strong intuition that future events do not yet exist and are yet to be determined, or that there is some genuine change occurring as time passes, do provide potential motivations for seeking a viable presentist view. In what follows, I will hence examine various candidates for such a view and consider whether they are consistent with special relativity and whether they are viable alternatives to eternalism.

One means of making relativity and presentism compatible which is readily apparent is the adoption of a particular frame of reference as privileged and to judge temporal order, as well as existence of entities, only by that frame. This, however, is an arbitrary specification which lacks the simplicity of other alternatives and provides no additional explanatory capacity. It also denies the basic intuition that the objects we perceive[6] around us are indeed real – if our velocity changes from that privileged frame then the time-slice present implied by that frame will be skewed on the Minkowskian diagram and the objects around us may be located in the non-existent future and/or past of that absolute present. Whether we travel by extremely fast spaceship away from Earth, or whether that privileged frame does not anthropocentrically (and against all likelihood) match our current velocity on the surface of a rotating, orbiting planet, this view entails that the objects and events which we see around us quite often do not exist simply because we are not in that privileged frame. It also discards the element of relativity that entails that physical laws (and presumably metaphysical laws too) act identically in all non-inertial reference frames. It may not be contradictory to dismiss this claim simply for a metaphysical definition of the present but, again, it is an unnecessary complication when the eternalist view is no less counterintuitive and is far more parsimonious[7].

An alternative method of overcoming Putnam’s argument at least is to dismiss his transitivity of realness – such that B may be real for A but that does not imply that C, which is real for B, is also real for A. To overcome Gödel then, we also require a means of specifying the present, which must avoid the arbitrariness seen above. One option is the ‘relativised presentism’ introduced by Hinchliff – “…the real events for an observer are the events simultaneous with that observer… in a relativistic setting [relativised] presentism is the view that the real events for an observer are the events simultaneous with the observer in the observer’s frame of reference…” (Hinchliff, 1996). Such a suggestion may initially appear to provide a clear choice of reference frame and to overcome Gödel’s objection, however the observer-dependence involved in selecting a frame denies the objective existence of any set of events. It is also highly counterintuitive – it denies the the intuitive notion that if we see some other observer then we are indeed real to them, as well as that what is real for them is also real for us (symmetry and transitivity). That is, if B is real for A then A must be real for B, and if A’ is real for B then A’ must be real for A. It does not seem plausible to deny that there can be some present B seeing some future event A’ without that A’ also being real. Due to this strong intuition, the transitive property is not so easily dismissed, nor is the symmetric property. Gödel’s objection might appear to be solved by defining present time-slices for each observer by their frame of reference, however this is insufficient without completely removing both such properties – A’s time-slice intersects B’s and each contains different events and objects which are real for each observer. The specification of what is real for A as dependent on A itself also introduces an observer-dependence which, as mentioned above, lacks the objectivity which we require when establishing an ontology of what is real and what is not. Relativised presentism may give a consistent response of whether some entity is real but this is only by removing observer-independence and by dismissing the transitive property, hence departing greatly from basic intuition and conceivability, arguably more so than eternalism does. Hence, even relativised in this way, presentism encounters difficulty[8].

The view proposed by Čapek, however, considers instead the exact implications of special relativity for the ordering of events. Events separated by time but not by space (for any given non-inertial frame of reference) have the same order in anyy such frame that we might choose. So too do any events separated by distance less than their separation in time t multiplied by c, the speed of light in a vacuum – that is, any events which can be linked causally by physically possible processes. If events are separated in space but not in time (according to some reference frame), or if the separation in space exceeds ct, then their order is not absolute, but this result does not extend to those events separated by spatial distance less than ct. For each point in spacetime, an extended light-cone of past or future points represents the region that is positioned as absolutely earlier or later than the given point, and this light-cone structure is invariant under changes in frame of reference (as all Lorentz transformations of the light-cone return the same light-cone). For any such point, an absolute becoming is indeed conceivable as points in an event’s future cone can never be present in any frame until after the event itself.

This does not, however, appear to establish a present and Gödel’s objection may still appear to hold. To overcome this, Čapek restricts the present from an extended slice in spacetime down to a single frame-invariant point. Absolute becoming cannot hold for ‘now’ (as in Hinchliff’s relativised presentism) but it can for ‘here-and-now’, so he modifies the view to accept only that here-and-now as present. This undermines Putnam’s argument as it does not even admit the initial step that B is real for A. It also overcomes Gödel’s argument since a single point has absolute order with its preceding and subsequent states, invariant under any difference in frame (or even generally under hyperbolic spacetime curvature). It also provides a region of spacetime absolutely earlier than and one absolutely later than that present, allowing for absolute becoming for any given pointlike present. In doing so, it also eliminates the possibility of backwards causation, at least without some non-hyperbolic curvature of spacetime, and of any such point being both earlier and later.

On first impression, Čapek’s revised form of presentism seems highly counterintuitive. If one sees a person across the room, it seems difficult to deny that that person, or any other simultaneous object, exists. However, this follows from a rudimentary Newtonian notion that instantaneous action at a distance is possible. Any impression of, or interaction with, a spatially distant object occurs in time over some finite interval. A perception of such an object is an effect of past events, just as occurs with children observing distant and long-dead stars. It is unintuitive just as it is for the child learning that those stars may already be long since dead. An object across the room is separated in space and cannot have any instantaneous effect on a distant observer so it is entirely inaccessible in the present, and can only interact with us through some future effect. The simultaneous object across the room, separated by space but not time according to our frame of reference, is no more present than a past or future event may be – in fact less so as it is causally inaccessible. A presentist denies the existence of past and future objects as they are simply not present, so denying the existence of so-called ‘present’ but distant objects which are even less accessible and imperceptible is not that bizarre a development. If a presentist view were to be justified by a sceptical denial of that which cannot be accessed, a denial of spatially separated objects would be consistent, if not a direct consequence.

Čapek’s ‘here-now’ presentism has the advantage of full compatibility with relativity. Also, unlike eternalism, it does not claim the reality of future events which, if one admits a principle of bivalence, may commit one to a determinate view of future events, as mentioned above. In addition, it does not imply the existence of objects which are not immediately present. This is more epistemically sound and allows for what appears to be a much simpler ontology. It conclusively rules out backwards causation and the contradictions which it might entail, and the view hence does not seem to be open to a great many possible objections. Čapek himself points out the relative simultaneity of causally unrelated events which may pose a problem for some, but this concerns events neither of which are present for the other and neither of which can possibly affect each other causally. Neither is present and hence existent for the other nor is either at a point in the absolute past which may leave effects in the present of the other. For relativistic presentism formulated with Čapek’s argument, neither event exists at the point of the other nor at any point taken as the ‘past’ or ‘future’ of the other, and hence they simply are not relevant to each other.

The restrictiveness of such a view, however, does lead to various problems. If the present is restricted to a point of ‘here-now’ and a typical presentist view that only that which is present exists, then there is only one point in space which exists for any observer at any given time. It departs from the psychological notion of a ‘specious present’ and from any extension of that point in spacetime. Were the point to be quantised and have some non-zero volume, then it would have spatial points at either end of its non-zero diameter which could be shifted in orienation by a change in reference frame so, for exactitude, we would prefer that points be without volume. However, whether the point have volume or not, no object larger than that point can exist. Given that it cannot have volume, due to shifts in simultaneity in different frames, this applies to all sized objects. A presentist who seeks to accept relativity in this way but maintain the non-existence of non-present objects cannot maintain the present existence of their own body. In fact, at no point in time does their body exist, even if points making up the body may causally influence later present points. Considering, for instance, to the metaphysics of mind, if such a presentist considers the mind to be material, then they accept the non-existence of that mind and most likely of all observers at every possible present. If they consider the mind immaterial and accept some form of solipsism, then the proposition might be conceivable if the brain’s interface to the mind were to occur at a sizeless point in space and they were to reject the notion of an extended physical world, accepting that there are only occurrences at that single point which influence the mind and which allow the sizeless conscious observer to perceive those occurrences which resemble effects of past causes. This may be a slightreductio ad absurdum, which could potentially be avoided by modifying the view in some way or by rejecting the ontological claim of presentism but retaining the Heraclitean claim of absolute becoming, however it highlights that, even with Čapek’s solution, presentism which maintains both claims encounters conceptual difficulties which pure eternalism successfully avoids. Eternalism does not rule out the existence of sized objects, even in a relativistic universe, so the presentist who does not wish to make such a denial or otherwise abandon the ontological claim of presentism has significant reason to not accept Čapek’s ‘here-now’ as that present. The view is still consistent but places greater conceptual restrictions on other areas of metaphysics which can otherwise be avoided with eternalism.

Savitt provides a rather deceptive escape from this. Either a single spacetime point is distinguished as present, which involves unnecessary arbitrariness much like the adoption of an absolute reference frame, or every spacetime point is present with respect to itself. Each and every point is then real with respect to itself, regardless of the observer’s position, which may allow for the existence of other points and of sized objects in some capacity but, as Savitt continues, “…if each point of spacetime is distinguished, then no point of spacetime is metaphysically distinguished from any of the others with respect to presentness.” (Savitt, 2000, S568) Analogously to the arguments against Hinchliff’s relativised presentism, this justifies a form of eternalism by which all points are real. Hence, without serious reformulation, the position of here-now presentism either denies the existence of a great many things, and arbitrarily so, or it is no presentism at all.

A straightforward and fundamental objection provided by Callender, which applies to presentism in general (excluding some modified forms such as that of Godfrey-Smith), is that it inevitably fails to account for past events. This is demonstrated by Callender’s example that a past New York Yankees victory in a baseball tournament, or perhaps by the colonisation of Australia, cannot be very well accounted for (Callender, 2000, S591). The man or woman on the street would accept that they did occur (provided they had sufficient knowledge of these events), or at least agree that the claim of them occurring refers to something real. Presentism in the forms that I have described deny the reality of such events as anything more than causal influences in the present, which may conceivably have been produced by some vastly different event (perhaps an enormous and now forgotten conspiracy to pretend that the Yankees won the tournament or that Australia was colonised at a certain time). For a presentism of the here-now, this is amplified to the even greater number of possible past events which do not directly influence a particular point. Without definitive well-determined facts in the present, no such facts of the past can be accounted for or claimed to refer to any real thing without expanding that which is real into the past in perhaps the manner of Godfrey-Smith (1979) or Broad (1927). The same applies for points spatially distant from the here-now under Čapekian relativistic presentism – if they fail to exist, then referring to objects or events at these points is problematic. Given the sizeless point which constitutes the here-now, accounting for reference to anything of size beyond that point is an ill-fated task.

In summation, Čapek’s response to the arguments of Putnam and Gödel does establish that causally related events do have an absolute order, excluding backwards causation and allowing that some pointlike event in spacetime may indeed become in an absolute Heraclitean manner without producing contradiction. If this approach is used to construct a presentist view, however, problems arise. To adhere to special relativity, the present must, at least according to Čapek, be restricted to a single point. Then, if the ontological claim of presentism is maintained (that only that which is present exists) then the existence of sized, past and/or distant objects is denied. Without major revision, the resulting form of presentism either collapses back into eternalism, as Putnam and Savitt describe, or it is restrictive to such an extent that it will be palatable only for the extremely narrow range of metaphysicians who accept the non-existence of all sized objects. Thus, relativity does not completely undermine presentism by exposing any major internal contradiction but still, in a largely intuitive sense, it leaves presentism as wholly unappealing in comparison to alternatives such as eternalism which encounter no relativistic difficulty and which may maintain greater parsimony, objectivity and, arguably, intuitive support.

Hayden Wilkinson completed a dual bachelor of arts and science last year and is now studying honours in philosophy at UQ.


[1] See (Michelson & Morley, 1887), (Kennedy & Thorndike, 1932), and (Ives & Stilwell, 1938).

[2] I will not dwell on these attempts for too long in this paper.

[3] See (McCall, 1976) and (Broad, 1927) for well-known examples. However, many such views, including those of Broad and McCall, do also suffer from similar relativistic objections as each has a set of existent events partly determined by what present time-slice of the universe is selected. Many of the same arguments from relativity, as described in the following paragraphs, demonstrate that these time-slices are not frame-invariant and hence that there is the potential for disagreement over what does and what does not exist, hence either greatly increasing the existent set or allowing existence to devolve into a frame-dependent and arguably non-objective characteristic. I will not address these other views in this paper, though it should at least be noted that analogous arguments can be made against them.
There are also views that claim to maintain presentism but which accept within the present various events which we would intuitively claim to be past, such as in (Godfrey-Smith, 1979, p233-244). Accepting that an ice age 10,000 years ago is as present as any action I undertake at this moment is arguably as problematic a view as any of the others considered here, and far more so than eternalism. Such views will hence also be largely overlooked in this paper.

[4] The general case of curved spacetime under general relativity is beyond the scope of this paper and will not be directly addressed. Neither will the various competing physical theories such as quantum gravity.

[5] In either frame of reference;

[6] Subject to a short delay of transmission between the object and ourselves;

[7] Some evidence and argumentative support for a privileged frame has emerged more recently. For instance: there are theories of quantum gravity which support a fixed foliation of spacetime (Monton, 2006); the approach of ADM Formalism to general relativity appears to imply a preferred foliation of spacetime (Pitts, 2004); and there are values of Lagrangian density which can be assumed and from which one can derive same equations as those of Einstein for general relativity, hence providing an empirically-identical theory (ibid.). However, these theories are still widely contested and general relativity remains the better-supported view (which, in a non-curved spacetime, adheres to special relativity). A comprehensive treatment of such theories is also, unfortunately, beyond the scope of this paper.

[8] This concludes my discussion of privileged-frame presentism and Hinchliff’s frame-dependent relativised presentism, as both appear to quite clearly be unacceptable positions, due to their lack of parsimony, objectivity and/or intuitive appeal in comparison with eternalism. There is also the view that the existent present is defined as the surface of the past light-cone (which is frame-invariant), however this falls to similar objections of lacking parsimony and intuitive appeal and won’t be fully addressed here. The remainder of the paper will hence deal primarily with Čapek’s view which I consider to be the strongest remaining candidate for a viable presentist theory.

References

Broad, C. D. 1927. The General Problem of Time and Change. Scientific Thought. London: Keagan Paul, Trench, Trubner and Co.

Callender, C. 2000. Shedding light on time. Philosophy of Science, S587-S599.

Čapek, M. 1975. The inclusion of becoming in the physical world. The Concepts of Space and Time: Their Structure and Their Development. Dordecht: Kluwer.

Gödel, K. 2006. A remark about the relationship between relativity theory and idealistic philosophy. Revista Brasileira de Ensino de Física, 28, 521-524.

Godfrey-Smith, W. 1979. Special relativity and the present. Philosophical Studies, 36, 233-244.

Hinchliff, M. 1996. The puzzle of change. Nous, 119-136.

Ives, H. E. & Stilwell, G. 1938. An experimental study of the rate of a moving atomic clock. JOSA, 28, 215-219.

Kennedy, R. J. & Thorndike, E. M. 1932. Experimental establishment of the relativity of time. Physical Review, 42, 400.

Mccall, S. 1976. Objective time flow. Philosophy of science, 337-362.

Michelson, A. A. & Morley, E. W. 1887. On the Relative Motion of the Earth and of the Luminiferous Ether. Sidereal Messenger, vol. 6, pp. 306-310, 6, 306-310.

Minkowski, H. 1910. Die Grundgleichungen für die elektromagnetischen Vorgänge in bewegten Körpern. Mathematische Annalen, 68, 472-525.

Monton, B. 2006. Presentism and quantum gravity. Philosophy and Foundations of Physics, 1, 263-280.

Pitts, J. B. 2004. Some Thoughts on Relativity and the Flow of Time: Einstein’s Equations given Absolute Simultaneity. Philosophy of Time.

Putnam, H. 1967. Time and physical geometry. The Journal of Philosophy, 240-247.

Savitt, S. F. 2000. There’s no Time like the Present (in Minkowski Spacetime). Philosophy of Science, S563-S574.

Stein, H. 1991. On relativity theory and openness of the future. Philosophy of science, 147-167.

Photo by Matt Benson

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