Here is a paper I wrote this year, regarding how ‘How Does Special Relativity Contradict the Claim of Endurantism and Support Perdurantism’.
It is “axiomatic for the endurantist view [of] the notion that objects are wholly present at each moment of their existence” (Hales “EP&SR” 532). The object has no temporal parts, for these parts are bound purely within three dimensions. An object “persists through time by being wholly present at different temporal locations. And, of course […] changes over time” (Benovsky 3). The claim of perdurantism is that “not all of an object’s parts are present here and now” (Barnard 183). Objects are comprised of three spatial dimensions and one temporal. Objects extend through time and space, rather than only extend in space. These “temporally extended objects persist through time by having temporal parts” (Sider 443). This is four-dimensional (4D). Things are coincident in time, but not wholly present at one specific time or another. The path to my university has spatial subregions that it occupies. So, too, do temporal subregions occupy the total region of the time ‘path’ that they occupy. I argue for the claim of perdurantism. I argue for this claim by employing a thought-experiment, using the Lorentz Transformation and Special Relativity (SR). In SR, “space time is conceived of as a multi-dimensional object, where one of the dimensions is temporal and the others are spatial” (Hales “EP&SR” 392). SR is based on two premises. First, that physics is the same in all inertial reference frames. Second, that the speed of light in a vacuum is constant. For SR the absolute moments of time of Classical Relativity, become “moments of time in a given reference frame” (Balashov “Relativ” 5). First, I shall briefly explore Balashov’s thought-experiment that, he argues, supports perdurantism. This also also introduces a key aspect of this paper: reference frames. I then anticipate one objection to this by the endurantist. I then shall use a thought-experiment to negate this objection, arguing for perdurantism as the preferred ontological claim.
Suppose that we are 2D ‘flatlanders’. We observe the passage of a 3D cylindrical object through our 2D world from two different reference point/time slices. Let’s call these two different reference points/time slices (a, b, t) and (a1, b1, t1). At (a, b, t), the flatlander observer sees a circle. At (a1, b1, t1) the flatlander sees a stretched out ovular shape. To the flatlander, the shapes in each event are 2D, appearing as two distinct shapes. They ‘wholly exist’ in each reference point (a, b, t) and (a1, b1, t1) as different shapes. But there is actually just one 3D shape. The flatlanders are seeing cross-sections of the cylinder from different 2D reference points. “Even if the object does not change its proper shape” it has “different shapes at time slices of its path drawn in different reference frames” (Balashov “Relativ” 41). Therefore, the “best explanation of the changing shape of objects relative to inertial frames is that they are 4D objects being seen from different three-dimensional perspectives” (Barnard 184). This thought-experiment supports the claim of perdurantism. However, an endurantist could argue that, despite these various time-slices overlapping with one another, if we pick out a certain reference frame, privileging it over the others, then this can be the ‘rest-frame’ of the object. For this argument of the endurantist, we can “restrict the LOCATIONS of persisting objects and their parts to […] regions representing subsets of moments of time in inertial reference frames” (Balashov Ont. 74). This would privilege the rest-frame (a fixed, ‘whole’ point) of an object at a space-time geometrical rest-point at given “position lines” (Balashov Ont. 77). But this argument has a prejudicial error. These locations, the geometric-positions in space-time, are useful but, privileging them over other slices is arbitrary. There is no necessary reason to conclude that we should privilege an imposed rest-frame in a geometric context over other reference points. These geometric-points have no claim to be the ‘rest point’ — an absolute time-slice of the object (and thus an enduring object) — over any others. Geometric-locations are useful, but are not the absolute rest-point, and are therefore not the site of a ‘wholly existing’ (to use the endurantist’s vernacular) object. As Gibson and Pooley argue, “one can equally choose to describe the content of spacetime with respect to some frame that is not so optimally adapted to the geometric structure of spacetime, or indeed, choose to describe it in some entirely frame-independent manner” (162). It is with SR and the Lorentz Transformation that one can see these other points of non-privileged reference. This shows how we cannot privilege one apparent ‘rest-frame’ over another. Therefore we cannot point to when an object has its parts wholly existing in the present.
To reiterate, endurantism posits that all objects are wholly present at each moment. An object “o is an enduring object iff o wholly exists at each moment of its existence. That is, at every time t at which o exists, every proper part of o is at t” (Hales “EP&SR” 533). All parts of the object co-exist simultaneously in the present. And so the inverse is that if parts of o do not co-exist simultaneously in t, then o is not wholly existing in the present at t. In the “‘rest phase’ of an object, each part of o is at a specific time t and this t is the same for all parts” (Hales “EP&SR” 532). But in SR, “for an inertial reference frame […] moving with respect to an object o, each proper part of o at a different position along the direction of relative motion is at a different time” (Hales “EP&SR” 536). Thus if “there is a reference frame moving with respect to an object o, then in that frame o has proper parts at t, before t and after t” (536). There are inertial frames that are not the same as the rest frame of an object. The whole parts of an object are not wholly present at one specific time. It is dependent on the frames of reference. Frames of reference are not simultaneous, and therefore the parts of an object cannot be simultaneous from different reference frames. That parts of an object can exist in the past, present and future appears to contradict the endurantist’s claim. But this requires elaboration.
Let us consider a thought experiment inspired by Hales (with a bit of flare from Sagan’s Cosmos). This thought experiment appears outlandish considering our current technological capacities. But this is just a device to explain something that goes on in the non-medium (our) planes of existence, commonly. This is something that was missed by the physics preceding SR. Vincenzo is sat by the road, next to a church. At t0, his friend Paolo starts driving his moped down the hill a few hundred yards away (I use these two ‘observers’/reference points as short-hand. There need not be a human observer in these situations; the points of reference can be anything). Both agree that t0 is the reference point that they share simultaneously — when the wheel first moves on the tarmac. They are ‘calibrated’ to one another in time, exactly. “t0 will represent the time of that event; everything in one’s reference frame that is simultaneous with that event is at t0” (Hales “Time” 504). Paolo drives his moped. This travels, nearing the speed of light c. Paolo draws even with Vincenzo, who is on the side of road at t1 (t1 is subsequent to t0). Both observe the church at exactly t1. Paolo sees a piece of slate roof flying off the church at t1. Surprised, due to the paucity of joy in his life, Paolo turns back round and rides back to Vincenzo at a normal speed. Paolo reports to Vincenzo that when he drew even with him on the side of the road (at t1), he viewed the slate roof fall off. For Paolo, the church had changed at t1. Vincenzo, perplexed, replies that, at t1, the slate roof had not yet fallen off the church. It was only shortly after t1 that Vincenzo perceived the piece of slate falling off — after Paolo had driven on by. Paolo and Vincenzo agree with the history of the church — its change from a church to a church lacking a slate roof. But they disagree with simultaneity—when the event happened. Paolo saw changed slateless roof in his present at t1. But for Vincenzo at t1, the roof had not changed. Thus, the broken slateless roof at t1 is in his future.
We have a quandary here. How can the church be both simultaneously changed and unchanged at the same t1? This apparent paradox is only a paradoxical if one considers simultaneity to be absolute –adhering to classical relativity. Endurantists would argue that the whole church is present at t0. Following the loss of the slate roof, they would argue the whole church (with all its
parts minus the slate) is present at t1. In the classical notion of spacetime that appeals to the endurantist, “locations of persisting objects, their parts, and temporary properties were indexed to moments of absolute time” (Balashov “Relativ” 5). But through the Lorentz Transformation, devised before SR but in accordance with it, there are no absolute moments in time. The Lorentz Transformation shows that observers moving at different velocities can measure different elapsed times, different orderings of events and different distances travelled in comparison to one another. Due to the differences of speeds between Paolo and Vincenzo, the simultaneity of the church’s slate roof falling off occurs out of sync, despite Paolo and Vincenzo both starting off at the same time t0. “Observers in different inertial frames that are simultaneous with each other will perceive the very same object as changed (in one frame) and unchanged (in the other frame)” (Hales “Time” 511).
For the church to endure, there can only be one whole set of church parts at t1. In SR, this is not the case. For Paolo on his near-c speed scooter at event t1, there is a church with parts that that has changed (lacking a slate roof) from t0. For Vincenzo at event t1, there is a church that has not changed since t0. These two events both occur at t1. “Observers in different reference frames find themselves simultaneous with different aggregates of the temporal parts of the object, with one series of temporal parts retaining a property and the other series changed and lacking the property.” (Hales “Time” 513). The church cannot have endured, for the parts of the object are not wholly present in the same moment — they overlap. The church has temporal parts. “If one is a spacetime realist then, barring conventionalism, things must have spatio-temporal parts” (Callender 225). Hales concludes that “if there is a reference frame [Vincenzo] moving with respect to an object o [the church], then in that frame o has proper parts at t, before t and after t” (Hales “EP&SR” 535). There is no way to factually conclude which events happened first, last, or at the same time as they all overlap. To return and conclude my original argument, then: we cannot privilege one reference point over another, non-arbitrarily. These two reference points, starting both at the co-existent reference point t0, lose their simultaneity at t1. This leads to the conclusion that o is comprised of parts that, from different points of reference, are not simultaneous, which is conducive with the claim of perdurantism. The church therefore has temporal parts that are extended throughout time in the past, present, and future, not comprised of parts ‘wholly’ in one moment. Vincenzo and Paolo are seeing different ‘time-slices’ of the same 4D spatio-temporally extended church. Just like the flat-worlders saw different 2D cross-sections of the 3D cyclinder. They view a spatio-temporally extended 4D object from different reference points. But they experience it as different 3D ‘slices’ of the 4D church at t1, due to their different velocities, caused by the Lorentz Transformation. But pointing at an object’s time-slice and assigning that as the rest-frame is disingenuous. There are many other equally valid reference points that one could point to, if one thinks outside of the trappings of Classical Relativity and positions in space being absolute, rather than relative. This is a “a distinctly relativistic phenomenon absent from the geometry of classical spacetime”(Balashov “Relativ” 42). Endurantism, intuitively, seems to hold for our perceptions of slow, “middle-sized” objects. However, a “predilection for slow-moving middle-sized dry goods is not a license for philosophy to pretend that such things are all we need consider” (Hales “EP&SR” 539). In order for endurantism to endure, one must constrain oneself to the classical relativistic view of our world. However, the claim of perdurantism, I argue, has a “natural and elegant fit with the physical facts of our world” (Hales “EP&SR” 525). Our immediate intuitions towards space and time can often fail us. Special Relativity’s elegant fit with perdurantism helps us to overcome these intuitive trappings.
Works Cited
Balashov, Yuri. “Relativistic Parts and Places: A Note on Corner Slices and Shrinking Chairs”. eds. Calosi, Claudio. Pierluigi Graziani. Mereology And The Sciences. Switzerland: Springer International Publishing, 2012. Web. 22 Mar. 2015
———. “Persistence and Multilocation in Minkowski Spacetime”. ed Dieks, Dennis G. B. J. The Ontology of Spacetime Ii. Amsterdam: Elsevier Science, 2008. Internet resource.
Barnard, Robert W. Neil A. Manson. The Continuum Companion to Metaphysics. London: Continuum, 2012. 180-190. Google Books. Web. 22 Mar. 2015.
Benovsky, Jiri. “On (Not) Being in Two Places at the Same Time: An Argument Against Endurantism”. American Philosophical Quarterly. 46.3. July 2009. Web. 22 Mar. 2015.
Callender, Craig. Time Reality and Experience. Cambridge: Cambridge UP, 2002. Google Books. Web. 22 Mar. 2015.
Ian Gibson. Oliver Pooley. “Relativistic Persistence”. Oxford UP, 2006. Web. PhilSci. 26 Mar. 2015.
Hales, Steven and Timothy Johnson. “Endurantism, Perdurantism And Special Relativity”. Oxford Journal (2003). PhilPapers. Web. 22nd March 2015.
———. “Time for Change”. Southern Journal of Philosophy 45.4 (2007): 497-513. PhilPapers. Web. 22 Mar. 2015.
Sider, Theodore. Four-Dimensionalism: An Ontology of Persistence and Time. Oxford: Oxford UP, 2001. Web. 22 Mar. 2015.
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