How we understand cosmology was altered by the development of Special and General Relativity. Here, I want to discuss a less appreciated change I think SR introduced to cosmology. In Aristotelian or Thomistic cosmology, there are two kinds of causal series, i.e., accidentally and essentially ordered causal series, and both Aquinas and Aristotle thought that only the latter can be used to infer that there must be a First Cause. However, on a relativistic understanding, we have a good reason to think that there are no essentially ordered causal chains, or at least no essentially ordered causal series with non-colocated members. Hence, Einstein provides a reason to reject the Aristotelian/Thomistic First Cause argument.

In a causal series, items are ordered in terms of cause and effect. For Aristotelians and Thomists, efficient causation involves one substance bringing about a change in another substance. When a substance is changed, Aristotelians and Thomists say that the efficient cause has actualized a potential. In an accidentally ordered causal series, each member has independent causal power to bring about its effect. Since the causal power of each member is independent of the prior members, no member requires the concurrent existence of a prior member to bring about its effect. For example, my parents caused me to exist. In turn, I am the cause of this blog post. However, my power to create this blog post is independent of my parents’ causal powers. Since my power is independent of theirs, my creating this blog post does not depend upon my parents’ continued concurrent existence. If they went out of existence, I would still have the causal power to produce this blog post. In an essentially ordered causal series, each member lacks its own independent causal power. Instead, each member borrows its causal power from a prior member. If a prior member went out of existence, then the successive members in the series would no longer have the requisite causal power to bring about their own successors in the series. All of the members must exist at once.

Aquinas offers a famous example involving a hand that moves a stick. The stick’s motion ceases if the hand’s motion ceases. In turn, the hand’s motion depends upon the arm’s motion. The arm’s motion depends upon the shoulder. The shoulder depends on the rest of the body; in turn, the body is standing on the ground, where the body is held fixed by a combination of the force of gravity and the ground’s normal force. And so on. Aristotle held that essentially ordered causal series can eventually be traced back to the motion of the celestial spheres, which are made to rotate by God. God has His own innate causal power, so there’s no need to trace essentially ordered causal series beyond God. Scientifically literate people no longer believe in the celestial spheres, but many present-day Thomists do believe that there are essentially ordered causal series. Each essentially ordered causal series must ultimately trace back to a First Cause, they say, precisely because each member in any such series, with the exception of the first member, must borrow its causal power from some other. We’re supposed to think that there wouldn’t be any causal power at all if there weren’t a First Cause to provide the causal power made use of by all of the succeeding members. And while it would be logically consistent with everything I’ve said so far for none of the essentially ordered causal series to share a first cause with any other series, it’s a simpler explanation to postulate one First Cause shared by all essentially ordered causal series.

Notice that the members of essentially ordered causal series must concurrently exist. Since any member borrows its causal power from a prior member, all of the members of an essentially ordered causal series must exist together at one time. Importantly, the Aristotelian/Thomistic First Cause argument does not require a finite past series of causes. Aristotle/Aquinas held that accidentally ordered causal series can be infinite; it’s only the essentially ordered series, they thought, that requires a First Cause. In fact, Aristotle held that the past must – as a matter of conceptual and metaphysical necessity – be infinite (as Aristotle argues in On Corruption and Generation), while Aquinas held that we know the past is finite only because the finitude of the past was revealed in scripture (as Aquinas argues in de Aeternitate Mundi). For this reason, in reply to the Aristotelian/Thomist First Cause argument, it’s no good to point out that (for example) our empirical observations are consistent with past eternal cosmological models.

While I don’t know of any sources that bring the two together, Aquinas’s example of the hand that moves the stick closely parallels an example frequently discussed in connection with SR. SR rules out the propagation of signals faster than the speed of light. Suppose that there existed a one light year long stick. If we push on one end, a signal must travel from the location we pushed to the end of the stick in order for the end to move. Since the stick is one light year long, the other end of the stick will not move until at least a year later. (In sticks composed of physically reasonable material, the signal will take much longer to transmit, where the transmission time depends upon the speed of sound in the material.) Since one end of the stick moves before the other end, the stick cannot possibly be perfectly rigid. Insofar as there is a prohibition on superluminal signalling, all objects — or at least all that are not point-size — are at least somewhat “squishy”. And while the light year long stick is a useful example, nothing conceptually crucial depends upon the fact that the stick is a light year long. Much the same is true for a meter long stick, except that it will take a small fraction of a second for the signal to transmit the stick’s full length. Aristotle and Aquinas were tricked into thinking that some causal series involve concurrently existing members because the speed of light is so large compared to the speeds we experience in our daily lives. Once we understand that the speed of light is finite and that nothing moves faster than light, we can surmise that rigid bodies do not exist. Since the hand-that-moves-the-stick example presupposes the existence of rigid bodies, the hand-that-moves-the-stick has presuppositions incompatible with SR. Nothing is special about the stick; a similar verdict obtains for all of the standard examples of essentially ordered causal series.

There’s another reason that SR is incompatible with the hand-that-moves-the-stick example. In SR, there is no such thing as absolute simultaneity. The only way for two items to be objectively simultaneous involves their being co-located at numerically one spacetime point. 

There are various prototypical examples of causal series, such as the hand-that-moves-the-stick, that are supposedly essentially ordered. However, none of the prototypical examples involve members that are co-located at numerically one spacetime point. Hence, none of the prototypical examples truly involve mutually simultaneous members. In essentially ordered causal series, each member, with the exception of the first, borrows its causal power from a previous member, so that the existence of any one member, again except the first, requires the concurrent – and so simultaneous – existence of the prior members. Since none of the prototypical examples truly involve successors that concurrently exist with the prior members, none of the prototypical examples are truly examples of essentially ordered causal series.

The prohibition on speeds greater than that of light rules out the possibility of a cause being space-like related to its effect. At least in SR, causes must always be either light-like or time-like related to their effects, or else they must be co-located. Thus, items must always be either co-located, temporally before, or temporally after their effects. (Presumably, before their effects, though Special Relativity, itself, does not deliver a verdict on whether retrocausation is possible.) Since a difference in time sufficed for distinguishing accidentally from essentially ordered causal series, SR rules out essentially ordered causal series with non-co-located members.

We may be able to make this argument a bit stronger. While controversial, many past and present metaphysicians have defended the view that spatiotemporal location is necessary for individuating material objects. I have my own reservations about whether this is really true; for example, in our current understanding of physical law, no law prohibits two bosons from occupying numerically one spacetime point. Can’t we still individuate two bosons when they are spatiotemporally co-located? There are various responses one could give. (For example, that when two bosons are spatiotemporally co-located, they are not actually numerically distinct.) But suppose that spatiotemporal location really is necessary for individuating material objects, as many metaphysicians are prepared to accept. This would entail that there are no instances where two distinct material substances share one spatiotemporal location. Aristotelians and Thomists maintain that cause/effect relations involve one substance actualizing the potential in another distinct substance. Consequently, insofar as spatiotemporal location is necessary for individuating material objects and SR rules out the possibility that items at numerically distinct spatiotemporal locations that occupy numerically one time, there cannot be cases where a material substance is a cause and its effect exists concurrently.

In any case, the foregoing suggests something like the following argument:

1. Various consequences of SR obtain (e.g., no absolute simultaneity, prohibition on superluminal signalling, etc).

3. If various consequences of SR obtain then there are no essentially ordered causal series.

4. Therefore, there are no essentially ordered causal series.

The Aristotelian/Thomist may try to save essentially ordered causal series by appealing to quantum field theory. According to various popularizations, one subatomic particle exerts an influence on another through the exchange of the appropriate boson. For example, one electron repels another electron because a photon moves from the first to the second. When the photon reaches the second electron, we might imagine that the second electron and photon share numerically one spacetime location. If so, there are at least some causal series – such as the two member series consisting of the photon and the second electron – where the members concurrently exist.

This reply involves a number of misunderstandings. First, it’s unclear that a subatomic particle could occupy only a single spacetime point. On some interpretations of quantum mechanics, that possibility seems ruled out, or at least made fairly implausible, by the Heisenberg uncertainty relation. Let’s set that objection to one side. Second, the reply involves an overly literal understanding of Feynman diagrams. As Paul Teller (1997) points out, Feynman diagrams represent the terms in specific series expansions. Whatever happens in a given quantum field theoretic process somehow involves the sum of all of the diagrams, so that any single diagram should not be understood as a literal representation of reality. Instead of a literal exchange of bosons, there is an exchange of energy and momentum between two localized excitations of the electron field, where the electromagnetic field (really, the quantized magnetic vector potential) acts as some sort of intermediary. Third, even if we do take Feynman diagrams literally, it’s unclear that the photon is ever co-located with the electron. The photon’s trajectory could be open on one end, where the photon exists at every point prior to the change in the second electron’s motion. If the photon and second electron are ever co-located, there is at most a two member essentially ordered causal series. We wouldn’t have reason to think that the essentially ordered causal series can be traced back further than the photon, and so wouldn’t have reason to endorse the presuppositions involved in the Aristotelian/Thomistic First Cause argument.

Here’s another possible objection. SR has been supplanted by GR. If SR has already been supplanted by another physical theory, why should we take seriously the negative verdict offered by SR? Notice that premise 1 claims only that some specific consequences of SR obtain and not that SR obtains. Some of those consequences – such as the prohibition on superluminal signalling – are required only by the empirical adequacy of SR. Since anti-realists accept that SR is at least empirically adequate, the argument cannot be evaded by appealing to anti-realism.

Moreover, GR arguably makes the situation significantly worse for the Aristotelian/Thomist. In SR, there’s a finite speed for the propagation of light, so that there are no rigid bodies, and there is no absolute simultaneity, so that no two numerically distinct items can concurrently exist unless they are spatiotemporally co-located. However, we could tweak SR slightly by “adding in” absolute simultaneity relations. For example, we could suppose that one of the inertial reference frames, call it R, is (somehow) metaphysically preferred over the other inertial reference frames. In that case, events A and B are absolutely simultaneous just in case they are simultaneous in R. This possibility is precluded in GR. In GR, the inertial reference frames from SR are preserved as part of the tangent space for each spacetime point. In turn, this means that in almost all relativistic spacetimes (with the exception of Minkowski space), there is no such thing as a reference frame shared by all spacetime points. If we pick out a preferred reference frame at one spacetime point, we haven’t added absolute simultaneity to spacetime. If we pick out preferred reference frames at all spacetime points, we still haven’t added absolute simultaneity. We could pick out some preferred foliation instead, but it’s not obvious why we should prefer any particular foliation. Moreover, arguments for absolute simultaneity (particularly in philosophy of religion) frequently appeal to our phenomenal experience of temporal passage, but it’s unclear how any preferred foliation could play the requisite role with respect to our phenomenal experience of temporal passage.

In sum, various features of the Einsteinian understanding of spacetime are incompatible with assumptions required for the postulation of essentially ordered causal series. Insofar as we have good reason to think the Einsteinian understanding is (at minimum) empirically adequate, we seem to have good reason to reject the Aristotelian/Thomistic First Cause argument. Is this argument correct? I think it is, though I’m still actively thinking about this topic.

Disclaimer: The posts on the Cosmotherium should never be taken as definitive and I am typically not completely convinced of what I post here. This is my place for working out my views without the pressure or rigor of publication.

References

Teller, P. 1997. An Interpretive Introduction to Quantum Field Theory. Princeton University Press.