The Real Presence and Relativity Theory

Jesus Christ like all human beings has an internal clock. One can measure that clock in heartbeats or in lower level physical interactions or in some other way. Let’s measure it in “internal years”. If Jesus was born in 4 BC, then in 4 BC, his internal clock was at about a year (he was conceived about 0.75 years before he was born). In 1 BC, it was at 4 years, in 1 AD, it was at 5 years, and in 30 AD, it was at 34 years.

I don’t know what Jesus’s internal clock was at in 100 AD, and it’s not immediately obvious that the question makes sense. For it is not immediately obvious that there is a correlation between time on earth and time in heaven of such a sort it makes sense to ask “What is happening in heaven right now?” After all, according to Relativity Theory, it doesn’t make sense to ask “What is happening right now in the Andromeda Galaxy” without specifying a reference frame for the “right now”, and it’s not immediately clear that there is a common reference frame between heaven and earth.

However, the real presence of Jesus in the Eucharist does provide a temporal correlation between heaven and earth. Around 22:45 UTC today, Jesus will come to be present in our campus parish. Moreover, Jesus will be present as an adult glorified human, not as the three-year-old he was in 1 BC. There thus appears to be a fact of the matter as to what his internal clock will be showing when he comes to be present at 22:45 UTC in Waco today.

Interestingly, this gives a temporal ordering on events scattered across the earth apparently independent of our ordinary relativistic reference frames. For if the Eucharist is celebrated around 22:45 UTC in Waco and around 22:45 UTC in London, there is a fact of the matter whether Christ as present in Waco is older or younger or at the same age (according to his internal clock), and this fact provides a reference-frame independent temporal ordering between these two Eucharistic celebrations.

Indeed, since according to Catholic and Orthodox faith, Christ remains Eucharistically present in the tabernacles across the world, we constantly have a temporal ordering between events scattered spatially across the world. In principle, this defines a theologically privileged reference frame between scattered events—a Eucharistic reference frame. Events at locations z₁ and z₂ in spacetime are Eucharistically simultaneous, we might say, provided that Christ as Eucharistically present at z₁ and at z₂ has the same value of the internal clock.

Of course, some philosophers of time think there is an objective reference frame in the physical world. If they are right, then very likely the theologically privileged frame is the same as the objective one.

All that said, it is not completely clear to me that Christ as Eucharistically present has to have a well-defined value of his internal clock. But I suspect so, because of the intuition that it is the adult and not toddler Jesus who is Eucharistically present.

Gale's criticism of Stump and Kretzmann's ET-simultaneity

Stump and Kretzmann give three main concepts of simultaneity in their famous paper:

• T-simultaneity between items in time

• E-simultaneity between items in eternity

• ET-simultaneity between items in time and items in eternity.

Stump and Kretzmann observe that ET-simultaneity is not reflexive: a temporal item is not ET-simultaneous with a temporal item and an eternal item is not ET-simultaneous with an eternal item. My mentor Richard Gale in his book on God argues that this is a serious problem: a relation that is’t reflexive just doesn’t have a hope of counting as a simultaneity relation.

But Gale is wrong. For T-simultaneity and E-simultaneity are clearly simultaneity relations, but neither of them is reflexive either! For an eternal item is not T-simultaneous with itself and a temporal item is not E-simultaneous with itself.

Now, granted, when we talk of reflexivity of a relation, it’s within a relevant domain. Thus, we say that being the same color is reflexive, even though St Michael the Archangel is not the same color as himself, because the relevant domain for sameness of color is things that have color, not immaterial intellects.

So we might say that T-simultaneity and E-simultaneity are reflexive because their respective domains are temporal and eternal things, and they are each reflexive in their domains.

We might, but we shouldn’t. Stump and Kretzmann’s investigation is of a domain of items that may or may not be simultaneous in different senses, a domain that includes both eternal and temporal things. And in that domain, none of the relations they consider are reflexive. And that’s OK.

Physicalism, consciousness and history

Many physicalists think that conscious states are partly constituted by historical features of the organism. For instance, they think that Davidson’s swampman (who is a molecule-by-molecule duplicate of Davidson randomly formed by lightning hitting a swamp) does not have conscious states, because swampman lacks the right history (on some views, one just needs a history of earlier life, and on others, one needs the millenia of evolutionary history).

I want to argue that probably all physicalists should agree that conscious states are partly constituted by historical features.

For if there is no historical component to the constitution of a conscious state, and physicalism is true, then conscious states are constituted by the simultaneous arrangement of spatially disparate parts of the brain. But consciousness is not relative to a reference frame, while simultaneity is.

Here’s another way to see the point. Suppose that conscious states are not even partly constituted by the past. Then, surely, they are also not even partly constituted by the past. In other words, conscious states are fully constituted by how things are on an infinitesimally thin time-slice. On that view, it would be possible for a human-like being, Alice, to exist only for an instant and to be conscious at that instant. But now imagine that in inertial reference frame F, Alice is a three-dimensional object that exists only at an instant. Then it turns out that in every other frame than F, Alice’s intersection with a simultaneity hyperplane is two-dimensional—but she also has a non-empty intersection with more than one simultaneity hyperplane. Consequently, in every frame other than F, Alice exists for more than an instant, but is two-dimensional at every time. A two-dimensional slice of a human brain can’t support consciousness, so in no frame other than F can Alice be conscious. But then consciousness is frame-relative, which is absurd.

Once we have established:

1. If physicalism is true, conscious states are partly constituted by historical features,

it is tempting to add:

2. Conscious states are not even partly constituted by historical features.

3. So, physicalism is not true.

But I am not very confident of (2).

Simultaneity, A-Theory and Relativity

Here is a standard story about Special Relativity and the A-theory of time:

• There is an objective metaphysical simultaneity, but

• this metaphysical simultaneity does not affect physical events and is unobservable.

Let’s assume the A-theory is correct and this story is also correct.

Now, when people talk about this metaphysical simultaneity, they normally think they it aligns with the frame-relative simultaneity of Special Relativity for some privileged reference frame. This seems reasonable. But it is an interesting question to ask for an explanation of this alignment.

Causation may put some constraints on metaphysical simultaneity. For instance, perhaps, there shouldn’t be any possibility of future to past causation. But a metaphysical simultaneity relation can satisfy such constraints without coinciding with any frame-relative simultaneity.

If God exists, I guess we might suppose that metaphysical simultaneity coincides with a frame-relative simultaneity because it’s more elegant if it does.

Absolute relativistic simultaneity

If we accept relativity theory as providing a metaphysically correct theory of time, the folk concept of temporal simultaneity needs revision. The standard way to revise it has been to relativize it to a reference frame. Instead of simultaneity being a binary relation between events (A is simultaneous with B) it becomes a ternary relation between events and a frame (A is simultaneous with B in F).

But another revision of the folk concept is possible: We keep simultaneity a binary relation, and specify that two events are simultaneous if and only if they are colocated in spacetime (this is roughly the same as saying that they are simultaneous according to every frame). Spatially distant events, on this revision, are never simultaneous.

The downside of the absolute simultaneity revision is that a lot of first-order
simultaneity judgments become false. Leibniz and Newton were not developing calculus simultaneously. I am not typing this at the same time as my daughter is playing a game on another laptop. Etc.

The upside is that colocation is a much more fundamental concept given relativity theory than the concept of a reference frame.

So we have a choice: We can keep our ordinary first-order judgments as to what events are in fact simultaneous or we can preserve the arity of the simultaneity relation and the judgment about the fundamentality of simultaneity. I think cases of revision of ordinary concepts, preserving ordinary first-order judgments tends to trump other things. So I am inclined to think the standard revision is superior as a way of doing justice to the language.

But the absolute revision may be better as a philosophical heuristic. For we might think that fundamental philosophical concepts should be frame-invariant, like fundamental physical concepts are.

Relativity, simultaneity, minds and brains

This is very much a thinking-in-progress post rather than a finished argument. But I've been toying with this line of thought:

1. The simultaneity relations between conscious mental states of an ordinary human (e.g., "itching while feeling cold") are not relative to reference frame.
2. The simultaneity relations of spatially extended states of an object are relative to a reference frame.
3. If conscious mental states are identical with or wholly constituted by brain states, then they are spatially extended states.
4. So, conscious mental states of an ordinary human are neither identical with nor wholly constituted by brain states.

The restriction to ordinary people rules out cases where someone has two or more centers of consciousness at a given time (e.g., due to brain-splitting, time travel, or multiple personalities). In the case of such a non-ordinary person, we can run the argument for each center of consciousness and conclude that the center's states are not identical with or constituted by brain states.

What makes this argument tricky—and this is the part I need think more about—is that of course the relativistic effects between different bits of the brain are practically negligible. The kind of time difference that would be involved in trying to see whether I started itching before starting to feel cold or whether it was the other way around would be so minuscule that I couldn't tell the difference as to which state started earlier or whether they started simultaneously. Nonetheless, there is some plausibility in thinking that there is a fact of the matter as to which state started earlier or whether they started simultaneously. Moreover, maybe we could imagine beings with bigger and faster brains where the effects would be real--and (1) plausibly isn't just a fact about us, but about any discursive agents with a single center of consciousness.

Here's an interesting thing. Suppose that one responds to the argument by saying that there is an absolute reference frame, despite relativity theory, much as defenders of the A-theory of time hold. That response doesn't get one completely out of the argument. We can argue: the absolute frame is insignificant for physics; yet it is significant for mind; so mind doesn't reduce to physics.

I also think the argument (though perhaps not the absolute-frame variant) may lead to some problems for supervenience theories of mind. But that's for future research.

Relativity of simultaneity

I've been thinking about Einstein's nice argument for the relativity of simultaneity in his popular book. The argument starts with the assumption that the speed of light is the same in every inertial reference frame, and uses this to construct a method for determining whether two events are simultaneous. Basically, this method involves having an inertial observer spatially equidistant between the two events checking whether light reaches her simultaneously from the two events. Given the constancy of the speed of light and the equidistance assumption, it seems to follow that the two events are simultaneous if and only if light reaches the observer simultaneously from the two events. And then Einstein gives a very nice argument that applying this method gives different answers depending on the osberve, and concludes that simultaneity is relative to the reference frame.

But there is something that has been worrying me conceptually about Einstein's account of simultaneity. That account takes for granted that we know what it means for the observer to observe two events simultaneously. But isn't the task to define simultaneity?

I guess not. Einstein seems to presupposing that we already have the notion of simultaneity of events at the location of an observer. Moreover, the details of Einstein's argument assume this principle which I think he doesn't discuss:

• Two events befalling the same observer occur simultaneously in the reference frame of the observer if and only if they occur at the same point in spacetime.

(Einstein also tacitly makes the simplifying assumption that observers are point-sized. I won't worry about that assumption in this post.) I am a little troubled by this principle. It's not clear that it's conceptually necessary (might we not think it's violated in cases of time travel?). Still, maybe the best way to take Einstein's account of simultaneity in the book is this. First, we define simultaneity for events befalling the observer who defines a reference frame by requiring sameness of spacetime location. Second, we use this and the equidistant-observer thought experiment to define simultaneity for events not both located at the observer. Third, we show that by this two-part definition of simultaneity, simultaneity is frame-relative.

Absolute simultaneity and common sense

It's common sense that there is absolute simultaneity, whether directly so or because it's common sense that there is an objective present. It is sensible for philosophers to want to hold on to what is common sense. But here we should not be so quick. For consider some common sense claims:

1. There is absolute simultaneity.
2. If A and B are absolutely simultaneous and C and D happen t units of time after A and B respectively, then C and D are absolutely simultaneous.
3. Properly functioning clocks correctly measure lengths of time.
4. Clocks continue to properly function when moving, as long as they are not accelerated so quickly as to damage them.

But while (1)-(4) are all common sense, we have empirical data (assuming some uncontroversial claims of how to determine cases of absolute simultaneity for side-by-side events) that they are not all true, namely the data confirming the Twin Paradox.

Now when a number of common sense claims cannot all be held together, it is not responsible simply to say that one of them is common sense and therefore true. For the same thing could be said about the others. One would need to say something about how one's preferred claim is more commonsensical than the others, and that's a judgment that may well go beyond common sense.

I think most defenders of absolute simultaneity will reject (3) or (4). But if we look at how we actually acquire our concepts of durations of time by using clocks, watches and internal timers, it's plausible that we are committed to (3). And our practices of blithely using clocks even after coming to think that the earth is rapidly moving around the sun suggest (4).

I actually think that an interesting strategy for defending absolute simultaneity is to deny (2). This would lead to a view with absolute simultaneity but purely relative temporal durations.

That said, I am happy to deny (1).

From relationalism about times to infinitesimal lengths of time

Assume that simultaneity is a reflexive and symmetric relation between events. I will, however, not think of it as transitive. This lets me say that an event that goes from 2 pm to 3 pm is simultaneous with one that goes from 2:30 pm to 3:30 pm. (This is important if there is to be any hope of the thesis that all causation is simultaneous being true.)

Can one construct times out of the simultaneity relation between events? Well, a natural attempt is to say that any maximal set T of pairwise simultaneous events is a time (we can use the Axiom of Choice to show that every event is contained in such a maximal set), and an event E happens at a time T if and only if E is a member of T.

This account, however, has a curious consequence. Consider some event E_n that starts right after noon, and ends right at noon plus 1/n hours. Thus, E_n takes place on the time interval (12,12+1/n] (non-inclusive at 12, inclusive at 12+1/n). Let T be any maximal set of pairwise simultaneous events that contains the E_n. (By the Axiom of Choice, T exists.) By the above account of times, T is a time, and all the events E_n occur at T. But when is T? It's not noon: none of the events E_n occur at noon. But for any positive real number u, most of the events E_n occur before 12+u, so T is not 12+u.

In other words, T is a time between 12 and 12+u for every positive real u>0. It is, thus, a time that is infinitesimally after noon. Thus, curiously, the natural construction of times out of the simultaneity relation very naturally leads to times that are infinitesimally close together, as long as there are events like E_n.

This is quite interesting, because it suggests that a hyperreal timeline may not be such an outlandish hypothesis (Rosinger has also suggested this hypothesis in a number of preprints, e.g., this one). It is a hypothesis that one is led to quite naturally from a relationalist picture, a hypothesis that given such a picture and such an account of times might very well be true.

Of course, the above depended on one particular way to construct times out of simultaneity. And it depended on a simultaneity, a somewhat fishy relation. But still, it's suggestive.

I think there is a way of seeing the above remarks as a reductio of the relationalist program. That's how I saw the observation when I started writing this post. And maybe that's right, but it's not clear to me that that's right.