Sunday’s on the Phone to Monday

Here’s something I’ve learned about spacetime and want to share.

We can thank Einstein’s theory of Special Relativity for the knowledge that time, velocity, and perspective are all observer-dependent; that the only thing constant wherever you are and however you move is the speed of light, c. We can also thank him for one creepy question: whether the future is already written.

A consequence of Special Relativity is that something in one observer’s future can already be in another observer’s past. Since there’s no simple limitation on how far this extends, an observer must therefore exist that has seen, as past or as “having become,” everything that’s going to happen to me, or to you, or to any perspective-point. (Roger Penrose has elaborated an example of this based on the moment of an Andromedan invasion of Earth.) Simultaneity is relative. So the question is, Do we live in a fatalistic universe?

No, says physicist Howard Stein. Here goes my interpretation— my attempt to rephrase what I’ve hearned— of his explanation why.

Stein starts by defining a relation Rxy such that y has already become, or is already definite, with respect to x. (I notice at x that the toaster has already spit out the toast at y. The toast has become toasted to me: for this relation, Rxy can be said to hold.) x and y, if I’m interpreting the Stanford Encyclopedia’s interpretation of Stein correctly, are four-dimensional variables: three dimensions of space, one of time.

So. If R can be said to define “having-become-ness,” two other things have to be true. First, R must be transitive. (Remember this term from algebra?) That is, if z has already become with respect to y and y has already become with respect to x, then z has already become with respect to x. If the parakeet has already chirped when the toast pops up, and I notice that the toast has already popped up, then, to me, the parakeet has already chirped. If Rzy and Rxz, then Rxy for all x, y, or z.

The second necessary relationship is that R is reflexive: that any perspective x has already become with respect to itself: Rxx, for all x. From my perspective at an instant, my perspective at that instant has come into being. (Got that?)

With transitivity and reflexivity in place, Stein argues that R defines “having become.” His last point is important in his argument against fatalism: he says that R does not hold between every two points in spacetime. That is, for any x, there’s at least one y that hasn’t become yet.

In fact, says Stein, there are a lot of such points: every point y in or on the “past light cone” of x.

Wait, what? Hold on, here’s my best attempt to explain: A past light cone is the range of points that could possibly be causally connected to x—that is, if they traveled within light speed, they could influence x. At one second in my past, it’s things 300,000 km away or less; at two seconds, it’s things 600,000 km away or less; etc. Something that happened 50 km away from me one second ago, could, in theory, reach me or influence me by this present moment: it’s inside my past light cone. Something that happened on Mars one second ago won’t reach me or influence me until after this present moment: it’s outside of my past light cone.

This structure of causality (that is, of the range of potential influence) is cone-shaped, more or less. If I see a star that’s ten light years away suddenly explode, it seems to happen right now. Really, it happened ten years ago. But, since it’s right on the edge of my past light cone (the light from the explosion racing toward me at light speed), the explosion seems to be an event in my present, rather than in the ten-years-ago past. Further, since the speed of light is a hard limit, there’s no way I could have known before this instant (or been influenced by the fact) that the star was going to explode, even though it happened—was over and done—ten years ago.

Here’s my best understanding of why Stein’s R represents a formal refutation of your-future-is-my-past fatalism: if Stein’s R does represent becoming, then my future from x could never be perceived as anyone’s past from, say, q, and then be returned to me in time for this knowledge-from-the-future to affect me. (That is, q could never warn me ahead of time that my toaster was going to catch fire at z, even if she saw it in her past.) I could never share, in a given moment, a causal relationship with someone who had seen my future past that moment.

Still with me? Here’s another weird consequence of Stein’s theory: Stein also demonstrated that an event’s present “is constituted by itself alone.” Each event is alone in its present. Including any other event in that event’s present—that is, saying that for each x a perspective y exists such that Rxy and Ryx both hold—requires the universal relation (meaning the relation of x = everything ever to y = everything ever), and no other.

So. The light cones and their ranges of influence topple backwards in time. From my perspective right now, I just noticed the toast pop up; from the perspective of the toaster as it pops, I haven’t yet noticed it. The toaster and I can’t share simultaneity.

This consequence is a major sticking point for philosophers of time, who seem nonetheless to be stuck between two firm conclusions. If you disagree with Stein and say that an event’s present can contain another event, then you live in a universe where the two events could influence each other and where, therefore, the future is definite—where fatalism holds. But if you reject fatalism, you live in a universe where every instant in every perspective is alone in its becoming.

(If you don’t mind a little more technical talk, please read SEP’s excellent article, by Dr. Steven Savitt, for a more extensive explanation.)

So (and this is my breath of breeze for poetry readers who’ve made it this far) this question gives me a new way to think of about the segmentation of experience. You know how, in poetic thinking or in a thickened apparent instant, thing A starts to B while thing B starts to A:

Flowers by the Sea
William Carlos Williams

When over the flowery, sharp pasture’s
edge, unseen, the salt ocean

lifts its form—chicory and daisies
tied, released, seem hardly flowers alone

but color and the movement—or the shape
perhaps—of restlessness, whereas

the sea is circled and sways
peacefully upon its plantlike stem


Filed under poetry, science, spirit

4 responses to “Sunday’s on the Phone to Monday

  1. Chris Robinson

    Assuming Stein is right about this not implying fatalism, does his statement have any implications for determinism? I can’t see them if there are any. We live in a deterministic universe because of absolute causality (or in a probabilistic universe which is no better in terms of free will). Reference points and relativity seem, to me, rather unimportant regarding the question of whether there is more than one possible future. That question is answered by macro-causality and QM probability, is it not? Tell me if I’m totally missing something here.

  2. The extended example of an alien invasion (seen from one person’s past, another’s future) presented by Roger Penrose and cited in Steven Savitt’s article— my sole firm source for this stuff– does actually call itself a deterministic argument. Savitt’s the one who renames it fatalism, but whatever the name, it’s what Stein’s formulation aims to disprove, by claiming that our present moment hasn’t yet become to anything whose past light cone our present moment lies in.

    But tell me more about “absolute causality,” it’s not a term I’m familiar with, tell me everything!

  3. Elizabeth Hartsig

    —Is your plucky brain a-faltering?

    No, I —

  4. Great stuff, which made me think: the future cone has a round tip, because the uncertainty principle disallows sharp corners in space-time; this might mean that several atoms can share the present. It kinda takes the edge off of loneliness…

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