How Special Relativity Thwarts Eternalism (And More)

Illustration of an argument for Eternalism

Image Credit: John D. Norton


INTRODUCTION. The image above illustrates a well-known argument due to Rietdijk and Putnam, which says that Special Relativity implies Eternalism (also called the “Block Universe” view). I recommend John Norton’s exposition if you’re not already familiar with the argument.

Norton has pointed out that the Rietdijk-Putnam argument requires assumptions that are not implied by Special Relativity (I review this in the Part I.) But the plight of the Eternalist is worse than that. After observing that observer-dependence is an essential part of the Eternalist claim (Part II), I’ll show that Special Relativity actually implies that there is no fact of the matter about Eternalism (or the “determinate present” itself, for that matter), since observers disagree about the Eternalist claim (Part III).

PART I: SR Does Not Imply Eternalism. Eternalism is the view that all events in the past and future have a kind of Platonic or “determinate” existence. But Norton points out there are two hidden assumptions in the Rietdijk-Putnam argument for this view. They are:

  1. IF two events lie on the same hypersurface of simultaneity, THEN they are equally determinate; and
  2. for all events e1, e2, e3: IF e1 and e2 are equally determinate and e2 and e3 are equally determinate, THEN e1 and e3 are equally determinate (transitivity of determinateness).

These assumptions seem to be independent of the theory of Special Relativity (SR). Therefore: SR does not imply eternalism.

PART II: Determinateness is Observer-Dependent. Notice that assumptions (1) and (2) only allow one to say that two events are equally determinate. There’s not yet a way to say that any event actually is determinate. So if the case for Eternalism is to be made, a third assumption needed, that

  1. There exists at least one event that is determinate.

How might one establish (3)? The only way to do it is through an observer. If a property of spacetime (like “determinateness”) isn’t in principle accessible by some observer, then we have good reason to suspect that it’s meaningless.

Fortunately, a precise kind of “observer-dependence” is already built into the Eternalist view, and into the view of (her nemesis) the Presentist. Both agree that an observer’s experience of the event “the present now” is required to first establish that an event is determinate. Therefore: both the Eternalist and the Presentist have only established the ability to say that an event is determinate for some observer.

In order to establish the Eternalist claim (that Minkowski spacetime is factually determinate), one would have to claim that spacetime in Special Relativity is determinate for all observers.

PART III: SR Thwarts Eternalism. Minkowski spacetime (the spacetime of Special Relativity) is not determinate for every observer. In fact, for every event e in Minkowski spacetime, there are observers who disagree about whether or not e is determinate. For example, consider Alice:

Alice in constant acceleration
(In this spacetime diagram, the vertical axis is time, the horizontal axis is space, and c = 1.) Alice accelerates uniformly from v = -c to +c over the course of her lifetime. Her hypersurfaces of simultaneity are indicated in red. But none of Alice’s hypersurfaces of simultaneity intersect any event in regions I or II. So Alice will claim that regions I and II are indeterminate.

On the other hand, suppose Bob travels with constant velocity for all of time. Bob’s hypersurfaces of simultaneity will collectively cover all of Minkowski spacetime. So Bob will conclude (by way of assumptions 1-3 above) that all events (and thus also the in regions I and II) are determinate.

CONCLUSION. Determinateness cannot be an objective property of spacetime, because observers disagree whether or not a given event is determinate. As a result, there is no fact of the matter about Eternalism, either.

This conclusion falls straight out of the assumptions (1-3) above, which were adopted by the Eternalist in the Rietdijk-Putnam argument. So insofar as one accepts these assumptions, Special Relativity not only thwarts Eternalism: it implies that the very notion of a determinate event is bogus.


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6 thoughts on “How Special Relativity Thwarts Eternalism (And More)

  1. Bryan

    Justin: yes, you won’t want to confuse those two concepts. Here’s the difference.

    Determinism is a mathematical property, which is (or is not) possessed by a theory. (Earman (1986) for more.)

    Determinateness is a (vague, Platonic) property that some suggest is possessed by the world.

    Here’s a way to pull the two ideas apart. In order to ask whether or not determinism holds, you will typically need an equation of motion and an initial state. If these two ingredients guarantee a unique way that the initial state can evolve in the future and past (a unique path through phase-space), the this system is deterministic.

    Notice that there is no question yet about what’s real and what isn’t. This was a question about the uniqueness of solutions to a differential equation.

    You don’t need any of that mathy stuff to talk about determinateness. In fact, you can (presumably) ask if an empty universe with no dynamical field equations has determinate spacetime points. The reason is, determinateness is supposed to be a question about what is real and what isn’t at various points in time and space. And I argue that the very idea is whacky.

    Hope that helps! -B.

  2. Richard

    Just to check I’ve understood the argument in part III correctly: there’s a frame of reference (namely, Alice’s) according to which some events (those in regions I or II) are not simultaneous with any moment whatsoever, and therefore not determinate/real. Is that it?

    But why does it matter if “there are observers who disagree about whether or not e is determinate”? You earlier talk about how a property must be “in principle accessible by some observer“. So why not stick with that, and say that an event is determinate/real so long as it fits within some frame of reference or other? Why require all? That stricter requirement seems unmotivated to me. Alice should simply recognize that there are blocks of spacetime which are inaccessible, in terms of simultaneity planes, from her frame of reference.

  3. Bryan

    Richard: you’ve got the idea, and your objection is well taken. My argument does depend on this claim:

    (*) The only factual properties of spacetime are those that are agreed upon by all observers.

    An objector could consistently discharge that assumption, and indeed avoid my conclusion. However, I claim that physics in practice assumes (*). For example:

    (1) The existence of an electric field depends on the motion of an observer, as in the famous example of a conductor around a magnet. 19th century ether-theorists assumed that there was one correct observer (namely, the ether rest-frame), and thus a fact of the matter about the field’s existence. But the 20th century saw the wide adoption of (*), and thus the rejection of the electric field by itself as an objective property of spacetime.

    (2) More recently, QFT-interpreters have noticed that Unruh radiation consists in particles that exist for accelerating observers (like Alice), but not for inertial observers (like Bob). My assumption (*) is often explicitly adopted to argue that “particle number” is not a fundamental property in QFT (for example, see Wald 1994, pp.116).

    Rather than list more examples, let me concede that (*) might still be wrong. In this case, I am willing to fall back to a more modest claim: Special Relativity together with modern physics practice thwarts eternalism.

    Thanks for the note! -Bryan

  4. Clark Goble

    Bryan, it seems this extra assumption ends up being problematic since it confuses what all observers would agree upon ontologically with what they’d agree upon epistemologically. That is you are in effect saying that epistemology (what they can measure) entails the ontology. I don’t think everyone would agree.

    Of course this ends up being a problem with uses of SR against presentism since the epistemology vs. realism issue is key. And the skeptic can always point to the epistemological issues.

  5. Anonymous

    Nice post, Bryan. It reminds me of Einstein’s Galilean relativistic dream, tweeked a bit.

    Imagine three cowbells, tuned to notes A, B, and C, hung a hundred feet apart in a straight line in the order A-B-C;
    Einstein stands in the middle and presses a button to simultaneously send an electrical signal through three equal length electric wires to sound the bells simultaneously.
    Assistant at A records the sequence ABC,
    Assistant at C records the sequence CBA,
    Einstein records B followed by an AC chord.
    Each of these three observations is repeatable and factual, yet contradicts the other two. All three event sequences are simultaneously true!
    Therefore, one must conclude that:
    1) All events are relative to space-time locality
    2) There are an infinite number of objectively inconsistent histories of the world, each originating in its here-now.

    Steve Gabor

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