A-Eternalism and B-Eternalism

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6 responses to “A-Eternalism and B-Eternalism”

1. 

   Malcolm Pollack

   April 29, 2025

   Bill,
   Thanks for another clarifying post. But now I’m back to raising the same issue for the A-eternalist that I did for the presentist:
   If I understand all of this correctly, A-eternalism (AE) models spacetime as a 4-D manifold in the usual way, but solves the mystery of our conscious experience of an ever-changing “now” by promoting “now” — the “fleeting whoosh” — to an objective reality.
   We might say that in AE the spacetime manifold M is an enormous sliced salami (sliced perpendicularly to the time axis) and something we can call “the passage of time” (PT) moves along that axis, lighting up one slice at a time (“the present”), and marking each slice behind it as “past”. So every point in the slice currently lit up as “the present” must therefore be simultaneous, because they occupy the same slice of time (which is what “simultaneous” means!).
   Leaving aside some puzzling questions — how “fast” does PT move? How thick is each slice? “How long” does each slice light up for? — we have another problem, courtesy of relativity, which tells us that there is no objective “fact of the matter” about how to slice the salami: observers in different reference frames will disagree about what “perpendicular to the time axis” looks like, and so will slice it at different angles.
   But this means that they must disagree about what that lit-up slice that AE wants to call the objectively existing, observer-independent “present”, because they will not be able to agree about which points belong in it!
   I’m sure this issue must have come up in the literature. So how does AE get around it?

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2. 

   BV

   April 30, 2025

   Malcolm,
   What I was trying to do above is to distinguish between two different problems.
   My problem: given the anti-presentist assumption that all events in time, whether past, present, or future, exist*, it seems we would have to say that the ancient gladiatorial battles, although not occurring at present, are occurring at temporal locations earlier than the present. And that sounds very strange!
   Your problem: How do we explain the experience of temporal passage? This is the “Whoosh” that Wuetrich mentions. Time is not a merely static ordering of events, but has a dynamic side: it seems to pass, flow, move, fly. Tempus fugit! Time flies. Your suggestion is that temporal passage is explainable in terms of our consciousness. I grant that your problem is legitimate and your solution plausible.
   It seemed to me that you were conflating the two problems. That is why I brought in the further distinction between A- and B-eternalism. A-eternalism allows for an explanation of temporal passage that is not subjective.
   You now bring up a third problem: >> another problem, courtesy of relativity, which tells us that there is no objective “fact of the matter” about how to slice the salami: observers in different reference frames will disagree about what “perpendicular to the time axis” looks like, and so will slice it at different angles.<< This brings us to the question of whether STR which is science is compatible or incompatible with such metaphysical theories as presentism and eternalism. Here is one issue. STR seems to presuppose the ontology of eternalism (which is the same for both A- and B-eternalism). Eternalism entails the transitivity of coexistence: if e1 coexists with e2, and e2 with e3, then e1 coexists with e3. But STR denies the transitivity of coexistence (across all rference frames). Inconsistency seems to result: 1. STR entails eternalist ontology. 2. Eternalist ontology entails trans. of coex. 3. STR is inconsistent with trans. of coex.

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3. 

   Tom T.

   May 1, 2025

   Bill,
   >>This brings us to the question of whether STR which is science is compatible or incompatible with such metaphysical theories as presentism and eternalism.<< I don't know if this solves anything, but an interesting thing about STR is that although there is no privileged reference frame to determine the time something happens, the order or sequence of events will be the same no matter the reference frame. In other words, it seems that the notions of an objective present and past are preserved, even though the measurement of time and the passage of time cannot be agreed upon. On the inconsistency you present, you seem to assume that STR is denying the coexistence of two events. Strictly speaking, STR only denies the possibility of measuring two events with some independent fixed time index. As to the actual coexistence of events, I think Einstein was not so much skeptical as unconcerned about what the reality might be behind his equations, so long as the equations were properly verified by experiments.

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4. 

   David Brightly

   May 2, 2025

   Tom,
   “…the order or sequence of [a pair of] events will be the same no matter the reference frame.” This is the case if and only if the two events are ‘timelike’ separated. That is, the spacetime interval between them (which all observers agree on) is positive or zero (*). Equivalently, light or a particle can be sent from one event to the other. And this means that all observers agree on the ‘causal structure’ of events, even if they cannot agree on all event orderings. For where they cannot agree an ordering there is no causation to be had. So not all is lost when we are forced to abandon simultaneity.
   (*) When the interval is given by Δs² = c²Δt² – Δx² – Δy² – Δz².

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5. 

   BV

   May 2, 2025

   Tom,
   You may be right. I am neither a physicist nor a philosopher of science, and in any case, this is difficult subject-matter and I’m no Einstein. So let me try to make a case for the inconsistency of STR with the transitivity of coexistence which eternalism requires. Maybe you or Brightly can show me where I go wrong.
   1. If spacetime points/events a, b, c, . . . each exists, then they all co-exist, which is to say that they all exist together as items in one and same sum-total of reality which is spacetime.
   2. Co-existence is an equivalence relation: it is reflexive, symmetrical, transitive.
   3. The reflexivity and the symmetry of coexistence are undeniable. So:
   4. The only way to deny that co-existence is an equivalence relation is by denying that co-existence is transitive.
   5. On STR, simultaneity is not absolute but relative to inertial reference frames (IRFs).
   6. Now suppose in IRF-1 events e1 and e2 are simultaneous. This implies that e1 and e2 co-exist in IRF-1. Suppose further that in IRF-2, e2 is simultaneous with e3, but that in IRF-3, e1 is not simultaneous with e3. This scenario is possible on STR.
   Therefore
   7. E1 and e2 coexist, and e2 and e3 coexist, but e1 and e3 do not co-exist. This is a violation of transitivity of co-existence.
   BUT
   8. On eternalism, all events are co-existent as items in the one sum-total of physical reality which is spacetime.
   THEREFORE
   9. If STR entails eternalism, then STR is false, and cannot be used to refute presentism.
   10. If, on the other hand, STR entails presentism, then it is also false because STR requires the relativity of simultaneity whereas presentism excludes it.
   THEREFORE
   11. Science and metaphysics are not in competition. In particular, STR as science is compatible both with the metaphysical doctrine of eternalism and with the metaphysical doctrine of presentism. What we have here are two different ‘magisteria’ (teaching authorities) that can peacefully ‘coexist’ (pun intended).
   Analogy: religion and science can peacefully coexist. In particular, divine revelation can coexist with the theory of evolution.

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6. 

   Tom T.

   May 4, 2025

   Bill & David,
   Bill, you argue that STR denies co-existence (simultaneity) and therefore contradicts eternalism and presentism. But I repeat what I said earlier that STR does not hold that there is no simultaneity of events, only that simultaneity cannot be objectively established between different IFR’s that disagree about the ordering of the events. It’s like the fact that it is impossible standing on earth with normal vision to see past the horizon. The impossibility does not mean there is nothing beyond the horizon, just that it cannot be seen. So too with simultaneity. In the metaphysics, you are talking about what is there (simultaneousness of events); STR is talking about what can be proven about what is there (simultaneousness of events). These two positions are not contradictory.
   You might say STR is agnostic about the reality of simultaneousness, but I think even that goes too far. Your #6 posits only the case of a series of events that are not in a reciprocal causation relationship wherein STR affirms that temporal ordering cannot be objectively established (i.e., proven between disagreeing observers). It seems to me that what STR identifies in the series of non-reciprocal events is that they are essentially atemporal. That is, discrete monad like events do not implicate time at all; they just are and there is no way to objectively distinguish their time sequence (simultaneous or not) between different IFR’s. In effect, STR is not saying there is no simultaneity or fixed time sequences, but that simultaneity or the time sequence of non-reciprocal events is irrelevant to the behavior of the spacetime matrix.
   The situation is quite different between events in which there is reciprocal causation. In that case, the linear, unidirectional relation of the past, present, and future can be objectively established between all IFR’s. Credit to David Brightly for presenting concisely the relation of reciprocal causation to the temporal ordering of events in STR: “And this means that all observers agree on the ‘causal structure’ of events, even if they cannot agree on all event orderings. For where they cannot agree on ordering there is no causation to be had.”
   If there is no causation, then no agreement on temporal ordering. But where there is causation, then there is agreement about the objective ordering of the sequence. Event A (falling rain) precedes Event B (striking the earth), whether I am standing on the earth or zipping along near the speed of light. In no IFR would the rain ever be seen as rising upwards from the earth (except, see the General Theory of Relativity, wherein this is not strictly true – but we’ll leave this complication aside).
   The only wrinkle in STR is that the objective “causal structure of events” is subject to time dilation between different IFR’s. That is, the objective passage of time in the order of past, present, and future stays the same in a fixed time sequence, but the rates of the passage of time are different between different IFR’s. This is counter-intuitive, of course, but not structurally different from classical notions of temporal succession.
   So, I see STR as consistent with eternalism and supportive of the reality of the past, present, and future. But to the extent presentism denies the existence of preceding causes in the production of existence in the present moment, then I think STR is inconsistent with presentism. The objective reality (existence) of causation and temporal succession along the time axis of spacetime are all rather fundamental to STR.
   But STR would not in any sense prove or disprove presentism or eternalism. As Bill says, STR and metaphysics are two different spheres of thought with very different agendas and never the twain shall meet. Einstein, for his part, was not a fan of metaphysics and was quite satisfied with theories so long as they could be verified by evidence and experiment. Metaphysics seeks something more.

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