# Does eternalism have testable implications in GR?

I have a PhD in theoretical physics, but little experience of GR. I have recently encountered the debate about eternalism v presentism, and I'm trying to determine whether it is purely metaphysical (and therefore probably futile) or whether it has physically testable implications. The particular question I would like to put to wiser members of the forum is as follows...

Assuming a 4-d block spacetime, the universe occupies some surface or time wise segment corresponding to the present. Supposing it were possible that other time-wise segments of time could likewise be occupied by matter- would the existence of that matter at another hyper-plane of time have any measurable impact on the segment of spacetime we occupy?

To make the scenario specific, suppose there were a parallel universe evolving through time ahead of ours. Would it leave any traces that could be detected? Would the size of the time lag between its existence and ours make a difference to our ability to detect it (eg if it were a billion years ahead of us or five minutes)?

I have convinced myself that we would be unable to detect light from a universe that either led or followed ours, regardless of the size of the time lag, as the light in that universe only exists in its version of the present (which by definition of the scenario is temporally separate from ours). However, I don't understand GR sufficiently to determine whether the warping effects of matter are confined to a present in the same way that EM radiation is, or whether they leave some kind of trail in the past. Does the theory have anything to say about that?

A clarification to my question in response to Ben...

If our universe currently occupies a space like surface at time T years (crudely speaking) then in a million years our universe will be at time T+1,000,000. I.E the space like surface will have advanced 1,000,000 years in a timelike direction. My point is this- could it be possible that the nature of time was such that another universe is already ahead of us at time T+1,000,000 years? It is not a future state of our universe as we understand it, but something separate at another space-like surface 1,000,000 years ahead of the one we occupy, and moving ahead through time 1,000,000 years ahead of us, so that by the time we get to T+1,000,000 years that other universe will be at T+2,000,000 years. In such a scenario we would never catch-up with the other surface, as it would propagate through time as our surface currently does.

In that scenario, the leading universe would have been at time T (ie the present for us now) when our universe was at time T-1,000,000 years.

If such a scenario were possible, would the universe at the surface ahead of ours leave behind it any effects on space that we could detect, or are the effects that mass and energy have on space confined, temporally, to the space-like surface in which the mass and energy exists?

• Very interesting - I had thought of the same idea of "multiple universes" "propagating" from past to future in the same way. – The_Sympathizer Sep 22 at 2:52
• One big problem with this is that there is no universal absolute simultaneity in relativity (in SR nor in GR). If I'm moving relative to you, our time axes are tilted relative to each other, so my spacelike "now" surface is not equal to yours. This is connected to the Andromeda Paradox. – PM 2Ring Sep 22 at 15:42
• Absolute simultaneity is a red herring. The surface that corresponds to the physical 'now' isn't a plane of simultaneity for any particular observer. Imagine your plane of simultaneity is tilted to mine so that at a certain distance I think it is noon on Monday but you think it is noon on Tuesday. Two observers at that point, one moving with your frame the other with mine, will disagree on what day it is, but they will both agree it is 'now'. – Marco Ocram Sep 22 at 18:41

Eternalism is an interpretation of general relativity. Predictions are generated using the mathematical formalism. An interpretation is an assignment of semantic values to the mathematical terms, and there are other interpretations possible which do not feature eternalism, while prediction is achieved through ultimately what amounts to formal manipulations of those terms to generate numbers with unambiguous semantic valence as the expected results of empirical observations.

Empirical science cannot answer questions regarding pure semantics - it is more of a philosophical matter, and the assignment of such semantics does not alter the predictive properties.

That said, it may be that there are theories which are more plausibly understood in terms of eternalism vs. presentism.

I'd also want to add some remarks here to better help clarify what the OP is talking about for the sake of future discussion as I believe I actually had the same idea the OP did that I think he is trying to thrust at, and that's regarding a possible theory of spacetime that unifies both the "four-dimensional spacetime" picture and the "non-eternalism" / "reality of change" point of view by imagining particles as entities bounded in both the spatial and "temporal" directions (as opposed to eternal, fixed "spacetime worms"), just as how Newtonian particles are bounded in three dimensions only, and that they are moving four-dimensionally through this space-"time" continuum, in one direction.

That is, what OP is after is that the "spacetime" of relativity should "really" be treated in a manner similar to the space (no "time") of Newtonian mechanics, i.e., as a theatre for actual motion, but a four-dimensional one, with a single "meta-time" parameterizing the motion and each particle constrained to broadly move in a unidirectional march from "past spacetime" to "future spacetime", i.e. from smaller to larger spacetime coordinate $$t$$.

Or in mathematical formalism, instead of talking about a particle simply as being described only by its spatial position $$(x, y, z)$$ and its evolution coordinate being $$t$$ (so that when both are put together you get a "worldline" or "spacetime worm"), you instead talk of the whole spacetime position, that is, the four-position $$^{(4)}x = (t, x, y, z)$$ as the dynamical entity, and there instead is a second meta-time $$\tau$$ that parameterizes this, i.e.

$$^{(4)}x(\tau) := (t(\tau), x(\tau), y(\tau), z(\tau))$$

which has meta-velocity

$$^{(4)}\mathbf{v}(\tau) := \frac{d[{^{(4)}x}]}{d\tau} = \left$$

which, looks very much like the four-velocity (and indeed, I've thought this quite suggestive) and when the meta-time $$\tau$$ is taken as the particle's own proper time, is equivalent. A "universe" would be a flat sheet of such particles perpendicular to the spacetime time axis, and since each particle is only at one spacetime position at every given meta-time, then it may be possible to put other particles "behind" it at earlier spacetime times and "in front of" it at later spacetime times just as you can arrange for there to be multiple moving particles in Newtonian space, some in front, some behind. And if interactions are suitably synchronized, a being made from such particles would not be able to ascertain it is so moving as opposed to $$t$$ being actual experienced time (something that may be made hard to realize as a possibility given how often a Lorentz frame is treated as a "viewpoint" instead of as simply a set of coordinates, when the truth is that no actual observer can really see such a Lorentzian "present", but only at most the surface of a past light cone as all information transfers are local.).

And OP's thesis about "universes ahead and behind" would come from that, given that if you had only one sheet of such particles marching toward higher $$t$$, things would be rather suspiciously empty ahead and behind, hence it would seem natural to wonder if there might be others given this apparent "loneliness" of that sole marching sheet.

To put this still another way, this theory would be one in which the "time coordinate" $$t$$ of relativity is not really "time" as we understand it, but simply another spatial dimension with a peculiar unidirectionality of permitted motion due to the pseudo-euclidean geometry, and given suitable synchronization of the motions of all constituting particles of the Universe may appear to us, mistakenly, as though it should be "actual time". On should note that this is a different theory (as per the understanding above) because it uses a different and inequivalent mathematical structure via the introduction of the meta-time. And though we can arrange a situation where it may be predictively equivalent, we can also perhaps arrange situations where it is not. In this regard, it bears a relationship to relativity theory similar to the relationship borne by Bohmian mechanics to "ordinary" quantum mechanics.

However, I'm not sure how good this goes for general relativity, because there we have the stress-energy tensor and I think that in order to work and produce the proper geometry of the spacetime manifold, it requires mass-energy distributed all along the time axis.

• Your statement that an interpretation is an assignment of semantic values is very edifying. – SpiralRain Sep 22 at 4:41
• I'm curious, how does your idea work for closed time-like curves? (Sorry if I'm over-burdening you with the question.) – SpiralRain Sep 22 at 4:43
• Which, of course, would be a predictive difference (hence a different theory). But one that could only be tested if CTCs actually exist. – The_Sympathizer Sep 22 at 4:48
• @Edouard : Yes, unfortunately my "easy language" facilities feel a bit #suppressed right now due to a mental disorder with a long story behind it. However, regarding your point about evidence: of course, this is only a hypothetical theory. My point in posting it is not to say that it's "correct", but rather only to try and better explicate what the asker of this question was talking about because we happened to have the same ideas. I had to put it in an answer because it would have been too long and too complex to nicely fit into comments. – The_Sympathizer Sep 23 at 1:22
• @Edouard : There is no quantum mechanics here - this is purely a classical (non-quantum) theory embryo. – The_Sympathizer Sep 23 at 1:43

What you're referring to as a "time-wise segment" is called a spacelike surface or Cauchy surface.

Supposing it were possible that other time-wise segments of time could likewise be occupied by matter

Why would there be any doubt about this? The same matter will continue to exist across a series of spacelike surfaces.

suppose there were a parallel universe evolving through time ahead of ours

This doesn't make sense. If it's ahead of us in time, it's not a parallel universe, it's just our future.

• Hi Ben, Many thanks. Your last sentence misses my point, so perhaps I've explained myself inadequately. I've added a clarification to my original post- could you take a look at it? Cheers. – Marco Ocram Sep 21 at 13:44

It appears to me that the testable implications of eternalism, in GR, might be the black-hole solutions to its equations, of which the Schwarzschild solution may be the simplest and best-known. Reality appears implausible because of the infinite brevity of the present, and yet it persists, with the contradiction between its brevity and its persistence resolved through the possibility of causal separation. Spatially-larger versions of the present may, through an application of the Weyl Curvature Hypothesis to GR which appears to be consistent with its mathematics, each contain a possibly-infinite number of arbitrarily (and perhaps sequentially) smaller versions of itself, although the objective examination of such versions through magnification would naturally be prevented, through GR's equivalence of mass and energy, by the fact that the addition of such mass would cause their further collapse to sizes even smaller.

The relativistic cosmology I've found to be the most compatible with the basic notion of this answer is Poplawski's "Costmology with torsion", described at https://arxiv.org/abs/1007.0587, and in several other papers he's written as recently as this year: In his theory of a "black-hole to white-hole bounce" (which is consistent with the CMB data), the spin of the fermions of a star undergoing gravitational collapse in a previous iteration interacts, partly through tidal effects, with the spin of much smaller-scaled fermions materialized by their separation from virtual partners in particle-antiparticle pairs by the collapsing star's outwardly-propagating event horizon. In this interaction, the trajectories of those newer fermions which subsequently form the white hole are reversed and greatly accelerated in the formation of that peculiarly irresistible dimension of spacetime which we (following Einstein) have designated simply as "time", wherein the velocities of particulate material makes its closest approach to that local limit which is the velocity of particles that are purely energetic.

The reason why I'm considering the causal separation to be susceptible to that experimental proof qualifying it as science is because of the astronomical evidence for black holes, mainly in the elliptical or nearly-circular trajectories of stars separated from their formerly-visible partners in binary pairs by the gravitational collapse of those partners.

For some related remarks on such variations in spatial scale as would necessarily occur in this model, as described by someone whose credentials (including thesis advice by Stephen Hawking) are far better than my own, see https://arxiv.org/abs/1703.08655.