Complying with the rule that discussions on Dr. Feser's blog articles can be started only "on articles one week (7 days, inclusive) old or more" but threads discussing "a topic inspired by the blog article but tangential to the article's main point" are acceptable, and given that the main point of the recent "Time, space, and God" article is, in Feser's words, the "theological problem", I want to discuss the fact that General Relativity (GR) theory makes it easier to understand that space and time are dimensions which are internal to the physical universe, and thus began to exist when the universe itself began to exist.

Though it is not easy to achieve the right balance between the required level of specificity regarding the physical theory and observations and the appropriate level of generality for a philosophy forum, I will give it a try.

1. A barely minimum theoretical background

When the GR equations are applied to a homogeneous and isotropic configuration, they lead to the Friedmann–Lemaître–Robertson–Walker (FLRW) metric (spacetime description). The geometry and evolution of the universe described by that metric depend on its contents and matter-energy density, with the following possibilities regarding each:

Possible cases of geometry:
- hyperbolic or open (negative curvature): infinite space.
- Euclidean or flat (zero curvature): infinite space. Case favored by current observations [1] but inherentely indistinguishable with certainty from the other two [2].
- hyperspherical or closed (positive curvature): finite space.

Possible cases of evolution:
- accelerated expansion for ever. Case confirmed by current observations [3] [4].
- linear (i.e. constant-rate) expansion for ever.
- decelerated expansion for ever.
- decelerated expansion up to a maximum, stop, and then accelerated contraction to singularity.

If the universe has a property which makes space expand - generically called "dark energy" (the darkness is epistemic) and, when it is constant in time, as observations point to be the case, specifically called "cosmological constant" - then any of the possible cases of geometry can have accelerated expansion for ever.

Otherwise, i.e. if there were no cosmological constant, then geometry would determine evolution thusly:
- hyperbolic: decelerated to linear expansion for ever,
- Euclidean: decelerated expansion for ever,
- hyperspherical: decelerated expansion to a stop followed by accelerated contraction to singularity.

2. Discussion of the consequences at the philosophical level

First, the physical model favored by current observations implies that the universe had a beginning (which was not a hot Big Bang from a singularity but the beginning of the inflationary epoch [5]). This means that time started to elapse at that initial moment.

Second, and most relevant to the "absolute space" nonsense, space expands. Light from faraway galaxies is not redshifted because the galaxies are moving away from us in some "absolute space", but because intergalactic space expands.

Third, current observations cannot discard that the universe is finite and geometrically closed, a 3-sphere. (BTW, a finite universe does not mean that there is something "outside" the universe, because a 3-sphere has no boundaries. If the expansion of a closed universe stopped, a ray of light sent in one direction would eventually return to the starting point from the opposite direction.)

So, time started to elapse and space expands, and it may also be finite. So much for the absolute, infinite time and space nonsense.

References

[1] Planck 2015 results. XIII. Cosmological parameters. P. 32.
Omega_K = -0.0001 +/- 0.005 or 0.0008 +/- 0.004, depending on observations selection.

[2] Mihran Vardanyan, Roberto Trotta and Joseph Silk, How flat can you get? A model comparison perspective on the curvature of the Universe, Monthly Notices of the Royal Astronomical Society, Volume 397, Issue 1, 21 July 2009, Pp. 431–444. https://arxiv.org/abs/0901.3354

Vardanyan et al (2009) wrote:

the geometry of the Universe is not knowable if the value of the curvature parameter is below |Omega_k| ~ 10^-4

[3] David Rubin and Brian Hayden, Is the expansion of the universe accelerating? All signs point to yes, The Astrophysical Journal Letters, Volume 833, Number 2 (2016). https://arxiv.org/abs/1610.08972

[4] Balakrishna S. Haridasu, Vladimir V. Luković, Rocco D’Agostino and Nicola Vittorio, Strong evidence for an accelerating universe, Astronomy & Astrophysics, Volume 600, L1 (2017). https://arxiv.org/abs/1702.08244

[5] Ethan Siegel, 21 09 2017, The Big Bang Wasn't The Beginning, After All. https://www.forbes.com/sites/startswithabang/2017/09/21/the-big-bang-wasnt-the-beginning-after-all/

Last edited by Johannes (2/16/2018 8:41 am)