Posted by Johannes  2/15/2018 5:22 pm | #1 |
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)
|
Posted by Ferinus 2/23/2018 11:34 pm | #2 |
This is a great intro post. What do you think about the A-theory in light of GR, specifically something like a growing block model. I am getting more into philosophy of physics and would like your opinion. I will find some of my better articles to contribute and share them when I get a chance. Also, I am new here, so hello everyone.
|
Posted by Johannes 2/24/2018 12:13 pm | #3 |
Hi, Ferinus, and welcome to the forum.
IMV, GR is compatible with both presentism and growing block/moving spotlight as long as the NOW is subjective, that is each observer has their own NOW. Thus, in presentism there is my present and your present, and in growing block, there is my moving spotlight and your moving spotlight. The simultaneity or absence thereof between two events depends on the observer, whereas the possible causality or necessary lack thereof between two events is the same for all observers, as expressed by the invariant interval.
Now, if the issue is precisely global simultaneity, e.g. if God wants to bring about a simultaneous end of the world (EOW) for all civilizations in the universe, then the solution is to choose a preferred Frame of Reference (FR) and make all local EOWs simultaneous in that FR. Let's have a look at two examples.
1. In SR, let's assume two FRs S and S' in standard configuration, moving with respect to each other at constant velocity v.
At t = t' = 0, when O and O' concide, the observers at O and O' have a vision that the remaining time to EOW is t_end, share their vision and wish each other well. After they have parted ways, they remember the Lorentz transformations and, assuming that EOW will occur simultaneously everywhere at t_end as observed from his own FR, think of each other "Poor guy, his remaining proper time to EOW is only t_end sqrt[1 - (v/c)^2]!" But neither of them thought that simultaneous EOW at t_end was as observed from the FR with respect to which both were moving at velocity u/2 in opposite directions [1], so that both had a remaining proper time to EOW of t_end sqrt{1 - [u/(2c)]^2}!
2. In FLRW cosmology, the obvious choice for preferred FR is the sum of all comoving FRs, any of which defined as a non-rotating FR in which the CMB dipole is zero. Then simultaneity in simply identity of cosmic time, which for comoving observers is identity of elapsed time since big bang.
This is clearly seen by noting that two observers A & B in immediate contact have the same "now". If they are fixed to a baloon that starts to inflate, they start to separate and eventually lose contact. But as long as they remain fixed to the inflating baloon, they will keep syncronized times, so that when A's clock marks tx, he knows that at that moment B's clock also marks tx.
The opposite case is that of a semi-relativistic hypervelocity star ejected by the merger of two massive black holes [2]. After ejection, the passage of proper time tau at the ejected system will be related to the passage of cosmic time t by:
Delta_tau = Delta_t sqrt[1 - (v/c)^2]
Thus, if 100 My ago in cosmic time a star was ejected towards earth with v/c = 0.5, when it encounters earth (hopefully without striking it!) the proper time elapsed since ejection at the ejected system will be [3]:
Delta_tau = 100 My sqrt[1 - 0.25] = 86.6 My
Notes
[1] Where v and u are related as: v = u / {1 + [u/(2c)]^2}
[2] Guillochon and Loeb (2014), "The fastest unbound stars in the universe".
https://arxiv.org/abs/1411.5022
[3] Assuming constant v is a valid approximation only for small relative increments of cosmic time, because the velocity of the ejected star with respect to the local comoving FR in to and t is:
v(t) = c / sqrt{[a(t) / a(to)]^2 [[c / v(to)]^2 - 1] + 1}
Last edited by Johannes (2/25/2018 6:40 am)
