How can space expand when it is only a perception of the separation between at least 2 objects. Isn't saying "space expands" implying it has properties?
$\begingroup$
$\endgroup$
6
-
2$\begingroup$ Space has properties, like curvature. $\endgroup$– jinaweeCommented Mar 2, 2014 at 19:40
-
1$\begingroup$ curvature is a property of matter - surely space is the perceived relationship between matter. $\endgroup$– PeterCommented Mar 2, 2014 at 19:57
-
1$\begingroup$ Einstein and every experiment of General Relativity disagrees. $\endgroup$– jinaweeCommented Mar 2, 2014 at 19:58
-
1$\begingroup$ @Peter A way to see that this view can never hold is by considering that it is, in fact, possible to have an empty space, i.e. with no matter or radiation. In fact, the space in which the theory of special relativity is set (Minkowski space) is a solution to the equations governing gravity with no matter content. $\endgroup$– DanuCommented Mar 2, 2014 at 20:21
-
$\begingroup$ I don't feel well-versed enough (yet) to venture an answer on the OP's good question, but, regarding questions about whether or not spatial expansion is driven by a "cosmic substratum" (which I've usually seen described as hydrogen & helium atoms), it's interesting to note that the Standard Model (presumably the one that's best-supported by observation &/or experiment) departs slightly from 1915's pure General Relativity, per a citation that I'll be including momentarily in a 3rd comment. $\endgroup$– EdouardCommented Feb 22, 2021 at 22:54
|
Show 1 more comment
2 Answers
$\begingroup$
$\endgroup$
2
We model spacetime as a manifold and a metric. Broadly, the manifold gives us the dimensionality and connectivity while the metric provides a method of specifying distances. The equations of General Relativity allow us to calculate the metric from the stress-energy tensor (or vice versa if you're Miguel Alcubierre).
The point that jinawee is making in his comments is that even in the absence of matter or energy the Einstein equation can still be solved to give a spacetime. These solutions are known as vacuum solutions. For example a common and potentially very important vacuum solution is the gravitational wave.
So we do not need matter/energy to be present to have a notion of distance. All we need is the metric. In the particular case of the FLRW solution the metric looks like:
$$ ds^2 = -dt^2 + a(t)(dx^2 + dy^2 + dz^2) $$
where $a(t)$ is the scale factor and increases with time. This metric tells us that the distance between two spacetime points increases with time regardless of whether or not there are chunks of matter at those two points.
answered Mar 3, 2014 at 14:57
-
$\begingroup$ --At arxiv.org/pdf/astro-ph/0610590.pdf, Chodorowski felt (in its Section 6) that the expansion of Milne's empty universe derives entirely from its coordinate system, quotes Lineweaver & Davis (2003) as claiming that spatial expansion isn't "a force or drag" carrying objects with it, and claims that the expansion of space, per se, only occurs thru an inappropriate extension of SR to cosmology. He doesn't mention gravitational waves: Might their observation (@2014) justify the difference between your conclusion and his own (that c might vary between any pair of inertial frames)? $\endgroup$– EdouardCommented Feb 21, 2021 at 14:04
-
1$\begingroup$ @Edouard The Milne metric is just the Minkowski metric written in curved coordinates. If you calculate the Riemann tensor from it the result is zero. $\endgroup$ Commented Feb 21, 2021 at 17:24
$\begingroup$
$\endgroup$
0
The (nearby) "separation between objects" you are referring to is the space-time metric. A metric in cosmology describes the expansion of space on large angular scales (low $\ell$ on the angular power spectrum of the universe). Without going into the mathematics, the expansion of space is driven by cosmic inflation, and is affected by things the amount and distribution of matter and energy in the universe. The origin of inflationary expansion is a major question in cosmology. "Space expanding" means that the scale of space itself is changing. By mentioning "properties of space" you are getting at the cosmological parameters in the current cosmological model (called $\Lambda CDM$) (e.g. $H_0$ the current rate of expansion, and $\Omega_k$ the curvature density) from the CMB power spectrum. So yes, space is described by physical parameters (some of which, like $H_0$ can change over time) that we measure on cosmological scales.
BTW, if by "perception" you are referring to different observers (frames of reference), you should note that there are both observer-dependent and observer-independent notions of curvature (not all observers agree on the curvature of space due to the presence of mass/energy density).
