One nice illustration of "space is really big" is a fact that if you take the cube with the side equal to the distance from the Sun to the nearest star and fill it with water, then the mass of this cube will be roughly equal to the mass of the whole visible Universe.
Another good one for me is that a cubic light year or butter would immediately collapse into a black hole with a Schwarzchild radius larger than the observable universe.
It's impossible for your fact and the fact you're replying to both be true. Water is denser than butter, and the nearest star to the sun is about 4.3ly away; if your fact were true, the universe would be a black hole.
A cubic lightyear is about 8.468e+50 liters, and butter weighs 911 g/L, giving the mass of a cubic lightyear of butter to be 7.714348e+50, whose Schwarzchild radius is about 121,103,293 lightyears, about 100x smaller than the radius of the known universe.
> if your fact were true, the universe would be a black hole
... maybe it is? Hear my pet theory out.
Extrapolating backwards from the expansion of our universe, the Big Bang model posits a hyperdense state that exceeds black hole levels originating from a singularity, yet it's thought that somehow it did not collapse back, handwaving it as "physics as we know it did not apply".
But maybe physics as we know it does apply. Notably physics as we know it does not imply a specific direction for the arrow of time.
So our universe might very well be a black hole, but we have time backwards compared to the usual way we think of black holes: what we think of as the origin of time and space is what we think of as the irremediable end of time and space in a black hole.
> a black hole, but we have time backwards compared to the usual way we think of black holes
Observations of our universe are straightforwardly understood -- and predicted -- by laying matter fields on an expanding Robertson-Walker metric. The same observations are not at all easy to understand by laying matter fields on a time-reversed Oppenheimer-Snyder-like black hole metric.
The first thing you run into is that at the largest scales (i.e., where the solid angles subtended by galaxy clusters are small for observers like us) visible matter is arranged roughly isotropically and roughly homogeneously: we detect typical spiral galaxies (and more importantly various atomic line transitions associated with them, like the <https://en.wikipedia.org/wiki/Lyman-alpha_forest>) at all sorts of redshifts.
Your homework would be to generate lightlike geodesics that can reproduce these observations at any time in a black-hole-like metric. If you can do that at for a single spacelike slice of your black hole, you then would want to work on evolving that slice using e.g. the <https://en.wikipedia.org/wiki/Initial_value_formulation_(gen...>.
Just scratching the surface of how you would go about doing that would be an interesting research project for a layperson. Among other things, you would end up learning a lot more about what's in your second paragraph, and likely develop an idea about how much work is involved in writing down even a simple "pet theory" of physical cosomology that accords with observational data. Or at least you'd have a better idea of what observational data there is that needs to be accounted for. You'd also confront all sorts of open questions about the interiors of black holes where there is significant matter; that would be timely given the recent preprint by Roy Kerr at <https://arxiv.org/abs/2312.00841>.
I like it! Not sure it works though. We observe the expansion of the universe accelerating, with gravity too weak to counter it. Reversing that would mean it's collapsing faster than the gravitational attraction of it's contents can account for. So either way, gravity isn't enough to explain what we observe.
IANAP, but possibly because you're measuring different attributes of the same thing - i.e., mass - but we as a species don't really understand the fundamentals of what mass actually is.
Before ANGRY KEYBOARD SOUNDS commence, I'm not saying we don't know what mass is, I'm saying fundamentals. I.e., why is mass. What causes it to come into being? Bulk entanglement, i.e., a function of probability or "mass as destiny"? Tiny signals? Lots of rubber sheeting? Etc.
The way it was explained to me is that at the big bang space itself was expanding at faster than the speed of light. So over blackhole density could evolve into less than blackhole density.
> if your fact were true, the universe would be a black hole.
The mass of ordinary matter in the universe is 2×10^53 kilograms, which would have a Schwarzchild radius of 31.39 billion light years. The explanation from popular science communicators on this topic have never satisfied me.
Your maths is correct for one cubic light year of butter. Proxima Centauri is 4.247 light years away, and that gives such a cube of water[0] a mass of 6.468×10^52 kilograms[1], which would have a Schwarzchild radius of 10.15 billion light years.
[0] At STP, which isn't realistic at all
[1] Close enough; I think it was Brian Cox who once joked that in cosmology it is standard practice to approximate π as 1.
This sounded completely false to me initially. When I think of taking mass and turning it into black holes, it involves squashing the mass into a strictly smaller volume.
Thus I would've expected the radius of the black hole to be necessarily smaller than the dimensions of the butter cube.
However, I now realize my mistake - in examples like squashing mount Everest or earth or a neutron star into a black hole, we're starting with masses that are stable/in equilibrium. This would not be the case for a cubic light year of butter!
Further, it looks like the radius is directly proportional to the mass. Given that mass grows cubic with respect to dimension, it's expected the radius of the black hole would eventually outgrow the cube of butter if made sufficiently large...
