Inspired by the thread about the speed of light. This is something I’ve been thinking about for a while, and I’ve come up with my own analogy as an alternative to the classic “stretched out rubber sheet”.
The classic. Space is like a rubber sheet, and as it expands, it’s like the sheet being stretched out. Unfortunately the implication seems to be that the density is then in some way decreasing due to being stretched out.
Flik’s alternative. Space is like a collection of a whole bunch of really small (maybe Planck size, maybe smaller or larger, but due to my own biases I like to imagine them as Planck length sized) pixels. As space expands, these pixels aren’t being stretched out. Instead more pixels are being added to the ones that already exist, pushing them all away from each other.
Are there any reasons to think the second explanation is closer to matching reality than the first one?
I don’t know but I like your second alternative better. I don’t think there is any sense in which space is getting thinner, whatever that would even mean.
Dots on a balloon and rubber sheet analogies explain how things can move away from each other in 2 dimensions. Yes, a balloon is 3 dimensional but the surface isn’t. For a pixel analogy I’d say consider a 3 dimensional array of pixels with each pixel expanding and the centers of the pixels are continuing to get further apart.
It might be somewhere in between. One plausible (but neither proven nor disproven) model has it that the “real” Universe only has two spatial dimensions, and the three dimensions we perceive are a holographic projection from those two dimensions. If that’s the case, and if there is some sort of fixed “pixel size” to the Universe, then the number of pixels is proportional to the square of the scale factor, while the volume is proportional to the cube, so there are both more pixels, and they’re less densely-packed.
That said, we not only don’t know if the holographic model is correct, but we also don’t know if space has “pixels”, or anything analogous to them.
I’d like to see a precise description of how these extra pixels can appear and maintain the anisotropy of space. I can’t quite picture it, even in 2D. I can imagine a rectilinear grid of all-black squares suddenly turning into a checkboard, wth exactly as many red squares interspersed with the black ones, but that would suddenly double the size of the universe. The universe doesn’t grow in discrete doubling steps. So somehow the extra pixels must appear gradually at various sites. As each new pixel appears, space cannot remain a rectilinear grid in its immediate neighborhood; there must be a “defect” in the grid at that point. Presumably there’s nothing in reality that corresponds to such defects suddenly appearing in the structure of space, so the stretching rubber sheet model seems to me to be closer to reality and easier to understand than the pixel model.
Another analogue might be something like a ball of cells dividing. Cells have an average size, but may grow big and divide, the two grow some more, and so on. The mass is growing, but there isn’t any sort of underlying rigid structure - no grid and nothing like pixels. But if you put two markers in the mass they will slowly move apart. How the cells obtain nutrients is an exercise for the reader. (Dark nutrients perhaps.)
The whole grid/pixel thing is curious in a way. The modern world sees people thinking in terms of the familiar computer based analogues. Perhaps a few decades ago the idea of a substructure more like film grain would have been more familiar.
Personally, I suspect the idea of some fundamental quantisation of space as a physical reality of structure isn’t the right answer. Ideas like extrapolating from the Planck length to a fundamental grid of that size are at best amusing thoughts.
‘Naive’ models of a pixelated spacetime at the Planck level should lead to observable violations of Lorentz invariance, leading to a dispersion of light (a dependence of its speed on energy) at energies comparable to the Planck energy. But such dispersion effects aren’t observed—all the light even from very distant, powerful sources, like gamma ray bursts, seems to arrive at the same time. This puts constraints on the discreteness of spacetime, such that if there is a scale at which it is discrete, it would have to be beyond the Planck scale.
There are also ways to build up a spacetime from discrete elements that uphold Lorentz symmetry. One is being pursued in causal set theory, where spacetime is a partial order of points, which gives it a certain causal structure. There, ‘sprinkling’ points into a manifold by means of a Poisson process, and giving to each an elementary unit of volume, leads to a Lorentz invariant manifold. Adding points to spacetime in the form of such a process then preserves its symmetries.
The one that makes the most sense to me I heard recently in that, space is like a loaf of raisin bread. As the loaf rises and expands, the raisins move away from each other in every direction at once. Simple enough for me to picture it in my peanut brain
While I think it is not currently favored the Big Rip is considered one possible end for our universe. Basically, the universe tears itself apart because the “rubber sheet” can’t keep stretching forever.
Why not? If matter warps space, why wouldn’t the density of space change? My understanding is that space (along with matter and time) was created at the moment of the Big Bang. As it’s been expanding ever since, it doesn’t seem that crazy to think of space as getting “thinner”.
To me, it seems weirder to think of space matter being created to fill in the gaps as it expands, rather than getting stretched out.
But then again, I know fuck-all about such matters.
To be clear, what I was proposing wasn’t “space stuff” being stretched out and new space being created to fill in the gaps. I was proposing that new “space stuff” is being created, and this new stuff pushes all the existing space stuff apart from itself. It doesn’t even have to be pixelated. It could be something that doesn’t change in character no matter how far you zoom down.
ETA: But I’m with you in that I don’t have any formal education in these matters. It’s me speculating on what I’ve learned from physics podcasts such as Daniel and Jorge Explain the Universe and Why This Universe and various popular physics books.
What we’re lacking is a precise definition of “space”. All we know is that space is NOT stuff as we normally recognize it; it’s what contains stuff. (I use stuff because matter and energy and fields and whatever the heck dark energy might be all are in space.) Trying to think of space as stuff is a category error.
My understanding (likely a misunderstanding) is that dark energy and the expansion of space are related, or at least that they have both been increasing since the Big Bang, and that the increase in both has been accelerating over the past 6 billion or so years. It only makes sense (at least to me) to at least consider that dark energy is some kind of property of space that makes it what it is, and that as it expands dark energy increases with it.
Your analogy describes hyperplasia, which involves an increase in the number of cells, and the expansion of the universe. But, hypertrophy—where cells grow larger rather than multiplying—seems like a more fitting analogy for how space expands. In the universe’s case, space itself stretches, much like how a cell expands during hypertrophy. This process causes galaxies to move apart, not because new space is being inserted between them, but because the very fabric of space is expanding. It’s similar to how markers embedded in a growing cell would drift farther apart as the cell increases in size. The objects remain the same, but the space between them increases due to the stretching of the medium itself.
I guess it depends really what the analogy is for. IMO either analogy can be used at various times.
The way I see it, analogies or metaphors to explain something that’s really come foremost from the maths should not be taken too seriously. Inferences like “Won’t the sheet get less dense as it gets stretched?” can always be made, and they usually don’t make any sense in the true mathematical model.
It’s why I stopped reading popular theoretical physics books. The authors mean well, but they are some of the least educational educational books IMO. The kinds of questions and inferences you might want to make based on their analogies often aren’t meaningful. And new developments in science are often hard to reconcile with old ways of describing the problem to a lay audience.
