I’m totally not agreeing here, man.
That’s fine, because it would probably take about three months of 12-hour conversations every day to lay the groundwork for a proper discussion about this. But maybe if I plant the seed of my viewpoint here, then after a few years of reading papers about general relativity and cosmology you’ll sit back and go “ohh…okay, that actually makes sense.” Because the prevailing view of all this stuff is so deeply rooted now that it's virtually impossible to see it differently -
everyone is married to the expanding spacetime idea these days. But let's see why that is.
The reason people say that spacetime is expanding at cosmological scales is because of the way that the Friedmann–Lemaître–Robertson–Walker (FLRW) metric is formulated. The FLRW metric defines something called a “comoving coordinate system,” where the “comoving distance” between galaxy clusters is fixed/unchanging. So if you start with that coordinate system, then you have to define the changing spatial separation between galaxy clusters using a different term which they call the “proper distance,” which as we know is constantly increasing between galaxy clusters. And the rate of this increasing distance is called the “scale factor.” Therefore, since the “comoving distance” is defined to be constant, while the observed “proper distance” is increasing, astrophysicists say that the spacetime between them is expanding. And using that coordinate system, that’s a perfectly legitimate way of looking at it.
But let’s back up for a minute, because we’ve skipped over the fundamental physics at the heart of all of this. The real issue here is the problem of defining a coordinate system in general relativity, because it’s nothing like the nice neat coordinate system that we humans tend to envision our world with, Euclidean geometry, where forces generate motion against a flat static geometrical background. Instead, we find ourselves in a cosmos where the geometry of spacetime is curved (or at least
appears to be curved, so Usual Suspect won't bristle at me ; ) - where gravitation isn’t a force at all, but rather the result of this curved geometry, which we can envision as curving both “up” and “down” for illustrative purposes. Within the galaxies, we have positive gravitational curvature, which we visualize as a dip downward. And in the vast distances between galaxy clusters, where the “dark energy” effect becomes dominant, we have negative gravitation, which we can visualize as a very slight hill lifted upward.
Regardless of which form of gravitational field that your galaxy is subjected to, either positive or negative, your galaxy remains in “free fall” – which GR calls “an inertial reference frame” (a reference frame that feels no forces acting upon it). Just as a rock dropped from a mountain is in free fall (neglecting atmospheric friction) and therefore feels no force acting upon it, the same is true of the galaxies undergoing positive or negative gravitational acceleration. In other words, locally, the galaxies are “at rest” in their own reference frames. And this is why the FRLW metric chose to define a “comoving coordinate system” - if all the galaxy clusters are locally at rest, then a coordinate system that defines their positions as a constant reference frame, is really the only way to define a global cosmological reference frame: there’s nothing else to reference, other than the galaxy clusters themselves.
You have to admit though, that it’s kinda weird to choose a coordinate system that’s physically expanding, and define that as a "rest frame.” And that’s how astronomers arrived at the idea that spacetime is expanding. Because if you start with the idea that the galaxy clusters are at rest and then define your unit of distance on that, when they’re clearly all flying apart from each other, then all you can say to explain it is by claiming that the spacetime between the galaxy clusters is expanding.
But general relativity itself is coordinate invariant – GR doesn’t define a cosmological coordinate system - it works for any self-consistent and well-defined coordinate system that you choose to use. So we can look at all of this quite differently, and I feel more intuitively in accord with its own formulation – which is simply geometrical.
Consider a simple example: two stars falling together via their gravitational interaction. Each star is in free fall: they don’t feel any gravity pulling them together, and yet they’re moving closer at an ever faster rate. From each star’s own point of reference – just as the FLRW metric defined each galaxy cluster as a point of reference – we can say that they’re at rest, even though they’re moving together at an accelerating rate. Applying the same kind of coordinate system that the FLRW metric employs, we can say with perfect validity that the spacetime between the two stars is shrinking.
But is it
actually shrinking, or is this “shrinking spacetime” simply a product of our choice of coordinate system? It’s relative, I suppose. From my point of view, I think it’s stupid to favor the view that spacetime is shrinking between those two stars, because the general theory of relativity can explain it far more simply: the two stars are merely following the geometry of spacetime curvature – the gravitational field – that exists between them. The spacetime between them isn’t shrinking; the stars are simply falling closer together.
And we can model cosmological behavior in exactly the same way, using the clear geometrical language of general relativity, without employing the comoving coordinate system of the FLRW metric. And in doing so, we can more clearly see the role of dark energy (or more precisely, the role of the negative gravitational field that we associate with dark energy) in cosmological evolution.
So let’s go back to our galaxy clusters separated, say, across a vast cosmic void. We’ll choose two galaxy clusters on opposite sides for simplicity.
The positive gravitational field surrounding each individual galaxy cluster produces an acceleration toward the other, but at the huge cosmic scale of distance between them, the negative gravitational field (which we can envision as a hill between the two clusters that’s highest at the center of the cosmic void) is greater than the positive gravitational field between them. So the two clusters free-fall away from one another as naturally as two balls on opposite sides of a hill roll away from one another. The spacetime between them isn’t
expanding – the distance between the two clusters is simply
increasing. And as all of the galaxy clusters at the periphery of this great cosmic void fall away from the center of the void, the positive gravitational acceleration between them gets even smaller. And since the distance between each galaxy cluster and the center of the cosmic void is 1 radius (the distance to the center of negative gravity), whereas the distance between galaxy clusters on opposite sides of the void is 2r (the distance between the centers of positive gravity), then by the inverse square law the galaxy clusters will increasingly accelerate away from the center of the cosmic void, and therefore each other. Which is what we observe.
By simply choosing a different, and local, coordinate system (in this case centered on the middle of the cosmic void in-between the galaxy clusters that we just considered), we’ve replaced the concept of expanding spacetime with the much simpler concepts of general relativity that we apply to every other gravitational system that we observe, from the planetary, to the stellar, to the galactic, and ultimately to the galaxy-cluster scales.
This is a perfectly valid way of looking at it: spatial separation is simply
increasing driven by negative gravitation…rather than spacetime itself
expanding. Both choices of coordinate system result in the same observations. But by focusing on the relative motion of observable galaxy clusters undergoing gravitational acceleration, instead of transforming it away with an accelerating coordinate system, we’ve eliminated the assumption that an unobservable empty volume of spacetime is increasing in size.
So that’s how I look at it. And that’s why I don’t have to resort to bizarre ideas like “spacetime repelling itself,” which suggests that you can push against a volume of nothing, and which overturns a century of general relativity that tells us that gravitation is not a force at all but rather a purely geometric phenomenon.
Possibly I took it quite too far. Here is how this guy explained time crystals. you have atoms experiencing effect before the cause and running ahead of themselves. But time crystals go back and forth, while positive & negative mass move in straight line.
Yep - time crystals are simply quantum oscillators, sorta like a spring-mass system. They're not related to negative mass, afaik.