Sorry for also asking a space 101 question, but since the fabric of space is expanding, does that mean that things are getting bigger as well? Naively, it would seem that way. In your balloon example, the dots would get bigger.
For the expansion to have a significant impact on relative distances, the distances involved have to be so extreme that there's no real other interaction between the objects you're measuring from.
That doesn't contradict strict conservation of energy - it just adds another energy source that has to be accounted for when balancing everything.
It might contradict the aphorism "energy is never created or destroyed", but I'm not sure that was ever science.
It's more fun to think about it in terms of thermodynamics. Can that extra energy be used to reverse the second law of thermodynamics? I'm guessing not - it's so diffuse that it's probably impossible to use it to reduce entropy. The math for actually doing those calculations is well beyond what I know, though, so I'll just say that one's no more than a guess.
Like other gravitational effects, locally, spatial expansion would manifest as a pseudo-force, but be too weak to overcome the nuclear and electromagnetic forces that keep matter bound.
However, Friedmann cosmology is only a large-scale approximation. A more realistic model is swiss-cheese cosmology, which comes with a different metric within the 'holes', and spatial expansion might indeed not act on galactic scales (though I would image it to have an indirect effect as boundary conditions at the edge of the hole have to be matched; I'm no expert on this part of the story, though).
The usual response of “it only affects space between galaxies not inside galaxies” is deeply unsatisfying, and feels like it must be an oversimplification.
What I think is meant, but I absolutely want someone wiser to confirm or refute, is that the rate of expansion is proportional to distance, and therefore so small inside a single galaxy it can be ignored.
What I don’t know is: can any orbits still be stable in an expanding universe?
(In theory I could simulate the orbits question easily; in practice, last time I tried to do astrophysics maths I made an elementary mistake).
I am not that person. But I feel like this can't work -- if all space is expanding equally, in proportion to its own extent, then we would perceive no expansion at all. If two points start out 1 light year apart, and over time 1 light year expands to be 10% longer than it was before... and also, everything in the universe expands to be 10% larger in all spatial dimensions... then the distance in meters between the two points hasn't changed, because meters grew too.
Really? These structure constants never involve any units of distance? Isn't distance changing at all levels?
If I have a meter stick, and then space expands by 10%, you're saying that my meter stick will end up being 0.91 new-meters long, yes? Wouldn't that require the structure constants to change, to allow for the same molecules to take up less space?
Let’s come at this from the other direction: if everything including the space between atoms and galaxies expands by 10%, how do you tell the difference between an old-meter and new-meter? For this to be observable, something has to still scale by the old-meter, or you wouldn’t be able to observe a difference at all. That something would be the physical constants with units, like the speed of light. This means the electrical force governing the chemical bonds in your meter stick will still try to restore the distance between them to their original old-meter distance, but in new-meter units.
Then if you define the actual meter by the length of your meter stick, or the physical constants, you end up getting the same meter that everything not macro-scale “snaps back” to.
The meter-long stick you put into that space to measure it is still one meter long at some time in the future because the force that pulls the space apart (dark energy) doesn't pull on the matter that makes up the meter stick strong enough to overcome the forces that hold the stick together. But even if it did, the idea of one meter hasn't changed its definition. It's just the tool you used to measure one meter has broken.
It obviously affects all space, inside galaxy or outside of it. Let's just check the rough math, not even bothering about the fact that expansion was not linear. The universe expanded to around 100BLY in about 10BY, i.e. got ten times bigger than its potential light cone. So, for every "initial" 1km, there is additional 9km in 10BY timespan, or 0.0009mm per year, or 0.00003nm per second. The general ratio is around 1e-17 per second per length unit.
Proton size is around 1e-15m, Planck size is around 1e-35m. A thousand Planck units per second is not that much, really. And on sub-milliseconds it just loses its effect completely, due to that Heisenberg guy. (If we take my bullshit math seriously, I mean.)
Of course, if you calculate out far enough time, you would eventually end up with the observable universe getting smaller (because the stretching of spacetime would take away more space than was added by light reaching us from further away), down to our galaxy, and eventually everything getting torn to shreds, even down to protons...
In the "near" term, the effect is so small that we have much more to worry about from the sun expanding in a few billion years than the Big Rip.
Every second, the tiles on the floor push away from all their neighboring tiles by one tile width and new tiles appear in their place. The tiles are small enough that the dancers are easily able to adjust their step/grip on eachother to simply maintain their dance routine.
However, even tho the dancers can stay together, the couples drift apart at an ever increasing rate. They start 10 tiles apart, after one second the couples will be 20 tiles apart from eachother, 40 tiles apart after 2 seconds, 80 tiles apart after 3 seconds (a new tile is being inserted between each pair of existing tiles). My tiling math is probably slightly off, but I think this illustrates the exponential increase in expansion.
The dancers are quarks, atoms, molecules, planets, galaxies, etc. Their grip on eachother is big enough to overcome the relatively small adjustment in the space that was created between them.
A few questions using this analogy arise.
Do the new tiles actually appear between the dancers, or is it more a case of the force of friction the dancers are applying to the floor prevents those tiles between them from moving apart ?
So when 'new space' is being created, is it created around strongly bound things and the things simply slide around through this new space to maintain their current configuration, or do the 'strong' forces prevent new space being formed around them ?
If the new space is not being created, what happens to the energy that would have gone into the creation of the new space ? Does it simply get applied to the nearest point where it can squeeze in more space ?
If the space is being created and the dancers pull themselves together to overcome it, where does this extra energy come from ?
As for the big rip, I always thought it was the equivalent to the dancers finally getting tired and not being able to hold onto eachother hence giving in to the expansion of space. ie. It happens around the heat death of the universe when everything has dissipated its kinetic energy so much that the energy of the expansion is more than is left in the system to keep things together.