Physics, Astronomy & Cosmology / Re: Is the inverse square law only approximately correct in general relativity?« on: Today at 02:58:44 »
Suppose it was something else like Beta particles being emitted isotropically by the source. Why would that not follow the 1/r2 law for the bombardment intensity received on the surface of a sphere held at a constant metric distance (a radius) r from the source?Presuming you didn't do anything funny like put detector/source at different potentials, the inverse square law would work given this constant r (say both held at opposite ends of a stick). Space expansion would make no difference. Dark energy probably would, but that counts as 'something funny' just like gravity does. Dark energy would put tension on the stick. Space expansion would not.
If we assume that the particles are traveling at (say) c/10, then there will be an event horizon beyond which these particles will not pass, because space will be expanding faster than c/10 by the time they got there.OK, but if distant detector is held at constant distance from this emitter, it will cross over that 'event horizon' (towards us) and the particles will get to it.
What you're talking about isn't the event horizon, it's the Hubble radius, the distance where Hubble's law yields c. The event horizon is a little further away from that, and it has to do with acceleration, and is not a function of the current expansion rate like the Hubble radius is. So a beta particle moving at 0.1c would get at most a 10th of the way to the Hubble radius, and would take an infinite time to do so.
This event horizon will be much smaller than the event horizon for light (which defines the limits of our observable universe).The light event horizon is about 16 BLY away. Current radius of the visible universe is about thrice that, so they're very different things. The latter is all the material in the universe which at some past time might have had a causal impact on a given event (Earth, here, now). The event horizon is the comoving distance of the nearest current event from which light can never reach here in any amount of time.
After all, the size of our observable universe is not at a fixed distance - it expands at the speed of c.The Hubble sphere expands at c (by definition). The visible universe expands at somewhat over 3c, which is why we can see galaxies that are currently about 32 BLY away (comoving distance). The event horizon is barely expanding at all.
so (in principle) there are distant galaxies that people on Earth could see today, butHate to disagree, but new galaxies become visible over time. The most distant ones were not visible several billion years ago, even if one used the best telescopes. Yes, the galaxies cross beyond the event horizon, but that doesn't mean we can't see them any more than we stop seeing somebody falling into a black hole.
which will not be visible in 10 billion years
The inverse square law is about the intensity received at a distance, r, from the source. That is a physical distance, so it is determined by the metric. It is not determined by reference to a difference in the values assigned to locations in the co-ordinate system we commonly use to describe an expanding universe.Just so, yes.
The usual co-ordinates used in an expanding universe are the called the co-moving co-ordinates. Galaxy 1 can have fixed co-moving co-ordinates and it's tempting to say it has a fixed position. Galaxy 2 can also have fixed co-ordinates and we can be tempted to say it has a fixed position.Right. The rate that a given galaxy changes its coordinates is called peculiar velocity, and the peculiar velocity of almost all objects is quite low, a few percent of c at best.
Quote from: evan_au
If you posit some particle that travelled at c/10 (and didn't slow down)In an expanding metric, the paricle will slow down without some force maintaining its peculiar velocity. Newton's laws only work in a static metric.