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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.
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.
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.
I was not thinking about a horizon at a fixed distance.OK - BUT you should be. 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.
But space can expand faster than c, so (in principle) there are distant galaxies that people on Earth could see today, butThis is correct. However, the light emitted by the distant galaxy will travel an infinite physical distance. It's just that how far it can go in 1 unit of time will not be sufficient to match the expansion of space that is occurring between the distant galaxy and earth.
which will not be visible in 10 billion years, because the expansion of space has carried them outside our visible universe.
If you posit some particle that travelled at c/10 (and didn't slow down), there would be regions of our visible universe that could never detect these particles, because the space in between is/will be expanding faster than c/10.Yes, total agreement. However, that has nothing to do with the particles crossing over a sphere at some fixed and pre-determined physical distance from the source.
You have to get copper down to 35K before it becomes superconductingI'm fairly sure that copper doesn't superconduct even at much lower temperatures than that.
Time dilation is so extreme within millimeters of the event horizon that the image of an infalling rock would be very quickly red-shifted into oblivion.I think we need to establish where the observer is and assume they are using a frame of reference where they are at rest. The distant observer = An observer at a fixed radial co-ordinate, r >> Schwarzschild radius. The rock = the rock or anyone close to the rock and falling in with it.
So: Very few photons, severely red-shifted: The rock would not "float" near the event horizon, it would just disappear.Bits of this are OK. However, it doesn't "just disappear", it fades away. It's like having a studio engineer with the slowest hands in the world, turning the fader knob so slowly that the universe will end before the stage actually goes dark.
...forming a black hole, with almost the same mass as the star before it imploded...Is that right? I know stellar collapse varies quite a lot and I'm not aware of the latest ideas for the typical behaviour. Old texts used to suggest that typically there is a supernova explosion where the outer layers of the star making up about 20% of the original mass of the star is blown away. Some sources put the amount of matter ejected far higher than that...
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in a sterile desert, more life will grow if the temperature fallsNo. In a sterile desert more life will grow if there is more water available at the surface. Of course - more water available at the surface will also cause surface temperatures to fall, due to increased evaporative cooling. Temperature is an issue in many hot arid areas - such as the Sahara - due to lack of water. The equator gets more sunlight above it, but also has more clouds, and more water (at the surface) to cool it. So water is the issue in arid areas - not temperature.
Do any Europeans care about cricket?Yes.
....and the idea of a massless particle transferring momentum really does confuse people.I'm definitely with you, or at least sympathetic to, a lot of what you've said alancalverd. It connects with something I was trying to get together and tidy up to make a post. I'm just going to post it now, scruffy as it is...
Massless particles (eg photons or the hypothetical graviton) which carry energy can only travel at "c"
(ES adjusted the spelling of the word "the")
is well defined for particles with timelike paths and then we can define Pμ = m Uμ. 
= 0 on a null path. It seems common to just introduce a new definition for the 4-momentum of a photon,So until there are some major breakthroughs, I suggest that researching limb growth is perhaps a thousand to a million times harder than producing a vaccine against one variant of COVID.If we think linearly, the obstacles are seemingly impossible to overcome. But technological progress is exponential. If the effectiveness of our technology improve by twice a year, we will get a million fold improvement in just 2 decades.
What would the scientific community's reaction be to a sudden volcanic eruption from a moonquake(s)?For about the first second, nothing at all.
In countries with a public health system (eg not the USA), the health system consumes a large fraction of the taxation income.The relevant difference between the US and the UK is that neither of them allow duelling.
- Dueling will only increase load on the health system, since it your taxes that pay to patch up the people who partially survive the dual.
- If there is no real public health system (eg the USA), gun violence is rife, and people are encouraged to get more guns to protect themselves from the idiots with guns. There is no incentive for the government to do much about it, because repairing the damage doesn't really come out of their pockets.
It was ironic to hear Donald Trump criticizing the mayor of London on a night when 3 people were killed in stabbings, when the homicide rate in New York was twice as high (you are much more likely to die from a gun attack than a knife attack).
See: https://www.bbc.com/news/uk-england-london-48651131
There is a branch of mathematics called Galois Theory, applied in 4G mobile phones and cable TV, among many others. Galois documented this in a letter at age 20. He had foolishly challenged a soldier to a duel, and died of gunshot wounds received the next morning.
See: https://en.wikipedia.org/wiki/%C3%89variste_Galois
The twin paradox comes about because the "stay at home" twin has a constant time coordinateActually, he has a constant spatial coordinate (at least in the Earth frame) and the time coordinate is the only one that varies (by a year).
and so has a "shorter" worldline through spacetime than the "leave home" twinE-S has the gist of it. Minkowskian spacetime isn't Euclidean. In Euclidean spacetime, 4D distances would be computed as √(t²+x²+y²+z²) but spacetime intervals subtract the xyz from the time: s² = t²-(x²+y²+z²). So the straight line (Earth result in the longest interval, and the shortest interval (that followed by light) is where t² equals distance². So I'd say the travelling twin has the shorter worldline, as measured as an interval.