* Although you can make the enveloping sphere as large as you want, the (anti-)equilibration process requires a sphere of some finite radius because if you wait long enough a few stars eventually get launched at escape velocity, and if these actually escaped they would effectively cool the remaining stars.
* Therefore, the characteristic time scale for this process (i.e., the timescale on which the average kinetic energy rises substantially) gets longer and longer as the sphere gets larger.
* In order for the pressure and average speed of the stars to keep rising, the gravitational potential needs to keep falling, so at least some stars need to get and stay very close. In real life, these turn into black holes, which cuts off the process by limiting the amount of gravitational potential energy that can be unlocked in any given volume with a given mass.
I think this is right, and I think he explicitly calls out that these calculations were done with Newtonian physics modeling point particles - and we know that those two factors severely limit the application of this to the real-world.
Basically, the issue is that you can’t end up in a stable equilibrium of binaries (and binaries of binaries) in a bounded phase space because the dynamics are time-reversible. The only way you get coarse-grained irreversible behavior is with an unbounded phase space where there are no recurrences.
This idea could have legs if the math works.
http://www.platonia.com/books.html
The related math and modelling goes under the name Shape Dynamics:
https://en.wikipedia.org/wiki/Shape_dynamics
Shape Dynamics - An Introduction
For one thing, squeezing the sphere smaller against pressure requires work. That's an external energy input. The system is not closed if some agent is available that can squeeze the sphere smaller.
What? Newtonian gravity is defined for point masses. Anything else you derive from that by integrating a mass density over a region.
>by integrating a mass density over a region.
exactly. When you do that for a disk galaxy you get much flatter curves that the 1/R the proponents of the dark matter insist on (that 1/R is exactly what one would get if the galaxy was spherical or the star was far outside of the disk)
B) “since stars rather rarely collide” still blows my mind. I did some napkin math on Reddit a while back on why there will be very few stellar collisions (really, one star falling into another’s orbit?) when andromeda collides with the Milky Way, and the answer is that space is just mind-bogglingly huge. Even the most dense clusters in our galaxy are akin to ~70 1cm diameter spheres per olympic swimming pool.
If god is real, he is surely a giant.
And GR fixes that by kind of moving the sphere walls farther away, ie. the space geometry changing by the changing gravitational potential.
This seems like an invalid assumption. We know that clusters of stars can eject some of their members. Lot of hand waving in this one.
We are gravitationally bound to Earth, but the Voyagers have left the solar system.
