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That still doesn't explain why energy exhibits the bizarre properties that it does (e.g. light interacting with matter and black holes the way it does....+similar references to energy in earlier posts.
I find it incredibly difficult to think of energy as anything but a thing.Many people would do the same. Sadly, nature doesn't really care what seems sensible to you (any of us).
Here's the picture3) The tetrahedron is the only platonic solid that lacks a hexagonal projection (it can’t make a hexagonal shadow). Best it can do is a square.The dodecahedron cannot throw a hexagonal shadow.
What you've depicted is a hexagonal cross section with all six visible faces truncated, but the shadow from that view would have 12 unequal sides. You've drawn some of the pentagons as triangles, which is impossible no matter what angle you view the pentagon.
3) The tetrahedron is the only platonic solid that lacks a hexagonal projection (it can’t make a hexagonal shadow). Best it can do is a square.The dodecahedron cannot throw a hexagonal shadow.
According to that page there is no water in rocks, but in reality, there's quite a lot.Could there be more water in the earth than on the surface?No, not even close.
Take a look at this: https://www.usgs.gov/special-topic/water-science-school/science/how-much-water-there-earth
As I understand it, the main idea underlying the cosmological principle is that no part of the universe is "special"..and I'm not sure that we (previous contributors) have really explained why isotropy is generally implied.
That seems a reasonable axiom, but where I have difficulty is that this appears to be widely interpreted as implying that the universe must be isotropic on some grand scale.
I think what my question down to is this: does the definition of "local anisotropy" scale with the scale that is being considered?This is very difficult to answer. If we go to small scales, then we are in the territory of quantum mechanics and most reasonable ideas go out of the window. If there is a fundamental Planck length then we cannot meaningfully divide space into smaller regions and calculate average densities or consider structures below this scale.
I cannot think of any structure larger than about 500 MpcI take that back. We're part of Laniakea at best, and that structure is only about 160 Mpc, and even that doesn't count as a 'local influence', but rather a collection of smaller local influences since Laniakea at large isn't a bound object and will break up in the long run. If the clusters comprising Laniakea are not bound to each other, we're certainly not bound to something larger like Shapley.
Perhaps we could also say that we can't observe any larger structures (with our current technology).Quasars are relatively small objects, and do not currently exist. My definition of local influence' seems reasonably to be an object that is bound in some way.
- We see distant quasars that happen to be beaming radiation in our direction, but that is hardly a representative sample...
Eternal Student's "preferred scale" is precisely what I am having difficulty seeing as an accurate depiction.....I think you (we) need to establish more firmly what definition or notion of the cosmological principle you are using before I (we) can discuss many specific details.
What is this preferred scale? Is there an unambiguous cutoff (that can be calculated like an even horizon?) Or is it just the idea that in the limit of larger and larger volumes, randomness balances out?It would be best to consider the notion on a statistical basis and therefore there is no clearly defined "cut-off" but instead the mean distribution of matter tends to become more symmetic as the volume over which averaging is done increases. However, there have been some attempts to put numbers on the sort of scales that would be required. Yor_on (earlier) has suggested some numerical values. I've found some estimates that are slightly larger than those (however, in Astronomical terms, getting agreement within a couple of orders of magnitude is acceptable):