[Filligree]

> We should determine c empirically, but we have already done so to exquisite precision.

As interesting as that is, what I meant we're narrowing down is the speed of gravity -- that is, that it's almost certainly equal to C. Not that we're narrowing down C itself, it's way more convenient to define that as 1.

Since you're here, though... the horizon problem. I can kind of understand the logic that makes it a problem, but...

If you have the same initial conditions everywhere, and the same laws of physics, wouldn't you expect everything we can see of the universe to look similar even if there hasn't been any communication?

That seems like an obvious implication of having deterministic physics, and sure, "same initial conditions" is a big assumption -- but I never see this hypothesis offered.

[raattgift]

> more convenient to define that as 1

Yes indeed. :-)

> ... I never see this hypothesis offered.

The tl;dr is that that hypothesis is a (subjectively) boring and (less subjectively) non-Copernican answer.

I'll expand on this.

Let's just accept arguendo that the laws of physics are everywhere the same and in particular that gravitation matched General Relativity from well before photon decoupling to the end of recombination.

You can indeed then take the position that the initial conditions of a hot big bang were extremely finely tuned, with overdensities at photon decoupling (and thus reflected in our CMB) being exactly encoded in the initial values.

However, the trend is to explore mechanisms that allow for much higher (Boltzmann) entropy in the early universe with overdensities evolving from fluctuations.

ETA, I'll steal a line from slide 6 at [1] : "don't explain low entropy by positing even lower entropy".

This trend has been productive in the sense that it has produced several progressive research programmes amenable to empirical tests.

For example, cosmic inflation (eta: in part by allowing the particle horizon and the Hubble horizon to be very different) allows for a much wider set of initial conditions (some with much higher entropy than is implied by maximally finely tuned initial conditions) that could produce our CMB and ultimately galaxies. Cosmic inflation in the broadest sense has produced a number successful predictions, so work is certain to continue.

Pragmatism, aesthetics, philosophy aside, I have trouble imagining in detail what observatories we would have constructed had late 1990s cosmologists simply pursued a programme of discovering the details of values surfaces at progressively earlier times, with the goal of simply discovering the initial conditions eventually, all without doing much theoretical speculating about what as yet unexplored early values surfaces might contain. What would have succeeded BOOMERANG? Instead, that sort of speculating raises all sorts of interesting questions about the behaviour of matter at extremely high densities and temperatures, how those behaviours might be encoded in a CMB that was not strictly fixed at the hot big bang, and what alternatives to the hot big bang (e.g. a big bounce cf. slides 7- @ [1]) could lead to our galaxy-filled sky.

So you practically hit the nail on the head in recognizing that assumptions about initial conditions is crucial to whether one sees the horizon problem as a problem in the first place. If you don't care about complaints about the apparent non-genericity of the initial conditions, there's no problem; likewise, if you are pretty sure that initial conditions can be highly generic yet lead to the universe we see, then there's also no problem. This is fertile ground for philosophers (and historians) of science. [2]

- --

[1] http://www.preposterousuniverse.com/blog/2017/01/25/what-hap...

[2] A quick search leads to Casey McCoy (University of Edinburgh)'s http://jamesowenweatherall.com/wp-content/uploads/2014/10/Wh... section 3 (edit: notably from the bottom half of p 15 where he has some pleasantly difficult questions in parentheses) and the second half of p 18.

[Filligree]

I'm with the first one, then. I consider the Kolomogorov complexity of the laws of physics to be important, and initial conditions to be part of said laws, but I don't think it adds much complexity to posit that the initial conditions are very, very simple (and thus low-entropy).

[raattgift]

Taking that position also gives you the answer to why we won't see black holes fissioning into outspiralling pairs of neutron stars, or shards of glass spontaneously reassembling into a wineglass that leaps off the floor into someone's hand. The only cost is extremely exquisitely finely placed stress-energy-momentum in the early universe into the infinite past.

If you have no problem with an infinite history of ever lower entropy, then luckily observations to date do not contradict this sort of cosmology, and under time-reversal the "movie" showing the universe crunching into an ever more orderly state forever isn't very shocking other than we arrange our lives with the movie playing the other way, sweeping up broken shards of glass rather than catching rising stemware. Maybe conscious life somewhere else in our Hubble volume arranges their lives in that way, though, unbreaking and unmaking their artefacts and thinking our way of doing things is strange.

Some other questions for you: how far does this cosmology's future grow? Do we get infinite entropy in the infinite future? If we don't have an infinite future, why do we have an infinite ever-more-orderly past? If we have an infinite future, do you suppress fluctuations? Do you wholly suppress Poincaré recurrence? How would you distinguish us here as us here now from a recurrence? Are we a recurrence? etc.

These questions do not seem as amenable to testing with current technology as questions arising from other cosmologies.

[Filligree]

Well, let's see. I don't have much time to spend on this, and I'm well aware that I'm an amateur anyway, but...

One point, at least. I see no reason why a theory being difficult to test should count even slightly against the probability of its being true. Sure, it's inconvenient -- and there's something to be said for focusing on ideas that can be tested -- but since when was nature ever constrained to convenience?

As to your other questions...

I'm not sure where the 'infinite past' comes from. There's a single slice of space-time that needs to be constrained; everything else can flow from there, in both directions. If it's a low-entropy constraint then causality would naturally flow away from that slice. The two sides should be mirrors of each other, though.

As to the far future... that's harder.

- My intuition is that, when you're trying to guess at which of many possible universes you actually live in, the amount of "runtime" the theoretical universe spends on computing you (that is, some form of life, at least) should matter. But that's problematic, since it seems to predict higher complexity of the physical laws in exchange for a universe that's denser with life, and it's not what we see.

- More realistically, perhaps, the big rip might be a thing. Recurrence could fail to happen because the far future doesn't allow for structures complex enough to have thoughts, not even by random chance.

I prefer to punt on the question, though. I don't know enough to have an informed opinion.