[defrost]

> If the conditions at the bottom of two black hole "singularity"s are the same - you would expect parallel, equal universes to be generated each time.

That's a strong no (for any sufficiently complex physical setup with moving parts, falling glasses won't shatter the same way twice).

Two things here are relevant:

1) Lorentz (Butterfly) and Smale (Horseshoe Map) both proved that in some physical systems you can always find initial conditions that are very close (for any arbitary epsilon of "close") that none the less end up far away from each other as time passes.

ie: Unless the initial starting points are absolutely precisely identical without question, then "close enough" isn't good enough to guarentee an identical outcome in the presence of "strange attractors"

2) The Uncertainty Principle tells us that at a fine enough grain (within a certain epsilon) initial conditions are like jelly - you cannot nail them to the wall and declare two systems identical.

[zoroaster]

Yes, note that I say the equal universes situation only occurs if the conditions are the same (which I agree is unlikely). They would have to be exactly the same to result in copy universes given even the slightest variation in initial conditions would compound into vastly different outcomes.

I think, in the black holes example this outcome is unlikely given even slightly more matter or quarks absorbed would differentiate the system. This would be the "parallelish" outcomes where slightly differences would compound over time. But if there's a limiting condition that only allows for one starting point, then you get the same duplicate outcomes.

In the same way that certain elements consistently arise as a result of fusion in a star, perhaps the same types of universes might arise here. You might have a "Hydrogen" universe, a "Helium" universe, an "Iron" universe dependent on the threshold that initiates a certain "big bang" / that create initial starting points that are "absolutely, precisely identical without question". This is a bit out there, probably wrong. I have no idea.

I'm not sure I'm explaining my thinking very well, but if only so much energy / matter can break through the other side of a black hole and it breaks through in the same way every time then you would get parallel, equal universes.

I am a huge fan of your usage of chaos theory to address this question - I appreciate it.

[defrost]

I have the advantage of knowing a few bright people in relevant fields.

Another point of interest is that our specific universe formed in a manner that left a "chaotic" biased imprint of early intial turbulence imprtinted across our sky in the Cosmic Microwave Background clumping.

While the variations are tiny deviations from uniformity they do exist and are thought to be random quantum fluctuations that expanded to a much larger size during inflation.

There is further conjecture about how these early random forces went on to seed the distribution and pattern of stars and galaxies.

In other words, the tiniest roll of dice during the seeding moments appear to have held sway over the form of entire galaxies.

[maxerickson]

What if there's an infinite, apparently random but actually fixed map underlying everything?

So like physics appears to have uncertainty but if you are outside it you can see that it's just playing back according to the map.

[defrost]

If our physics is actually deterministic,

Then

- how do you measure with sufficient accuracy to (well) beyond the Heisenberg limit, everything within a relativistic radius in order to counter chaotic turbulence

and, then, once you have done so,

- how do you compute forward the rather large number of "grains" just measured in the fine time steps required to counter chaotic turbulence?

Leaving aside just how difficult (against the scale of the universe) such exercises are, let's return to the mathematical certainty of proof by both Lorentz and Smale ... any tiny deviation, even magnitudes of order finer than Heisenberg will eventually bite any claim to the certainity of determinism hard in the arse.

[maxerickson]

And yet it's unknowable.