For instance, it’s incorrect that “if the rule isn’t deterministic… then a single repetition doesn’t guarantee infinite repetitions.” The jellyfish example is just a random walk on a finite 2D grid, so we are mathematically guaranteed it would return to its initial configuration eventually. Determinism vs. randomness is irrelevant. Moreover, the same would hold on a 3D grid (or higher) as long as we have finitely many states (jellyfish).

Infinite recurrence would also hold for a single jellyfish on an infinite 1D or 2D grid (the so-called “gambler’s ruin” phenomenon), but not on an infinite 3D grid. This is another place where the description is deceptive. The universe is certainly not 2D, so even if it could be conceivably mapped to a stable grid with 3 or 4 dimensions (3 space + 1 time), recursion is not going to be guaranteed, at least not by the same ideas as the pigeonhole principle and the gambler’s ruin. One would need much stronger assumptions on the structure of the dynamic phenomena.

]]>First, it seems to me that if we draw truly random numbers, say in a computer that is pseudorandomly seeded by internet access, we can wait eternity truly before a repetition. Then the number he gives is an average estimate, not a truly random outcome of an infinite volume of state combinations. It is only if we draw without replacement so we move within a finite phase space that the ‘ergodic assumption’ underlying Poincaré recurrence applies [ https://en.wikipedia.org/wiki/Poincar%C3%A9_recurrence_theorem ].

Second, in quantum mechanics theory there is arguably fundamental randomness in observation outcomes, even if states evolve deterministically [ https://en.wikipedia.org/wiki/Quantum_mechanics ]. So the analysis of laws seems somewhat lacking.

Third, when cosmologists such as Tegmark has looked at repetition in a spatially infinite universe they have relied on the finiteness of number of free quantum field particles, not possible field states, within a general relativistic sound comoving patch. As far as I understand the quantum vacuum simplifies that state space a lot, a quantum field vacuum void of free particles seems to have just one thermodynamic state, i.e. its entropy is 0, close to 0 K.

Which finally brings me to the grid idea, which I think Tegmark would argue/is arguing is irrelevant. As far as I understand, if eternal inflation applies for sufficiently long it should have dispersed matter and its thermal energy to near enough 0 K for the 0 entropy vacuum state to apply. That should be self consistent*, with no particles that would seem to heat up when we look back, the system can run on for ever in the parts that fluctuate randomly to keep inflating.

So now we must consider the comoving patch that cosmologists do. Since space simply inflates to larger scale with no problem, the classical comoving patch which is big bang associated with “close before our universe stopped inflating” must be scaled too as we look further back. Then it seems to me there must be an absence of ‘grid’ states in such a model.

* Which Site Physicist ™ Sean Carroll implies is not enough for him, because it has some topological problems if you want to argue that it can not expand for ever (has a non-zero vacuum energy). Others say that adiabatic expansion cooling cannot approach 0 K, but they seem to assume non-adiabatic processes so I cannot simply agree. And I have even seen the argument that an eternal system is unlikely to be in its steady state, but I do not think that is assumed either. This is just extrapolating likeliest model from observation as far as I understand Planck probe data. If the system inner state does not need to change as we move along the pathway from our universe back, except obviously the random exit from inflation, why assume the opposite?

]]>I am thinking that I know of no one else

who goes here but … … I do: http://www.reason.com

for stuffs such as thus: http://www.reason.com/archives/2017/10/18/how-to-end-the-fight-over-contraception.

Blue

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