The discrete-time physics hiding inside our continuous-time world

phys.org ^ | 04/15/2019 | Santa Fe Institute

[BenLurkin]

Scientists believe that time is continuous, not discrete—roughly speaking, they believe that it does not progress in "chunks," but rather "flows," smoothly and continuously. So they often model the dynamics of physical systems as continuous-time "Markov processes," named after mathematician Andrey Markov. Indeed, scientists have used these processes to investigate a range of real-world processes from folding proteins, to evolving ecosystems, to shifting financial markets, with astonishing success.

In a pair of papers, one appearing in this week's Nature Communications and one appearing recently in the New Journal of Physics, physicists at the Santa Fe Institute and MIT have shown that in order for such two-time dynamics over a set of "visible states" to arise from a continuous-time Markov process, that Markov process must actually unfold over a larger space, one that includes hidden states in addition to the visible ones. They further prove that the evolution between such a pair of times must proceed in a finite number of "hidden timesteps", subdividing the interval between those two times...

The authors stumbled on the necessity of hidden states and hidden timesteps while searching for the most energy-efficient way to flip a bit of information in a computer. In that investigation, part of a larger effort to understand the thermodynamics of computation, they discovered that there is no direct way to implement a map that both sends 1 to 0 and also sends 0 to 1. Rather, in order to flip a bit of information, the bit must proceed through at least one hidden state, and involve at least three hidden time steps.

It turns out any biological or physical system that "computes" outputs from inputs, like a cell processing energy, or an ecosystem evolving, would conceal the same hidden variables as in the bit flip example.

[SunkenCiv]

Thanks BenLurkin.

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[SuperLuminal]

"This actually happened to me 60 years ago while waiting for a traffic light to change - one moment the light as there and the next gone, only to reappear a few intervals later "

Yep! Know what you went through... Several years ago one of my socks instantaneously disappeared while I was carrying the laundry basket downstairs... Last year it reappeared underneath my bed inside one of my gun cases...

I started to write a paper on the subject to publish in Physical Review, but changed my mind when the first draft of the paper I was writing instantaneously disappeared while my wife was dusting my bookcases...

[DungeonMaster]

1 chronon = one unit of discrete time.

Well that's what I heard 30 years ago. That was a long time ago.

[PIF]

Don’t worry, it will turn up in your car boot under the spare tire next year.

[Redcitizen]

“In heaven we’ll be outside of time”.

We’ll be in eternity marked by time as I understand it based on the passage from revelation 22 verse 2“On each side of the river was the tree of life, which bears fruit twelve times a year, once each month; “.