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Discrete-time physics hides in our time-continuous world



  Discrete-Time Physics Hiding in Our Time-Continuous World
Markov processes were used to model the accumulation of piles of sand. Picture credits: Santa Fe Institute Press

Scientists believe that time is continuous, not discreet ̵

1; roughly speaking, they believe that it does not progress into "chunks", but rather runs "smoothly" and smoothly and continuously. Therefore, they often model the dynamics of physical systems as time-continuous "Markov processes," named after mathematician Andrey Markov. In fact, scientists have used these processes to study a range of real-world processes, from protein folding to ecosystem development to changing financial markets, with astounding success.

However, a scientist can only observe the state of a system at certain times, separated by a gap, and not continuously. For example, a stock market analyst could repeatedly observe how the market situation at the beginning of the day is related to the market situation at the beginning of the next day and builds a conditional probability distribution of the stock market on the second day, the state is given on the first day.

In a pair of papers, one published this week Nature Communications and one recently published in the New Journal of Physics . Physicists at the Santa Fe Institute and at MIT have shown that from a continuous Markov process, such two-fold dynamics can emerge through a series of "visible states" that the Markov process actually needs to unfold over a larger space, closing hidden states in addition to the visible one. They further prove that the evolution between such a pair of times must occur in a limited number of "hidden time steps", with the interval being divided between these two times. (Strictly speaking, this proof applies whenever this development is noise-free from the earlier to the later times – technical details can be found in the documentation.)

Scientists use it to study such systems, "says co-author David Wolpert (Santa Fe Institute) In a very limited sense, we also say that time runs in discrete time steps, even if the scientist models time as if it were running continuously, and scientists have these hidden variables and these hidden time steps But they are there and play a key behind-the-scenes role in many of the papers these scientists have read, and almost certainly in many of the papers they write. "

In addition to discovering hidden states and time-lapses the scientists also made a compromise between the the; The more hidden states there are, the less the minimum number of hidden time steps required. According to co-author Artemy Kolchinsky of the Santa Fe Institute, "these results surprisingly show that Markov's processes have some sort of trade-off between time and memory, often in the separate mathematical domain of analyzing computer algorithms."

  The discrete physics hides in our Time-Continuous World
The minimum configuration for flipping information from 1 to 0 requires three states and three consecutive time steps: Credit: David Wolpert

To illustrate the role of these hidden states, co-author Jeremy A. Owen (MIT) presents the example of a biomolecular process that is observed for hours: When coupled with a protein in state & # 39; a, & # 39; and begin Over an hour, usually "b" is displayed, and after another hour, it usually returns to "a". There must be at least one other state "c" – a hidden state – that influences the dynamics of the protein. "It's there in your biomolecular process," he says. "If you have not seen it yet, you can search for it."

The authors stumbled upon the need for hidden states and hidden time steps as they searched for the most energy efficient way to mirror a bit of information in a computer. In this investigation, which is part of a larger effort to understand the thermodynamics of computation, they found that there is no direct way to implement a map that sends both 1 to 0 and 0 to 1. Rather, to slightly reflect information, the bit must pass through at least one hidden state and contain at least three hidden time steps. (See attached Multimedia Diagram)

It turns out that a biological or physical system that "calculates" output of inputs, e.g. A cell processing energy or evolving ecosystem that would mask the same hidden variables as in the bit flip example.

"This type of model actually occurs naturally," Owen adds, "based on the assumption that time is continuous and that the state you are in determines where you are going next . "

"One surprising thing that makes us more general and surprising is that all these results apply without thermodynamic considerations," Wolpert recalls. "It is a very pure example of Phil Anderson's mantra" more is different "because all these low level details [hidden states and hidden timesteps] are invisible to the higher level details [map from visible input state to visible output state]."

It's like the limit of the speed of light, "says Wolpert. The fact that systems can not exceed the speed of light is not an immediate consequence for the vast majority of scientists. However, it is a limitation of permissible processes that is applicable everywhere and something should always be kept in mind. "



Further information:
Nature Communications (2019). DOI: 10.1038 / s41467-019-09542-x

Provided by
Santa Fe Institute




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Discrete-time physics hides in our time-continuous world (2019, April 15)
retrieved on April 15, 2019
from https://phys.org/news/2019-04-discrete-time-physics-continuous-time-world.html

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