To a large extent, scientists believe that time is continuous and not discrete. Scientists hold a conviction that it does not progress in chunks, but flows continuously and smoothly. Consequently, they model the dynamics of physical systems as a continuous-time Markov process.
Scientists have utilized these processes, no doubt about it, to investigate a range of real-world processes from folding proteins to shifting financial markets, evolving ecosystems, with extraordinary success.
A physicist at the Santa Fe Institute and MIT have shown in a pair of papers that will be appearing in Nature Communications and recently in the New Journal of Physics revealed that for such two-time dynamics over a set of visible states to arise from a continuous-time Markov process. He said that Markov process must indeed unfold over a larger space, one that includes hidden states in addition to the obvious ones.
The papers also proved further that the evolution between such pair of times must proceed in a finite number of hidden timesteps that will subdivide the interval between those two times.
Also from Santa Fe Institute, one of the authors of the papers, David Wolpert, further said that their claim is there are hidden variables in dynamic systems, implicit in the tools scientists are using to study such systems. Furthermore, in a certain limited sense, time proceeds in discrete timesteps even if the scientist models time as though it advances continually. It is possible for scientists to have been overlooking those hidden variables and those hidden timesteps, but they are there, playing a key, behind-the-scenes role in several papers those scientists have read, and quite certainly also in many of the documents those scientists have written.
To discover more of the hidden states and time steps, the scientists also found out a tradeoff between the two, that is, the more hidden states there are, the smaller the minimal number of hidden timesteps that are needed. Artemy Kolchinsky, another co-author of the paper, said that it is surprising that these results demonstrate that Markov processes exhibit a kind of tradeoff between time versus memory, which is often encountered in the separate mathematical field of analyzing computer algorithms.
In the illustration of the role of these hidden states, Jeremy A. Owen, another co-author gave the instance of a biomolecular process, observed at hour-long intervals. If one starts with a protein in state 'a,' and over an hour it usually turns to state 'b,' and then after another hour it usually turns back to 'a,' there must be at least one other state 'c' - a hidden state - that is influencing the dynamics of the proteins. Owen concluded that it is there in the human's biomolecular process.
