viernes, septiembre 26, 2008

Entrophy, Arrow of time and Life

Sam Wormley , in the second message, repost this article in which there is a phrase:

"In the universe we observe a very definite direction in time. No-one is really sure why time flows the way it does but if it didn't flow intelligent life as we know it would not exist because of our reliance on the second law. "

I´m very interested in the relation between entropy and our perception of time. This was my response, that try to answer the question:

This is not only true, but the key for the understanding of arrow of time from my point of view:
The Arrow of time is, at last, a common subjective experience experimented by living beings. According with the laws of physics, time is just a dimension.. or not even that . The solutions of the equations of General Relativity are cuasy arbitrary four dimensional manifolds.where time is just a local dimension. That is, can be approximately suppossed that in a certain point, the time could be considered as a dimension, but the direction of this dimension can change from point to point. Superstring theory suggest even more bizarre 11-dimensional, geometrical figures. No intuition about the arrow of time or any other subjective experience can be extracted from phisical theories.

The only natural law that lthat links with subjective experience is the anthropic principle applied to life in general. Life imposes strong restrictions in the particular form that our Universe (or portion of Universe) has in the infinite sea of optional solutions of General Relativity and String Theory. These restrictions also applies to the initial conditions. of this universe. The observed increase of entropy with time in our visible universe means that it started with a very improbable configuration. But this reasoning is circular: If we try to elucidate what really is the arrow of time, we can not use concepts that presupose a certain direction of the arrow of time !!

The quesition, reformulated in strict physical terms is as such: In the four or eleven-dimensional manifold described by the equations of relativty or the superstring theory respectively, why our lifes follows a line from less to more probable configurations of matter, that is, from less to more entrophy, that is, from less microstates to more microstates for each observable state?. Why ?

This last view in terms of micro-states is the key for the explanation: causes are in the side of less microstates. Effects are in the side of more microstates, because there are less causes than effects. In the other side, life is all about prediction of the future. An organism can not make use of the environment for its own ends if he can not predict what will follow at the chemical, biological, instinctive or rational levels. Computationally, it is much more easy to simulate the evolution of a system where entrophy increse than in the opposite direction. The precision demanded for a reverse simulation is much higuer: The calculus of the fragmentation of a glass is not very difficult. Essentially, the results are not very different using a precission or another. But a reverse simuation from a broken glass never will reach the re-composition of the glass, no matter how precise the measure of the real position of the pieces from a real case were introduced in the simulation.

But the fact is that in our univese, glasses do recompose themselves, the flame of the candles do recombines liberating oxygen and make grow the candle, objects lighter than water sink. Why? because these events exist in our space time; Just go in the reverse time dimension in our space-time manifold to see them. The laws of physics permits them. They are just reversible chemical reactions, reversible object collisions at the particle or macroscopic level.

In terms of our perception of time, the outcomes we see happens just because they are cuasi-infinitely probable and the reverse counterparts, cuasi infinitely improbalbe. But, that is also an illlusion of the arrow of time, because , In terms of time-agnostic spacetime manifold reasoning, our life vector in space-time go along the increase of entrophy, not the other way around. That is: the outcomes of probability laws are a consequience of our trajectory in space time. Why our life follow this direction?. The reason is computational, as I said before.

The essence of life is to identify risks and opportunities, that is, to identify causes to react accordingly in order to achive efffects that permit survival and reproduction, while maintaining the internal disorder controlled. This happens at all levels of life. From the chemical to the neuronal level, the living beings look at the present to predict the effects in the phisical direction of entropy increase. life can not operate in other but in such direction, because this is the computable direction.

Computation is done at all levels. chemically a cell computes by generating proteins triggered by an stimulus, these proteins will aid the cell to cope with what will come nest, either engulf food in the protoplasma and diggest it or to expell toxins to scape from a predator. For this reason life chooses the esasy path in the universe-manifold: because computationally it is easier

he key here is that neiter our universe is simulated nor time has meaning outside our psichology. There are simulaton, but this simulation is carried out by us, the living beings. We are the ones that simulate in advance the events along a direction fo the manifold in order to advance actions for the next point in this coordinate. Why? because we need to planify furter actions in order to grow and reproduce in succesive progression in this direction. This progression along this direction is what we perceive as time.

Because living beings are the ones that must simulate in advance what comes next, at the chemical, instinctive, rational level, this iimposes very serious computational restrictions to the direction of time. Simply, the reverse simulation , along the enthropy increase demands infinite or near infinite resources computational resources. It is also possible simulate in any lateral direction, any direction in the manifold, but I hipotesize that they are also very heavy to calculate. Thinking in terms of Natural Selection: The living beings that tried to progress along other directions are extinct, They needed too much computational resources!!!. Or even never appeared in the first place!.

For this reason, the perception of time, enthrophy and probability, and the initial conditions of the universe are a byproduct of this restriction of computability in living beings.

living beings are like fractals that grow, reproduce and die along the temporal coordinate. There are two ways to express a trajectory , and here I use the Max Tegmark coined frog/bird view; The frog view is time dependent and uses the input of the previus step, wich is the view of computers, living beings and us, and the other is the bird view that contemplates the manifold or part of a manifold . The first type of beings strugle for anticipating the next step,. The second see the enlarged mandelbrot figure of all our life, and this figure is part of the manifold described maybe by a single formula The M formula or whatever may be the grand unification theory.

This is not so difficult to understand: This is the difference between the expression of a integral in mathematical terms versus the step that a computer must perform along the integrration coordinate to calculate its numerical value.

1 comentario:

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