Arrow of time determined by life´s easiest direction for computation Entropy, Time and life (Alberto G.Corona agocoronaDELETE@gmail.DELETEcom) you are here
Life is computation• Living beings maintain homoeostasis by making predictions about the environment so that they anticipate. So they must compute.• Computation is not only at the brain, but also at te chemical level. Plants and bacteria also compute. chains of chemical reactions are analogous to algorithms in a computer language. its purpose is to produce an ouput that is good for the organism, given an input.• To open the mouth in the precise moment that the small fish pass nearby, the big fish has to calculate in advance the small fish trajectory.• Even a seed has to compute the right moment for germination given temperature, humidity etc.
What I want to demonstrate• The increase of entropy is a precondition for life• Therefore, the low entropy of the universe at the beginning is a consequence of the anthropic principle (and the concept of "begining" too)• For computational restrictions, evolution and life operates in the direction of systems that go from lower to higuer probabilities• Causality and time itself is a psichological experiece, a product of the way life can predict to survive.• Reichenbach “direction of time”: time proceed in the direction of positive gradients of entrophy• Time is just a perception product of the computations living beings have to do to survive and specially, conscientious beings that learn from experience.
Mathematical Multiverse Hypotesis (MMH)Reality is mathematicalHilbert: mathematics means "absence of contradictions"Progressive unification of phisical laws suggest that ouruniverse appears to be isomorphic with a single mathematicalstructure.Tegmark: each mathematical structure creates its own universehttp://space.mit.edu/home/tegmark/toe.htmlTo avoid paradoxes, Gödel incompleteness, non computabilitya subset with good properties are the decidable, computablestructures (tegmark The Mathematical Universe http://tinyurl.com/6zvv5h)
Life as criteria for universe existence• According with MMH, existence of self aware structures (SAS) is the requirement for an observable universe.• An alternative criteria for existence may be the existence of life, understood as self preserving structures (so they must compute) without mathematical restrictions a priori• Life then is not a criteria for observability but for existence.• But life and natural selection demands a mathematical universe somehow• Existence of Intelligent life (self aware structures) remains as the criteria for observability.• This is not a topic of this presentation.• A mathematical universe hypothesis is accepted as starting point.
Causation• According with general relativity, time is local, there is no absolute notion of simultaneity, it depends on the observer.• All natural laws (KUN) are reversible, this do not match with experience.• Natural laws do not distinguish forward or backwards in time• Therefore, causation is also an illusion caused by the arrow in which life and natural selection flow due to computational restrictions (forward)
What "life computes" means in the static mathematicalfigure of an spatio-temporal, immutable universe?• Computations need computers and data. They need energy and building materials and sensors. Living beings have to transport them.• To permit life, an Universe must facilitate smooth physical laws and a direction in which predictions are feasible with a small set of inputs and computational load. This direction is locally perceived as arrow of time.• Seeing from outside, living beings and his environment form intermingled trajectories in the space-time that maintain low entropy along their paths thanks to apropriate interactions of his constituent particles and the environment.• For the time-aware living being these internal collisions are the computations that permits life and, if intelligent, interpret past interactions with the external world as causalities, anticipations, and sucessful actions for survival,
Causation and effects. forward and backward examples• Forward (in the arrow of time): Heat is applied to water, water evaporates. o Molecular collisions and photons excitate vibration in water molecules, that evaporate.• Backward (in reverse arrow of time): very unlikely and fortunate molecular collisiona makes water molecules to increase its speed in the down direction (while air molecules decrease its own). Very unlikely, their directions make them to join and very unlikely further collisions make then go down to the liquid water of the recipient
Causation. forward and backward examples 2 electric light bulb• Forward: o electrons trough a resistence in the light bulb produces infrared and visible photons that escape outside• Backwards o Very unlikely, reflected photons are focused in the light bulb. The electrons of the philament absorb the photons and its speed increases. Very unlikely their directions are aligned so that their movement produce electricity back
Causation. forward and backward examples 2 backward ninja jumps• Forward (entropy increase): o A ninja fall from a building o The legs muscles tighten to mitigate the impact, in the process, heat radiation that is absorbed by surrounding air molecules• Backward (entropy decrease): o Very unlikely the surrounding air molecules emit infrared photons that impact the muscular fibers in a way that they add to the energy of muscle contraction and the ninja jumps back to the top of the building. Air in the ground is colder now.
Entropy in terms of micro and macrostates• A single macroscopic state (you in your room reading this) has many microscopic states (the possible combinations of positions and velocities of all the particles in the room).• A macrostate has more entropy than other when the number of possible combinations of microscopic states is greater. A ninja in the ground after the forward jump and the surrounding hot air has more entropy than the ninja in the top of the building, because higer temperature has more possible combinations of particle speeds.• If I were living in the reverse arrow of time, to predict that the ninja in the ground flexing his legs will jump to a three floor building I have to track the concrete microscopic state of the ninja, that is the positions and velocities of all the particles in the legs of the ninja plus the surrounding air molecules• In the right arrow of time, I can do an educated guess of
computational needs for survival in forward and backward arrow of time
• Distance in space-time is well defined• Simultaneity appears when two objects are in the same space and time coordinates• Space-time is four dimensional• Time is an arbitrary name, it is the direction of entropy increase• Particle trayectories must not loop in the entropic arrow or causality may not be extracted
Causality as a consequence of lifes computation• Emission and absortion of photons, collisions with loss and gain of energy are individually probable.• But coordination of many of such phenomena to reduce entropy are very very unlikely.• Living beings can anticipate from ordereed to less ordered states because the correlation of more disordered states from less disordered states is computationally easy while the opposite is much more difficult. This also produces the psychological sense of causality in conscious beings who learn from experience.
Computation in other arbitrary direction is even more difficult Weird time Ordinary time Collision between Collision between A particle in the "past" Two particles in With other in the "future" space They bounce back to their time • In four-dimensional coordinates, when two particles touch in the same moment of time no matter where time coordinate points to. however the weird time being see the particle going to and coming back from collision before seeing the collision. Their computations must be very difficult