Saturday, June 27, 2015

email to arto annilo concerning least action and evolution

The principle of least action shows a preference for the integral combination of higher potential energy bonds, less kinetic energy, and a shorter time path. Higher potential energy bonds and lower kinetic energy is a state of less entropy. Outside of the 2nd law, the shorter time interval "sought" by the principle of least action does not imply an increase in entropy.  Copies of higher potential energy bonds (such as crystal formations or DNA) instead of a larger-number of different levels of potential energy is less entropy.  Lower kinetic energy from different sources will result in less heat and entropy.

A cheetah gaining stronger teeth (higher potential energy structure) and therefore more successful follows the principle of least action. An immediate result that can be seen by the differential form of least action (Newton's law) will be that other potential energy sources (free energy) are depleted more rapidly.  However, the more holistic form, least action, anticipates that gazelles of the future will carry higher potential energy structure as a result of the stronger cheetahs, if there is a free energy influx and an entropic efflux.  So my view of least action is that it is the missing key in evolution. You have the same intuitive feel, but you have an opposing view of least action that causes you to see least action as an "exploitive" rather than "generative" key. Genes are not selfish because they carry no force. They are the memory system that maintains higher potential energy structures. Life is not exploitive, it's creative. Life is more symbiotic than mutually-destructive. Life maintains order, not an accelerator of disorder.

Least action is usually calculated for a given system, but the Earth has a net free energy influx. The energy coming in equals the energy going out which is maintaining the surface temperature. The larger number of lower-energy photons leaving Earth compared to the incoming light is higher entropy for the Universe.  So the 2nd law can be allowing least action to decrease local entropy on the Earth's surface. The minimum energy principle is a special case of the 2nd law that applies to the Earth. It is enabling least action to create life.

For a given time interval, the principle of least action implies a preference for lower entropy via the preference for potential over kinetic energy. It is a mistake to turn this around and say the quantity of L=T-V (entropy generation) is fixed and therefore a shorter time period is sought by least action, and therefore more entropy can be created in a given time period.

So I see no reason that physics does not dictate that life should arise and continually decrease entropy on Earth.  Identical (lower entropy) black solar cells covering the planet would cause a great increase in the entropy the Earth generates for the Universe due to inefficiency in the solar cells causing infrared radiation. But the energy captured could turn photons from the Sun into mass (a potential energy) by storing energy on flywheels, made of very high potential energy carbon-carbon bonds, not to mention the silicon-silicon bonds in the solar cells which store more potential energy compared to the original SiO2. The flywheel can be viewed classically as kinetic energy, but it is not random motion, so that in relativity it is a potential energy due to the mass increase, without the entropy generated by conflicting kinetic energy masses.  As "solar cells and flywheels" (or whatever methods) get more efficient, the universal entropy increase will decrease, giving less opportunity for a decrease in entropy on Earth, but it could still get blacker and more difficult to detect by light emissions. The ultimate would be a Dyson sphere around the sun, storing the excess energy as mass which could take the form of a lot of kinetic energies all "working together" without "conflict" like simple flywheels or very complicated but strictly organized movement.

As a concrete example of free energy creating less local entropy, imagine a Newton's cradle where the balls on the strings are not of equal weight, have irregular striking surfaces, and are made of a mixture of materials (like steel and rubber) where some of the material is less efficiently elastic and of lower potential energy bonds compared to their oxidized state (the rubber).  Now imagine an external free energy source, like Sun energy, that brings the striking ball back up to the original height after each cycle. The movement will be chaotic and not pretty due to the different weight balls and irregular striking surfaces. Eventually, the rubber will wear away, leaving more potential energy in the bonds per volume (and per mass) of the balls. The heavier balls will loose rubber and steel faster due to trying to store more potential energy in the striking process (surface compression) which will result in more heat. Conversely, the smaller balls will endure less wearing away due to acquiring kinetic energy. So the system is evolving towards less potential energy.  However, the potential energy per mass or per volume is increasing, as a direct result of a continual influx of free energy and an efflux of entropy. After a great deal of time, even steel ball irregularities and weights will equalize and a better Netwon's cradle will have "evolved".  Copies of a ball were created and it has lower entropy even on a per mass basis.  The striking cycle has less action: it is reduced in time has a smaller KE-PE difference in that interval.  The "creator" was time, free energy, and the constraints of the strings and gravity.  The strings had a pre-existing order but it resulted in a larger level of order for the device, a higher potential energy per mass, and less action in a striking cycle.
2nd email (to which I received a reply):

Feynman said Newton's differential form of least action is not as fundamental because it allows for non-conservative forces like friction. So if you start with a differential form, you might be automatically  preventing the possibility of local order from arising out free energy.
3rd email:
On the last page of Feynman's lecture on least action, he gives two examples of least action [edit: no, he said they are different minimum principles from mechanical and electromagnetic least action] seeking minimum entropy as it seeks minimum energy [edit, no it seeks min energy only under isothermal].  I am trying to show qualitatively in my last email that this is true for the general case. [edit: feynman mentioned possibility that QM could have a min entropy law, that could give rise to a very general principle, in which case it could be the law I seek, and it may even underlay the least action cases so that my path above is correct]

Since the Earth has an external source of free energy and an entropy "sink" (as I explained) it seems the principle of least action requires life to evolve into a lower entropy (copies of genes, copies of solar cells) of higher-energy bonds, which it is doing, especially if you view our use of silicon, metals, and carbon-carbon bonds as part of that "life".

I could not have made the argument (that least action in the presence of free energy and an entropy sink demands the existence of  life) with F=dp/dt because it allows for frictional forces. It mistakenly allows for entropy generation to be a legitimate force (a potential field) so that it does not allow the user of the equation to see that least action prefers lowest possible entropy.
4th email:

To answer your two questions in reverse order:

I am not seeking a stationary action (optimization) for a known L=T-V path over time, but asking what happens if free energy is applied to stationary action where the L=T=V path and end state has many non-constraints.

Stationary action is used in many calculations that are intractable by F=ma, apparently because stationary action takes away an extra useless variable that F=ma retains, namely non-conservative forces like friction. There is no such fundamental thing as "friction" and non-conservative forces.   It's not a force, it's generating heat and entropy rather than changing position in a potential field.  If you start with F=ma, you can't get order out of it because it assumes disorder generation is another type of real potential.  It would be like writing the Langrangian as (T-V-F*dx) where F is the friction and the last term is generating heat. This only works classically.
F=ma implies a force causes an action, but in relativity and QM the acceleration can be viewed equally well as the cause of the F.  By thinking F is a cause, people want to look at past forces to see how they determined the present. Relativity and QM overthrew this classical view. The past did not create life. An entire action (event) creates life.  The end L state determines the path as much as the initial L state. The assumption that F is a cause is based on the everyday false impression that friction is a real force.

I doubt I can do this over a sequence of macroscopic events where the classical view seems real enough, so I would guess the microscopic bond changes have given rise to brains that seek optimization in a manner similar to stationary action, such that even the global economic system is doing the same. It seems like F=ma implies selfishness is legitimate due to legitimizing friction, but people agreeing before hand to have optimal (more orderly) paths and outcomes is copying least action. We retain F=ma as a view in everyday life such as being forced to go to work, but our legal/economic systems enforce least action on a system-wide basis.  Least action is working together for an optimal path and outcome when there are many non-constraints on our Langrangian. Force and selfishness can be at every point in the details (F=dp/dt), but the wholistic function of least action is love?  Even Feynman's chapter on it was a bonus (gift) chapter, not one of the
"forced" curriculum chapters. It was also the only chapter where he gave a final written note, to mention that some systems spontaneously discover minimum entropy.

Entropy is being released to space, some of it from offsetting least action creating copies of higher-and-higher energy potentials that know better-and-better how to capture and use the free energy of photons, minimizing kinetic energy release that would have otherwise lead to wasted (non-life) heat/entropy. In the creation process that is still going on, there is plenty of energy being "lost" kinetically but there seems to be an upward long-term trend as seen by today's technology.  Life feeding off life is a complicating detail that on first sight seems extractive of potential energies but it is part of the process from initial L to end L, leading to system-wide higher potential energy bonds that are more efficient at  creating copies.

All the new technologies that are replacing biological life due to greater efficiency depend on higher-energy bonds and many copies of themselves.  Solar cells are 20x more efficient per area than photosynthesis.  Electrical motors are about 100x more cost-effective than muscle. CPU's are about 1 million times more cost efficient than brains for implementing any specific algorithm. Mobile energy storage is shifting from hydrocarbons to metal-air batteries. The economic winners can spread like wildfire, and they are. Copies are lower entropy.
5th email:

F=dp/dt allows for the possibility that p(t) is legitimate for the range of functions p(t)= p'(t) + Constant where any non-zero Constant would create a non-conservative momentum, which would in turn allow for a non-existence force like friction.  [edit: p'(t) is not a derivative of p(t) ] Friction is a statistical measure that is not fundamental.  Life is created via processes that occur beneath the data-discarding, macro-quantity of friction.

The stationary action minimization process removes any possibility of the Constant, such that p'(t) is what it finds instead of p(t) where p'(t) is a subset of p(t) which means least action has higher order, i.e., that it has higher algorithmic compression value satisfying Occam's razor better, and can thereby lead to discovering deeper rules, like the originating impulse for the existence and development of life.

This is why action can solve problems F=dp/dt can't, but the converse is not true.  You can strictly derive F=dp/dt from action, but you can't derive action from F=dp/dt unless you arbitrarily throw away the constant.
6th email

It seems to me that evolution is headed towards creating a maximum amount of order and potential energy that can be provided by the Sun's free energy and the available mass, not that it is accidentally finding the quickest ways to expend the free energy, as I would have expected from thermodynamics, and as I thought you had written. Also, I am thinking of what's happening on Earth as a whole closed system with limited resources, not of evolution existing in an open system.   I'll study your writings more and let you know if I think of something that you may find interesting.  I was reading your 2008 paper and thought it seemed overly complicated and wondering why it did not start with classical mechanics or electromagnetic least action an immediate and direct "explanation of life's order" from there.  I've had a long history of armchair interest in evolution, but still lack a satisfactory explanation for its spontaneous development.  That the  thermodynamics does not forbid it is not enough. It is not clear to me that it seeks an acceleration towards heat death. It is not clear to me, as a skeptical and pessimistic scientist might assume, that intelligence is meant ultimately for quicker depletion of order and potential energy instead of their creation.
The photons emitted by even the smallest change of state are not likely to be under the control of my least-action-initiated view of life, but those photons would just be a cause of the net entropy the Earth emits to space, leaving behind the higher order.  Being more in the infrared, they are higher in number with same total energy (or less, if my view of life has its way) of the incoming photons that had less entropy. 
I did not think about photons having mass and therefore the Earth is not closed.  But then even a closed system that receives work via piston action is receiving photons, so that if photons are included, there is no such thing as a thermodynamically closed system that maintains constant mass and can exchange other variables. Your definition of closed would then be equivalent to isolated.

It is not true that my thoughts on entropy are textbook. First, there are many different ways to state it, but all of them have some error or are good for only a specific domain.  Only a QM view would be correct, and I do not know that view or if there is an official exact view.  But I can prove to my own satisfaction that physical and informational entropy are the same, not just equations of a similar form.  For example S=k*ln(states) has fundamental units of bits except for the constant conversion factor of ln(2) that is needed to convert a ln() to a log base 2.  k effectively removes physical considerations, bringing things back down to a theoretical absolute zero and having no real units ( Joules per Kelvins is fundamentally no units because kelvins is a rigid measure of a distribution of kinetic energy). Conversely, there is no such thing as a purely informational bit because in order to have one in the physical world there must be a difference
in potential energy states. So bits on a computer have more mass/energy than physical entropy because physical entropy is a mathematical construct about the organization of matter. I can also show to my own satisfaction that a Maxwell demon disproof does not need to refer to entropy, and that it should not because there is an energetic cost of bit erasure, but not all entropy increases require an energetic cost.

Photons do not have charge.

The brain has 6 layers of neurons in the cortex which always for 3 degrees of freedom when compressing time-based data. In order words, our brains seem to insist that we believe there are 3 dimensions of space, and a lot of our physics follows from that.  For example, if we had 10 layers instead of 6, 4D space would be what we use, and instead of E= - m*c^2 we would think in terms of a E = - i*m*c^3 where the E and m are not energy and mass, but a different type of conserved quantities.  E is negative mass because meters=i*c*seconds and if you follow the math to remove unitless c, energy is shown to be negative mass.  Different number of dimensions also changes the way spin is viewed.  E and m are in units of 1/time^2 or 1/length^2 once unitless c is removed, so they are shown more directly to be some sort of convolution of space-time.  The logical way to express physics would be to use 1D space instead of the 2D space the holographic view of the
universe is trying to say is more fundamental. Maybe in a 1D view, the connection between mass, photons, charges, and spin would be more readily apparent. 

My main interest is in seeing the connections between evolution, intelligence, and economics.
There is a big difference between life and crystals and such.  Life has found a way of affecting a macroscopic sequence of Lagrangians instead of being like a snowflake that is subject to a single fixed Lagrangian.  Our brains model the larger world before affecting it. We decide we want a sequence of least action events that lead to the most money in our bank accounts. So we model and change the sequence of Lagrangians that are available to and affect us. Even when we only seek minimal time for a given amount of free energy, we are choosing from different paths over a macroscopic scale that normal least action isn't supposed to be able to affect.

So there is an optimality that could occur on Earth, given Earth's constraints, and that nature is somehow working backwards in time at a hugely macroscopic level (billions of years, planet wide) to start affecting matter in the beginning that would eventually arrive at an optimal arrangement of efficiency at the end.  If you think everything is made of photons, then this should be agreeable since there is no time from the perspective of photons.  So I guess my interest is in understanding if and how least action could be (or is being) applied across a sequence of microevents, choosing its own Lagrangians, not just minimizing Langrangians it is stuck with.  Then I want to know how this can be applied to economics and A.I.  Can it choose the optimal Lagrangians only on a QM level?  It this why it takes a long time to discover the best sequence of macro-level Lagrangians to create on Earth?  I mean, maybe life is a process by which QM-level Lagrangian
processes are remembered better if they can affect maco-level Langrangian options in an optimal way.   If creating entropy as fast as possible were a "desire" of physical law, then a black Earth doing nothing but getting hotter would have been the end result long ago. The trend seems to be the opposite way, so what in physical law shows us that this should be the case?

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