Synopsis [8/9/04]

 

The essays published on this site address the question of whether known physical laws can adequately account for complexity in general, and life in particular.¹  My  answer is that known physical laws appear to suffice, but only if generalized to areas where they have not normally been applied.

 

It appears that the orthodox set of laws governing dynamics and thermodynamics is incomplete. The seeming conflict between the origin and evolution of life and the Second Law of thermodynamics has been noted by numerous thinkers on the subject, beginning with Erwin Schrödinger in What Is Life?, a book commonly cited as the seminal work on the relationship between biology and physics.²  Thus there appears to be a missing link between laws governing the two fields of science.

 

A related topic is the “time paradox”, which is universally commented upon in writings on the subject of thermodynamics.  The paradox is due to the observation that the Second Law determines a direction in time, whereas the laws of dynamics are symmetrical with respect to whether time proceeds toward the future or past.³ This indifference to the direction of time holds not only for Newton’s laws of motion, but for their quantum and relativistic counterparts as well.   

 

The Fourth Law of Thermodynamics

 

The question of how life can emerge in the face of the Second Law has become the preoccupation of complexity theorists, who have suggested the need for modification of the Second Law or the formulation of new “laws of complexity”.⁴  I believe that the Second Law, properly understood, is adequate as it stands but that a “new” law of thermodynamics is necessary to account for the observed complexity of the universe in both its animate and inanimate manifestations.

 

This new law, which I call the Fourth Law of thermodynamics, is simply an extension of the principle of least action (PLA), from which the classical laws of motion can be derived.  The PLA also underlies the theory of quantum electrodynamics as formulated by Richard Feynman as well as Einstein’s relativistic laws of motion.⁵ The logic employed in extending the PLA to thermodynamics is straightforward:  If each of the particles in a flow follows the path of least action, then the action of a large aggregation of such particles must also be a minimum, since the sum of the minimums must be the minimum of the sum.

 

The Fourth Law can be stated in thermodynamic terms as follows.

 

The flow of energy and matter through a system is such that the thermodynamic efficiency of the process is maximized, given the structural constraints on the system.

 

Alternately, this law can be stated as:

 

The flow of energy and matter through a system is distributed such that the heat dissipated by the process is minimized.

 

This law provides a universal basis for selection which applies to both the animate and inanimate realms of nature and bridges the ontological gap between physics and biology.

 

The Second Law of Thermodynamics

 

Investigation of the Fourth Law leads to a clearer understanding of the Second Law, which has been the source of perhaps more confusion in physics than any other topic except quantum mechanics.  The confusion appears to revolve around whether the Second Law provides an ontological description of reality or is merely epistemological statement concerning the state of our knowledge.⁶  If it has an ontological basis, then the Second Law should be discernable in the laws of motion and the time paradox would be resolved.

 

The solution to the time paradox is to see that the Second Law is merely the extension of Newton’s first law, the law of inertia, to thermodynamics.  Since the law of inertia as conventionally presented is clearly indifferent to the direction of time, there must be something missing.  To see what this might be, consider that the Second Law, like a good story, has a beginning, a middle and an end.  If we consider the simple example of the expansion of gas from a small container into a larger isolated system, the beginning corresponds to the initial conditions by which the gas is constrained to a relatively small area.  The middle is the expansion of the gas to fill the larger container, with the gas molecules moving according to the law of inertia (and the law of conservation of momentum, in the case of collisions).  The end is the new equilibrium state where the gas molecules have spread out to fill the expanded space.  If a movie were made of this process, we would be able to tell whether it was being run forward or in reverse, since only one direction would be consistent with our real world experience of time flowing from the past to the future.

 

The same logic can be applied to the law of inertia, taking as an example the motion of two bodies moving at a constant relative velocity with respect to one another.  At the beginning the two bodies are in proximity to one another, relative to the size of the universe.  This is the hidden assumption in dynamics that has not been recognized.  Having established the initial conditions, we can observe the relative motion.  At first, the objects could be moving closer together or farther apart.  If one were to watch a movie of this motion, it would be impossible to determine whether it was being run forward or in reverse.

 

However, after a time determined by the initial separation of the two bodies, they will necessarily be moving apart and will continue to do so as a consequence of the law of inertia.  Therefore, if we watch a movie that is significantly longer than the time it would take the bodies to pass each other (or collide) if they started off moving together, we will be able to tell if the movie is being run in forward or reverse.  At the end of this movie, the bodies will always be further apart than they were at the beginning.

 

So there is a delay determined by the initial separation of the objects before Second Law behavior becomes established.  If we define a sphere with a diameter equal to the initial separation of the two objects, and then add more objects moving at the same velocity to this space at the beginning, the delay will become shorter as more objects are added, since the time required for the paths to cross will vary inversely to the number of objects contained within the sphere (assuming that the objects are evenly spaced to begin with).  So for the large number of objects (billions or trillions) that we would expect in the thermodynamic experiment described above, the delay would be infinitesimal and the expected Second Law behavior would be seen over all observable time frames down to the point where intermolecular distances became significant.

 

One can reverse this thought experiment to see clearly how the Second Law transforms smoothly into the law of inertia.  If we start with a large collection of molecules contained in a balloon and then pop the balloon, the molecules will disperse.  If we then repeat the experiment with fewer and fewer molecules, the result will be the same.  This will continue to be true for two molecules (or even one).

 

The First Law of Thermodynamics

 

The logic extending the law of inertia to the Second Law parallels the logic extending the PLA to arrive at the Fourth Law.  The result is symmetry between the laws of dynamics and those of thermodynamics.

 

Another symmetry between the two sets of laws is that the law of inertia and the Second Law govern motion in the absence of forces.  The PLA and the Fourth Law, by contrast, govern motion in the presence of forces.  However, if these forces are gradually reduced to zero, then we are left with the inertial cases, so it can be seen that the inertial laws are just special cases of the least action laws.

 

As a further simplification, it can be demonstrated that under the assumption of locality (as required by the theory of relativity), the principle of least action can be derived from the law of conservation of energy, the First Law of thermodynamics, and vice versa.⁷  Therefore, the laws of motion governing both dynamics and thermodynamics can be interpreted as manifestations of the law of conservation of energy applied locally.  This statement explicitly encompasses electrodynamics as a logical consequence of the unification of the laws of motion with the laws governing electricity and magnetism.⁸  If one accepts the First Law as universal, the same principle would also apply to nuclear forces.

 

The Physics of Biology

 

The extension of the principle of least action to thermodynamics via the Fourth Law provides a causal bridge from physics to biology and provides an avenue for exploring the origin of life and biological evolution which avoids both dualism and teleology.  Once the passivity of the Second Law is accepted, it ceases to become a distraction, opening the way to the more fruitful approach to the questions of biology indicated by the Fourth Law.  The origin of life is seen to depend most crucially on encapsulation, rather than replication.  The encapsulation of organic compounds by lipid membranes or pores in subterranean rocks would have provided the individuation necessary for the operation of selection based on the Fourth Law.^9,10  Replication could have at first taken the the form of simple cell division without the need for genetic material.  Primitive genes may have developed still later, possibly adapted from metabolic systems using membrane templates to sequence multi-step catalysis.  This gradualist approach avoids the invocation of divine intervention or the miracle of "spontaneous self-organization" as explanations for overcoming the vast improbability of the genesis of life.

 

The second mystery of biology illuminated by the Fourth Law is the physical basis for the theory of evolution.  The fact that the basic premise of biological evolution, survival of the fittest, is tautological goes largely unnoticed or unmentioned in the scientific literature.  Since the mid-twentieth century the seemingly broader premise of reproductive success has gained widespread acceptance, representing a kind of "present-value" view of natural selection.  However, both premises can only be applied retrospectively and lack the predictive power of causal explanations.  In the first case, only the differential survival of individuals is taken into account.  Reproductive success, on the other hand, must be evaluated after two or more generations have elapsed.  Since this evaluation is necessarily retrospective, the jury is always out on the question of which ancestral traits provide advantage and the final verdict is pushed into the indefinite future.  The Fourth Law provides means of comparison that allows prediction, at least in theory, of which traits are likely to prove most advantageous, assuming of course that there are no abrupt changes in the environment.  It also provides a physical basis for predicting optimal tradeoffs between time spent in foraging versus reproduction, or between activity and idleness.¹¹  While these tradeoffs have been extensively examined by means of modeling and field studies, only those evaluations which are based on efficiency criteria can have predictive value.

 

 

Footnotes and References:

 

¹ An excellent discussion of these topics and how they interrelate is given by Donald Haynie in Biological Thermodynamics, Cambridge University Press, 2001, pp. 64-67.

³ Erwin Schrödinger, What Is Life? with Mind and Matter and Autobiographical Sketches, Cambridge University Press, 1967.  First published in 1944.

³ For a book-length treatment of this subject, see Ilya Prigogine, The End of Certainty, The Free Press, 1997.

⁴ Stuart Kauffman, Investigations, Oxford University Press, 2000.

⁵ Feynman, Leighton, Sands, The Feynman Lectures on Physics, Addison-Wesley Publishing Co., 1964, Volume II, Chapter 19, "The Principle of Least Action."

⁶ E. T. Jaynes,"Clearing Up Mysteries – The Original Goal", In the Proceedings Volume, Maximum Entropy and Bayesian Methods, J. Skilling, Editor, Kluwer Academic Publishers, Dordrecht-Holland. 1989. pp. 17, 20.

⁷ Jozef Hanc and Edwin F. Taylor, "From conservation of energy to the principle of least action:  A story line", in The American Journal of Physics, Special Issue on Mechanics, Spring 2004.

⁸ Richard Feynman, QED: The Strange Theory of Light and Matter, Princeton University Press, 1988.