A New Theory of Evolution That Trumps Darwin?

A new theory of evolution has been advanced by Jeremy England, a young MIT professor who’s proposed a thesis based on thermodynamics, showing that the emergence of life was not accidental, but necessary. In an article in Quanta magazine early in 2014, that’s since been republished by Scientific American and, more recently, by Business Insider, he’s  quoted as saying, life itself evolved out of simpler non-living systems. In his words:

"Under certain conditions, matter inexorably acquires the key physical attribute associated with life,”

In a way this touches on the theory of the origin of life, abiogenesis. This is generally distinguished from the theory of evolution which shows how life evolves and speciation occurs.  Creationist Ken Ham’s Answers in Genesis (AiG), after one Cosmos episode on the issue last April, asserted:

"Abiogenesis has never been observed in experimental biology and violates the most fundamental law in biology, the law of biogenesis. Nevertheless, the authors of the review are confident there was a naturalistic chemical origin for life.” [Biogenesis is the natural law that life comes from reproduction by living things].

But curiously, around the same time, a remarkable find was published in The New Scientist (Vol. 209, No. 2794, p. 11), by two investigators: Kunikho Kaneko and Atsushi Kamimura. The pair made a remarkable breakthrough in devising a testable model that was able to replicate the Abiogenesis process. The two basically solved the problem of how a lipid-coated proto-cell can divide into two (displaying reproduction) when the genetic material replicates.

Enter now, Jeremy England. According to the Quanta magazine piece:

From the standpoint of physics, there is one essential difference between living things and inanimate clumps of carbon atoms: The former tend to be much better at capturing energy from their environment and dissipating that energy as heat. Jeremy England, a 31-year-old assistant professor at the Massachusetts Institute of Technology, has derived a mathematical formula that he believes explains this capacity. The formula, based on established physics, indicates that when a group of atoms is driven by an external source of energy (like the sun or chemical fuel) and surrounded by a heat bath (like the ocean or atmosphere), it will often gradually restructure itself in order to dissipate increasingly more energy. This could mean that under certain conditions, matter inexorably acquires the key physical attribute associated with life.

This means that “under certain conditions” where life is possible — as it is here on Earth, it is also quite probable, if not, ultimately, inevitable. Indeed, life on Earth could well have developed multiple times independently of each other, or all at once, or both. It does not mean that life is ubiquitous and can emerge on any planet anywhere in the galaxy or the universe. There still remain limiting factors defined by what we call the "habitable zone" around our own star -  which is of specific spectral type (G2).  Thus,  if the same conditions are found elsewhere then Earth-like planets circling other suns would have a much higher likelihood of carrying life as well.  See e.g.

http://brane-space.blogspot.com/2014/01/finding-second-earth-we-better-make.html


If England’s theory proves to be consistent and is confirmed, it will  be an epochal scientific advance but also be a fitting rebuke to pseudo-scientific creationists. Recall they have long mistakenly claimed that thermodynamics disproves evolution (specifically the 2nd law).  The error of the AiG crowd is two-sided :a) They assumes that evolution means more primitive organisms develop into more complex or organized ones, and, b) They misunderstand the second law (because it refers to increasing disorder or "entropy") as applicable to all living things- hence believe it is impossible they can "evolve" to more orderly, organized forms.

Consider (a) first: At no point and no place do evolutionists claim that more organized forms are the inevitable manifestation of natural selection and adaptation, and represent evolutionary success. What evolution states- which any high school biology student learns -  is that the species which survive best are the most well adapted to their environment.

Thus, the humble cockroach beats just about all other species on Earth for evolutionary success given it's been around for 150 million years. Humans, though much more complex and organized than cockroaches, have only been around in their modern form for barely 1.5 million years, if that. Humans, up to now, have enjoyed  barely 1/100 th the evolutionary success of the cockroach, measured in time!

Now, as to (b), this is a common error of those who've never taken advanced physics, but just read Googled excerpts. It's basically a direct result of misinterpretation of the 2nd law, something I often see from those who've never taken a serious physics course. Strictly speaking,  the law states:

Entropy (the state of disorder) will tend to increase over time in any closed system

This is generally expressed in statistical mechanics terms as:

s = log g

Where 'g' denotes the number of accessible states. In other words, in a closed system we will expect the probability of increasing entropy and that means increasing accessible states.  This was discussed at length when we looked at assorted spin systems (see the posts on 'Order and disorder'  on April 5th and 9th, 2013) and note that higher entropy - as in a state with low excess spin- corresponds to the most probable state. Say a  closed magnetic spin system S(2), has 10 spin ups while S(1) has five, then S(2) has a much higher degree of order (less entropy) than the system S(1). 

The part about closed systems is crucial since it is exactly the part that the creationist-ID crowd omits, which renders their complaints using the 2nd law non-starters. The reason is that neither the Earth nor its biological systems are "closed" systems, hence do not exhibit constantly increasing disorder. The Earth, for example, receives a constant input of radiant energy from the Sun - quantified as some 1360 joules per square meter per second. Plants on the Earth are likewise OPEN to solar energy, and receive it and then use it in the process of photo-synthesis.

Bottom line: Evolution is no more a violation of the Second Law than life itself is.

Germane to the point of England's thesis is that flows of energy — whether from the Sun or some other source — can give rise to what are known as dissipative structures, which are self-organized by the process of dissipating the energy that flows through them. Russian-born Belgian physical chemist Ilya Prigogine won the 1977 Nobel Prize in Chemistry for his work developing the concept. Common to all the examples is that order can arise from disorder.

In the thermodynamic study of chaos, similar approaches to equilibrium can be examined but permitting far from equilibrium changes. Given the right fluctuations, it’s even possible to generate self-organization from pre-existing chaos.

One of the simplest examples of a non-equilibrium system is a simple chemical reaction of the form:

X + 2Y <-> 3Y

X <-> W


where X, Y, W are arbitrary reactants that meet the conditions and the symbol (<->) denotes a two-way equilibrium process. We note here that at equilibrium detailed balance requires (with k1, k2, k3 and k4 the respective concentrations):

k1 xy² =  k2 y³

k3 y = k4 w

Similarly, a stationary state ‘far from equilibrium’ is disclosed by the concentration equation:

k1 xy² + k3 y = k2 y³ + k4 w

Or:

k1 xy² + k3 y - k2 y³ - k4 w = 0

 Note that in such a state, far from equilibrium, it isn’t necessary for each separate chemical reaction to balance in both directions. Clearly, non-equilibrium discloses aspects of the system that are inhibited when it is at equilibrium.  Prigogine in his monograph 'Order Out of Chaos'  cited the example of  individual tumor cells, for example, emerging from a disordered background (cf. Garay, R.P. and Levefer, R.: 1978, Theoretical Biology, 417, p. 73.) The cell appears as a fluctuation,  and is then able to develop by replication.

In a true sense, then, Prigogine’s work laid the foundations for what England is doing today, which is why it might be overstated to credit England with originating this theory. Several commentators at Quanta have pointed this out, noting other progenitors as well (here, here and here, among others).
 

In a sense then, it may be more accurate to say that rather than Jeremy England and his research group advancing a whole new theory, they are instead formulating an alternative multidisciplinary,his theoretical approach to evolution and abiogenesis. (You can search his research group home page for more.)  As the Quanta article puts it:

Above all, as described on the home page mentioned above, England is involved in knitting together the understanding of life and various stages of life-like processes combining the perspectives of biology and physics:

Living things are good at collecting information about their surroundings, and at putting that information to use through the ways they interact with their environment so as to survive and replicate themselves. Thus, talking about biology inevitably leads to talking about decision, purpose, and function.

Hence, it will be the development of a detailed body of specific mutually interrelated results that will distinguish England’s articulation of his theory from other earlier formulations- that have yet to be cast into a testable research approach. And whether or not England’s approach is validated in the end, he’s already doing a lot to build bridges between worldviews and inspire others to make similar efforts.  As the Quanta article explained:

England’s theoretical results are generally considered valid. It is his interpretation — that his formula represents the driving force behind a class of phenomena in nature that includes life — that remains unproven. But already, there are ideas about how to test that interpretation in the lab. 

“He’s trying something radically different,” said Mara Prentiss, a professor of physics at Harvard who is contemplating such an experiment after learning about England’s work. “As an organizing lens, I think he has a fabulous idea. Right or wrong, it’s going to be very much worth the investigation.”

Those readers who fancy themselves science nerds might enjoy this hour-long presentation of his work. 

Order from Disorder (Pt. 3): Bifurcation Examples

In two earlier blogs on statistical mechanics and its applications to simple systems (e.g. spin systems) we saw how order can emerge naturally out of disorder. What one looks for, say in an electron spin system (or Ising model of larger scale magnetizations) is rapid fluctuations that quickly alter the state from one of disorder to order, or from equilibrium to order - say like a 16 spin magnet system with 8 up and 8 down that evolves to one with 14 up and 2 down, giving a spin excess of 12 up, denoting higher order.

Accessing such simple systems allows us to infer fundamental measures applicable to the systems, for example the "magnetic moment" of a state, as well as the "degeneracy function". Consider an N= 2 model system with either 2 ups (two up arrows) or 2 downs. Then, if m denotes the magnetic permeability we can have:

M = +2m or M = -2m

where the first is the magnetic moment for two spins up particles, and the second for two spins down. One can also, of course, have the mixed state inclusive of one spin up plus one spin down, then:

M = O m or O

Meantime, the degeneracy function computes the number of states having the same value of m (individual spins) or M such that:

g(N,m) = N!/ (½N + m)! (½N - m)! [M_av]


where [M_av] denotes the average value of the total magnetic moment summed over all states (e.g. with m_s)

Accessing these quantities helps to see at which point a system is likely to be subject to what we call "bifurcation" - which was illustrated generically in the last blog on statistical mechanics and order.Let's look at a couple of examples of this, starting out with more or less prosaic systems. An actual example from fluid dynamics is the famous ‘pitchfork bifurcation’, which has nothing to do with demons! It arises by considering the complex interactions of a controlled water channel whose flow continuously recycles. At some point, beyond a critical value of the Reynolds number (R_c), the single flow relinquishes its symmetry and two stable flows result. These are shown in Fig. 1.

The critical value (where the vertical dotted line intersects the abscissa) turns out to be 40.5. As before, with the Ising model, we see that hidden complexities manifest in a kind of order or self-organization for each of the bifurcation paths. Indeed, each one of these paths can be thought of as mirror images of the same Markov process, tending to some new ‘equilibrium’ displaced from the original one.

An interesting but somewhat more complex example from plasma physics is the ‘two stream instability’. In this case we have the plasma dispersion function F(w) which leads to two bifurcation ‘paths’, including a split symmetrical one and a symmetrical one similar to that shown- but in a different direction relative to coordinate axes. This is shown in Fig. 2.

In finding conditions under which it operates, one considers treating a dispersion relation for plasma waves such that, viz.:

F(w) = F(x, y) = (m_e/m_i)/ x² + 1/ (x² - y²)

where (m_e/m_i) denotes the electron to ion mass ratio, and we define the variables x, y as follows:

x = w / w _e

or the ratio of the plasma frequency to electron plasma frequency.

Meanwhile:

y = k V_o/ w _e

or the ratio of the product of the wave number k by the electron thermal velocity (V_o) to the electron plasma frequency.

Plotting the graph on the axes yields a bifurcated graph with 4 roots (Fig. 2). It will always feature a local minimum F_m such that: 0 (less than or equal) F_m (less than or equal) x=y.

When: F(x_m, y) = F_m  < 1 there will be four real roots.

When F_m  > 1 there will be two real and two complex roots with suitable approximations, e.g. k² V_o ²    £  w _e ² then the 2 complex roots are found to be:

w / w _e  =   - ½ + i((Ö3/2) ,   - ½ -  i((Ö3/2)

 

These will give the limits for the instability for when F_m >1

Order Arising from Disorder (Pt 2)

In the previous blog on order and disorder in statistical mechanics, I focused on some basic principles, and simple illustrations, including the basis for a Markov process, and the Ehrenfest effect. We confined the basis to very simple systems while now we want to turn our attention to actual spin systems, such as occur in quantum mechanics. In conjunction with this, some readers may find it useful to go back to the blogs dealing with electron spin to refresh memories, e.g.  http://brane-space.blogspot.com/2010/07/more-quantum-mechanics-electron-spin.html

and http://brane-space.blogspot.com/2010/07/spin-orbit-coupling-in-quantum.html


Consider two systems of atomic magnets possessing different ‘spins’. We look at what happens when they undergo changes, and what is observed at the quantum level, as well as macroscopic scales. A fact of 20th century physics is that all electrons have a property called spin that’s either up (+½) or down (-½).

The numbers are "spin quantum numbers" and the main thing to remember about them is that they refer to different directions in the atom, and differing energy states. (The plus state slightly higher than the minus). An atom can assume a net spin as a result of the spins of the constituent electrons. Helium, for example, has two electrons which are forbidden (by the Pauli Exclusion Principle) to have the same spin numbers at the same time and so the net spin of the Helium atom cancels out: (-½) + (+½) = 0.

At a more detailed level, spin is assessed in atoms for particular (x, y, z) orientations. That level of detail is omitted here to keep the presentation simple. Also, the details of the experiment by Stern and Gerlach (1921) to infer electron spin using the magnetic moment are omitted, though these were given in a much earlier blog. Basically, they passed a narrow beam of silver atoms through an unequal magnetic field and found it split into two beams: one for the ½ spin, the other for minus ½ spin. Historically, it was Wolfgang Pauli who introduced electron spin into quantum mechanics in 1927, after S. A. Goudsmit and G. E. Uhlenbeck first postulated it in 1925.

Observationally speaking, spin is inferred from fine splitting of atomic spectral lines, cf. Fig. 1, wherein the unperturbed line splits into two separate lines of slightly differing energy. The appropriate inferences are derived by applying a set of quantum rules for combining angular momentum vectors and their quantum numbers in what is known as ‘L-S coupling’. A spin-orbit interaction results with a total angular momentum J’ = L’ + S’, where L’ denotes total angular momentum = L1 + L2 etc. = {l’ (l’ + 1)}^1/2  ħ , and S’ the total spin angular momentum = S1 + S2 etc. = {s’ (s’ + 1)}^1/2 ħ, then:

 J’ = {j’ (j’ + 1)}^1/2  ħ.

And recall here  ħ = h/ 2π , where h is the Planck constant.  One applies these to a particular atomic configuration, say: 2p 3d then goes through a procedure of taking differences, assigning values etc. based on selection rules. (See prior blogs on quantum mechanics)

Let's now look at an elementary, statistical mechanical spin system. For starters, let's say that there is a system consisting of 16 atomic magnets. These atomic magnets exist temporarily in the state S(1) as shown in Fig. 2 (i.e. each arrow denotes the net spin of the atom based on the sum of electron orientations within it). We want to find the degree of order applicable to the system, say at time t(o) and do the appropriate counting of "spin ups" and spin downs" as shown in the left side of Fig. 2 below the system at t(o). We find on doing so (which the reader can verify) that we get 8 spin ups - 8 spin downs = 0 net spin, or in other words the system is at equilibrium.

The degree of order, as well as information, for the simple spin system shown is determined from what is called "the spin excess", or the net spin difference (up minus down or vice versa). The larger this number, the greater the degree of order, and the lower the entropy of the system. Obviously, since 0 denotes an extremely low number, we can deduce large entropy.

 

Consider then another system but at a different time, for which we behold the right side orientations of the elementary spin magnets. Here we get: 14 spin ups - 2 spin downs = 12 spin ups, or in other words the spin excess = 12. This system, call it S(2), has much higher degree of order (less entropy) than the system S(1). (We should add here that higher entropy - as in S(1) - corresponds to the most probable state, defined by the minimal spin excess of zero.

Now, it is also important to note that one can dramatically generalize what's depicted in Fig. 2 via the "Ising Model" of statistical mechanics. In the 2-dimensional Ising Model for ferromagnetic matter, for example, one finds magnetic domains or regions which can, after a time, undergo a change such as that shown from S(1)-> S(2) (looking at the same system!) Here the Ising model system, by virtue of undergoing spontaneous magnetization, discloses a higher degree of order at the later time t(0) + t, where t could be in billions of years or hundreds of seconds. (Depending on the system).

The reader should also note that each arrow can be generalized to represent a region of indefinite scale size. For example, the depiction given in Fig. 2 might conceivably represent the evolution of an (essentially) two-dimensional current sheet in a highly compressed magnetic region near a sunspot. The arrows would represent plasma flows and current densities that follow magnetic field lines.

Chaos theory, spurred on by a number of notable successes, sheds new light on the numbers. Particular offshoots of Chaos theory disclose entities such as ‘strange attractors’ that can actually spur a system toward an enhanced degree of self-organization. We call such a turning point a bifurcation. Bifurcations represent sudden, abrupt changes toward higher degrees of organization of a system. These include the sudden alteration of system development from equilibrium (maximum entropy) to non-equilibrium.

In the thermodynamic study of chaos, similar approaches to equilibrium can be examined but permitting far from equilibrium changes. Given the right fluctuations, it’s even possible to generate self-organization from pre-existing chaos. The ultimate example is the formation of matter in the universe. From amidst a sea of pure energy, the ambient temperature cooled, re-setting the so-called Higgs Field H(f) from a zero to a non-zero value. This re-setting of the cosmic thermostat enabled the production of material particles in a sudden and spontaneous breakdown of symmetry.

One of the simplest examples of a non-equilibrium system is a simple chemical reaction of the form:



X + 2Y <-> 3Y

X <-> W


where X, Y, W are arbitrary reactants that meet the conditions and the symbol (<->) denotes a two-way equilibrium process. We note here that at equilibrium detailed balance requires (with k1, k2, k3 and k4 the respective concentrations):

k1 xy² =  k2 y³

k3 y = k4 w

Similarly, a stationary state ‘far from equilibrium’ is disclosed by the concentration equation:

k1 xy² + k3 y = k2 y³ + k4 w
Or:

k1 xy² + k3 y - k2 y³ - k4 w = 0

 
Note that in such a state, far from equilibrium, it isn’t necessary for each separate chemical reaction to balance in both directions. Clearly, non-equilibrium discloses aspects of the system that are inhibited when it is at equilibrium. To assist in identification of far from equilibrium states, bifurcation diagrams can be of use. A typical form or template for such a diagram is depicted in Fig. 3, where F is some state function, and lambda (Greek letter) is called a control parameter.

Note also that the equilibrium solution associated with the above is valid up to some critical value of the control parameter. Beyond this value there are multiple solutions, viz. the two separated or bifurcated ones. Meanwhile, the use of the classical (Newtonian) order paradigm for the cosmos is now recognized as the byproduct of a bygone era in which astronomers didn’t have access to the wide range of instrumentation available today. It also hearkens to an era in which the assumption prevailed that what one saw was what was actually there.

 

The prevalence of dark matter and dark energy, of course, resoundingly refutes this. We now know formidable problems occur when one postulates a supernatural agent, in this case an allegedly "eternal" deity to create order. Logically, such an entity must be outside all temporal reference frames. However, the action of transforming disorder to order would require this being to exist within time. This inconsistency also intrudes on its being ‘all-knowing’ or ‘omnipresent’. We have then a logical contradiction. The point is that any being postulated to exist outside time (eternal) can exhibit no activity which determines natural laws or processes.

In th next instalment I will give examples of systems undergoing bifurcation and subject to spontaneous emergence of order from chaos.

Order Arising from Disorder? Not Strange At All! (Pt. 1)

 

The concept of order emerging out of disorder or even chaos, is not new. Some examples include: a normally functioning cell suddenly becomes malignant; the molecules/particles of a liquid, initially with random arrangements, suddenly assume an orderly, lattice-type of structure when the liquid freezes (e.g. when water turns to ice); elementary atomic ‘magnets’ originally distributed randomly, suddenly oriented in the same basic direction - creating magnetism in a ferrous material. In each instance, the system has undergone a transition from a more disordered state, to a more ordered one.

The discipline is also an important one in that it reinforces and validates the arguments and position of scientific Materialism, i.e. in not having to invoke supernatural agents to account for a broad spectrum of natural phenomena. In the course of this, we also find that the ultimate supernatural agent, 'God', is rendered redundant in terms of explanations.


Issues of order and disorder occupy the top rungs of that branch of physics we call statistical mechanics. In this discipline, we apply principles from classical mechanics as well as microscopic thermodynamics to arrive at properties of complex systems and their evolution. In so doing, we can expose the conditions under which spontaneous order can arise from chaos, as well as ascertain systems in which equilibrium applies.


One example is the so-called Markov process which is at the heart of an important model used in statistical mechanics. As an example of this (Ehrenfest) model, one can consider a number of marbles, N, distributed among containers C1 and C2. At precise periods, say every 2 seconds, one marble is randomly selected from C1 (with X initial marbles at time to) and moved to C2 which must have N – X marbles by inference. It can be shown that at some arbitrary future time: t(o) (less than or equal to) t Iess than or equal to) t(o) + tN/2.


There will be either X + 1 or X –1 marbles, with transition probabilities: X/N corresponding to X -> X - 1, and 1 – X/N for X -> X + 1. Eventually, assuming the initial number of marbles large, equalization (‘equilibrium’) will occur with N/2 marbles in each container. The sketch of the approach to equilibrium is shown in Fig. 1.


We expect that as the process continues, oscillations will stabilize about the line X = N/2, so effectively the transition probabilities equalize. The important point of this process is that each such transition is independent of the system’s prior history. Say, there are just 16 marbles in all initially with 11 in C1 and 5 in C2 at t(o). Then successive distributions might appear like this, leading toward equilibrium (equalization of C1-C2 distributions):


C1: (11) -> (10) -> (9) ->(7) -> (9) -> (7) -> (9)


C2: (5) -> (6) -> (7) -> (9) -> (7) ->(9) ->(7)


Notice how the numbers relative to each container ultimately settle into small deviations from the equilibrium value (N/2 = 8). Of course, the probabilities reflect this, and can be represented on a separate graph for probability density plotted against X. This is shown in Fig. 2. In effect, this is the standard ‘Gaussian’ distribution. Mathematically, one can obtain it starting with the basic diffusion equation:


¶ r/ ¶ t = D DIV² ( r)


The preceding necessitates applying suitable boundary conditions, then using a Fourier transform to solve. This indicates all Markov processes can reduce to a form of diffusion.


The probability density peak at N/2 discloses this to be the most probable state. The reader should again bear in mind, however, that we are assuming thousands of marbles, transitions, to get it! Fig. 2 illustrates the direction in which all physical processes tend to run: from more order to more disorder.[1] By definition, in physics the equilibrium (or ‘equalized’ distribution) state is the one with the greatest disorder.


An interesting analog to the above is based on polymers, using Monte Carlo simulations in what is called ‘the two space algorithm’.[2] In one such computation it is found that a characteristic scale size for the polymer (given by a defined ‘radius of gyration’) fluctuates about some final equilibrium value. Such simulations would seem to have direct bearing on work[3] that provides a model for pre-biotic evolution. In particular, that in given environments a single macromolecule can emerge to dominate, with all others fluctuations only[4].


What about processes that more clearly give rise to order out of chaos? Is such a thing possible? To address this, one needs to venture outside the domain of equilibrium processes, and delve into non-equilibrium ones. Indeed, these are observed in the cosmos at large. Thus, the formation of large scale structures like galaxies, galaxy clusters, gaseous nebulae and even superclusters can arise entirely from chaotic processes!


One interesting model for the origin of all the matter in the universe is based upon a quantum fluctuation in its earliest epoch, engendering a primitive superdense radiation state followed by the non-equilibrium production of matter.[5]

The key point is we need not invoke any supernatural inventions to explain aspects of nature we associate with order!
-----


[1] This, of course, is from a thermodynamic viewpoint. In order to elicit thermodynamics from Markov processes, one must somehow assure that the probabilities in question approach that for the Boltzmann distribution, viz. P = exp(-E/kT)/Z, where Z is the partition function.



[2] See, e.g. Yaneer Bar-Yam, 1997: Dynamics of Complex Systems, Addison-Wesley, p. 499.


[3] See, e.g. Eigen, M. and Schuster, P.:1979, The Hypercycle, Springer-Verlag.


[4] The magnitude of a fluctuation can be obtained from probability parameters, in this case multiplying the rms deviation [N]^1/2 by 1/N, or in the case of the polymers, [R_G]^1/2  by 1/[R_G]^1/2


[5] Padmanabhan, T.: 1982, Universe Before Planck Time: A Quantum Gravity Model, in Physical Review D, Vol. 28, No. 4 (15 August, 1983), p. 756