Quantum Evolution is the attempt to describe space-time itself as an evolutionary system. It is a possible candidate for a theory of everything. A real theory of everything should explain the emergence of space, time, and the most fundamental particles in it. Where does space-time come from in the first place?
We know that the only thing that has not changed in the last 14.6 billion years since the universe exists is evolution itself. Everything else emerged during the course of time, particles, atoms, inorganic matter and organic life-forms. Life and its complete history can be generated just by starting with a simple short self-replicating DNA, and then let it evolve for 4 billion years.. If the universe is evolving (in some form of cosmic evolution), what is the corresponding space-time code? Is nature subject to eternal laws, or do laws evolve like everything else ? Can we use in this case the theory of evolution to gain more insight into fundamental particles and processes ? If yes, then we must start at the most fundamental level, at the level of space-time itself, as a result of the interplay between expansion (the three spatial dimensions are expanding) and contraction (the force of gravity).
A theory of Quantum Evolution would describe the evolution and emergence of space-time.
Are Laws immutable ?
In the time of Leibniz and Newton scientists thought that the world is a great machine going on without the interposition of God, like a clock which continues to go without a clockmaker. But they still believed that God has made the eternal (mathematical) laws, like a clockmaker determines the composition and the laws of his clocks (see ).
Many physicists today still think physical laws are immutable. Some even think there is a fundamental, universal theory. Yet the search for a TOE "Theory of Everything" is maybe misleading, because there is probably no such eternal law except evolution. The very concept of a physical law is maybe an emergent property. This has proposed for example by John A. Wheeler. In his book "Frontiers of Time" Wheeler writes about "Law without law" :
- "It is preposterous to think of the laws of physics as installed by a Swiss watchmaker to endure from everlasting to everlasting when we know that the universe began with a big bang. The laws must have come into being."
Paul Davies summarizes Wheeler's point of view about the laws of physics in the following way 
- "Perhaps there are no ultimate laws of physics, only chaos. [...] Lawlike behavior might emerge stepwise from the ferment of the Big Bang at the cosmic origin, instead of being mysteriously and immutably imprinted on the universe at the instant of its birth. [With this considerations] Wheeler was breaking a 400-year-old scientific tradition of regarding nature as subject to eternal laws."
Sudden and unpredictable emergence of structures is an important concept in the evolution of complex systems . Even the Big Bang itself can be considered as the "emergence" of space-time. What is more likely, that particles and laws have co-evolved together gradually, or that with the Big Bang suddenly a 11-dimensional String Theory (or M-Theory) appeared which governs the behavior of the universe for all times ?
Are physical laws, as Wheeler doubts, really "engraved on a tablet of stone for all eternity", or do they evolve in a process of cosmic evolution together with the rest of the universe ? The latter possibility is more probable. If elementary particles really emerged and appeared in the course of evolution, which is a generally accepted fact, there is no need to assume that immutable laws which described their behavior have been valid earlier. The laws for certain particles or phenomena make no sense if there are no such particles or phenomena.
Evolution is important
Most of the fundamental physical laws are conservation laws based on symmetries. Energy conservation is a direct consequence of the fact that the laws of nature do not change with time, and momentum conservation derives from the simple fact that the laws of physics do not change as you move from one place to another . Conservation of something is related to invariance under a certain transformation:
- Energy (and Mass) - Invariance under Time Transformations
- Linear Momentum - Invariance under Tanslation
- Angular Momentum - Invariance under Rotation
- Electric Charge - Invariance under Gauge Transformations (Invariance of "electric" potentials, a global "voltage" shift )
Symmetries, while mathematically elegant, do not extend scientific understanding of the underlying nature of matter. The basic physical laws do not change with time in the region we can observe now. But in the early universe or near the planck scale, it is possible that the laws of physics are changing from one place to another, or from one moment to another. Since conservation laws, invariance and symmetries are closely connected, it is possible, that conservation laws emerge on a larger scale, if symmetries appear on a larger scale and vice versa.
It is possible that the fundamental laws of physics emerge from such a spacetime foam, where particles and laws are changing from one place to another, or from one moment to another ? If yes, is there a consistent formulation of processes in the spacetime foam near the Planck scale which is able to topple (or to underpin) the twin pillars of 20th century physics, the theory of relativity and quantum mechanics ? Can particles *and* laws emerge from nothing except spacetime foam ?
To answer this question, it is useful to try to look for a connection between the basic physical theories - Quantum Theory and the theory of relativity - and evolution. If all the physical, chemical and biological particles with their corresponding scientific laws emerged bit by bit during the course of evolution, the theory of evolution is the only important and fundamental theory left, because the only thing that has not changed in the last 14.6 billion years since the universe exists is evolution itself. If you want to know why the world is as complex as it is, the theory of evolution is the right choice.
Evolution and Quantum Theory
Can you apply notations and principles of Quantum Mechanics to explain the evolution of complex systems ? George Simpson had a similar idea already 1944. He formulated the idea of a "quantum evolution" in his book "Tempo and Mode in Evolution" (Columbia Press, 1944), where rapid "all or nothing" changes are possible.
Johnjoe McFadden has written a book about "Quantum Evolution" in 2000. McFadden is or was a microbiologist at Surrey (UK) University. But there are doubts if you can apply wavefunctions to macroscopic objects like an entire cell. Matthew J. Donald has argued in http://arxiv.org/abs/quant-ph/?0101019 that McFadden's use of quantum theory is deeply flawed. McFadden clearly has the benefit of understanding the biology much more than most physicists, but many physicists doubt that his understanding of QM is sufficient to give his theories any weight. It is certainly easier to understand evolution for a physicist than to understand Quantum Mechanics for a biologist. Even physicists themselves do not understand Quantum Mechanics well, a theory which relies on many strange principles: Quantization, Wave-particle duality, Spin, Complex amplitudes, Probabilism, Amplitude and State Superposition, Uncertainty Principle,.. As Wolfram says in his NKS book on page 1058, it is not clear which are really fundamental. McFadden seems to have concentrated himself on the wrong ones.
Yet there is evidence  that certain principles of Quantum Mechanics can be used to explain complex phenomena in evolutionary systems on a different level, for example tunneling processes related to the borrowing of energy and the uncertainty principle, or the energy band levels and gaps known from semiconductors. The former correspond to tunneling processes through fitness barriers due to borrowing of complexity, the latter correspond to certain band levels in complex evolutionary systems.
Prof. Eric J. Chaisson says about evolution in his article "Complexity: An Energetics Agenda", Complexity Vol.9 No.3 (2004) 14-21 "Evolution knows no disciplinary boundaries. As such, the most familiar kind of evolution-biological evolution, or neo-Darwinism-is just one, albeit important, subset of a much broader evolutionary scheme encompassing more than mere life on Earth."
If evolution is so fundamental, can you apply the principles of evolution to construct a fundamental description of physical reality near the Planck scale as well ? Here are some basic ideas and suggestions:
1) If everything is subject to evolution, then why should laws and theories be constant ? There is no constant TOE "Theory of Everything", because if new complex structures evolve, new laws will evolve, too, which describe new symmetries and emergent properties. Because there was no particle at the beginning, there were probably not many laws, either. The question who was first, the particles, strings and elements or the corresponding rules, forces and laws, is simple. Particles and laws co-evolved together. Matter constituents and Force carriers, Fermions and Bosons probably evolved together, too.
2) For evolution we need basically only multiplication (replication or reproduction), heredity (inheritance) and variation (mutation or recombination). Maybe the most fundamental structure of space-time involves some process of multiplication or replication, and this process is either related to a fundamental time step itself, or to the continuous expansion of the universe.
Of course an expansion with each time step would result in exponential growth. This is the scenario of the inflation originally proposed by Alan H. Guth. Yet once inflation starts, it never stops completely. Thus it must be balanced by opposite gravitational forces.
It is possible, that all particles emerge as whirls or disturbance in the space-time foam due to constant interaction of expansion (visible in extreme, pure form during inflation) and gravitation (visible in extreme, pure form in black holes) ? Usually "emergence" processes and self-organization take place in open systems with a constant inflow, throughput and outflow of energy or information.
3) A biological species is composed of related organisms that share common characteristics and can interbreed. Is a particle type (or "species") similarly composed of related particle that share common characteristics and can interact (instead of interbreed) with each other ? Elementary particles can be created and annihilated like species.
4) Bifurcations in evolutionary lineage trees or phylogenies have certain similarities with vertices in Feynman diagrams. In evolution bifurcation of species and lineages are possible because a species has an internal structure of a certain complexity or diversity. This internal complexity is based on constant genetic or memetic recombination within the common genetic or memetic pool. The bifurcation or branching point is only a transfer of internal complexity within a species to external complexity between species. Complexity within a species is reduced, and complexity between species is increased in such a transfer. Therefore the ability to absorb and emit particles is a signal or sign for an internal structure, if the evolutionary analogy has any significance.
If this is true for vertices in QFT and string theory, too, then everything that interacts strongly through emission and absorption of particles is probably not elementary: the electrons, the quarks and the gluons. Particles like the electron and the quark should have an internal structure based on constant recombination of space-time structures at the Planck-Scale. If a species (or lineage) splits into two branches, the new emerging species have a common ancestor. Of course the electron is not composed of photons, and the quark is not composed of gluons. But it is possible, that they have like species a common "ancestor" ?
5) There is an important lesson to learn from the evolution of complex systems: the most abundant, primitive and tiniest elements are often the oldest and most fundamental ones. For example bacteria are countless, tiny and primitive, but they belong to the most ancient life-forms on earth. Thus the smallest particles, the insignificant neutrinos with their strange inclination to oscillate, are perhaps more important than we think, exactly because they interact only very weakly with normal matter.
6) Pauli's Exclusion Principle for fermions (electrons and quarks) is very similar to the concept of an evolutionary niche, which can only be filled by a single species at a time. Is there any connection between these completely different concepts ? The Pauli exclusion principle says that two identical fermions can never occupy the same quantum state. Likewise, two species can never occupy the same niche in the ecological landscape (the species correspond to the particles, and the ecological landscape to the quantum state). Species occupy a certain niche, just as fermions occupy a certain quantum state.
Evolution of Time
On the most basic level, space and time may evolve together. Past, present and future may also co-evolve together. Imagine a microscopic world where time is connected to the replication rate of the universe. What would it be like in a universe where time flows forward *and* backward, e.g. at the Planck Scale of Quantum Gravity ? If positive time is related to the expansion of the universe, then negative time is perhaps related to contraction and gravitation (this would be the case, if time is connected to the replication rate of an evolutionary universe, and lightspeed is a somehow a measure how fast the universe replicates itself --- the inflationary universe would be a universe where each point replicates itself without being balanced by gravitation). So there are regions in this universe where time runs backwards (the universe shrinks), and other regions where time runs forwards (the universe expands). Regions in the universe where time runs backwards (or at least not forward) are perhaps Black Holes - can information spread at all if gravity is stronger than the speed of light ? What does negative time or time travel mean ? Time traveling is only possible if the present already contains the effects of time traveling although you might not be aware of them i.e. if the present is not possible without the time travels which have already happened. Of course this is not possible on the macroscopic scale of the world we know, but maybe on a much smaller microscopic scale. If time travel is possible, then deadlock situations can appear where the present is not possible without the past, but the past is not possible without the present, either. Thus both must co-evolve together, somehow. Maybe through a replication or evolution of elementary space-time structures.
|Quantum (Field) Theory||Theory of Evolution|
A testable and predictable consequence of "Quantum Evolution" is individuality and uniqueness: in evolution, no instance of a species is completely identical to another instance of the same species. Each person has a unqiue fingerprint and look, a nonrecurring history and an unparalleled brain. We are all "individuals". Similarly, every culture and every language is unique. The constant genetic or memetic recombinations, variations and mutations which are necessary for natural selection in Evolution are responsible for strong individuality and uniqueness.
If this principle applies to fundamental particles, then there are not two particles would have exactly the same properties: the same mass, the same charge, etc. There would be intrinsic and inherent small differences. Like each person is unique, each particle would be unique, too. On first sight these differences may look like measurement errors. But if the elementary particles are a product of some evolutionary process, these differences would be an inherent property. (Is there eventually a connection to Heisenberg's Uncertainty Principle ??)
 The Book of the Cosmos Imagining the Universe from Heraclitus to Hawking Dennis Richard Danielson, Perseus Books Group, 2000
 Science and Ultimate Reality Quantum Theory, Cosmology and Complexity Edited by John D. Barrow, Paul C.W. Davies, Charles L. Harper Jr. Cambridge University Press, 2004
 according to Noether's theorem, see http://en.wikipedia.org/wiki/Noether's_theorem
 The Emergence of Everything: How the World Became Complex Harold J. Morowitz Oxford University Press, 2002
The Major Transitions Evolution John Maynard Smith, Eors Szathmary Oxford University Press, 1997
 The Emergence of Complexity Jochen Fromm Kassel University Press, 2004
- Eric J. Chaisson, Complexity: An Energetics Agenda, Complexity Vol.9 No.3 (2004) 14-21
- Addy Pross, Toward a general theory of evolution: Extending Darwinian theory to inanimate matter, Journal of Systems Chemistry (2011) Vol. 2