"Physics and Life"
in: The First Steps of Life in the Universe
Proceedings of the Sixth Trieste Conference on Chemical Evolution.
Trieste, Italy, 18-22 September.
Editors: Chela-Flores, J., Owen, Tobias and Raulin, F.
Kluwer Academic Publishers: Dordrecht, The Netherlands. (In
Physics and Life
Lecture in honour of Abdus Salam
London SW7 2AY
Fifty years ago, physicists seemed on the verge of solving the
problem of life. Inspired by Erwin Schrödinger's book What is Life?
(1944), researchers began unraveling the molecular basis of the
living cell, in the belief that a solution to both the nature and
the origin of life would soon be found. Today, these hopes seem very
naïve. Indeed, physics is regarded by most investigators as not
especially relevant to the problem of life.
To be sure, physics plays an indirect role in life, in two ways.
First, life operates in accordance with the laws of physics, but so
does everything else, including, for example, the Italian
Constitution. Physics is universal, its laws simple, mathematical
and general. But life, like the Italian Constitution, is complex,
non-mathematical, and very special. Precisely because physics is
universal, it is unusual that its principles are crucial for
explaining any particular physical system.
The second way in which physics has an indirect bearing on life is
by providing the basic 'tool kit' which biology requires. It is well
known that the existence of life (at least as we know it) depends
rather sensitively on the precise nature of the laws of physics, and
particularly on the numerical values that nature assigns to various
coupling constants and particle masses. This topic often goes under
the name 'the anthropic principle' and has been much reviewed
(Barrow & Tipler, 1986). Here I shall restrict myself to two simple
examples, the first due to Fred Hoyle (Hoyle, 1954). Life is based
on carbon. This element did not exist at the birth of the universe,
but was made inside large stars. A carbon nucleus forms from the
fusion of three helium nuclei. This reaction has a tiny
cross-section, and the carbon yield would be paltry were it not for
the fortuitous existence of a resonance at just the right energy to
correspond to the temperatures of stellar cores. If the strong
interaction did not have the strength it does, the universe could
have been largely devoid of this life-giving substance.
The second example has been discussed by Freeman Dyson (Dyson,
1971), and also concerns the strength of the strong nuclear force.
If it were just two per cent stronger, then it would be possible for
two protons to overcome their electric repulsion and bind to form a
di-proton. This would soon decay via the weak interaction to a
deuteron. Dyson considers the consequences of this for the hot big
bang theory of the universe. One second after the origin of the
universe, the cosmic material was a soup of free protons, neutrons,
electrons, etc. During the subsequent few minutes, about 25 per cent
of the nuclear matter was converted into helium, the rest being left
as hydrogen. If di-protons were possible, the leftover protons would
rapidly convert into deuterons, which would then combine to form
more helium. The result would be that all the hydrogen would be
consumed, leaving a universe composed entirely of helium. There
would then be no stable stars like the sun and no water. Life would
almost certainly be impossible in such a universe. There is a long
list of similar happy accidents in particle physics that make for a
remarkably bio-friendly universe - analogous to what science
administrators call 'a well-found laboratory'.
All this is well and good, but is physics relevant to life's
specific and peculiar properties? One person who was convinced that
physics plays a direct role in life, at least in its genesis, was
Abdus Salam, in whose honour this paper is delivered. His work on
molecular chirality (Salam, 1991, 1992) was a bold attempt to trace
the well-known handedness of biological molecules to parity
violation in electroweak interactions, a subject that he himself
founded. If this link is correct, it provides a key biological role
for one the most fundamental aspects of particle physics. Whilst not
wishing to revisit the topic of chirality here, I shall argue, in
the spirit of Salam's work, that physics may enter into biology at a
basic level in a number of important ways.
In approaching this problem, it is helpful to be reminded of Jacques
Monod's celebrated distinction between chance and law, or necessity
as he termed it (Monod, 1972). All physical systems come about from
a combination of these factors. Some, like crystals, are almost
completely determined in their structure and properties by the laws
of physics alone, which embody the relevant crystal symmetries.
Others, like clouds in the sky, are shaped mostly by chance. In
between are systems such as snowflakes, for which the overall
hexagonal structure is determined by physics, but the specific
filigree details are a matter of happenstance. Where, on this
spectrum from pure chance to pure law, does life lie? Opinions vary
widely. Monod himself argued that life was pretty much the product
of chance, a stupendous chemical fluke unique in the observable
universe. By contrast, Christian de Duve (de Duve, 1995) thinks life
is a 'cosmic imperative,' more or less bound to occur wherever
earthlike conditions prevail.
The belief that life is 'written into' the laws of nature is
sometimes called biological determinism (Shapiro, 1986). In its most
extreme form, as advocated for example by Sidney Fox (Fox, 1988), it
asserts that the laws of the universe are cunningly rigged to coax
life into being from lifeless chemicals, by favouring the production
of just those molecules that life needs. On this manifestly
teleological view, life's information content derives from the
physical laws that generate the informational molecules. This view
is hard to sustain, since the information content, as measured
algorithmically (Chaitin, 1990), of the known laws of physics at
least, is demonstrably low (Yockey, 1992). That is why crystals,
which are determined by those laws, have low information content,
being just regular arrays of atoms. By contrast, DNA is a random
string of atoms - the 'aperiodic crystal' famously predicted by
Schrödinger (1944) - and so has high algorithmic information
content; it is then hard to see how such an entity could be a
product of law alone. In this respect it is worth noting that
although the backbone structure of DNA is determined by the laws of
physics and chemistry, the precise sequence of nucleotides - the
'letters of the genetic alphabet' - are not. There are no chemical
bonds between successive nucleotides; chemistry is indifferent to
the sequence chosen.
Those like de Duve who espouse a less teleological and
conspiratorial form of biological determinism argue that because the
stuff of life is common in the universe, then so must life be.
Oft-cited is the commonness of the life-giving elements C,H,N,O,P,S,
and the ubiquity of simple organic building blocks like methane,
formaldehyde, alcohol and even amino acids. These molecules are easy
to make, and are found across the universe, in meteorites, comet
tails and even interstellar clouds. Therefore, the argument goes,
life should be common too.
This argument is, however, flawed. The building blocks of life are
easy to make because their synthesis is thermodynamically favoured.
But stringing them together in an aqueous environment into complex
molecular chains like proteins and RNA is thermodynamically 'uphill.
' Just as a pile of bricks alone don't make a house, so organic
building blocks alone don't make life. Put a stick of dynamite under
a pile of bricks, and you don't make a house, you just make a mess.
In the same way, merely throwing energy willy-nilly at a collection
of amino acids, for example, to drive it against the thermodynamic
gradient, won't produce a protein. Just as a house requires the
delicate assembly of bricks into an elaborate and specific
arrangement, so amino acids need to be carefully linked in a precise
way to make a functional protein, rather than gunk. The same goes
for nucleic acids.
A hundred years ago, it was commonly supposed that life is some sort
of magic matter, and that life's origin would be analogous to baking
a cake. All it needs is the right ingredients mixed in the right
order under the right conditions. Today we know that the living cell
is less magic matter, more a supercomputer; i.e. it is an
information processing and replicating system. The key property that
distinguishes life from other forms of complexity is the
informational aspect, the message in the genes. Chemistry cannot
explain information. Chemistry is the medium of life, but one must
not confuse the medium with the message.
In the living cell, nucleic acids and proteins, which are scarcely
on nodding terms chemically, deal with each other via an information
channel, i.e. using software rather than hardware, written in a
triplet mathematical code. The advantage of life 'going digital' in
this way is much greater flexibility and fidelity (as is also the
case with digitization in electronic devices). The situation can be
likened to flying a kite versus a radio-controlled plane. A kite is
hard-wired to the controller, and is clumsy to control by pulling on
the strings. By contrast, a radio-controlled plane is easier to fly
because the controller's instructions are digitized and transmitted
to the plane, where they are decoded and used to harness local
energy sources. The radio waves themselves do not push and pull the
plane around; they merely convey the information. Analogously,
nucleic acids do not themselves assemble proteins, they relay the
instructions for ribosomes to do it. This frees protein assembly
from the strictures of chemistry, and permits life to choose
whatever amino acid sequences it needs. So, far from deriving from
physics and chemistry, biological information is quasi-independent
of it. To explain the origin of this information-based control, we
need to understand how mere hardware (atoms) wrote its own software.
Note that we must do more than simply explain where information per
se came from. A gene is a set of coded instructions (e.g. for the
manufacture of a protein). To be effective, there must exist a
molecular milieu that can decode and interpret the instructions, and
carry them out, otherwise the sequence information in the DNA is
just so much gobbledygook. The information is therefore semantic in
content, i.e. it must mean something (Küppers, 1985). So we are
faced with the task of understanding the nature and origin of
semantic, or meaningful, information. Since the very concept of
information emerged from communication theory in the realm of human
discourse, this is no trivial matter. Information is not like mass
or energy: you can't tell by looking whether a molecule has it or
not. As yet, there is no 'info-dynamics' comparable to the dynamics
of matter, let alone an understanding of how 'meaning' emerges in
The central puzzle, as it seems to me (Davies, 1998), is that life
possesses two apparently contradictory properties. The first is that
the key informational content demands randomness (in the algorithmic
sense) since order is by definition low in information content. The
second is specificity; arbitrary randomness is no good. A protein,
for example, is a specific random sequence of amino acids; any old
higgledy-piggledy sequence will almost certainly be biologically
useless. Individually, randomness and specificity are not hard to
create. Chance (in the form of thermal chaos say) generates
randomness, and law generates specificity. But what combination of
chance and law generates specific randomness?
One solution is Darwinism. Chance mutation and lawlike natural
selection has what it takes to produce the right mix of randomness
and specificity. But Darwinism kicks in only after life gets going;
it cannot be used to explain the origin of life. Some researchers
suggest defining life as any system that undergoes replication,
variation and selection, and argue for 'Darwinism all the way down'.
The system may be simply a collection of replicating molecules that
could plausibly form by chance in a prebiotic soup.
Can molecular Darwinism explain biogenesis? Maybe, but we have scant
idea what those first replicating molecules might be. Examination of
real organic replicator systems like RNA/proteins indicates that
even the simplest replicators are extremely large and complex
molecules, unlikely to form by chance. Moreover, the smaller the
molecules the sloppier they copy, suggesting that molecules small
enough to form by chance would be very bad at replicating
information, and thus subject to Eigen's error catastrophe (Eigen &
Schuster, 1979), whereby information is eroded by the inaccurate
copying process faster than natural selection can inject it.
I concede that if something like the RNA world (Cech, 1986) were
given to us ready-made, it has the capacity to evolve into life as
we know it. But it strains credulity to suppose that the RNA world
sprang into being in one huge chemical transformation. Likely it
would be the product of a long series of steps. We can liken the
situation to a vast decision tree of chemical reactions, with the
RNA world as one tiny twig on the tree. (There is the question of
whether there are other twigs that could lead to life, but I shall
assume here that the RNA route is the only one.) So we need to
understand how a hypothetical class of simple, small replicators
navigated through that decision tree and 'found' the RNA twig. Was
this just a lucky fluke, or is there something other than a random
Now searching databases and navigating decision trees is an
interesting branch of science that we might term informational
physics. I wish to conjecture that some new discoveries in this
field just might help explain how life's decision tree was
The first point I want to make is that informational physics
encompasses mechanisms capable of converting random motion into
directed motion. An example of current interest is the so-called
Brownian ratchet, based on a device first studied in detail by
Smoluchowski (1912). It consists of a ratchet and pawl connected via
a rod to a set of vanes, and immersed in a gas in thermodynamic
equilibrium. The ratchet allows the vanes to rotate in one
direction, but not the reverse. The random motion of the molecules
bombarding the vanes will cause the system to rotate, thereby
apparently converting undirected chaotic molecular motion into
directed macroscopic motion. This seems to violate the second law of
thermodynamics, because the rotation could be used to perform work,
e.g. by lifting a weight. The resolution of the paradox was
essentially spotted by Smoluchowski (1912) and refined by Feynman
(Feynman, Leighton & Sands, 1963) and Abbott (Abbott, Davis &
Parrondo, 1999), in which it was pointed out that in thermodynamic
equilibrium the position of the pawl will fluctuate due to thermal
noise, and allow the ratchet to slip backwards as often as it is
driven forwards. There is then no net rotation on average.
Moreover, a type of Brownian ratchet that serves to convert random
into directed motion has been devised by Magnasco (1993), and
studied by Doering (1995) and Harmer & Abbott (1999). In this
system, an ensemble of randomly bouncing balls can be made to
diffuse uphill if driven by a tilted sawtooth forcing potential that
flashes on and off - the so-called flashing ratchet (Ajari & Prost
1993). The ratchet thus drives the system 'the wrong way' from a
thermodynamic viewpoint (though there is no violation of the second
law because the system is not closed on account of the external
potential). The relevance of this discussion to life is that
Darwinian evolution is an example of a ratchet, because advantageous
random changes are locked in, thus also giving a superficial
appearance of going against the second law of thermodynamics.
Derived from the physical example of the Brownian ratchet is the
curious paradox of Parrondo (Harmer & Abbott, 1999; Parrondo et.
al., 2000), involving games of chance. Parrondo has proved that two
fair games that individually have an expectation of loss to the
player can be played in combination with an expectation of gain!
Again, the relevance of this to biological evolution is clear:
Darwinism is a type of game of chance in which the winners, driving
against the thermodynamic gradient ('climbing Mount Improbable', to
use Richard Dawkins' evocative description (Dawkins, 1996)) are the
survivors. If chance variations could lead to ordered evolution as
opposed to random diffusion, then canalization within the chemical
decision tree may result. (Of course, if nature obligingly directs
the activity preferentially towards the RNA world we are back to
My remaining examples concern the possibility that quantum mechanics
may have a more direct role to play in life than merely providing
the mechanism of chemical bonding. The founders of quantum mechanics
generally believed that life required some extraordinary physics to
explain it. Thus Schrödinger wrote (Schrödinger, 1944, p. 81), 'We
must be prepared to find a new kind of physical law prevailing.'
Several researchers have suggested that quantum mechanics might be
biologically relevant. An early conjecture along these lines is
Fröhlich's theory (Fröhlich, 1983) that collective vibrational modes
(coherent phonons) in biological membranes can create conditions
similar to a Bose-Einstein condensate, leading to ordered,
cooperative behaviour in which the vibrational energy is
concentrated into the lowest mode.
A more recent example has been given by McFadden (2000), who points
out that certain mutations occur as a result of quantum tunneling
events in the pair bonds within DNA. He conjectures that the
biological environment might 'select' certain mutations by affecting
the tunneling probabilities. Is this credible? Certainly the theory
of quantum transitions involving strong coupling to the environment
involves some unusual features. For example, in the watchdog or
quantum Zeno effect (Itano et. al., 1990), continuous
measurement-like interaction with by the environment can serve to
paralyze a quantum system in its initial state. The inverse watchdog
or Zeno effect (Altenmuller & Schenzle, 1993; Kofman & Kurizki,
2000) can amplify certain transitions and 'steer' a quantum system
through a sequence of states by environmental interactions. McFadden
conjectures that competing quantum transitions with biochemically
very distinct consequences might have very different transition
rates, so that adaptive mutations might be quantum mechanically
favoured. Applying this to biogenesis, it is possible to imagine
that states that are in some sense 'more lifelike' (e.g. more
complex, more organized, more information rich) might also be
favoured. The trouble is, it's very hard to pin down a precise
attribute for 'lifelike' that can exercise a well-defined physical
effect. The most obvious candidate is replication, which has a clear
physical basis. In a quantum system with feedback, it may be that
the production of a replicator in a complicated network of chemical
reactions acts like an attractor, with the feedback amplifying, via
something like the inverse watchdog effect, the transition
probabilities leading to replicating molecules.
These ideas hint that maybe quantum mechanics can 'fast-track' a
chemical soup to complex biologically-relevant states. Since the
object of the exercise is to explain the origin of biological
information, the appropriate theoretical framework would seem to be
quantum information theory. This subject is currently of intense
interest because of the possibility of constructing a quantum
computer (Milburn, 1998; Bennett & DiVincenzo, 2000). The key
property of quantum information processing is that it is far more
powerful than classical information processing. That is because the
wavefunction of a collection of entangled particles can store
information in the phases. So long as quantum coherence is
maintained, transformations of the wavefunction can simultaneously
process exponentially more information than the corresponding
classical system. Farhi and Gutmann (1998) have applied quantum
information theory to decision trees, and found an exponential
improvement in the search time. Treating the biogenesis problem as
the need to navigate the molecular decision tree to 'find' the RNA
world, or something similar, then a quantum search would obviously
be vastly quicker.
Building upon these ideas, a fruitful line of investigation would be
to apply quantum information theory to ratchets. Quantum ratchets
might combine quantum search efficiency with the directionality
property of ratchets. Another related field under active
investigation is quantum game theory (Meyer, 1999; Eisert et. al.,
1999). This is closely related to the molecular evolution decision
tree problem: if competing chemical reactions are regarded as
participants in a game, with the 'winner' being life (or simply a
replicator), then quantum strategies are expected to be much more
efficient than their classical counterparts.
Hameroff (1998), and more recently Nanopoulos (Mershin et. al.,
2000), have suggested that quantum information processing may play
an important role in protein folding - another famous decision tree
problem, where this time the branches of the tree are alternative
conformational states. These researchers point out that the protein
tubulin can undergo quantum flips between two specific
conformational states, and thus form a binary quantum switch - the
basic component of a quantum computer. In a microtubule of the sort
found within living cells, ordered arrays of tubulin molecules
constitute a sort of quantum cellular automaton, potentially capable
of prodigious information processing. Penrose and Hameroff (Penrose,
1994) have also suggested that quantum information processing takes
place in microtubules, and, more controversially, that this process
may be involved in the phenomenon of consciousness.
There is some circumstantial evidence in favour of the theory that
quantum computation plays a crucial role in life. Grover's algorithm
was devised to apply quantum information processing to search an
unsorted database of N objects by posing Q yes-no questions. Grover
(1999) proved that this would produce a N1/2 improvement in the
search time. The relationship between N and Q in Grover's algorithm
(2Q + 1) sin-1(N-1/2) = p/2
which has the intriguing solutions Q = 1, N = 4, and Q = 3, N =
20.2. Patel (2000) has suggested that these numbers could explain
the genetic code. N = 4 corresponds to the four nucleotide bases, Q
= 3 to the triplet code and N @ 20 to the twenty amino acids life
uses. He has developed a scenario of molecular assembly using
quantum interrogation in which these numbers may crop up naturally,
as a consequence of quantum mechanics.
Another hint of quantum physics at work in the genetic code is the
discovery that the coding assignments possess a compact description
in terms of supersymmetry (Bashford et. al., 1999). Supersymmetry
arises in particle physics as a unified description of fermions and
bosons, and is a subject to which Salam made important
contributions. To find supersymmtery appearing in a biological
context is remarkable, and still somewhat mysterious. Unless it is a
weird coincidence, it points to a deep link between the quantum
realm of particle physics and the quasi-classical realm of protein
Exciting though these various quantum conjectures may be, they all
come up against a major obstacle - decoherence. Explicitly quantum
effects may be manifested only so long as the phase relationships
between various branches of the wave function are maintained. But
these phase relationships are exceedingly delicate, and will be
disrupted by even slight interactions with a noisy environment
(Zurek, 1991). A simple-minded calculation (Tegmark, 1999) for the
conditions inside a living cell, for example, indicates decoherence
timescales of 10-13 s or less - too fast to be biochemically
relevant, and far too fast to navigate a decision tree of
If this obstacle is to be circumvented, there have to be special
reasons why certain organic systems are screened from decohering
influences. There is a claim that water and proteins could have a
shielding effect on electromagnetic disturbances (Mershin et. al.,
2000). Moreover, most decoherence calculations assume linear,
near-equilibrium systems. In biology one is dealing with highly
nonlinear systems involving strong feedback loops, often driven far
from equilibrium by an energy throughput. The quantum theory of such
systems is more or less nonexistent; greatly extended decoherence
times may not be impossible under such conditions. Also, decoherence
calculations are applied primarily to electromagnetic disturbances
on charged particles. In the case of coherent vibrational modes of
bio-polymers and membranes, phonons are the relevant quantum
particles, and these are likely to have much longer decoherence
times than electrons and ions.
Although the case for quantum information processing in living
systems is far from proved, I think Salam would have approved of the
following philosophical observation. Given that quantum mechanics
provides the possibility of stupendous information processing power,
why does nature have need of it? To what use is it put? Does this
extraordinary power just go to waste, or is it harnessed somewhere?
I believe it is indeed harnessed, in bringing life into existence,
and maybe mind too. That is not a scientific conclusion, of course,
but the history of science does show that what can happen in physics
usually does happen somewhere in nature. If quantum computation
turns out to technologically feasible, I would find it hard to
believe that nature didn't get there first.
I should like to thank Derek Abbott, Carlton Caves, Johnjoe
McFadden, Peter Jarvis, Gerard Milburn, Lee Smolin and Duncan Steel
for their help and encouragement in preparing this paper.
Abbott, D., Davis, B. and Parrondo, J.M.R. (1999) The problem of
detailed balance for the Feynman- Smoluchowski engine (FSE) and the
multiple pawl paradox, in Proceedings of the Unsolved Problems of
Noise (UpoN99), American Inst. Phys. 511, 213.
Ajari, A. & Prost, J. (1993) Mouvement induit par un potentiel
periodique de basse symmetrie: dielectrophorese pulsee, C.R. Acad.
Sci. Paris II 315, 1635.
Altenmuller, T.P. & Schenzle, A. (1993) Dynamics of measurement:
Aharonov's inverse quantum Zeno effect, Phys. Rev. A48, 70.
Barrow, J.D. & Tipler, F.J.(1986) The Anthropic Cosmological
Principle, Clarendon Press, Oxford.
Bashford, J.D., Jarvis, P.D. & Tsohantjis, I. (1998) Supersymmetry
in the genetic code, in Physical Applications and Mathematical
Aspects of Geometry, eds. H.-D. Doebner, P. Nattermann, W. Scherer
and C. Schulte, World Scientific Press, Singapore.
Bennett, C.H. & DiVincenzo, D.P. (2000) Quantum information and
computation, Nature 404 (2000).
Cech. T. (1986) RNA as an enzyme, Scientific American 255, No. 5,
Chaitin, G. (1990) Information, Randomness & Incompleteness: Papers
on Algorithmic Information Theory, second edition, World Scientific
Davies, P. (1998) The Fifth Miracle: The Search for the Origin of
Life, Penguin, London.
Dawkins, R. (1996) Climbing Mount Improbable, Viking, London.
De Duve, C. (1995) Vital Dust, Basic Books, New York.
Doering, C.R. (1995) Randomly rattled ratchets, Nuovo Cimento, 17D,
Dyson, F. (1971) Scientific American 225 (September issue), 25.
Eigen, M. & Schuster, P. (1979) The Hypercycle: The Principle of
Natural Self-Organization, Springer-Verlag, Berlin..
Eisert, J., Wilkens, M. & Lewenstein, M. (1999) Quantum games and
quantum strategies, LANL preprint quant-ph/9806088.
Farhi E. & Gutmann, S. (1998) Quantum computation and decision
trees, Phys. Rev. A58, 915.
Feynman, R.P., Leighton, R.B. and Sands, M. (1963) The Feynman
Lectures on Physics, Addison-Wesley, Reading, Mass., vol. 1, sec.
Fox, S. (1988) Prebiotic roots of informed protein synthesis, in The
Roots of Modern Biology, ed. H. Kleinkauf et.al., de Gruyter,
Berlin, p. 897.
Fröhlich, H. (1983) Coherent Excitations in Biological Systems,
Grover, L. (1999) Quantum computing, The Sciences, July/August
Hameroff, S.R. (1998) Quantum computation in brain microtubules? The
Penrose-Hameroff "Orch OR" model of consciousness, Phil. Trans.
Royal Soc. (London) A356, 1869.
Harmer, G.P. & Abbott, D. (1999) Parrondo's paradox, Statistical
Science, 14, 206.
Hoyle, F. (1954) Astrophys. J. Supplement 1, 121.
Itano, W.M., Heinzen, D.J., Bollinger, J.J. & Weinland, D.J. (1990)
Quantum Zeno effect, Phys. Rev. A41, 2295.
Kofman, A.G. & Kurizki, G. (2000) Acceleration of quantum decay
processes by frequent observations,' Nature 405, 546.
Küppers, B.-O. (1985) Molecular Theory of Evolution,
Magnasco, M.O. (1993) Forced thermal ratchets, Phys. Rev. Lett. 71,
Mershin, A., Nanopoulos, D.V. & Skoulakis, E.M.C. (2000) Quantum
brain?, LANL preprint quant-ph/0007088n.
McFadden, J. (2000) Quantum Evolution, HarperCollins, London.
Meyer, D.A. (1999) Quantum strategies, Phys. Rev. Lett. 82, 1052.
Milburn, G. (1998) The Feynman Processor, Perseus Books, Reading,
Monod, J. (1972) Chance and Necessity, trans. A. Wainhouse, Collins,
Parrondo, J.M.R., Harmer, G.P. & Abbott, D. (2000) New paradoxical
games based on Brownian ratchets, Phys. Rev. Lett. 85, 3386.
Patel, A. (2000) Quantum algorithms and the genetic code, LANL
Penrose, R. (1994) Shadows of the Mind, Oxford University Press,
Salam, A. (1991) The role of chirality in the origin of life, J.
Mol. Evol. 33, 105.
Salam, A. (1992) Chirality, phase transitions and their induction in
amino acids, Phys. Lett. B288, 153.
Schrödinger, E. (1944) What is Life?, Cambridge University Press,
Shapiro, R. (1986) Origins: A Skeptic's Guide to the Creation of
Life on Earth, Summit Books, New York.
Smoluchowski, M. (1912) Experimentall nachweisbare, der üblichen
Thermodynamic widersprechende Molekularphänomene, Phys. Z. 13, 1069.
Tegmark, M. (1999) The quantum brain, LANL preprint
Yockey, H. (1992) Information Theory and Molecular Biology,
Cambridge University Press, Cambridge.
Zurek, W.H. (1991) Decoherence and the transition from quantum to
classical, Physics Today, 44, No. 10, 36.