Additional evidence of the fact that biomolecules are phase-correlated is provided by thermodynamics. The Second Law of Thermodynamics prescribes that the yieldof a thermal engine, whereis the heat absorbed at the temperatureandis the performed work, should not exceed the quantitywhereis the temperature decrease of the energy flow within the engine. In a typical living organism at room temperaturecannot exceed a few percent, whereas bio-electrochemical evidence of the membrane processes gives a value of about 70% [ 7 ]. To avoid a thermodynamic inconsistency, we are forced to conclude that a living organism is not a thermal engine, so that its component molecules are not independent but are phase-correlated; actually, the ensemble of coherent molecules is able to receive energy as, since its entropy is vanishing. The above statement is corroborated by the result quoted in the literature [ 8 ] that a muscle is not a thermal engine but a quantum machine. In conclusion, we should accept that liquid water, at least within living organisms, should exist in a coherent state, supporting the suggestion coming from QED analysis.

Therefore, coherent correlations span at least 5 nm. The correlated molecules, as all biomolecules, are of course immersed in water, which accounts for the large majority (70% of mass and 99% of molar concentration) of the components of living organisms. Therefore, the coherent correlations among biomolecules should be propagated by water. However, G. Scholes 6 ] produced a study, based on Molecular Dynamics, showing that EM correlations within a liquid obeying the assumptions usually made for water, fall off within a distance smaller than 2 nm. Consequently, we should conclude that the usual picture of liquid water is unable to account for the observations of the coherent structure of living organisms.

“Intriguingly, recent work has documented that light-absorbing molecules in some photosynthetic proteins capture and transfer energy according to quantum-mechanical probability laws instead of classical laws at temperatures up to 180 K. This contrasts with the long-held view that long-range quantum coherence between molecules cannot be sustained in complex biological systems, even at low temperatures. Here, we present two-dimensional photon echo spectroscopy measurements on two evolutionarily-related light harvesting proteins isolated from marine cryptophyte algae, which reveal exceptionally long-lasting excitation oscillations with distinct correlations and anti-correlations, even at ambient temperature. These observations provide compelling evidence for quantum coherent sharing of electronic excitation across the 5-nm-wide proteins under biologically relevant conditions, suggesting that distant molecules within the photosynthetic proteins are ‘wired’ together by quantum coherence for more efficient light-harvesting in cryptophyte marine algae.”

In the above equation,is the magnetic vector potential, V is the electric potential, h is Planck’s constant and e is the electron electric charge. Consequently, the phase correlations within the ensemble of coherent molecules are kept not by the EM fields but by their potentials, which, by the way, propagate in space at the phase velocity, which, as is well-known, could be larger than c. In Reference [ 4 ] a detailed mathematical theory, based on QED, is presented, discussing the appearance of coherent solutions in the system, which give rise to the liquid.

In the last two decades a conceptual change has occurred in the physics of condensed matter. For a long time condensed matter has been conceived as an ensemble of atoms/molecules kept together by static short-range forces. Liquid water has been no exception to this trend. In references [ 1 2 ] much material has been presented to describe the formation of a network of water molecules tied by the bindings named, which should emerge from highly directional protuberances protruding from the molecule electron clouds. However, a conceptual difficulty emerges here, since, in order to fit experimental data [ 3 ], H-bonds should be conceived as short-lived; the lifetime varies with temperature from 20 ps at 250 K to 2 ps at 300 K. How is it possible to treat in a static approximation an electric charge structure (the H-bond) which lives so short a time? An electromagnetic (EM) field having at least the same time of oscillation should be necessarily introduced. Therefore the physical system of water molecules tied together would demand necessarily, in the framework of present knowledge, the explicit consideration of the interaction between water molecules and a radiative EM field. However when this problem is addressed in the theoretical framework of Quantum Electrodynamics (QED), a configuration of the system molecules + field emerges different from the usual network of molecules kept together by forces. In the new configuration, molecules oscillate in unison between two single-particle states, in tune with a non-vanishing EM field trapped in the ensemble of molecules. In this new state, termed, the relevant physical variable is phase. QED connectsto the EM potentials through the equations (in SI units)

2. Emergence of Coherence

In this section we will try to provide a physical intuition of the emergence of coherence within a composite quantum system, such as an ensemble of atoms/molecules. According to first principles, a quantum system (either particle or field) cannot but fluctuate; in particular vacuum also fluctuates, as shown by the phenomenon of the Lamb shift of the energy levels of hydrogen atoms. These levels exhibit energy values slightly below (about 1 ppm) the ones calculated by quantum mechanics, which is based on the assumption that the Coulomb field that connects the proton and the electron is classical (non-fluctuating). The above difference between measured and calculated values of the hydrogen energy levels, first detected by Lamb in 1947 [ 10 ], is the evidence that actually a fluctuating field should be present, just the one produced by the quantum fluctuations of the vacuum oscillators. Therefore, according to quantum physics, we should always assume that molecules are coupled to a quantized EM field.

In order to give to the reader a qualitative understanding of the origin of the collective interaction among molecules induced by their interaction with the EM field, we give a simple scale argument. The size of a molecule is about a few Angstroms (Å); in the case of water slightly more than 1 Å. The typical energy difference E exc between two levels of an atom/molecule is in the order of some eV (say 10 eV); the photon supplying this energy could be extracted from the environment, at the very least from the quantum fluctuations of the vacuum, and its size (we mean by size the extent of the region where the photon can be located) is of course its wavelength λ = hc/E exc which for E exc = 10 eV gives λ = 1200 Å. We find, therefore, the surprising result that the tool able to change the internal structure of the molecule is about one thousand times more extended than the molecule itself. At the usual densities of gases on Earth (in the case of water vapor at the boiling point 2 × 1019 molecules∙cm3) one single photon able to affect the molecular structure would include within its own volume some 20,000 molecules! Hence the collectivizing feature of the interaction between molecules and EM fields.

Let us describe now how this process of interaction could occur. A fluctuation of the EM mode having the frequency corresponding to the energy jump among molecule levels emerges either from the quantum vacuum or from the thermal bath. This fluctuation involves simultaneously all the molecules present in the volume λ 3 spanned by its wavelength λ , in the case of water some 20,000 molecules, as candidates to be excited. It excites one of them with a probability P which can be calculated from the Lamb shift. The molecule remains excited for a time t decay (the decay time of the excited level) and then decays giving back the EM fluctuation, which could fly away or excite a second molecule. The probability P N that this fluctuation would give rise to an excitation of one out of the N molecules present within the ensemble would be, of course:

When this number is smaller than 1, the EM fluctuation would disappear eventually in the original background, but when the density reaches the critical value (N/V) crit such that:

(2)

The EM field loses the chance of leaving the ensemble of molecules and gets permanently trapped within the region, bouncing from one molecule to another. In a short time more photons undergo the same fate until a sizeable EM field grows in this region that will be called from now a Coherence Domain (CD) attracting from the environment other molecules of the same species that are, by definition, able to resonate with the growing EM field. In this way the system self-produces a negative pressure which counteracts the positive pressure of the vapor. An attractive dynamic arises which binds molecules together, giving rise to a large increase of the molecular density and of the EM field until a value of the molecular density is reached, where, as we will see in detail in the following, the trapped EM field grows exponentially (runaway) inducing a further increase of density. This runaway brings the density of the system to a limiting value given by the intermolecular distance at which the repulsive forces produced by the molecule hard cores come into play. The final result is a closely packed ensemble of molecules oscillating in phase with an EM field. This field is trapped within the CD since its oscillation time is renormalized by the interaction with molecules; the time of oscillation of the free photon should be actually supplemented by the time spent within the molecules in the form of excitation energy. Consequently, the frequency of the fields (matter and EM) in the CD, ν CD , becomes smaller than the frequency ν 0 of the free field and the squared mass of the photon, m2 , becomes, according to the Einstein equation:

(3)

since we know that the mass of a free photon is zero. On the contrary, the above equation tells us that the mass of the photon oscillating in the CD becomes imaginary; therefore this photon is no longer a particle, is unable to propagate and gets trapped in the CD in form of a cohesion energy, not static but at the origin of the coherent oscillation of molecules. The outcome of the above complex multi-step dynamics is the actual spontaneous formation of a cavity for the EM field.

Let us address now the problem of the selection of one specific level in the above lasing dynamics in the case of multi-level molecules, as is the case of water molecules. Phenomenological evidence gives us the indication that the transition vapor-liquid occurs basically in two steps. In a first step, molecule condensation occurs at several points simultaneously giving rise to a slow growth of density; this step takes almost the whole time of transition, until a threshold is reached where very fast condensation dynamics takes place, bringing the system to the final liquid phase.