In spontaneous symmetry breaking (SSB), the symmetric properties of the microscopic dynamics imply the presence of fields which, distributed throughout the system, cause the formation of ordered configurations of the elementary components.
The quanta associated with such dynamics (i.e., SSB) are called Nambu-Goldstone (NG) quanta (or particles or modes)
[8][11][12][13][3,19,20,21], and include the phonons in crystals, the magnons in ferromagnets, the polarons in ferroelectrics, etc. Quanta of NG and responsible for the space–time arrangements observed in such systems, which, depending on the case (geometric, magnetic, rotational, electric, etc.), carry the specific correlations that generate the observed order. Even at very different scales, as in cosmology
[5][14][9,22], or where non-trivial forms of order occur, as in biological systems (a very special case of condensed matter), the breaking of several kinds of symmetry underli
nes the appearance of order parameters
[6][8][11][15][16][3,10,19,23,24].
The NG quanta are bosons, i.e., many of them can occupy the same physical state
[17][25]. Under ideal conditions (without “edge effects”) they have zero mass, and in their low-momentum state they do not contribute to the energy of the ground state (vacuum): the emergence of order is therefore a condensation effect of the NG bosons in the vacuum (ground state). The NG quanta are the mediators of correlation and are structural elements.
In a liquid or gas, the atoms (or molecules) are in a state where their positions in space can be shifted without changing the macrostate. A shift in any direction of space therefore produces a configuration equivalent with identical free energy (and entropic content). In practice, a gas or liquid are symmetric systems with respect to the degrees of freedom of spatial displacement.
Therefore, when the system is open and capable of dissipating a certain amount (i.e., entropy, latent heat of condensation), a phase transition from a disordered state to a more ordered state occurs spontaneously
[1][6][1,10]. This new state, the vacuum level, is energetically lower than the previous one. This energy gap (in electron volts, eV) characterizes its thermodynamic stability. The translational symmetry is broken, and it is no longer possible to move along another direction of the system experiencing the same potential landscapes.
This suggests that (i) continuous symmetry breaking as a result of the guided pathways in biotic systems that seeks to maintain a viable homeo
stasis leads to a lack of symmetry and (ii) is the consequence of quantum dynamics in which the components of the matter field phase their oscillations and create a correlation that manifests itself as a field consisting of a discrete set of bosons (in this case phonons)
[9][17]. This correlation field is indeed a classical field (the order parameter), since it is insensitive to quantum fluctuations and causes the macroscopic (classical) stability of large quantum systems (such as a crystal)
[6][10].
However, phonons cannot be “detached” from the system, i.e., there are no freely propagating phonons outside a crystal because they exist only as long as the crystal exists. This implies that the quanta of NG are identified with the function of the specific order for which they are responsible and thus also express the functionality, the mode of being of the system. Without them, the system is “another system” with completely different physical properties (functionality and therefore structure).
2.2. Condensed Matter from a Field Perspective: Water, the Matrix of Life
The principles of SSB described above—applied to condensed matter such as liquid water—allow a fully consistent picture to emerge accounting for phenomena occurring in both plain water and living matter.
Once a critical threshold density (below a critical temperature) is reached, SSB induces condensation of matter in coherently coupled domains
[6][10]. For water, such thresholds are reached at 0.32 g/cm
3 and 373.15 K (at 1 atmosphere pressure)
[18][31].
Experimental evidence
[19][20][21][22][32,33,34,35] and descriptive approaches
[23][36] have demonstrated that liquid water must be a two-phase system. According to QED
[1], part of the molecules in such a system (whose abundance is in “inverse proportion” to the temperature) are organized in collective, coherent vibrational domains corresponding approximately to the size of a wavelength of the coupled electromagnetic mode. Their energy range corresponds to the spectral distance between the two energy levels at which the electron of each water molecule oscillates. Such regions are called coherence domains (CDs), and, in liquid water, where coherence is established between the sp
3 and 5d levels, their size is ideally the wavelength of the corresponding electromagnetic mode (photon), about 100 nm (neglecting thermal fluctuations, which correspond to a frequency of the field in vacuum of 3 PHz, which, during the coupling with the matter field given by the resonating molecules, will be renormalized down to the IR range, about 6 × 10
13 Hz).
The new ground state (known as a “spontaneous superradiant phase transition”) associated with coherently oscillating molecules is lower than that of incoherent, isolated molecules. The difference of this energy gap expresses the thermodynamic stability of the coherent state with respect to decohesion agents acting from outside (such as temperature, photons, fields in general, and mechanical forces). If the excitations are small enough (smaller than the energy gap), the CD receives them as a whole; if they are larger, one or more oscillators are released from coherence and “spilled back” into the normal (incoherent) part
[1][24][1,37].
If the fluid is confined by hydrophilic surfaces, the coherent fraction is stabilized, and possibly other degrees of coherence (such as dipole rotation) can be set. This is the typical condition in living matter as described further below
[25][26][38,39].
As water CDs are self-generated total-reflectance cavities for the EM field, the presence of an externally supplied cavity and pump (as is the case in laser physics) is not required. Indeed, the self-trapped electromagnetic field cannot be externally irradiated as
it an intrinsic phenomenon related to the coupling of molecules and as such implies total internal reflection
[24][27][37,40]. Interestingly, almost four decades ago, Persinger
[28][41] noted that the effects of therapeutically active substances are due to their electromagnetic oscillations rather than due to the biochemical properties; that is, a drug’s electromagnetic oscillations already induce an effect before it is ingested.
Each molecule participating in the coherent dynamics is endowed with an electron that spends about 10% of its time at the 5d energy level, 12.07 eV above the sp
3 hybrid orbital (ignoring collective storable electron excitations). This level is at most 0.53 eV below the ionization threshold (I
th), which for water is 12.60 eV.
These quasi-free electrons can also escape from a CD through the quantum tunneling and in doing so become available to suitable reaction partners (such as the oxygen molecule, non-coherent water molecules, or other species) or are extracted by small excitations
[29][42]. Tunneling of electrons from the CD leaves behind ionized water molecules. These ions no longer participate in the coherent oscillation and therefore pass to the non-coherent fraction—exactly as described in the Landau model of liquid helium
[24][37].
The extracted electron on the other hand could be captured by an oxygen molecule dissolved in water, creating a negative ion. The resulting ion pair, after some chemical steps
[30][43], eventually leads to the formation of a proton and reactive oxygen species such as a hydroxyl. Thus, the CD is an electron donor and then a chemical reducer, which, together with the non-coherent moiety, forms a “redox pile”
[30][31][32][4,43,44].
Because water CDs are easily excitable, they can collect many small external excitations (high-entropy energy) and generate unique coherent vortices whose energy is the sum of all small, collected energy excitations but whose entropy is low (high-degree, low-entropy energy)
[33][48].
In turn, to generate coherence between the CDs, it is necessary to make them oscillate, which means that in one part of the oscillatory cycle the CDs should be able to release energy to the outside, and in the other part of the oscillatory cycle they should recover this energy from external excitations
[31][33][34][4,16,48].
Thus, if external non-aqueous molecules present in the fluid contain in their own spectrum at least one frequency close to the vibrational frequency of the water CD (resonance), then these molecules could participate in the coherent dynamics of the fluid and would be subject to dynamics that we now outline
[29][42].
2.3. Living Phase of Matter: Time-Dependent Order and Morphogenesis
The molecules belonging to the coherent fraction form a set in which the phase is well defined: their common wave function is defined by eigenstates of the phase (
φ), complementing the observable “number” (
N): the uncertainty relation (Δ) expressed in natural units (with
h/2π =
c =
kB = 1, where ”
h” is Planck’s constant, ”
c” is the speed of light in vacuum, and ”
kB” is Boltzmann’s constant), results in the “fundamental uncertainty relationship” expressed as Δ
φΔ
N ≥ ½
[1].
In a perfectly coherent state, the number of oscillators is completely indeterminate, while the phase, the wave-like aspect of the field, is precisely defined. This means that in a coherent state, the individuality of the oscillators loses physical meaning, since the matter field of uncountable quanta coupled to an electromagnetic field whose massless part defines itself as a quasiparticle in the coherent phase
[35][36][37][38][39][53,54,55,56,57] is the only definable object
[1][3][1,7].
This is equivalent to minimizing the uncertainty of the phase (Δ
φ) and thus maximizing the uncertainty of the number of quanta (Δ
N). In order for this to happen, the system tends to have a large number (
N) of quanta because Δ
N ≤
N, with a continuous transition, i.e., an exchange between the coherent phase and the external environment. Since the coherent state is thermodynamically more stable (lower vacuum level than the disordered state), coherent systems tend to share their oscillations with other systems, with which they can resonate as to increase
N. This is a fundamental feature for understanding that living systems are de facto (super)coherent systems. The open flow of matter and energy quanta is thus possible as they share a common vibrational phase with everything capable of doing so.
Since phase correlations are nonlocal correlations that do not imply an exchange of kinetic energy
[40][41][58,59], the definition of the term “ecosystem” in the theoretical framework of QED is appropriate. In this context, the term “ecosystem” is considered a region of spacetime, in which living systems share an oscillation phase of certain electromagnetic modes that cover very large spatial domains (extending over
100s of kilometers and
even more) at long wavelengths
[42][43][15,60].
Quantum-mechanically, the density of water does not significantly alter with or without a solute. When the solute concentration is high, the concentration of water coherence domains is low. As the concentration of the solute decreases, the concentration of water coherence domains increases
[44][67] Thus, by modulating the ionic concentration,
the a the cell is capable of regulating the degree of water CDs.
The size of coherent domains is never smaller than the maximum distance between any surface (membrane, molecular chain, etc.) and another
[29][42]. Such supramolecular organization of water molecules into CDs has two major important implications: (i) the topology of the quasi-free electrons circulating around CDs cannot be tridimensional
[45][46][69,70] (this does not exclude that CDs occupy 3D volumes and can exist in bulk pure water
[19][32], in contrast to Sen et al.
[45][69]) and (ii) no supercoherence can be observed in pure liquid water
[29][47][42,71]. In order to self-organize on further levels, CDs require the presence of other species with which to
co-resonate or some surfaces such as nano-particles (e.g., ions or bubbles) and/or hydrophilic walls
[31][44][48][4,67,72]. Only then will the entire water matrix in living matter be able to experience multimodal coherence, termed supercoherence, which allows for general “multiplexed” phase correlation throughout the system—be it a single cell or a multicellular organism
[31][49][4,62].
One of the most difficult aspects of molecular biology to understand has always been the fact that biochemical processes occur with incredible efficiency, with an extraordinary degree of precision and timing
[30][50][43,64]. This capacity for biochemical activity also allows living matter to express one of its most challenging properties that cannot be simulated in vitro, namely the ability to perform chemical reaction cycles
[50][64] that are perfectly selected from a large number of educts that are present together in the cellular landscape—a good example is the Krebs or Calvin cycle. How can this be explained?
In trying to summarize this very illustrative aspect (for details, see
[31][51][2,4] it should be remembered that any chemical species is first and foremost a physical species, i.e., an oscillator characterized by its own precise proper frequencies (modes).
In the coherent phase, there are regions where a background field oscillation acts as a director and coordinator of the molecular encounters. Inside the CD, however, and due to the high dielectric constant
𝜀𝑐𝑜ℎ~160, fields are strongly shielded.
Once the reactive species have been brought together and activated, the water CD catalyzes the biochemical reaction (typically an oxidation–reduction reaction) by releasing electrons (which in the coherent phase occupy states close to the ionization threshold and are therefore readily released at charges below 0.4 eV
[48][72] or by emitting field quanta
I in the form of
ultra-weak photon emissions (biophotons
) [52][53][54][55][61,77,78,79].
These reaction paths (guided by the sequence of vibrational modes of the coherent fraction) are deterministic and by no means random. On the other hand, they are also unpredictable, since they are determined by (i) the preceding overall thermodynamic history at a given time, (ii) the coherent configuration of the CD at that time, and (iii) the current boundary conditions according to the available reagents and their concentrations, ambient fields, phase correlations, macroscopic thermodynamic variables, etc.
2.4. A Sensible Case: Ions and Ultraweak Fields
Although dissolving salt in water is a common and everyday occurrence, it holds very deep mysteries: How can solvation begin? How can a small molecule like water, which is about 3 Å in size and whose dipole amplitude is no more than 0.38 Å, be able to detach ions from an ionic crystal whose stability is determined by a considerable bond strength (bond strength for most common salts is approx. 5 eV)? Although it is known that the dielectric constant
(𝜀bulk) of water at room temperature is about 80, the question arises of why calculations based on the molecular properties of H
2O using the Langevin equation give a value of about 13. And why does the solvent power increase with an increase in temperature while at the same time the dielectric constant decreases? These questions cannot be answered consistently from either the CP or the QM points of view and can only be explained by considering coherence
(2nd quantization) in liquid water. The empirically measured high value of the dielectric constant in liquid water (
εbulk = 80 at 300 K) applies only macroscopically to the bulk liquid. This could justify the steady state of the already dissolved ions, which provides a rationale for their separation from each other. But it does not realistically support any process involving the onset of dissolution (its dynamics).
The first transition of the electric dipole of water occurs at about 7.4 eV, i.e., in the full UV spectrum, and the oscillator strength (f) of such dipolar transitions is very low (f∼0.05)
[56][84]. Thus, the water molecule is an electric object that is rather rigid, which contradicts the high polarizability required by the pair potentials used in the second-order perturbation theory. This means that the only electrostatic effects water can produce are related to its modest electric dipole and are too tiny to keep oppositely charged ions apart and separated. The attractive Coulomb potential between charged ions in the crystal lattice of the salt can be overcome only if a lower-energy state is accessible; a component is needed that must be able to balance the large enthalpy of ionic bonding, which reaches values in the range of 5–7 eV on average in common salts. The dissolution of ions can take place only if the dielectric constant of water is lower than the known value of
εbulk = 80 (in fact, within the QED picture, the incoherent phase has a value of
εinc = 13, whereas the coherent phase of water with
εcoh~160 is quite high. It can be concluded that the ions oscillate in phase with each other and in a cross distribution of ions and counterions. Thus, the energetic gain of the system Δ, which allows it to overcome the strong stability given by the Coulomb ionic bonds, is associated with the creation of new dynamical structures that are ordered and coherent and embedded in the noncoherent phase of the solvent.
The energy gap depends only on the temperature and the value of the dielectric constant of the incoherent part of the liquid (which in turn also depends on the temperature), and this energy gap corresponds to values of the order of a few eV. Each ion coordinates around itself a 3D plasmatic cage of counterions (with opposite charge). The constraint of coherence (i.e., all ions must vibrate in the same phase and at the same frequency as their counterparts) means that the counterion cages must be identical to avoid collisions (collision implies that these cages to be torn apart), with the concomitant loss of coherence. This comes at an energetic cost and therefore does not occur within certain concentration and temperature thresholds. Furthermore, once temperature increases, the solubility in water increases with the rise in the incoherent fraction of water, increasing the space available for ion dissolution (Figure 15).