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International Letters of Chemistry, Physics and Astronomy
2 (2014) 1-10 ISSN 2299-3843
Quantitative Convergence Between
Physical-Chemical Constants of the Proton and the
Properties of Water: Implications for Sequestered
Magnetic Fields and a Universal Quantity
Michael A. Persinger
Laurentian University, 935 Ramsey Lake Road, Sudbury, Ontario P3E 2C6, Canada
E-mail address: mpersinger@laurentianl.ca
ABSTRACT
The ratio of the magnetic moment and charge of a proton when multiplied by the viscosity of
water results in forces that when applied over the distance of O-H bonds provides quantum increments
in the order of 10
-20
J. Precise coefficients of this order of magnitude are consistent with the
mechanisms associated with proton (H
+)
mobility and duration of the hydronium atom. When applied
to aggregate properties of water that involve exclusion zones defined by boundaries containing marked
proton density and coherent domains within which specific patterns of applied magnetic fields can be
contained for protracted periods, these intrinsic properties suggest that the major features of the cell
plasma membrane and living systems can be accommodated by proton movements within water.
Water exposed in the dark to weak magnetic fields displayed a ~10 nm shift in peak wavelength as
measured by a fluorescence spectrophotometer. Given the persistent emergence of 10
-20
J as a
functional unit of energy across the universe, the physical significance of the interaction between
weak, temporally patterned magnetic fields and the organization of water within astronomical and
abiogenic contexts may have been underestimated.
Keywords: proton magnetic moment; hydronium ion; aggregate water properties; magnetic fields;
spectrophotometry; 10
-20
J; cosmological parameters
1. INTRODUCTION
Discerning the quantitative bases for the physical-chemical properties of water is
important to relate the different levels of scientific discourse. In the tradition of Bohr and
others [1] the basic properties of the unit particles, the electron and proton, should be reflected
in the spatial and temporal characteristics of larger aggregates. Establishing the quantitative
relationships between the properties of water, the primary constituent of living systems and
the most voluminous solvent on the planet, and the fundamental constants that define the
characteristics of matter may facilitate our understanding of the mechanisms and processes by
International Letters of Chemistry, Physics and Astronomy 2 (2014) 1-10
2
which mass and energy interact within this medium. Here I present quantitative evidence that
the basic physical units predict the major properties of water that define living systems and
that the energies associated with these interactions could reflect universal constants.
2. PROTON PROPERTIES AND THE UNIVERSAL QUANTAL UNIT
Dividing the magnetic moment of a proton (1.41∙10
-26
A∙m
2
) by the unit charge (1.6∙10
-
19
A∙s) displayed by a proton (or an electron) results in a term of diffusion which is 0.88∙10
-7
m
2
∙s
-1
. When applied to the average viscosity of water (8.94∙10
-4
kg∙m
-1
s
-1
) around 25°C the
force is 7.87∙10
-11
kg∙m∙s
-2
.
If this force is applied over the distance of two O-H bonds (1.92∙10
-10
m) that would
constitute a water molecule the intrinsic energy would be 1.5∙10
-20
J. For comparison, the
resulting quantity of energy for biological temperatures (37° C) where viscosity is ~6.3∙10
-3
Pa∙s, is 1.1∙10
-20
J and at 20°C (the classic standard temperature) where viscosity is 1.00∙10
-3
Pa∙s the energy would be 1.7∙10
-20
J.
The order of magnitude of 10
-20
J is relevant for several reasons. First it is the quantum
of energy associated with the resting membrane potential produced by the electrical force
between potassium ions each separated by about 11 nm over the surface of the membrane [2].
Second, this magnitude defines the energy associated with the effects of the net change in
voltage of an action potential (~1.2∙10
-1
V) on a unit charge.
Third, the energy is within measurement error for the second shell hydrogen bonds (2.6
kcal∙M
-1
) that have been shown to be primarily contributory to the capacity for proton
mobility [3] within water.
As aptly articulated by Decoursey [3] the proton is unique among cations because it is
interchangeable with the protons that form water. Consequently water maintains its structure
while the constituent protons move through space and time. This capacity is coupled to a very
small concentration of free protons (H
3
O
+
), the hydronium ion, particularly in physiological
systems. Whereas the concentration of H
+
in water is 110 M, the concentration of hydronium
ions is ~40 nM. Only one proton in about a billion comprises H
3
O
+
at any given instant [3].
The average life time of the H
3
O
+
ion has been estimated by more than a dozen
researchers to range between 0.24 to 3 ps with a median of ~1 ps. When this temporal
parameter (10
-12
s) is multiplied by the ratio of the proton’s magnetic moment and charge
(0.88∙10
-7
m
2
∙s
-1
), the resulting area is 8.8∙10
-20
m
2
, or 2.97∙10
-10
m (0.297 nm).
The actual distance between water molecules is usually measured as 2.9 A or 0.29 nm.
In other words, the duration of the hydronium ion is coupled to the diffusivity of the dynamics
of H
2
O.
Proton mobility in water, which is ~3.6∙10
-7
m
2
∙V
-1
∙s
-1
[3], has been shown
quantitatively to be related to the movement of photons through tissue, including the human
brain [4] through a Grotthuss chain-like effect associated with free protons.
The subtle effects of weak, extremely low frequency magnetic fields generated from the
geophysical environment within the cerebral tissue upon water containing physiological
concentrations of ions may be primarily mediated by these proton movements [5].
Recently we have shown that experimentally-induced shifts in pH between two non-
local reactions that shared weak magnetic fields (~1 µT) with specific temporal parameters for
changing, accelerating and decelerating angular velocities exhibited the conspicuous excess
correlation that has defined entanglement [6].
International Letters of Chemistry, Physics and Astronomy 2 (2014) 1-10
3
3. RELEVANCE TO AGGREGRATE PROPERTIES
Water molecules do not behave only as singular entities whose primary structure
remains remarkably stable. Large numbers of water molecules exist for short periods as
clusters whose numbers and structures depend upon ambient temperature. Flickering clusters
with durations of ~10
-11
s have been estimated to contain ~50 molecules at 20 °C and 40
molecules at 37 °C. Above 35 °C the clusters display configurations more typical of networks
[7].
The spatial order of water adjacent to hydrophilic surface areas, interfacial water, differs
remarkably from bulk water. The existence of “exclusion zones” whereby colloidal and
molecular solutes suspended in aqueous solutions are profoundly excluded from the vicinity
of the surface has been shown by Pollack and his colleagues [8]. These widths of solute free
zones were at least 100 µm in width. Within the exclusion zones there was a 10 fold increase
in viscosity. Between the exclusion zone and the bulk water the potential difference was
within the order of 100 mV (up to 150 mV). This EZ-bulk water boundary was occupied by
protons. The most conspicuous implication of these measurements was that the properties of
the exclusion zones of interfacial water might be the primary bases of living systems that has
been traditionally attributed exclusively to the plasma cell membrane. This would suggest that
the primary role of the physical lipoprotein boundary that defines the cell membrane would be
to ensure spatial-temporal stability of these functions rather than causing their occurrences.
Chai et al al [9] examined the absorption and fluorescence characteristics of aqueous
solutions of sugars, salts, and amino acids by employing UV spectroscopy and
spectrofluorometry. They found clear evidence of peak emissions of photons with
wavelengths ~270 nm within the exclusion zones adjacent to various hydrophilic surfaces.
This empirical observation is congruent with the intrinsic force associated with the product of
viscosity and the diffusivity ratio for the magnetic moment of the proton and charge
developed in the present paper.
For example, when the force (7.87∙10
-11
N) associated with the product of the viscosity
of water and the ratio of the magnetic moment to unit charge of the proton is applied across a
plasma membrane (assuming 10 nm) the energy would be 7.87 ∙10
-19
J or a frequency
equivalence, when divided by Planck’s constant (6.626∙10
-34
J∙s
-1
) of 1.19∙10
15
Hz. Assuming
c, the velocity of light in a vacuum, the peak wavelength would be ~252 nm. This is within
measurement error and statistical dispersions for the ranges of experimental temperatures that
were reported by Chai et al [9] to be emitted from exclusion zones along hydrophilic surfaces.
More precisely, if the functional width of the membrane were 9.3 nm the peak wavelength
would be ~270 nm, which was their empirical result. This solution, if valid, would couple
quantum phenomena (by Planck’s relations) to the fundamental units (the proton magnetic
moment and charge) to the wavelength of electromagnetic energy (light) emitted by water
molecules within this particular organization.
4. INTERACTIONS WITH APPLIED MAGNETIC FIELDS
Although the hydrogen bond comprises only ~5 % of the O-H bond energy it
significantly determines the interactions between water molecules and their solutes [10]. With
a typical range of 4 to 4.5 kCal (16.74 to 18.82∙10
3
J) per mole or the equivalent electrostatic
energy of between 2.75∙10
-20
J to 3.1∙10
-20
J per molecule, this means that the intrinsic energy
is a factor of 2 greater than the energy applied from intrinsic forces over the distance of two
International Letters of Chemistry, Physics and Astronomy 2 (2014) 1-10
4
O-H bonds. Although the precision of this doubling must be established, what is important is
that only about 20 hydrogen-bonded sequences of water molecules would be required to
extend the distance of the phospholipids that comprise the typical plasma membrane. Such a
“water wire” has the capacity to conduct protons [3].
The dielectric relaxation time, the temporal latency between the onset of of an electric
field and the induced polarization of water, displays a common activation energy of 4.6 Kcal
per mole. When the two H
+
that organize the polarity of water are accommodated this is
equivalent to 1.6∙10
-20
J as a quantum per hydrogen unit. Because voltage is energy divided by
charge (1.6∙10
-20
J divided by 1.6∙10
-19
A∙s), the resulting intrinsic value would be 100 mV.
This quantity is the median value for the potential difference generated between bulk water
and interfacial water that has been attributed to the shell of protons that separate the
boundaries.
The rotational relaxation time (“time constant, τ”) of water can be estimated by:
τ = 4πδa
3
(kT)
-1
(1)
where a = 9.6∙10
-11
m (0.96 A) for the length of a single O-H bond, which is the radius of that
dipole, δ is the viscosity of water, k = the Boltzmann constant and T is temperature.
The quantification is:
[(12.58) ∙ (8.94∙10
-4
Pa∙s) ∙ (9.6∙10
-11
m)
3
] ∙ [(1.38∙10
-23
J∙T
-1
) ∙ (2.98∙10
2
K)]
-1
or 2.4∙10
-12
s.
This is within the range of the life time of the hydronium ion. For comparison the
estimated time between “jumps” of a water molecule into a new position is estimated to be
~4∙10
-12
s. Stated alternatively, the relaxation time of water (when an electric field associated
with the application of an external magnetic field is considered) results in the duration of the
life time of a hydronium ion. This strongly suggests that application of magnetic energy
within a volume of water could be mediated through the ubiquitous and continuous
movements of protons through the water matrix. Integrating the rationale concerning the
nature of the cell membrane from the previous section, one would predict that the
appropriately patterned magnetic field could displace energetic wavelengths within the range
of the visible spectrum by the width of a membrane.
We have recently demonstrated this effect. Murugan et al [11] have demonstrated a
reliable and robust shift of ~10 nm in the peak fluorescent wavelength of light through 1 cc
aliquots of spring water that had been exposed, in 50 cc containers within the dark, for 18
days to weak (1 µT) magnetic fields with temporal structures that exhibit physiological
patterns and intrinsic but complex frequency modulation. This is the same field that, in
association with a second pattern, completed dissolved the aqueous flat worm: the planarian
[12]. In multiple experiments sets of three beakers were placed at the edge of an active coil,
at the edge of an inactive coil at a distance of 1 m, and in a central position between the two.
The three specific intensity ranges were high (4.4 to 11.5 µT), low (0.11 to 0.15 µT), and
medium (0.3 to 0.6 µT), respectively. In each experiment a fourth beaker (control) was placed
outside this geometry in the background intensity from ambient 60 Hz (power frequencies) of
0.1 µT.
We found that the critical temporal factor that determined the effects of this magnetic
field upon photon emissions was the duration of the point durations that determined the
sequential voltages generating the magnetic field pattern. The effect was only evident with 3
ms point durations but not with either 1 or 2 ms or 5 and 10 ms point durations. We have
International Letters of Chemistry, Physics and Astronomy 2 (2014) 1-10
5
shown previously that 3 ms point durations are very likely to be associated with the intrinsic
cosmological properties of the proton as inferred from Hubble’s parameter [13].
Employing fluorescence spectrophotometry (Ultrospec 2100 pro uv visible
spectrophotometer) with a stimulation wavelength of 250 nm we measured photon
transmission over successive 1 nm wavelengths between 250 and 500 nm. An example of
these results is shown in Figure 1. It shows the mean values of photon counts for triplicate
replications for each successive 1 nm λ between 350 and 466 nm. The 10 nm shift to the
longer wavelength occurred only in the water exposed to the < 0.3 to 0.6 µT fields but not to
the more intense strengths. At this wavelength the shift of 10 nm is equivalent to a net change
of 10
-20
J.
One interpretation is that continuous application of this magnetic field pattern to spring
water in darkness altered the intrinsic organization of the protons. This condition particularly
affected the distribution of energy from the second shell hydrogen bonds that contribute to
proton movements. If classic processes are assumed, then a shift occurred such that different
vibrational phases within the ground state were produced by the maintained exposure to the
magnetic field pattern.
That the quantitative shift in the wavelength (and intrinsic energy) reflects magnetic
energy contained within the spring water from the magnetic field exposures can be estimated
by quantification. The net increase in photon counts s
-1
for the medium intensity field was
~100 (Figure 1).
Figure 1. Photon counts from the fluorescence spectrophotometer over wavelengths through water
that had been exposed to the high, medium, and low intensity magnetic fields in darkness.
