S. M. Korotaev, V. O. Serdyuk, and M. O. Sorokin
Geoelectromagnetic Research Institute, Troitsk, Moscow Region, Russia
Received November 28, 1998
Number of the statistically reliable facts on dependencies of some observables, which can not have direct or indirect relations on the base of any known local interaction (e.g. relationship between the velocity of some physical or chemical reaction and the solar activity) have been collected in geophysics and astrophysics [Adamyan et al., 1972; Alekseenko et al., 1989; Alekseev et al., 1989; Eroshev and Sheynina, 1986; Kozyrev, 1971; Richter-Bernburg, 1963; Sazeyeva, 1986].
Kozyrev [1971] suggested interpretation of such facts within developed by him causal mechanics, based upon recognition of fundamental irreversibility of time and following a new type of physical interaction between any dissipative processes. But there was rather negative reaction to Kozyrev's hypothesis in his time because of a week formalisation of the theory and doubts in strictness of the experiments.
Recently the situation has changed. Basic statements of the concept of causal mechanics have been strictly formulated [Korotaev, 1993]. Some geophysical phenomena, e.g. asymmetry of the Earth figure, structure and distribution of physical fields have been explained quantitatively on the base of development of Kozyrev`s theory [Arushanov and Korotaev, 1996]. Kozyrev`s experiments have been successfully reproduced by Savage [1985, 1986, 1987] and though some doubt on their strictness have remained. On the other hand Home and Majumdar [1995] suggested theoretical reasons on preservations of the effect of quantum nonlocality in the strong macroscopic limit and, though an idea of experimental verification had not been proposed, the properties of the possible macroscopic nonlocality must be very similar to the Kozyrev`s interaction. Our work aims to conducting an experiment which would first verify a strictly formulated hypothesis and second fit the modern level of strictness.
Generalization of previous results of development of causal mechanics [Korotaev, 1996] might be formulated in the following statements.
(1) A new type of interaction between the dissipative processes of any nature exists.
(2) This interaction transmit the energy, the rotational moment, but not the momentum.
(3) The energy of interaction is directly related to the entropy production and inversely related to the squared distance.
(4) The interaction is screened by the matter, but the screening properties of the matter does not coincide with such properties for the electromagnetic field.
(5) The interaction can have positive, zero and symmetrical negative time lag.
With the exception of the dissipativity one can see a similarity to the quantum nonlocality. But the dissipativity may be included by interpretation of the nonlocality within Wheeler-Feynman action-at-a-distance electrodynamics [Cramer, 1995]. This theory considers the electromagnetic field as a superposition of retarded and advanced parts. The latter one is unobservable due to specific interference and is manifested only through the radiation damping which is a dissipative process. Moreover, any dissipative process is ultimately related to the radiation and therefore to the radiation damping. The third time derivative of position x appearing in the formulae for the radiation damping can be directly related to the entropy production. Indeed, for oscillating charge q the advanced field E adv is related to the retarded one E ret and radiation damping [Hoyle and Narlikar, 1995] as:
| (1) |
On the other hand, the radiation power is
 | (2) |
The entropy (dimensionless) production per a particle at a temperature T is S= P/kT and therefore
 | (3) |
One can see from (1)-(3) that advanced fields carry a relationship between the dissipative processes. Moreover according to the modern treatment of action-at-a-distance electrodynamics [Hoyle and Narlikar, 1995] the efficiency of absorption of the advanced field must be imperfect (Statement (4)). It means a possibility of advanced field detection (Statement (5)).
From the above operational consideration, it is possible to formulate the following hypothesis:
 | (4) |
where
Sd is the entropy production in the absorber
(detector),
s is the density of the entropy production in the sources,
s is the cross-section of the interaction,
x is a distance,
t is time, velocity
v is bounded by
v2 
c2, the
integral is
taken over an infinite volume
V.
The task of the experiment is the detection of connection of the entropy change in some testing process with the entropy change in the environmental medium according to (4) under condition of all known kinds of the classical local interactions. Although any dissipative process may be used as a detector, not the entropy, but one or other circumstational connected with its observable is measured. Therefore the choice of the detector type depends upon the expected value of the relative effect. Two types of the detectors had been chosen by this criterion. The first was based on measurements of self-potentials of the weekly-polarized electrodes in marine water, the second was based on measurements of the dark current of the photomultiplier. As the experiment implied, the first type turned out much more appropriate, therefore consider its work in great detail.
Self-consistent solution for the potential u in the liquid phase is [Korotaev, 1979]:
 | (5) |
where q is the charge of the main ion of the liquid phase, x is a dimensionless length ( x=1 corresponds to half of the distance between the electrodes), z is the full (electrokinetic) potential. The entropy S can be expressed in terms of the normalized potential j:
 | (6) |
 | (7) |
Substituting (3) to (6) and (5), after a number of transformations one can obtain the expression for the entropy production:
 | (8) |
where
 | (9) |
Prefactor of w is always positive, therefore from (8) and (9) it follows that S and z change in opposite phase. So far as the variations of z are small in comparison with the averaged value, one can linearize (8) and obtain final simple expression:
 | (10) |
All known local factors influencing z (temperature, pressure, chemism, illumination, electric field etc.) must be excluded or stabilized. In fact, only difference U = z1 - z2 of a pair of electrodes can be measured. Except external screening, the influence of the noise-forming factors mentioned above might be minimized by measuring U at a minimum spatial separation of the electrodes. In this case:
 | (11) |
where zc are constants, g is the efficiency of the detector, the averaged measure of which is the variability coefficient.
For the detector based on the photomultiplier analogue, U is the work function. Noise-forming factors to be excluding or control are: temperature, electric and magnetic fields, illumination, moisture, feed voltage unstability.
The experimental setup included the two types of detectors and the apparatus for accompanying measurements.
The detector based on weakly-polarized electrodes was constructed as follows. As the electrodes marine geophysical C-Mn ones were chosen. The electrodes were positioned in the glass vessel with marine water, space separation between contact windows measured 1.5 cm. The vessel was rigidly encapsulated so that evaporation as well as atmospheric pressure variations were fully eliminated. The vessel was positioned in the dewar, covered on the outside by the additional layers of light and heat insulation. For the control of the temperature variations remained the sensor of temperature (allowing to measure it continuously accurate to 0.001 K) was positioned between the internal wall of the dewar and the electrode vessel. Thus influence of all noise-forming factors, except temperature, was eliminated. Influence variation of the last was minimized and controlled. The quantity U was measured continuously with the accuracy of 0.5 m V.
The second type detector was constructed on the basis of a photomultiplier with the small-area Cb-Cs cathode. The photomultiplier was positioned in the similar dewar with the temperature sensor and the additional external electric field screen. Possible magnetic field influence was controlled by quantum modulus magnetometer accurate to 0.01 nT. The dark current I was measured continuously accurate to 0.05 nA.
Magnetic field measurement served also as indicator of the most important geophysical process - dissipation of ionospheric electric current. Lastly, the overall air temperature in the lab was recorded continuously accurate to 0.1 K. Thus measurements on the setup included 2 major channels and 4 satellite ones.
Accidentally during the part of the period of our experiment and absolutely independently, similar measurements of electrode self-potentials for other purposes were conducted by Nalivayko, who bindly presented us with his data. His setup did not provide measurements of the noise-forming factors and had no protection against them. Nonetheless, if a signal associated with the geophysical processes in U variations is sufficiently strong then, taking into account relatively small distance between the labs (300 m), one would hope for a correlation of the data.
The measurements carried out in continuous regime from December 10, 1996 till December 11, 1997.
The data were processed by the methods of causal, correlational, regressional and spectral analysis.
The first should be particularly mentioned because of its adequacy to modern treatment of theoretical foundation of the causal mechanics [Korotaev, 1993]. In essence the method is the following. For the observables X and Y the independence functions are introduced through conditional and unconditional Shannon`s entropies H:
 | (12) |
For example, if Y is one-valued function of X then iY X = 0, if Y does not depend on X then iY X = 1. Next the causality function is considered:
 | (13) |
and it determines that the cause X and effect Y are called observables for which g< 1. The case g = 1 means adiabatic (non-causal) relation between X and Y. It has been shown by theoretical and numerical experimental examples (see, for example, Korotaev [1992, 1995] and Korotaev et al. [1993]) that such a formal definition of the causality does not contradict intuitive understanding of causality in obvious situations and can be used in unobvious ones.
The important preliminary stage was to study of the temperature influence. The results are presented in [Korotaev et al., 1998], where it has been shown that besides trivial local retarded influence of the internal temperature TU, there is advanced nonlocal influence of the external temperature Te, violating a microscopic analogue of the Bell inequality. In the geophysical results described below, if it is not mentioned specially, all temperature effects had previously been rejected.
First of all, it is reasonable to compare our measurements
U with
the ones on remoted (300 m) setup
Ur. It immediately allows us to
establish, that the variations of these quantities are not merely
internal noises. A fragment of the synchronous record of
U and
Ur is shown in Figure 1. The correlation coefficient turned out
to be
0.68 
0.01. Only one common trivial cause is possible,
that is
the internal temperature. After eliminating the influence of the
internal temperature
TU of the detector
U the partial correlation
coefficient turned out to be
0.74 0.01. Therefore the local
influence of the temperature was not a common cause of the
correlated potential variations. It remains to consider such common
cause nontrivial influence of the external geophysical processes.
There is no reason to consider U depending on the magnetic field F in any way. Therefore detection of the relation of the potential with the Earth magnetic field variations would be a good test for hypothesis (4), as these variations could be easy related to electric current dissipation in the source (ionosphere). Special experiments on influence on U by artificial magnetic field (up to 100 A m -1 ) in the frequency range from 0 to 1 Hz had confirmed absence of any reaction of U within sensitivity of the apparatus.
Analysis of long-time series have shown existence of stable
correlation
rUF = -0.56
0.01 with a great advancement of
U relative to
F (t = 48.0h). In the
causal analysis at this
t there is a minimum
iF U = 0.79+0.02-0.01
(g = iU F/iF
U = 1.03+0.01-0.01). Thus relation
between
U and
F is statistically reliable, but both from the prior
reasons and advancement of
U relative to
F, it can not be a result
of a direct influence of
F on
U. Therefore
F is an indicator of
some process interacting with
U.
The spectral analysis showed that the period dependence of the amplitude ratio U/F is approximated by formula
 | (14) |
In terms of spectral densities U and F (14) turns into
 | (15) |
where
r0 = 8.5 
10-5 Wm2
and
f is the frequency.
(15) describes
1/f -noise, although we can not localize the noising
resistivity.
Whereas
U(f)/F(f) depends on frequency
f, it has turned out that
U(f)/F2(f) does not depend on
f:
U(f)/F2(f) = (1.7 0.2) 10-5
Wm2/A. It is the most
important result pointing to a
relation of
U to the entropy production.
For proof, let us consider an application of (4) to the particular case. The magnetic field F is related to the electric currents in the source (ionosphere), and also to the induced currents in the Earth. For simplicity of the problem, we neglect the latter and consider entropy production only in the source of F. It is easy to express the density of entropy production through the electric field E(f) (which in turn through impedance Z(f) is related to F(f) ), resistivity r, and medium temperature T. For the sake of simplicity we consider r and Z(f) as scalars. Then:
 | (16) |
Combining (4), (10), (11), and (16) and using for the electromagnetic field the plane wave approximation in homogeneous medium, we have:
 | (17) |
Thus the experimental fact U(f)/F2(f) = const is explained within hypothesis (4).
It is of interest to estimate the constant
s from
observations. If presented reasoning with references to Kozyrev's
concept has a meaning, the
s value could be related to known
Kozyrev's constant of course of time
c2 (velocity of the causal
effect transition at the microscopic level). From theoretical
consideration
c2 
in the classical limit, while from
causal-mechanical experiments
c2 = +(2.2 0.1) 106 m s
-1 [Kozyrev, 1977].
Since only an order of
s is of
interest on this stage, for its estimation we simplify (17),
supposing, that similarly to an ordinary electromagnetic field, it
is possible to use the plane wave approximation. Then, instead of
(17), we have
 | (18) |
where
h is a thickness of the dynamo-layer. For estimation of
s we accept the parameters corresponding to the
detector:
TU= 3 102 K,
q = 1.6 10-9A
s,
g = 6 10-2, and known typical
values of the ionospheric parameters:
T = 103 K,
h = 5 104 m.
Then
with the value
U(f)/F2(f) mentioned above we obtain from
(18)
s = 2 10-21 m
2.
It is the most reasonable value and is of an
order the atom cross-section. And really this value may be related
to
c2, mass and charge of an electron:
 | (19) |
If (19) is true, then in the classical limit
s 0.
An interesting manifestation of ionosphere activity in U variations was revealed. It turned out that the probability of sudden ionospheric disturbances during the phase decrease. The probabilities ratio is 4.5. If only sudden enhancements of atmospherics were selected such probability ratio would be 7.1.
The following qualitative interpretation of these facts may be suggested. Sudden ionospheric disturbances are sharp increase of ionization in the lower ionosphere. That corresponds to a decrease of the entropy resulting, according to (4) and (10), from increasing potentials. In the case of sudden enhancements of atmospheric there is an additional effect related to enhancements of the thunderstorm activity.
The spectral analysis showed similarity of the spectra U and solar activity indices. In particular, there is a maximum with 27-days period with the amplitude of about millivolt.
The analysis in time domain gives more detailed information. So for as time averaged solar-terrestrial data always demonstrates stronger dependence, we processed our data with daily and monthly averaging. The former were processed by the causal and correlation analysis, the latter were processed only by the correlation one (because the causal analysis needs larger statistics).
Consider daily averaged data. Figure 2 shows the synchronous
independence function
U of the solar radio wave flux
R (in the
standard range
245 
15,400 MHz) and their correlation function.
Both curves point out the optimal frequency 1415 MHz, corresponding
radiation coming from the level of the lower corona and upper
chromosphere, where the most intense electromagnetic dissipative
processes take place. At this frequency
iU R = 0.66+0.02-0.00
(g = iU R/iR
U = 0.81 0.01),
rUR = 0.68
0.02. All these series
R were reduced
to 1 AU. One can expect that the use an observable series
R instead of reduced one has to increase correlation slightly. Indeed
at a frequency of 2800 MHz for which both series of
R are available
in the "Solar-Geophysical Data", it turns out that for the reduced
R:
rUR = 0.59
0.02, while for the observable
R:
rUR = 0.62
0.02.
One can suggest the cosmic ray flux as a possible local mechanism
of the solar activity influence on the detector. We have tested it
by the data of the IZMIRAN neutron monitor, situated in the
vicinity (100 m) of our setup. Correlation of
U with the cosmic ray
counting rates turned out much less of the above mentioned
correlation
U with
R:
-0.30 0.03 under daily averaging and
-0.4 (not significant) under monthly averaging. Therefore cosmic rays do
not carry the interaction.
A maximum in dependence of
U on
R (corresponding to min
iU R) is discovered under large
advancement of
U relative to
R. For
the optimal frequency 1415 MHz min
iU R = 0.59 (and min
g = 0.71 0.01 )
at
t = 39 days. The ratio of
iU R at the advancement
t = 39 days and symmetrical retardment
t = -39 days are inverted to the ratio of
corresponding
rUR: rU R
ret / rU R adv =
rUR adv / rUR
ret = 1.3.
Monthly averaged data have demonstrated this advanced connection
even more visually. The data of
U and
R shifted to 1 month are
presented in Figure 3. Strong correlation is obvious. At
t = 1 month
rUR = 0.76
0.08. At the symmetrical value
t = -1 month the
correlation is insignificant ( 0.5 0.2 ).
Thus we have to consider influence of the solar activity on the U as a direct (nonlocal) impact with an advanced lag of about a month.
All the effects mentioned above (except of the sudden ionospheric
disturbances) were discovered also with the detector of dark
current
I, they were rather week as compared with
U. In particular,
for the magnetic variations min
iF I = 0.76+0.05-0.00, max
rFI = -0.42
0.02 occurred at
advancement
t = 35.0 hours. As this takes place, a strong
interplay
of
I and
U (which can not be reduced to a trivial influence of the
single common local cause, which is the laboratory temperature
Te )
has been discovered. It might be demonstrated by set of the partial
correlations:
rU Te = 0.78 0.01,
rUTe I =0.24 0.02,
rITe U = 0.09
0.02 (not significant).
A peculiarity of
I as an indicator of the natural dissipative
processes is that sometimes the standard deviation of
I displays
more spectacular relationship with them than the averaged
I. Figure 4
shows the amplitude spectra of the solar radio wave flux
R and
the standard deviation of
I. The left amplitude peak has the period
exactly 27 days.
The results of the long-term experiment conducted at the modern level of rigour allow us to make positive inference on the nonlocal interaction of the dissipative geophysical processes. Understanding of nonlocality as a new type of interaction may lead to understanding of nature of a number of unusual geophysical and astrophysical correlations, particularly concerning some statistically reliable, but physically unexplained solar-terrestrial relationships. The characteristic property of the nonlocal interaction is existence of an advanced time lag. It allows to develop a new method of the geophysical forecast which is not based upon an extrapolation of previous evolution. However admittedly our approach was essentially heuristic, and further development of the theory at intersection of causal mechanics, quantum nonlocality in strong macroscopic limit and action-at-a-distance electrodynamics is needed.
Adamyan, R. A., A. D. Alekseev, and N. I. Kolosnitsyn, On correlation of gravitational signals in Weber experiments with the Earth magnetic activity, Pisma Zh. Eksp. Teor. Fiz., 15 (5), 277, 1972.
Alekseenko, V. V., V. T. Sborschikov, and A. E. Chudakov, Microvariations of cosmic rays intensity and atmospheric electric field, Izv. Akad. Nauk SSSR Ser. Fiz., 48 (11), 2152, 1989.
Alekseev, E. N., et al., Correlation between phone events of LSD setup and Baxan telescope on February 23, 1987, Pisma Zh. Eksp. Teor. Fiz., 49 (9), 480, 1989.
Arushanov, M. L., and S. M. Korotaev, Geophysical effects of causal mechanics, in On the Way to Understanding the Time Phenomenon, Part 2, p. 101, World Scientific, 1996.
Cramer, J. C., Generalised absorber theory and the Einstain-Podolsky-Rosen paradox, Phys. Rev. D, 22 (2), 362, 1995.
Eroshev, M. E., and A. V. Sheynina, Fluctuations of gases output by water radiolize, J. Phys. Chem., 60 (3), 187, 1986.
Home, D., and A. S. Majumdar, Incompatibility between quantum mechanics and classical realism in the "strong" macroscopic limit, Phys. Rev. A, 52 (6), 4959, 1995.
Hoyle, F., and J. V. Narlikar, Cosmology and action-at-a-distance electrodynamics, Rev. Mod. Phys., 67 (1), 113, 1995.
Korotaev, S. M., Filtration electromagnetic field of the submarine springs, Izv. Akad. Nauk SSSR Fiz. Zemli, 8, 91, 1979.
Korotaev, S. M., On the possibility of causal analysis of the geophysical processes, Geomagn. Aeron., 32 (1), 27, 1992.
Korotaev, S. M., Formal definition of causality and Kozyrev`s axioms, Galilean Electrodynamics, 4 (5), 86, 1993.
Korotaev, S. M., Role of different definitions of the entropy in the causal analysis and its employment to electromagnetic induction in the sea currents, Geomagn. Aeron., 35 (3), 116, 1995.
Korotaev, S. M., Logic of causal mechanics: Observations-theory-experiments, in On the Way to Understanding the Time Phenomenon, Part 2, p. 60, World Scientific, 1996.
Korotaev, S. M., O. A. Hachay, and S. V. Shabelynsky, Causal analysis of the process of horizontal informational diffusion of electromagnetic field in the ocean, Geomagn. Aeron., 33 (2), 128, 1993.
Korotaev, S. M., et al., Geophysical manifestation of interaction of the dissipative process through the active properties of time, Phys. Chem. Earth, 6, 81, 1998.
Kozyrev, N. A., On the possibility of experimental investigation of properties of time, in Time in Science and Philosophy, p. 111, Academia, Prague, 1971.
Kozyrev, N. A., Astronomical observations by physical properties of time, in Flaring Stars, p. 209, Armenian Acad. Sci., Erevan, 1977.
Lavrentyev, M. M., et al., On remote influence of the stars upon the resistor, Dokl. Akad. Nauk SSSR, 314 (2), 352, 1990a.
Lavrentyev, M. M., et al., On registration of actual position of the Sun, Dokl. Akad. Nauk SSSR, 315 (2), 368, 1990b.
Lavrentyev, M. M., et al., On registration of reaction of the matter upon the external irreversible process, Dokl. Akad. Nauk SSSR, 317 (3), 635, 1991.
Lavrentyev, M. M., et al., On scanning of star sky by Kozyrev`s sensor, Dokl. Ros. Akad. Nauk, 323 (4), 649, 1992.
Richter-Bernburg, G., Influence of solar activity circles and other climatology circles on band evaporates genesis, in Problems in Paleoclimatology, p. 336, Interscience Publishers, 1963.
Sazeyeva, N. N., On correlation of the results of measurements on gravity wave detections with the geophysical factors, J. Tech., 56 (5), 741, 1986.
Savage, D., Time stress and other properties of time, The Toth-Maatian Review, 4 (2), 1899, 1985.
Savage, D., Conservation of momentum at a distance, The Toth-Maatian Review, 4, 2257, 1986.
Savage, D., Measuring local time dilation using sandglass egg timers, in Progress in Space-Time Physics, p. 242, Wesely Press, Blumberg, 1987.