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1 Introduction 2 Preliminary Remarks on the Biological Situation 3 Evidence of the Coherence of Biophotons 4 Biological Implications 5 Conclusions

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3 Evidence of the Coherence of Biophotons

It is well known¹⁰ that a necessary condition of coherence of an ergodic stationary electromagnetic field is the Poissonian distribution of its photocount statistics (PCS), This fact is based directly on the definition of coherent states as eigenstates of the annihilation operator.

Actually, the representation of a coherent field in terms of number states leads to the probability amplitudes <n|a>=exp(1/2|a|²) aⁿ/ where |n>, |a> are the number states and coherent states, respectively.

Consequently, if one prepares a biological system in a stationary state and measures the PCS, one is able to examine whether this necessary condition of coherence of biophotons is fulfilled or not. We started these measurements in 1981¹¹ and continued with more and more refined methods up to now. After direct methods, where we compared the measured statistical distribution with the best fit of a Poissonian distribution, we changed to measurements of the normalized factorial moments which have the advantage of being independent of special properties of the photomultiplier². As long as the normalized factorial moments of all orders keep the value 1, one can be sure that the PCS is Poissonian.

It turned out that in a quasistationary state all biological systems under study approach rather accurately a Poissonian PCS (Fig.2)¹²

Figure 2:
Agreement of the Photocount Statistics of different biological systems with a Poissonian distribution.

It is important to know whether the Poissonian distribution is only some kind of an average over the measurement time interval or whether it is valid at any instant. In the first case it could be an indication of a chaotic field which in a small time interval compared to its coherence time follows a geometrical distribution, but with increasing measurement time approaches more and more a Poissonian distribution. Consequently, in the case of a sufficiently long measurement time interval that is large compared with the coherence time of a chaotic field, one would measure a Poissonian distribution as well for a chaotic field as for a fully coherent field. Consequently, as soon as there is no knowledge about the coherence time of a chaotic field, there may be no way of distinguishing with certainty a fully coherent and a chaotic field. This was the reason why we changed the measurement time interval to rather low values and always measured the PCS.¹³ We hoped to see then the possible changes in the Poissonian distribution. As far as we have results, there is no indication that with a decreasing measurement time interval down to 10^-5 s there is a less accurate agreement to a Poissonian distribution.In fact, we found just the opposite, where with decreasing measurement time interval the normalized factorial values approached better and better values around 1 (and even lower), whereas with increasing measurement time intervals up to 10 s and more, the PCS of some amoebae had the tendency to follow a geometrical distribution.² However, because of the rather difficult procedure of keeping a biological system in a stationary state and the uncertainties of measuring at the outside but not within the living system do not allow us at present to draw final conclusions from these observations.

It is very important to find out whether the Poissonian distribution of PCS governs the system at any instant, even in a nonstationary state. In the case of a Poissonian distribution at any instant during relaxation after the system has been excited, it has been shown that the relaxation dynamics is ergodic and follows a 1/t-law, where t is the time after excitation. ^14-15 The agreement of relaxation dynamics of biophoton emission after excitation to hyperbolic (1/t) law and the disagreement to exponential decay including the validity of the Poissonian distribution at any instant are therefore sufficient conditions for a fully coherent ergodic field.^14-15 It is now accepted that all living systems display hyperbolic relaxations dynamics rather than exponential one.¹² Even the theoretically possible multi-exponential decay can be truthfully excluded by describing the relaxation function of delayed luminescence. Consequently, there is already proof of the coherence of biophotonic emission.

In order to demonstrate experimentally that the hyperbolic decay is a consequence of instantaneous Poissonian distribution during relaxation, we built a double measurement chamber with two multipliers and registered the coincidences of counts during the "delayed luminescence" of biological systems. The double chamber is built up in such a way that channel 1 measures the photon counts of a system under inverstigation in chamber 1, while channel 2 registers the counts of an other system in chamber 2. By a channel 3 the coincidence rate between channel 1 and channel 2 are registered. A photon in channel 2 is registered in channel 3 as a coincident one as soon as at least one other photon has been counted in channel 1 in a preset time interval dt before the photon counting happens in channel 2 (Fig.3).

Figure 3
Coincidence counting of biophotons, where at least one photon in channel 1 has to be registered in a time interval t<t<D t before a registered photon in channel 2.

For t=0, the number of random coincidences Zj in the j-the time interval, is then Zj = n_2j . pl(dt, n_1j>0), where n_2j is the number of counts in channel 2 within the j-th time interval dt, and p1 (dt, n_1j>0) is the probability of counting at least one photon in channel 1 in a time interval dt. Since pl(dt,n_1j>0) = 1-pl(dt,n_1j=0), where pl(dt,n_lj=0) is the probability of measuring no photon in dt in channel 1, we then have Zj = n_2j-(1-p1(dt, 0)). Consequently, by observing the delayed luminescence of a biological systern in channel 1 and another arbitrary system in channel 2, we register Zj and n_2j and are able to compare the measured value p1(dt, 0) = (1-Zj/n_2j) with the theoretical one of a Poissonian distribution which is simply p1(dt, 0) = exp (-n_1j.dt). Fig. 4a displays the result of such a measurement. It is obvious that the Poissonian distribution of PCS of a biological system is valid at any instant of the relaxation giving rise to the hyperbolic relaxation (Fig.4b) and showing evidence that the biophotons originate from a fully coherent field. On the other hand a geometrical distribution according to p1 (dt, 0) = 1/(1+ n_1j^.dt) can be truthfully excluded.

Figure 4a

Agreement of the Poissonian distribution with the PCS of biophoton emission of a leaf. The value Zj/n_2j is displayed in dependence on n_1j^.dt.

Figure 4b

Relaxation of the leaf of figure 4a, where the logarithm of the intensity is displayed versus the logarithm of the time.

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