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Introduction Coherent State Approach to Biophotons The Cancer Problem Acknowledgements References

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As has been demonstrated by several groups, cancer tissues

• display in general higher intensities of both biophoton emission and delayed luminescence [1, 2, 11, 12],
• show a shorter relaxation time of delayed luminescence [2],
• change from hyperbolic relaxation for normal cell populations to an exponential one for tumor cells [13],
• lose the capacity for oscillatory relaxation in cases where the normal tissue exhibits distinct oscillations during delayed luminescence [2].

All these features are understandable in terms of eq.(18) as a consequence of the transition from coherent to chaotic states of the biophoton field. Actually, number states become eigenstates of the Hamiltonian as soon as  and the non-diagonal elements of  disappear. The total energy is then stored in a rather higher photon number than in the case of coherent states. Consequently, the transition from coherent to chaotic states has to be accompanied by an increase of photons provided that possible energy loss in the case of cancer development does not over-compensate this increase of photon number. Second, in contrast to coherent states which relax according to a hyperbolic function, chaotic states are subject to exponential decay under just the same ergodic conditions.

The relaxation time then is smaller with respect to the lack of reabsorbance during the phase of emission, caused by -terms. It is evident that under these conditions the non-diagonal elements (where  are number states. This means that the oscillations disappear.

In order to display a concrete and impressive example, let us discuss the problem of chemical carcinogenesis. Several polycyclic hydrocarbons have been investigated to find correlations between electronic properties and their carcinogenic activity. These compounds are most interesting, since they are chemically rather inert, and there is reason to believe that the mother-substances are at the same time the "ultimate carcinogens" which do not require metabolism into epoxides for inducing cancer in the case that they are carcinogenic at all.

Some years ago we showed a highly significant correlation [14] between the transition momenta of electronic states of these compounds (eq.21), i.e. the second lowest singlet state of an energy of 3.25 eV and a transition to the lowest singlet state at an energy of about 3.10 eV (Fig.1).
 
 
 

(21)

are resonance energies in the UV- and IR- range respectively,  are the corresponding transition momenta and  are the life-times of the transitions i®l, with k a proportionality constant.

Figure 1.
The couplings f_jk in resonance regions are decisive for the biological effects of compounds. For carcinogenic polycyclic hydrocarbons a strong correlation can be found between optical transitions E₀₂ of about 3.25 eV and E₂₁ of about 0.15 eV.

Both these states are in the range of singlet- triplet- transitions, but also exciplex- or dimer- transitions of the DNA. Tables 1a-f display the correlations between the electronic features of these compounds and their carcinogenic activities. All compounds - with the exception of TCQ - have been selected according to the original work of Pullmans [15], who tried to find correlations between the capacity of metabolic transformation into epoxides and carcinogenic power. It should be noted that Pullmans' correlation is rather insignificant. TCQ has been added to this list since it is known that it is not metabolised despite its belonging to the most efficient carcinogenic substances. The interpretation of this correlation is easy. It is well known that photorepair has a high activity in the range of 3.25eV (corresponding to about 380 nm). Taking the case that biophotons of this energy, around 380 nm, work permanently for photorepair, of modes around 380nm should work then with high efficiency for repair, leading to stabilisation of coherent states. At the same time there should be a strong coupling  between k-modes around 3.25 eV and j-modes around 3.1 eV, since the energy difference 0.15 eV can be devoted to a carrier wave which may stabilise the coherence and the transport of signals within the dimension of a cell. Actually, the wavelength of 0.15 eV fits the size of a cell. Consequently, the coupling might play a rather decisive role for cancer induction and growth regulation as soon as k is in the UV-range (at about 3.25 eV) and j in the infrared ( at about 0.15 eV). Actually, as long as , the coherence is conserved, as can be seen from eq.(18). However, as soon as an imbalance  becomes chronic, the transition to number states is unavoidable. Actually, for,  according to eq.(18) contains only real numbers such that there is no change of  However, for  we get a chronic overshoot or undershoot of coherent photons which can be expressed in terms of an additional operator

, where  is the difference .

As a consequence,  of eq.(10) deviates from the norm of 1 according to

(22)

which is a real quantity , as long as and  are not in phase.  is a measure of the deviation from perfect coherence.

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