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Introduction Basic Considerations Elements of a Theory Sucking Force Summary References

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Sucking Force

The mechanism under considerations describes the capacity of a system to use phase information in order to store and distribute energy. This process is not passive absorbance but an active process where energy is stored by constructive interference within the system against an energy gradient of removed energy at the outside. It is evident that this leads to a force which is defined by the gradient of stored to destructed energy between the inside and the outside.This force has the opposite direction to the force of the radiation pressure of the incoming wave like that of a vacuum cleaner which moves its sucking tube towards the incoming air flow instead of getting pushed away. In order to calculate this sucking force we use for simplicity the model of a cavity with a resonator value Q. It shall represent the relevant energy content of the photon sucking biological system.

Let us remind ourselves that the radiation pressure, pn_, is identical to the energy density of radiation at the surface of the incoming wave that is pn= nnhn , where nn is the spectral component of the photon density and hn the photon energy. From the spectral radiation pressure one arrives at the spectral force
 

equ. 17

of radiation pressure simply by multiplying with the surface area F which is the target of the incoming wave.
 

The photon sucking force, on the other hand, has to be assigned to the energy gradient dU/dz, where U is the relevant part of the stored energy, defined by Q times the energy flow i which, on the other hand, corresponds to the Poynting vector of the "destructive interference" outflow. Consequently we have then
 

	equ.18a
	equ.18b
where
	equ.18c

We expect consequently that for Q=1 and a double layer of a thickness of wavelength l the photon sucking force is just compensating the radiation pressure. This is, as one can see from equ. 18c actually the case. One sees that the photon sucking force exceeds the radiation pressure just by a factor of the orderA=Q times l /(D z), where D z is the thickness of the double layer. Take, for instance, the exciplexes of neighboured base pairs of the DNA as the effective double layer, we may have a strong and highly efficient photon sucking. The radiation pressure of sun rays on the earth is about 1 mp/m², corresponding to the solar constant. Take for sunrays a Q-value of 10⁶, corresponding to their coherence time t of some nanoseconds (where Q=tn ) and take for simplicity the thickness of the double layer of the order of the wavelength, then one gets a photon sucking force which is 10⁶ times higher than the radiation pressure of sun rays. This may well be the reason for the unexplained phenomenon that plants (like sunflowers) are able to turn the surface area of parts of the plants always perpendicular to the incident light. The force of 1 kp/m² is just of the correct order to move the plant into the sunlight stream. Dependent on the Q-value and the thickness of the layer, for a cell of a surface area F of about 10^-10 m² the photon sucking force for one photon is about 1.6 10^-14Ntimes A, where A is the amplification factor Ql /(D z). This force may well come into the order of known attractive forces between cells which reqire a value A of about 100 in case that there is a permanent exchange of at least one photon between neighboured cells.

Quantum Description of the Phenomenon

It is very likely that the mechanism of destructive interference by phase conjugation phenomena is based on quantum optics where one sees low intensities of biophotons. Actually, the possibility of squeezing light provides a powerful tool of fixed phase relations for adjusting light to highly polarizable matter and vice versa.

We are free to start with a boundary condition that shall define the effect of the double layer which has been introduced classically by equ.10.

We require that any two waves of amplitudes g and -g shall interfere within the two layers which establish the boundaries of the vacuum state. We express this by means of the well known displacement operator

D(g ) = exp(g a+g^*a), where a+, a are the creation operator and annihilation operator, respectively. Now, destructive interference by phase conjugation shall be defined by the following requirement:
 

equ.19

At first, let us note again that most suitable candidates for this mechanism are the exciplex states of biological matter, in particular those of the DNA. In fact, as soon as a photon excites one of the base pairs of the DNA, it gets squeezed between the two molecules which are subjects of strong Casimir forces.

Second, an immediate consequence of equ. 19 is the violation of the semigroup law (which holds for a chaotic photon field) in a way that hyperbolic relaxation takes place. We have shown in several papers [13, 17] that hyperbolic relaxation of delayed luminescence is a general property of biological systems. Straightforward calculations prove this statement of hyperbolic relaxation. Apply D(a )D(ß) to equ. 19. Then we have
 

equ.20

The l.h.s. can be reformulated to give ½(D((a +ß)/2)(D((a +ß)/2+g )+D((a +ß)/2-g )) which, after the arbitrary choice of g = + or - (a -ß)/2 results finally in
 

equ. 21

Now, let us transform D(g ) by an unitary transformation U(t,g ) into time development operator

where H is the Hamiltonian.

D(t) = U(t,g )D(g )U⁺(t,g ) which results in the corresponding equation of equ.21:
 

equ.22

In contrast to chaotic states which follow D(t₁)D(t₂) = D(t₁+t₂) and consequently are subject to an exponential decay law, equ.22 cannot be satisfied by exponential relaxation. However, hyperbolic decay following D(t) = D(0)/t fulfills exactly equ. 22, since
 

equ.23

This makes obvious that a necessary condition of photon sucking is the coherence of the field under consideration described by equ. 22 in addition to definite boundary conditions. It is worthwhile to note that this general condition 22 originating from equ.19 is already sufficient for destructive coherence of the reflected wave after phase conjugation.

Actually, any ket =/u> can be written in the form
 

equ. 24

where the operators T and R are defined according to
 

	equ. 25a
	equ.25b

In view of equ. 19 and because of R² = T, T²=T and RT=R, the first term on the r.h.s. of equ. 24 describes the penetrating part(z>0), the second term the reflected part (z<0) of the wave under examination. Straight-forward calculation shows that the expectation value of the penetrating part provides energy conservation while the expectation value of the reflected part vanishes in accordance to ideal desctructive interference. At the same time we have /u>* = -/u> for the reflected part, thus satisfying as well the condition of phase conjugation as of perfect destructive interference. It is evident that any solution can be constructed in terms of the solutions of equ. 24, describing then the basis of phase conjugation as well as of destructive and constructive interference. It is not our goal to go here into more details.

However, a combination f(a,a+)T + g(a,a+)R, may then well describe the whole process of the interaction with the double layer.

In addition we would like to say that it is very likely that the quantum description of photon sucking in biological systems requires squeezed states [18] since the flexibility in tuning the uncertainties of amplitude and phase of the electromagnetic field is a most powerful instrument of biological organization and communication. This could also explain why biophoton emission is limited to weak intensities, since only a few photons in the field allow the perfect application of non-classical light for communication.
 

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