E(k)= x× E0(k) ,
Here x is a numerical factor taking into account the geometry of the space-time sheet and equals to x=1 for cubic geometry.
The liberated zero point kinetic energy in the case that the particle drops to a space-time sheet labelled by kf=k+Δ k with same value of x is
ΔE(k,Δk)=x× E0(k)×(1-2-Δ k) .
The transitions are seen as discrete lines for some resolution Δ k≤Δ kmax. At the limit k→ ∞ transitions give rise to a quasicontinuous band. The photon energy for k→ ∞ transition is same as the energy from k-1→ k transition, which brings in additional option to the model building.
For a proton dropping from the atomic space-time sheet k=137 to very large space-time sheet (Δ k→ ∞) one has ΔE(k)= E(k)≈ x× .5 eV. Since the ratio of electron and proton masses is mp/me≈ .94× 211, the dropping of electron from space-time sheet ke=kp+11 liberates zero point kinetic energy which is by a factor .9196 smaller. For kp=137 one would have ke= 148. This energy corresponds to the metabolic energy currency of living systems and the idea is that the differences of zero point kinetic energies define universal metabolic energy currencies present already in the metabolism of pre-biotic systems. In the following fit electron's zero point kinetic energy will be taken to be E0(148)=.5 eV so that for proton the zero point kinetic energy would be E0(137)=.544 eV.
The hypothesis predicts the existence of anomalous lines in the spectrum of infrared photons. Also fractally scaled up and scaled down variants of these lines obtained by scaling by powers of 2 are predicted. The wavelength corresponding to .5 eV photon would be λ= 2.48 μm. These lines should be detectable both in laboratory and astrophysical systems and might even serve as a signature for a primitive metabolism. One can also consider dropping of Cooper pairs in which case zero point kinetic energy is scaled down by a factor of 1/2.
Interestingly, the spectrum of diffuse interstellar medium exhibits three poorly understood structures: Unidentified Infrared Bands (UIBs), Diffuse Interstellar Bands (DIBs), and Extended Red Emission (ERE) allowing an interpretation in terms of dropping of protons or electrons (or their Cooper pairs) to larger space-time sheets. The model also suggests the interpretation of bio-photons in terms of generalizes EREs.
1. Unidentified Infrared Bands
Unidentified infrared bands (UIBs) contain strong bands at λ=3.3, 6.2, 11.3 microns. The best fit for the values of k and Δk assuming dropping of either electron or proton are given by the following table. The last row of the table gives the ratio of predicted photon energy to the energy characterizing the band and assuming x=1 and E0(148,e)=.5 eV. Discrepancies are below 8 per cent. Also the dropping of protonic Cooper pair from k=137 space-time sheet could reproduce the line Δ E= .2 eV. The fit is quite satisfactory although there is of course the uncertainty related to the geometric parameter x.
Table 1 .
According to this article, UIBs are detected along a large number of interstellar sight-lines covering a wide range of excitation conditions. Recent laboratory IR spectra of neutral and positively charged poly-cyclic aromatic hydrocarbons (PAHs) has been successfully used by Allamandola to model the observed UIBs (L. J. Allamandola, M. P. Bernstein, S.A. Sandford (1997), in Astronomical and biochemical origins and the search for life in the universe, Ed. C.B Cosmovici, S. Bowyer, D. Wertheimer, pp. 23-47, Editrice Compositori, Bologna.). It is believed that PAHs are produced in reactions involving photosynthesis and are regarded as predecessors of biotic life (see this). This would conform with the presence of metabolic energy quanta.
DNA sugar bone, some aminoacids, and various hallucinogens involve 5- and 6-cycles and the proposal is that these cycles involve free electron pairs, which possess Planck constant hbar= n×hbar0, n=5, 6. These free electron pairs would explain the anomalous conductivity of DNA and would be an essential characteristic of living matter. The emergence of n=5,6 levels could be seen as the first step in the pre-biotic evolution.
2. Diffuse Interstellar Bands
There are diffuse interstellar bands (DIBs) at wavelengths 578.0 and 579.7 nanometers and also at 628.4, 661.4 and 443.0 nm. The 443.0 nm DIB is particularly broad at about 1.2 nm across - typical intrinsic stellar absorption features are 0.1 nm (see this). The following table proposes a possible identification of these lines in terms of differences of zero point kinetic energies. Also now the best fit has errors below 7 per cent.
Table 2 .
The peak wavelengths in chlorophyll and photosynthesis are around 650 nm and 450 nm and could correspond to second and third row of the table. 3. The Extended Red Emission
The Extended Red Emission (ERE) (see this and this) is a broad unstructured emission band with width about 80 nm and located between 540 and 900 nm. The large variety of peak wavelength of the band is its characteristic feature. In majority of cases the peak is observed in the range 650-750 nm but also the range 610-750 nm appears. ERE has been observed in a wide variety of dusty astronomical environments. The necessary conditions for its appearance is illumination by UV photons with energies E≥ 7.25 eV from source with T≥ 104 K. The position of the peak depends on the distance from the source .
According to the current interpretation attributes ERE to a luminescence originating from some dust component of the ISM, powered by UV/visible photons. Various carbonaceous compounds seem to provide a good fit to the observational constraints. However, the real nature of ERE is still unknown since most candidates seem to be unable to simultaneously match the spectral distribution of ERE and the required photon conversion efficiency.
a) Consider first the band 650-750 nm appearing in the majority of cases. The most natural interpretation is that the lower end of the band corresponds to the zero point kinetic energy of electron at k=135+11=146=2× 73 space-time sheet. This would mean that the lines would accumulate near 650 nm and obey the period doubling formula
[(λ(k)-λ(∞)]/λ(∞)= 2-k/(1-2-k) .
By the estimate of Table 2 the lower end should correspond to λ=628.4 nm with a correction factor x< 1 reducing the zero point kinetic energy. The reduction would be smaller than 4 per cent. Δk=3 transition would correspond to 744 nm quite near to the upper end of the band. For Δk=2 transition one has λ=867 nm not to far from the upper end 900 nm. Δk=1 corresponds to 1.3 μm.
b) For proton with k=135=146 the energy band would shift by the factor 211me/mp≈ 1.087 giving the range (598,690) nm.
c) The variation for the position of the peak can be understood if the charged particles at the smaller space-time sheet can have excess energy liberated in the dropping to the larger space-time sheet. This excess energy would determine the position of the lower end of the band in the range (540,650) nm.
d) One should also understand the role of UV photons. UV photon with energy E≥ 8 eV could kick electrons from large space-time sheets to k=144=146-4 space-time sheet where they have zero point kinetic energy of 8 eV plus possible additional energy. One possibility is that these electrons drop first to k=145 by the emission of ≈ 4 eV UV photon and then to k=144 by the emission ≈ 2 eV photon corresponding to 650 nm line. The further dropping to larger space-time sheets would produce besides this line also the lines with longer wavelengths in the band.
4. Could UV photons have some metabolic role?
The correlation between UV photons and ERE brings in mind the vision that high temperature plasmoids are primitive life-forms possibly having universal metabolic energy quanta in UV range. One can imagine that the development of chemical energy storage mechanisms has made it possible to use visible light from Sun as a source of metabolic energy and get rid of UV quanta having disastrous biological effects. Ozone layer shields out most of UV light and also air absorbs the UV light below wavelength 200 nm, which justifies the term vacuum UV (VUV) for this range.
Table 3 .
From Table 3 one finds that Δk >2 electronic transitions cascading to 8 eV (155 nm) by period doubling belong to vacuum UV (VUV) absorbed by air. The lines 310 nm and 207 nm corresponding to Δk=1 and Δk=2 could however define frequency windows since these lines need not correspond to any atomic or molecular electronic transitions.
In the solar photosphere the temperature is about 5800 K, roughly half of the minimum temperature 104 K needed to generate the UV radiation inducing ERE in interstellar dust. Solar corona however has temperature of about 106 K, which corresponds to a thermal energy of order 100 eV and the UV radiation from corona at above mentioned discrete frequencies resulting in dropping of electrons could serve as a metabolic energy source for pre-biotics in the interstellar space. This raises obvious questions. Should the stellar sources inducing ERE possess also corona? Could 4 eV and 6 eV UV photons from the solar corona serve as a source of metabolic energy for some primitive organisms like blue algae?
5. What about bio-photons?
Also the wave length of bio-photons are in the range of visible photons. Their spectrum is claimed to be featureless, which would suggest that identification in terms of photons resulting in dropping of electrons and protons to larger space-time sheets might not make sense. The variation of the geometric shape of space-time sheets, the possibility of surplus energy, and the clustering of the transition lines around the lower end of wave length spectrum might however give rise to effectively featureless spectrum.
For details see the chapter About the New Physics Behind Qualia of "Quantum Hardware Of Living Matter".