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Quantum Hardware of Living Matter

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Year 2007

Fractional Quantum Hall effect in TGD framework

The generalization of the imbedding space discussed in previous posting allows to understand fractional quantum Hall effect (see this and this).

The formula for the quantized Hall conductance is given by

σ= ν× e2/h,ν=m/n.

Series of fractions in ν=1/3, 2/5 3/7, 4/9, 5/11, 6/13, 7/15..., 2/3, 3/5, 4/7 5/9, 6/11, 7/13..., 5/3, 8/5, 11/7, 14/9... 4/3 7/5, 10/7, 13/9... , 1/5, 2/9, 3/13..., 2/7 3/11..., 1/7.. with odd denominator have bee observed as are also ν=1/2 and ν=5/2 state with even denominator.

The model of Laughlin [Laughlin] cannot explain all aspects of FQHE. The best existing model proposed originally by Jain [Jain] is based on composite fermions resulting as bound states of electron and even number of magnetic flux quanta. Electrons remain integer charged but due to the effective magnetic field electrons appear to have fractional charges. Composite fermion picture predicts all the observed fractions and also their relative intensities and the order in which they appear as the quality of sample improves.

I have considered earlier a possible TGD based model of FQHE not involving hierarchy of Planck constants. The generalization of the notion of imbedding space suggests the interpretation of these states in terms of fractionized charge and electron number.

  1. The easiest manner to understand the observed fractions is by assuming that both M4 an CP2 correspond to covering spaces so that both spin and electric charge and fermion number are quantized. With this assumption the expression for the Planck constant becomes hbar/hbar0 =nb/na and charge and spin units are equal to 1/nb and 1/na respectively. This gives ν =nna/nb2. The values n=2,3,5,7,.. are observed. Planck constant can have arbitrarily large values. There are general arguments stating that also spin is fractionized in FQHE and for na=knb required by the observed values of ν charge fractionization occurs in units of k/nb and forces also spin fractionization. For factor space option in M4 degrees of freedom one would have ν= n/nanb2.

  2. The appearance of nb=2 would suggest that also Z2 appears as the homotopy group of the covering space: filling fraction 1/2 corresponds in the composite fermion model and also experimentally to the limit of zero magnetic fiel [Jain]. Also ν=5/2 has been observed.

  3. A possible problematic aspect of the TGD based model is the experimental absence of even values of nb except nb=2. A possible explanation is that by some symmetry condition possibly related to fermionic statistics kn/nb must reduce to a rational with an odd denominator for nb>2. In other words, one has k propto 2r, where 2r the largest power of 2 divisor of nb smaller than nb.

  4. Large values of nb emerge as B increases. This can be understood from flux quantization. One has eBS= nhbar= n(nb/na)hbar0. The interpretation is that each of the nb sheets contributes n/na units to the flux. As nb increases also the flux increases for a fixed value of na and area S: note that magnetic field strength remains more or less constant so that kind of saturation effect for magnetic field strength would be in question. For na=knb one obtains eBS/hbar0= n/k so that a fractionization of magnetic flux results and each sheet contributes 1/knb units to the flux. ν=1/2 correspond to k=1,nb=2 and to a non-vanishing magnetic flux unlike in the case of composite fermion model.

  5. The understanding of the thermal stability is not trivial. The original FQHE was observed in 80 mK temperature corresponding roughly to a thermal energy of T≈ 10-5 eV. For graphene the effect is observed at room temperature. Cyclotron energy for electron is (from fe= 6× 105 Hz at B=.2 Gauss) of order thermal energy at room temperature in a magnetic field varying in the range 1-10 Tesla. This raises the question why the original FQHE requires so low a temperature? The magnetic energy of a flux tube of length L is by flux quantization roughly e2B2S≈ Ec(e)meL(hbar0=c=1) and exceeds cyclotron energy roughly by factor L/Le, Le electron Compton length so that thermal stability of magnetic flux quanta is not the explanation.

    A possible explanation is that since FQHE involves several values of Planck constant, it is quantum critical phenomenon and is characterized by a critical temperature. The differences of the energies associated with the phase with ordinary Planck constant and phases with different Planck constant would characterize the transition temperature. Saturation of magnetic field strength would be energetically favored.


[Laughlin] R. B. Laughlin (1983), Phys. Rev. Lett. 50, 1395.
[Jain] J. K. Jain (1989), Phys. Rev. Lett. 63, 199.

For more details see the chapter Dark Nuclear Physics and Condensed Matter .

The photons emitted in the dropping of protons and electrons to larger space-time sheets as signature of many-sheeted space-time

The dropping of particle to a larger space-time sheet liberates energy, which is the difference of the energies of the particle at two space-time sheets. If the interaction energy of the particle with the matter at space-time sheet can be neglected the energy is just the difference of zero point kinetic energies. This energy depends on the details of the geometry of the space-time sheet. Assuming p-adic length scale hypothesis the general formula for the zero point kinetic energy can be written as

E(k)= x× E0(k) ,

E0(k)=(3/2)×(π2/mL2(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.

Could one demonstrate the existence of large Planck constant photons using ordinary camera or even bare eyes?

If ordinary light sources generate also dark photons with same energy but with scaled up wavelength, this might have effects detectable with camera and even with bare eyes. In the following I consider in a rather light-hearted and speculative spirit two possible effects of this kind appearing in both visual perception and in photos. For crackpotters possibly present in the audience I want to make clear that I love to play with ideas to see whether they work or not, and that I am ready to accept some convincing mundane explanation of these effects and I would be happy to hear about this kind of explanations. I was not able to find any such explanation from Wikipedia using words like camera, digital camera, lense, aberrations..

Why light from an intense light source seems to decompose into rays?

If one also assumes that ordinary radiation fields decompose in TGD Universe into topological light rays ("massless extremals", MEs) even stronger predictions follow. If Planck constant equals to hbar= q×hbar0, q=na/nb, MEs should possess Zna as an exact discrete symmetry group acting as rotations along the direction of propagation for the induced gauge fields inside ME.

The structure of MEs should somewhat realize this symmetry and one possibility is that MEs has a wheel like structure decomposing into radial spokes with angular distance Δφ= 2π/na related by the symmetries in question. This brings strongly in mind phenomenon which everyone can observe anytime: the light from a bright source decomposes into radial rays as if one were seeing the profile of the light rays emitted in a plane orthogonal to the line connecting eye and the light source. The effect is especially strong if eyes are stirred.

Could this apparent decomposition to light rays reflect directly the structure of dark MEs and could one deduce the value of na by just counting the number of rays in camera picture, where the phenomenon turned to be also visible? Note that the size of these wheel like MEs would be macroscopic and diffractive effects do not seem to be involved. The simplest assumption is that most of photons giving rise to the wheel like appearance are transformed to ordinary photons before their detection.

The discussions about this led to a little experimentation with camera at the summer cottage of my friend Samppa Pentikäinen, quite a magician in technical affairs. When I mentioned the decomposition of light from an intense light source to rays at the level of visual percept and wondered whether the same occurs also in camera, Samppa decided to take photos with a digi camera directed to Sun. The effect occurred also in this case and might correspond to decomposition to MEs with various values of na but with same quantization axis so that the effect is not smoothed out.

What was interesting was the presence of some stronger almost vertical "rays" located symmetrically near the vertical axis of the camera. The shutter mechanism determining the exposure time is based on the opening of the first shutter followed by closing a second shutter after the exposure time so that every point of sensor receives input for equally long time. The area of the region determining input is bounded by a vertical line. If macroscopic MEs are involved, the contribution of vertical rays is either nothing or all unlike that of other rays and this might somehow explain why their contribution is enhanced.

Addition: I learned from Samppa that the shutter mechanism is un-necessary in digi cameras since the time for the reset of sensors is what matters. Something in the geometry of the camera or in the reset mechanism must select vertical direction in a preferred position. For instance, the outer "aperture" of the camera had the geometry of a flattened square.

Anomalous diffraction of dark photons

Second prediction is the possibility of diffractive effects in length scales where they should not occur. A good example is the diffraction of light coming from a small aperature of radius d. The diffraction pattern is determined by the Bessel function

J1(x), x=kdsin(θ), k= 2π/λ.

There is a strong light spot in the center and light rings around whose radii increase in size as the distance of the screen from the aperture increases. Dark rings correspond to the zeros of J1(x) at x=xn and the following scaling law for the nodes holds true

sin(θn)= xnλ/2πd.

For very small wavelengths the central spot is almost pointlike and contains most light intensity.

If photons of visible light correspond to large Planck constant hbar= q× hbar0 transformed to ordinary photons in the detector (say camera film or eye), their wavelength is scaled by q and one has

sin(θn)→ q× sin(θn)

The size of the diffraction pattern for visible light is scaled up by q.

This effect might make it possible to detect dark photons with energies of visible photons and possibly present in the ordinary light.

  1. What is needed is an intense light source and Sun is an excellent candidate in this respect. Dark photon beam is also needed and n dark photons with a given visible wavelength λ could result when dark photon with hbar= n×q×hbar0 decays to n dark photons with same wavelength but smaller Planck constant hbar= q×hbar0. If this beam enters the camera or eye one has a beam of n dark photons which forms a diffraction pattern producing camera picture in the decoherence to ordinary photons.

  2. In the case of an aperture with a geometry of a circular hole, the first dark ring for ordinary visible photons would be at sin(θ)≈ (π/36)λ/d. For a distance of r=2 cm between the sensor plane ("film") and effective circular hole this would mean radius of R ≈ rsin(θ)≈ 1.7 micrometers for micron wavelegnth. The actual size of spots is of order R≈ 1 mm so that the value of q would be around 1000: q=210 and q=211 belong to the favored values for q.

  3. One can imagine also an alternative situation. If photons responsible for the spot arrive along single ME, the transversal thickness R of ME is smaller than the radius of hole, say of of order of wavelength, ME itself effectively defines the hole with radius R and the value of sin(θn) does not depend on the value of d for d>R. Even ordinary photons arriving along MEs of this kind could give rise to an anomalous diffraction pattern. Note that the transversal thickness of ME need not be fixed however. It however seems that MEs are now macroscopic.

  4. A similar effect results as one looks at an intense light source: bright spots appear in the visual field as one closes the eyes. If there is some more mundane explanation (I do not doubt this!), it must apply in both cases and explain also why the spots have precisely defined color rather than being white.

  5. The only mention about effects of diffractive aberration effects are colored rings around say disk like objects analogous to colors around shadow of say disk like object. The radii of these diffraction rings in this case scale like wavelengths and distance from the object.

The experimentation of Samppa using digi camera demonstrated the appearance of colored spots in the pictures. If I have understood correctly, the sensors defining the pixels of the picture are in the focal plane and the diffraction for large Planck constant might explain the phenomenon. Since I did not have the idea about diffractive mechanism in mind, I did not check whether fainter colored rings might surround the bright spot. In any case, the readily testable prediction is that zooming to bright light source by reducing the size of the aperture should increase the size and number of the colored spots. As a matter fact, experimentation demonstrated that focusing brought in large number of these spots but we did not check whether the size was increased.

For details see the chapter Dark Nuclear Physics and Condensed Matter.

Burning salt water with radio waves and large Planck constant

This morning my friend Samuli Penttinen send an email telling about strange discovery by engineer John Kanzius: salt water in the test tube radiated by radiowaves at harmonics of a frequency f=13.56 MHz burns. Temperatures about 1500 K which correspond to .15 eV energy have been reported. You can radiate also hand but nothing happens. The orginal discovery of Kanzius was the finding that radio waves could be used to cure cancer by destroying the cancer cells. The proposal is that this effect might provide new energy source by liberating chemical emergy in an exceptionally effective manner. The power is about 200 W so that the power used could explain the effect if it is absorbed in resonance like manner by salt water.

The energies of photons involved are very small, multiples of 5.6× 10-8 eV and their effect should be very small since it is difficult to imagine what resonant molecular transition could cause the effect. This leads to the question whether the radio wave beam could contain a considerable fraction of dark photons for which Planck constant is larger so that the energy of photons is much larger. The underlying mechanism would be phase transition of dark photons with large Planck constant to ordinary photons with shorter wavelength coupling resonantly to some molecular degrees of freedom and inducing the heating. Microwave oven of course comes in mind immediately.

  1. The fact that the effects occur at harmonics of the fundamental frequency suggests that rotational states of molecules are in question as in microwave heating. Since the presence of salt is essential, the first candidate for the molecule in question is NaCl but also HCl can be considered. The basic formula for the rotational energies is

    E(l)= E0×(l(l+1), E0=hbar2/2μR2. μ= m1 m2/(m1 +m2).

    Here R is molecular radius which by definition is deduced from the rotational energy spectrum. The energy inducing transition l→l+1 is ΔE(l)= 2E0×(l+1).

  2. By going to Wikipedia, one can find molecular radii of heteronuclear di-atomic molecules such as NaCl and homonuclear di-atomic molecules such as H2. Using E0(H2)=8.0×10-3 eV one obtains by scaling

    E0(NaCl)= (μ(H2/μ(NaCl)) × (R(H2)/R(NaCL)2.

    The atomic weights are A(H)=1, A(Na)=23, A(Cl)=35.

  3. A little calculation gives f(NaCl)= 2E0/h= 14.08 GHz. The ratio to the radiowave frequency is f(NaCl)/f= 1.0386×103 to be compared with the hbar/hbar0=210=1.024×103. The discrepancy is 1 per cent.

Thus dark radiowave photons could induce a rotational microwave heating of the sample and the effect could be seen as an additional dramatic support for the hierarchy of Planck constants. There are several questions to be answered.

  1. Does this effect occur also for solutions of other molecules and other solutes than water? This can be tested since the rotational spectra are readily calculable from data which can be found at net.

  2. Are the radiowave photons dark or does water - which is very special kind of liquid - induce the transformation of ordinary radiowave photons to dark photons by fusing 210 radiowave massless extremals (MEs) to single ME. Does this transformation occur for all frequencies? This kind of transformation might play a key role in transforming ordinary EEG photons to dark photons and partially explain the special role of water in living systems.

  3. Why the radiation does not induce spontaneous combustion of living matter which contains salt. And why cancer cells seem to burn: is salt concentration higher inside them? As a matter fact, there are reports about spontaneous human combustion. One might hope that there is a mechanism inhibiting this since otherwise military would be soon developing new horror weapons unless it is doing this already now. Is it that most of salt is ionized to Na+ and Cl- ions so that spontaneous combustion can be avoided? And how this relates to the sensation of spontaneous burning - a very painful sensation that some part of body is burning?

  4. Is the energy heating solely due to rotational excitations? It might be that also a "dropping" of ions to larger space-time sheets is induced by the process and liberates zero point kinetic energy. The dropping of proton from k=137 (k=139) atomic space-time sheet liberates about .5 eV (0.125 eV). The measured temperature corresponds to the energy .15 eV. This dropping is an essential element of remote metabolism and provides universal metabolic energy quanta. It is also involved with TGD based models of "free energy" phenomena. No perpetuum mobile is predicted since there must be a mechanism driving the dropped ions back to the original space-time sheets.

Recall that one of the empirical motivations for the hierarchy of Planck constants came from the observed quantum like effects of ELF em fields at EEG frequencies on vertebrate brain and also from the correlation of EEG with brain function and contents of consciousness difficult to understand since the energies of EEG photons are ridiculously small and should be masked by thermal noise.

In TGD based model of EEG (actually fractal hierarchy of EEGs) the values hbar/hbar0 =2k11, k=1,2,3,..., of Planck constant are in a preferred role. More generally, powers of two of a given value of Planck constant are preferred, which is also in accordance with p-adic length scale hypothesis.

For details see the chapter Dark Nuclear Physics and Condensed Matter.

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