**Basic ideas about refraction**

Absorption, reflection, and refraction are basic phenomena of geometric optics describing the propagation of light in terms of light rays and neglecting interference and diffraction making it possible for light to "go around the corner". The properties of medium are described in terms of refraction index n which in general is a complex quantity. The real part of n gives the phase velocity of light in medium using vacuum velocity c as unit, which - contrary to a rather common misconception - can be also larger than c as a phase velocity which cannot be assigned to energy transfer. The imaginary part characterizes absorption. n depends in general on frequency of the incoming light and the resonant interactions of light with the atoms of medium make themselves manifest in the frequency dependence of n - in particular in absorption described by the imaginary part of n.

What happens at the boundary of two media - reflection or refraction - is characterized the the refraction index boundary conditions for radiation fields at the boundary, which are essentially Maxwell's equations at the discontinuity. Snell's law tells what happens to the direction of the beam and states essentially that only the momentum component of incoming photon normal to the boundary changes in these processes since only the translational symmetry in normal direction is changed.

**How refractive index is determined?**

What determines the index of refraction? To build a microscopic theory for n one must model what happens for the incoming beam of light in medium. One must model the scattering of light from the atoms of the medium.

In the case of condensed matter X ray diffraction is excellent example about this kind of theory. In this case the lattice structure of the condensed matter system makes the situation simple. For infinitely large medium and for an infinitely wide incoming beam the scattering amplitude is just the Fourier transform of the density of atoms for the change of f the wave vector (or equivalently momentum) of photon, which must be a vector in the resiprocal lattice of the crystal lattice. Therefore the beam is split into beams in precisely defined directions. The diffracted beam has a sharp maximum in forward direction and the amplitude in this direction is essentially the number of atoms.

In less regular situation such as for water or bio-matter for which regular lattice structure typically exists only locally the peaking to forward direction, is even more pronounced, and in the first approximation the beam travels in the direction that it has after entering to the system and only the phase velocity is changed and attenuation takes place. Diffraction patterns are however present also now and allow to deduce information about the structure of medium in short length scales. For instance, Delbrueck diffraction from biological matter allowed to deduce structural information about DNA and deduce its structure.

This description contains an important implicit assumption. The width and length of the incoming photon beam must be so large that the number of atoms inside it is large enough. If this condition is not satisfied, the large scale interference effects crucial for diffraction do not take place. For very narrow beams the situation approaches to a scattering from single atom and one expects that the beam is gradually widened but that it does not make sense to speak about refraction index and that the application of Snell's law does not make sense. Incoming photons see individual atoms rather than the lattice of atoms. For this reason the prevailing wisdom has been that it does not make sense to speak about bending of gamma rays from solid state. A gamma ray photon with energy of one MeV corresponds to a wavelength λ of about 10^{-12} meters which is of same order as electron Compton length. One expects that the width and length of gamma ray beam is measured using λ as a natural unit. Even width of 100 wavelengths corresponds to 1 Angstrom which corresponds to the size scale of single atom.

**Surprise**

The real surprise was that gamma rays bend in prisms made from silicon! The discovery was made by a group of scientists working in Ludwig-Maximilians-Universität in Munich. The group was led by Dietrich Habs. The article about the discovery is also published in Phys Rev Lett May 3 issue. The gamma ray energies where in the range .18-2 MeV. The bending known as refraction was very small using every day standards. The value of the refractive index which gives the ratio c/v for light velocity c to the light velocity v in silicon is 1+10^{-9} as one learns from another popular article. When compared to the predictions of the existing theory, the bending was however anomalously large. By the previous argument it should not be even possible to talk about bending.

Dietrich Habs suggests that so called Delbrueck scattering of gamma rays from virtual electron positron pairs created in the electric fields of atoms could explain the result (see this). This scattering would be diffraction (scattering almost totally in forward direction as for light coming through a hole). This cannot however give rise to an effective scattering from a many-atom system unless the gamma ray beam is effectively or in real sense scaled up. The scattering would be still from single atom or even part of single atom. One could of course imagine that atoms themselves have hidden structure analogous to lattice structure but why virtual electron pairs could give rise to it?

In the following I discuss two TGD inspired proposals for how the diffraction that should not occur could occur after all?

**Could gamma rays scatter from quarks?**

There is another strange anomaly that I discussed for a couple of years ago christened as the incredibly shrinking proton. It was found that protons charge distribution deviates slightly from the expected one. The TGD inspired explanation was based on the observation that quarks in proton are rather light having masses of 5 and 20 MeV. These correspond to gamma ray energies. Therefore the Compton wave lengths of quarks are also rather long, much longer than the Compton length of proton itself! Parts would be larger than the whole! The explanation for this quantum mystical fact would be that the Compton length corresponds to length scale assignable to color magnetic body of quark. Could it be that the scattering gamma rays see the magnetic bodies of 3× 14 = 42 valence quarks of 14 nucleons of Si nucleus. The regular structure of atomic nucleus as composite of quark magnetic would induce the diffractive pattern. If so, we could do some day nuclear physics and perhaps even study the structure of proton by studying diffraction patterns of gamma rays on nuclei!

**Could part of gamma beam transform to large hbar gamma rays?**

Also the hierarchy of Planck constants comes in mind. Scaling of hbar for a fixed photon energy scales up the wavelength of gamma ray. Could some fraction of incoming gamma rays suffer a phase transition increasing their Planck constant? The scaling of Planck constant make gamma rays to behave like photons with scaled up wavelength. Also the width of the beam would be zoomed up. As a result the incoming gamma ray beam would see a group of atoms instead of single atom and for a large enough value of Planck constant one could speak of diffraction giving rise to refraction.

For years ago I considered half jokingly the possibility that hierarchy of Planck constants could imply quantum effects in much longer scales than usually (see this). Diffraction would be a typical quantum effect involving interference. Perhaps even the spots seen sometimes in ordinary camera lense could be analogous to diffractive spots generated by diffraction of large hbar visible photons through a hole (they should usually appear in the scale of visible wavelength about few microns, see this). Take this as a joke!

I also proposed that strong classical em fields provide the environment inducing increase of Planck constant at some space-time sheets. The proposal was that Mother Nature is theoretician friendly (see this). As perturbation expansion in powers of 1/hbar fails, Mama Nature scales up hbar to make the life of her theorizing children easier;-). Strong electric and magnetic fields of atomic nuclei believed by Habs to be behind the diffraction might provide the manner to generate large Planck constant phases and dark matter.

## 3 comments:

Your remark on quark wavelengths is very interesting. JC Slater thought nuclei constantly exchange radiation, but Bohr did not want him to pursue the idea, and he walked out. So we stumble on with much loose talk about "delocalization", "correlated electrons" and isospin.

Astrophysicists take the electron wave to be operative in the photoelectric effect, and will take the same line with electron-positron scattering. A source in the nucleus does not mean the effect is restricted there. One could say the same for quarks.

As I said at the outset, I'm interested in measure theory. From Cartan's Corner, the site for TTD: http://www22.pair.com/csdc/car/carhomep.htm. Relying on sympletics and separable Hilbert representation, you have their T2 topology. But the strictly topological distinctions are T0, with Kolmogorov's automorphisms and entropy of predictability. And there's also the rogue not-T0 category, which haunts the boundary of the observable.

As Louis Althusser notoriously said, "The system is overdetermined and contradictory." Hence Plato's dialectic, "politics as usual". But we owe distinctions in geometry to Leon of Byzantium, where the herbal of Dioscourides was remembered.

Kähler automorphisms come with all kinds of strings attached. Here's a direct lead on Hamed's question that gives regularization, stringiness and self-duality (so quarks of proton can equal proton of quarks).

http://arxiv.org/abs/hep-th/9906028

Dear Matti

would it be possible to use silicon dusts to scatter the gamma ray produced by ( or coming out from ) earth faults?

I am working on a project " frequent accidents spot" in Hong Kong

regards

Owen Chow

+852-92728777

owenchow@bestset.org

owenchow1@gmail.com

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