Laue: right or wrong?

Abstract

In 1912, Laue spots were discovered in x-ray scattering 'photograms' of crystals, which were amongst the most consequential experimental findings of the 20th century. Inter alia, spots established the x-ray waves and crystal lattice; plus, for the first time ever, revealed atoms as real physical objects. Laue, a protégé of Planck and a wave-optics expert, had theoretically predicted these spots, and promptly won the Physics Nobel Prize for 1914. The prize did not come easy: executing his experimentum cruces, over the judgments of Sommerfeld and Wien, required force of will and a certain amount of diplomacy. Besides, his explanation for missing spots and x-ray diffraction were proven wrong by Moseley, Darwin and the two Braggs. Traditionally, Laue's three-dimensional diffraction model is reconciled with Bragg's reflection formula by Ewald's construction using reciprocal lattice space. Laue had overlooked that his fundamental equations violate Euclidean length invariance. This article shows that implementation of invariance consolidates Laue's system of three (multi-parameter) equations into a single formula containing one integer, one angle and two distances; plus validating Bragg's conjecture of reflection. This new derivation demonstrates that the mechanism of Laue spots is akin to the anti reflection coating the colour-plays in soap bubbles and oil slicks-reflection and interference not diffraction. Yet, Laue stimulated countless breakthroughs: Nobel Prizes and scientific innovations, with an enduring legacy of inspiration a century later.

The Imperatives in Atomic Structure Analyses: Lessons from Three- Dimensional Diffraction Gratings, Specular Reflection and Quasi- Crystals

“…In 1925 Alver Gullstrand, Chairman of the Royal Swedish Academy of Sciences would declare [11], " This epoch-making discovery [Laue spots], which not only bore upon the nature of X-radiation and the reality of the space lattice assumed in crystallography, but also placed a new means of research into the hands of Science …". Paradoxically, although Max Laue anticipated the 'Laue effect', but his new 3-dimensional vector diffraction theory had some serious flaws [12]. As a matter of fact, this theory shockingly misinterpreted the observed patterns.…”

“…Incredibly, it was Max Laue's own 3-d diffraction grating theory that was problematic and consequently failed to interpret Friedrich and Knipping's experimental data [12]. As a matter of fact simultaneously satisfying the dispersive equations along all the three Cartesian axes was overwhelming and Laue's results came out erroneous, including a wrong answer for the crystal density!…”

“…As a matter of fact simultaneously satisfying the dispersive equations along all the three Cartesian axes was overwhelming and Laue's results came out erroneous, including a wrong answer for the crystal density! Incidentally, Laue was aware of some of the problems with his theory, because in his Nobel lecture he stated, " … the three specified numbers… I made no secret of the fact that I could not attribute to these values the same degree of reliability…" But Max Laue did not realize that he did not properly constrained the system of equations and lacked Euclidean length invariance; so the theory was producing too many solutions [12]. As a matter of fact, it is not generally known that Euclidean geometry and dimensionality of the space-time have a significant influence on what physical phenomena are permissible; vector product and Huygen's principle for wave are two classic peculiarities of 3+1 dimensional space-time [15].…”

“…In equation 5, wave dispersion is effective only along dB a direction perpendicular to the planes. Freed from the direct considerations of 3-dimensional lattice periodicity, Bragg's law also dispenses of Laue's desperate conjectures including the infamous 'missing spot' proposal, invoked to interpret the patterns recorded by Friedrich and Knipping [12]. Unsurprisingly Bragg's formula is computationally frugal.…”

The Janus Called Citizen Scientist a Closer Look

“…Interestingly, ever since the Hellenic times pure science has had no masters and occupied the reserved position on top of the pedestal marked 'knowledge for the sake of knowledge' [3]. In contrast, because it may never violate any laws of science plus neither shall it transgress the laws of the society that creates it, technology serves many a master.…”