„Noone has ever been able to define the difference between interference and diffraction satisfactorily. It is just a question of usage, and there is no specific, important physical difference between them.“
In physics and chemistry, the Lyman series is the series of transitions and resulting ultraviolet emission lines of the hydrogen atom as an electron goes from n ≥ 2 to n = 1 (where n is the principal quantum number referring to the energy level of the electron). The transitions are named sequentially by Greek letters: from n = 2 to n = 1 is called Lyman-alpha, 3 to 1 is Lyman-beta, 4 to 1 is Lyman-gamma, etc. The series is named after its discoverer, Theodore Lyman.
The Balmer series is particularly useful in astronomy because the Balmer lines appear in numerous stellar objects due to the abundance of hydrogen in the universe, and therefore are commonly seen and relatively strong compared to lines from other elements.
The spectral classification of stars, which is primarily a determination of surface temperature, is based on the relative strength of spectral lines, and the Balmer series in particular are very important. Other characteristics of a star can be determined by close analysis of its spectrum include surface gravity (related to physical size) and composition.
Because the Balmer lines are commonly seen in the spectra of various objects, they are often used to determine radial velocities due to doppler shifting of the Balmer lines. This has important uses all over astronomy, from detecting binary stars, exoplanets, compact objects such as neutron stars and black holes (by the motion of hydrogen in accretion disks around them), identifying groups of objects with similar motions and presumably origins (moving groups, star clusters, galaxy clusters, and debris from collisions), determining distances (actually redshifts) of galaxies or quasars, and identifying unfamiliar objects by analysis of their spectrum.
Balmer lines can appear as absorption or emission lines in a spectrum, depending on the nature of the object observed. In stars, the Balmer lines are usually seen in absorption, and they are „strongest“ in stars with a surface temperature of about 10,000 kelvin (spectral type A). In the spectra of most spiral and irregular galaxies, AGNs, H II regions and planetary nebulae, the Balmer lines are emission lines.
In stellar spectra, the H-epsilon line (transition 7-2) is often mixed in with another absorption line caused by ionized calcium known by astronomers as „H“ (the original designation given by Fraunhofer). That is, H-epsilon’s wavelength is quite close to CaH at 396.847 nm, and cannot be resolved in low resolution spectra. The H-zeta line (transition 8-2) is similarly mixed in with a neutral helium line seen in hot stars.
The Rydberg constant, symbol R∞ or RH, named after the Swedish physicist Johannes Rydberg, is a physical constant relating to atomic spectra, in the science of spectroscopy. The constant first arose as an empirical fitting parameter in the Rydberg formula for the hydrogen spectral series, but Niels Bohr later showed that its value could be calculated from more fundamental constants, explaining the relationship via his „Bohr model“. As of 2012, R∞ is the most accurately measured fundamental physical constant.
The Rydberg constant represents the limiting value of the highest wavenumber (the inverse wavelength) of any photon that can be emitted from the hydrogen atom, or, alternatively, the wavenumber of the lowest-energy photon capable of ionizing the hydrogen atom from its ground state. The spectrum of hydrogen can be expressed simply in terms of the Rydberg constant, using the Rydberg formula.
Huygens‘ principle can be seen as a consequence of the isotropy of space – all directions in space are equal. Any disturbance created in a sufficiently small region of isotropic space (or in an isotropic medium) propagates from that region in all radial directions. The waves created by this disturbance, in turn, create disturbances in other regions, and so on. The superposition of all the waves results in the observed pattern of wave propagation.
Isotropy of space is fundamental to quantum electrodynamics (QED) where the wave function of any object propagates along all available unobstructed paths. When integrated along all possible paths, with a phase factor which is proportional to the path length, the interference of the wave-functions correctly predicts observable phenomena.
„Because of the regularity of those ancient waves, there’s a slightly increased probability that any two galaxies today will be separated by about 500 million light-years, rather than 400 million or 600 million,” says Daniel Eisenstein of the Harvard-Smithsonian Center for Astrophysics, director of SDSS-III and a pioneer in baryon oscillation surveys for nearly a decade. In a graph of the number of galaxy pairs by separation distance, that magic number of 500 million light years shows up as a peak, so astronomers often speak of the “peak separation” between galaxies. The distance that corresponds to this peak depends on the amount of dark energy in the Universe. But measuring the peak separation between galaxies depends critically on having the right distances to the galaxies in the first place.
That’s where BOSS comes in. “We’ve detected the peak separation more clearly than ever before,” says Nikhil Padmanabhan of Yale University, who along with Percival co-chairs the BOSS team’s galaxy clustering group. “These measurements allow us to determine the contents of the Universe with unprecedented accuracy.
In addition to providing highly accurate distance measurements, the BOSS data also enable a stringent new test of General Relativity, explains Beth Reid, a NASA Hubble Fellow at Lawrence Berkeley National Laboratory. “Since gravity attracts, galaxies at the edges of galaxy clusters fall in toward the centres of the clusters,” Reid says. “General Relativity predicts just how fast they should be falling. If our understanding of General Relativity is incomplete, we should be able to tell from the shapes we see in BOSS’s maps near known galaxy clusters.
Reid led the analysis of these “redshift space distortions” in BOSS. After accounting for the effects of dark energy, Reid’s team found that the rate at which galaxies fall into clusters is consistent with Einstein’s predictions. “We already knew that the predictions of General Relativity are extremely accurate for distances within the solar system,” says Reid, “and now we can say that they are accurate for distances of 100 million light-years.”