Dirac Large Numbers Hypothesis - Later Developments and Interpretations

Later Developments and Interpretations

Dirac's theory has inspired and continues to inspire a significant body of scientific literature in a variety of disciplines. In the context of geophysics, for instance, Edward Teller seemed to raise a serious objection to LNH in 1948 when he argued that variations in the strength of gravity are not consistent with paleontological data. However, George Gamow demonstrated in 1962 how a simple revision of the parameters (in this case, the age of the solar system) can invalidate Teller's conclusions. The debate is further complicated by the choice of LNH cosmologies: In 1978, G. Blake argued that paleontological data is consistent with the 'multiplicative' scenario but not the 'additive' scenario. Arguments both for and against LNH are also made from astrophysical considerations. For example, D. Falik argued that LNH is inconsistent with experimental results for microwave background radiation whereas Canuto and Hsieh argued that it is consistent. One argument that has created significant controversy was put forward by Robert Dicke in 1961. Known as the anthropic coincidence or fine-tuned universe, it simply states that the large numbers in LNH are a necessary coincidence for intelligent beings since they parametrize fusion of hydrogen in stars and hence carbon-based life would not arise otherwise.

Various authors have introduced new sets of numbers into the original 'coincidence' considered by Dirac and his contemporaries, thus broadening or even departing from Dirac's own conclusions. Jordan (1947) noted that the mass ratio for a typical star and an electron approximates to 1060, an interesting variation on the 1040 and 1080 that are typically associated with Dirac and Eddington respectively. Various numbers of the order of 1060 were arrived at by V. E. Shemi-Zadah (2002) through measuring cosmological entities in Planck units. P. Zizzi (1998) argued that there might be a modern mathematical interpretation of LNH in a Planck-scale setting in the context of quantum foam. The relevance of the Planck scale to LNH was further demonstrated by S. Caneiro and G. Marugan (2002) by reference to the holographic principle. Previously, Carneiro (1997) arrived at an intermediate scaling factor 1020 when considering the possible quantization of cosmic structures and a rescaling of Planck's constant.

Several authors have recently identified and pondered the significance of yet another large number, approximately 120 orders of magnitude. This is for example the ratio of the theoretical and observational estimates of the energy density of the vacuum, which Nottale (1993) and Matthews (1997) associated in an LNH context with a scaling law for the cosmological constant. Carl Friedrich von Weizsaecker identified 10120 with the ratio of the universe's volume to the volume of a typical nucleon bounded by its Compton wavelength, and he identified this ratio with the sum of elementary events or bits of information in the universe. T. Goernitz (1986), building on Weizsaecker's work, posited an explanation for large number 'coincidences' in the context of Bekenstein–Hawking entropy. Genreith (1999) has sketched out a fractal cosmology in which the smallest mass, which he identified as a neutrino, is about 120 orders of magnitude smaller than the mass of the universe (note: this 'neutrino' approximates in scale to the hypothetical particle m_H mentioned above in the context of Weyl's work in 1919). Sidharth (2005) interpreted a typical electromagnetic particle such as the pion as a collection of 1040 Planck oscillators and the universe as a collection of 10120 Planck oscillators. The fact that a number like 10120 can be represented in a variety of ways has been interpreted by Funkhouser (2006) as a new large numbers coincidence. Funkhouser claimed to have 'resolved' the LNH coincidences without departing from the standard model for cosmology. In a similar vein, Carneiro and Marugan (2002) claimed that the scaling relations in LNH can be explained entirely according to basic principles.