Dirac's Large Numbers Hypothesis Research Articles

Drake equation of search for extraterrestrial intelligence: A proposal for modification in the light of Dirac’s large number hypothesis

In the light of Dirac’s Large Number Hypothesis (LNH), we try to relate the Drake equation with the extra-terrestrial intelligence (ETI), specifically in terms of cognitive science. This argument has been drawn from the ratio of smallest time scale (i.e. 40[Formula: see text]Hz oscillation in neuronal system of brain) to the smallest timescale (i.e. the Planck time in the present universe) which provides a very large dimensionless number [Formula: see text]. Under this LNH, we emphasize on the issue of the alien equation of Drake and provide a modified version of it by considering consciousness of the ETI. Thus, the Drake equation, which basically represents a statistical conjecture with random and arbitrary values, can be related with a feasible as well as applicable background philosophy.

Universality of minimal length

We present an argument reinterpreting the generalized uncertainty principle (GUP) and its associated minimal length as an effective variation of Planck constant (ħ), complementing Dirac's large number hypothesis of varying G. We argue that the charge radii (i.e. the minimal length of a scattering process) of hadrons/nuclei along with their corresponding masses support an existence of an effective variation of ħ. This suggests a universality of a minimal length in measurement of scattering process. Varying ħ and G explains the necessity of Von Neumann entropy correction in Bekenstein-Hawking entropy-area law. Lastly, we suggest that the effective value of ħ derived from various elements may be related to the epoch of their creation via nucleosynthesis.

Deformed special relativity with an invariant minimum speed as an explanation of the cosmological constant

This paper shows the need of the emergence of a universal minimum speed in the space-time by means of a more thorough investigation of Dirac's large number hypothesis (LNH). We will realize that there should be a minimum speed $V$ with the same status of the invariance of the speed of light $c$, however $V$ has gravitational origin. Hence, such a minimum speed forms a new kinematic basis in the space-time, thus leading to a new Deformed Special Relativity (DSR) for the quantum world so-called Symmetrical Special Relativity (SSR). Furthermore, we will show that such a new structure of space-time (SSR) reveals a connection between $V$ and a preferred reference frame $S_V$ of background field that leads to the cosmological constant $\Lambda$, which can be associated with a cosmological anti-gravity. We will also investigate the effect of the number of baryons $N$ (Eddington number) of the observable universe on the Hydrogen atom. Finally, we will show that SSR-metric plays the role of a de-Sitter (dS)-metric with a positive cosmological constant, which could assume a tiny value.

Dirac's large number hypothesis: A journey from concept to implication

Large dimensionless numbers, arising out of ratios of various physical constants, intrigued many scientists, especially Dirac. Relying on the coincidence of large numbers, Dirac arrived at the revolutionary hypothesis that the gravitational constant [Formula: see text] should vary inversely at the cosmic time [Formula: see text]. This hypothesis of Dirac, known as the Large Number Hypothesis (LNH), sparked off many speculations, arguments and new ideas in terms of applications. Works done by several authors with LNH as their basic platform are extensively reviewed in this work. Relationship between some of those works are pointed out here elaborately. Possibility of time variations of physical constants other than [Formula: see text] as well as large numbers in various realm of physical and biological sciences are also discussed.

Cosmological constant decaying with CMB temperature

Recent observations of the dark energy density have demonstrated the fine-tuning problem and the challenges faced by theoretical modeling. In this study, we apply the self-similar symmetry (SSS) model, describing the hierarchical structure of the universe based on the Dirac large numbers hypothesis, to Einstein’s cosmological term. We introduce a new similarity dimension, [Formula: see text], in the SSS model. Using the [Formula: see text] SSS model, the cosmological constant [Formula: see text] is simply expressed as a function of the cosmic microwave background (CMB) temperature. The result shows that both the gravitational constant [Formula: see text] and [Formula: see text] are coupled with the CMB temperature, which simplifies the solution of Einstein’s field equations for the variable [Formula: see text]–[Formula: see text] model.

Time evolution in a geometric model of a particle

We analyse the properties of a (4+1)-dimensional Ricci-flat spacetime which may be viewed as an evolving Taub-NUT geometry, and give exact solutions of the Maxwell and gauged Dirac equation on this background. We interpret these solutions in terms of a geometric model of the electron and its spin, and discuss links between the resulting picture and Dirac's Large Number Hypothesis.

From Dirac theories in curved space‐times to a variation of Dirac's large–number hypothesis

An overview is given of recent developments in the field of Dirac equations generalized to curved space-times. An illustrative discussion is provided. We conclude with a variation of Dirac's large-number hypothesis which relates a number of physical quantities on cosmological scales.

EXTENDED MASS RELATION FOR SEVEN FUNDAMENTAL MASSES AND NEW EVIDENCE OF LARGE NUMBERS HYPOTHESIS

A previously derived mass relation has been extended to seven equidistant fundamental masses covering an extremely large mass range from ~10-69 to ~1053 kg. Six of these masses are successfully identified as mass of the observable universe, Eddington mass limit of the most massive stars, mass of hypothetical quantum “Gravity Atom” whose gravitational potential is equal to electrostatic potential e2/S, Planck mass, Hubble mass and mass dimension constant relating masses of stable particles with coupling constants of fundamental interactions. The seventh mass, ~10-48 kg remains unidentified and could be considered as a prediction of the suggested mass relation for an unknown fundamental mass, potentially a yet unobserved light particle. First triad of these masses describes macro objects, the other three masses belong to particle physics masses and the Planck mass appears intermediate in relation to these two groups. Additionally, new evidences of dirac Large Numbers Hypothesis (LNH) have been found in the form of series of ratios relating cosmological parameters and quantum properties of space-time. A very large number on the order of 5×1060 connects mass, density, age and size of the observable universe with Planck mass, density, time and length, respectively.

Is dark energy a consequence of quantum fluctuations?

In this issue we present two speculative but exciting papers which may help provide insight into the nature of the dark energy of the Universe. The first of these by Hajdukovic (2010) is yet another exploration of the rich world of “cosmic coincidences” which are often described under the general heading of the Dirac large number hypothesis (Dirac 1938), but whose intellectual origins go back to Weyl a couple of decades earlier. Many such “coincidences” have now been investigated and discussed in the pages of this journal, most recently by Dinculescu (2009), Alfonso-Faus (2008) and Sorrell (2008). These attack the problem from a number of different viewpoints and working hypotheses, but involve similar expressions connecting fundamental atomic constants with cosmological quantities such as the Hubble Constant, the Black-Body temperature of the Universe and the Cosmological Constant. To quote Dinculescu (2009):

Variation of the fine-structure constant from the de Sitter invariant special relativity**Supported by National Natural Science Foundation of China (90403021) and PhD Program Funds of Education Ministry of China (20020358040)

We discuss the variation of the fine-structure constant, α. There are obvious discrepancies among the results of α-variation from recent Quasi-stellar observation experiments and from the Oklo uranium mine analysis. We use dS Sitter invariant Special Relativity (\U0001d4aeℛc,R) and Dirac large number hypothesis to discuss this puzzle, and present a possible solution to the disagreement. By means of the observational data and the discussions presented in this paper, we estimate the radius of the Universe in \U0001d4aeℛc,R which is about ∼2√5×1011l.y.

A Theory of Evolving Natural Constants Based on theUnification of General Theory of Relativity and Dirac's Large Number Hypothesis

Taking Dirac's large number hypothesis as true, we haveshown [Commun. Theor. Phys. (Beijing, China) 42 (2004) 703]the inconsistency of applying Einstein's theory of generalrelativity with fixed gravitation constant G to cosmology, anda modified theory for varying G is found, which reduces toEinstein's theory outside the gravitating body for phenomena ofshort duration in small distances, thereby agrees with all thecrucial tests formerly supporting Einstein's theory. The modifiedtheory, when applied to the usual homogeneous cosmological model,gives rise to a variable cosmological tensor term determined bythe derivatives of G, in place of the cosmological constantterm usually introduced ad hoc. Without any freeparameter the theoretical Hubble's relation obtained from themodified theory seems not in contradiction to observations, as Dr.Wang's preliminary analysis of the recent data indicates[Commun. Theor. Phys. (Beijing, China) 42 (2004) 703]. Asa complement to Commun. Theor. Phys. (Beijing, China) 42(2004) 703 we shall study in this paper the modificationof electromagnetism due to Dirac's large number hypothesis in moredetail to show that the approximation of geometric optics stillleads to null geodesics for the path of light, and that the generalrelation between the luminosity distance and the proper geometricdistance is still valid in our theory as in Einstein's theory, andgive the equations for homogeneous cosmological model involvingmatter plus electromagnetic radiation. Finally we consider theimpact of the modification to quantum mechanics and statisticalmechanics, and arrive at a systematic theory of evolving naturalconstants including Planck's ℏ as well as Boltzmann'skB by finding out their cosmologically combined counterpartswith factors of appropriate powers of G that may remain trulyconstant to cosmologically long time.

A Unification of General Theory of Relativity with Dirac's Large Number Hypothesis

Taking a hint from Dirac's large number hypothesis, we note the existence of cosmologically combined conservation laws that work cosmologically long time. We thus modify Einstein's theory of general relativity with fixed gravitation constant G to a theory for varying G, with a tensor term arising naturally from the derivatives of G in place of the cosmological constant term usually introduced ad hoc. The modified theory, when applied to cosmology, is consistent with Dirac's large number hypothesis, and gives a theoretical Hubble's relation not contradicting the observational data. For phenomena of duration and distance being short compared with those of the universe, our theory reduces to Einstein's theory with G being constant outside the gravitating matter, and thus also passes the crucial tests of Einstein's theory.

Holography and the large number hypothesis

Dirac's large number hypothesis is motivated by certain scaling transformations that relate the parameters of macro and microphysics. We show that these relations can actually be explained in terms of the holographic $N$ bound conjectured by Bousso and a series of purely cosmological observations, namely, that our universe is spatially homogeneous, isotropic, and flat to a high degree of approximation and that the cosmological constant dominates the energy density at present.

Modified large number hypothesis

In the Brans-Dicke theory, a certain large number hypothesis is equivalent implicitly to an equation of state. The equation of state corresponding to Dirac's large number hypothesis, however, is not reasonable. The Whitrow-Randall relation is regarded as a modification of Dirac's large number hypothesis, but it is not in fact in keeping with Dirac's original intention to relate only a single cosmological parameter to the gravitational “constant.” In view of those facts, an alternative modification of Dirac's large number hypothesis is proposed.

Derivation of the mass of the observable universe

Using solely microphysical arguments, we arrive at an expression for the overall mass of the universe in terms of the constants of nature and the parameters describing the elementary particles. The link between cosmology and the microscopic world is thus highlighted in the spirit of Dirac's large number hypothesis.

The Unification or Interconnection of the Gravitational Constant G to the Electron Charge e and to Other Fundamental Parameters Interlinked with Equations Describing the Strong and Weak Forces in Terms of the Same Fundamental Parameters via a Nonstationary Axi‐Symmetric Space‐Time and Corresponding Thermodynamics

The decay times for the neutron and Orthopositronium and the binding energies for Helium and Deuterium are calculated from the SSM. In addition, the mass, age, Helium abundance, average density, background photon and neutrino temperatures, and overall entropy associated with the SSM universe are analytically determined. The theoretically determined SSM results agree substantially with empirical findings. In addition, calculations, using the SSM, predict that actual astronomical red shifts are greater than they appear to be, which may result in biased values for the Hubble constant and may make the universe appear younger than the 15.25 Billion years it is, as calculated from the Super Spin Model. The SSM also provides a solution to the Earth-Moon problem along with an analytically derived foundation for the Dirac Large Numbers Hypothesis. The Super Spin Model supplies answers to these and other cosmological puzzles. See Table I (Preface) and Table II (at end of Section 4) for the values, definitions and symbols used for the various constants and parameters employed in this paper. See Section 8 for a compendium of results.

Dirac's cosmology with varying cosmological constant

The phenomenological approach to investigating the decay of the vacuum energy density is generalized in the spirit of Dirac's large number hypothesis. Different arguments are outlined to justify an universal dependence of the type λ=ΒH2 (Β is a pure number andH is the Hubble parameter). Such time-varying A does change the predictions of the earlier Dirac's cosmology. The deceleration parameter (q0=(2−Β)/(1+Β)) and the age parameter (H0t0=(1+Β)/3) are now compatible with the observations. The model also allows a “power-law” inflationary phase and a rate of matter creation smaller than the one present in the steady state universe.

The large numbers hypothesis and the cosmological constant

A recent generalization of Dirac's large numbers hypothesis has implications for the cosmological constant problem. We show that this generalization follows from the usual large numbers hypothesis.

On a generalized large number hypothesis

By generalizing Dirac's large number hypothesis, we find that the cosmological “constant” varies witht−2, as expected from earlier studies.

Large number hypothesis

Dirac's large number hypothesis (LNH) and the Whitrow-Randall-Sciama relation are related to some cosmological models. The LNH and Whitrow-Randall-Sciama relations are neither equivalent nor consistent in general relativity, but they may both be valid in the Brans-Dicke theory and in another theory considered in this paper.