Arbab I Arbab

Arbab I. Arbab
Residence	Khartoum, Sudan
Nationality	Sudanese
Known for	Variable-G and variable-Λ cosmology, quaternionic formulation of physics, the electromagnetism–hydrodynamics analogy
Scientific career
Fields	Professor of Physics
Institutions	University of Khartoum; Qassim University, Buraydah

Arbab Ibrahim Arbab is a Sudanese theoretical physicist, professor of physics at the University of Khartoum and in recent years based at Qassim University in Saudi Arabia, whose work runs along two main lines: a cosmology in which the gravitational "constant" G and the cosmological term Λ both vary with time, and a programme of rewriting the equations of physics over the quaternions in the hope of unifying them.

He is an unusual entry in this catalogue in one respect that should be said at the outset. Arbab is not an isolated author publishing only in marginal venues: he has published in Physical Review D, Classical and Quantum Gravity, General Relativity and Gravitation, JCAP and EPL, has accumulated on the order of two thousand citations with an h-index around 25, and holds fellowships of the Royal Astronomical Society and the Institute of Physics. His heterodoxy is real, but it sits inside a working mainstream career rather than outside it.

Career

Arbab took his first degree at the University of Khartoum in 1989, a diploma at the Abdus Salam International Centre for Theoretical Physics in Trieste in 1992, and his doctorate at Khartoum in 1997. He has held posts at Omdurman Ahlia University, at the Teachers College of King Saud University, and as dean at Comboni College for Computer Science, and has served as Deputy Director for Scientific Research and Cultural Relations at the University of Khartoum and as Secretary of the Sudanese National Academy of Sciences. He co-founded and served as an associate editor of the African Physical journal and is managing editor of the Sudan Journal of Science. He remains active, publishing as recently as 2025.

Variable constants and cosmology

Arbab's earliest and most-cited work, from the mid-1990s, develops Friedmann models in which G and Λ are functions of time rather than constants, generally with Λ scaling as a power of the density, and frequently combined with bulk viscosity treated causally in the Israel–Stewart manner.

The claims made for these models are substantial. They are argued to be compatible with observation while producing inflation as a special case rather than as an added ingredient; to resolve the horizon, flatness and monopole problems on that basis; to give nonsingular cosmologies, avoiding the initial singularity altogether; and to yield cosmic acceleration with a positive cosmological constant while addressing the fine-tuning problem that makes Λ so awkward in the standard model. He has also argued that the various dark-matter and dark-energy scenarios are formally equivalent to one another, and extended the framework to phantom and viscous dark energy.

A distinctive sub-programme uses the Earth–Moon system as a laboratory: he has argued that the tidal evolution of the Moon's orbit and the length of the day in the geological past can be used to constrain a varying G and the cosmological parameters.

This line of work belongs to a heterodox but respectable tradition descending from Dirac's large-numbers hypothesis, and it is cited in the ordinary general-relativity and cosmology literature — his 1997 paper on variable G and Λ with bulk viscosity has been cited well over two hundred times, and his 1994 Physical Review D paper on nonsingular cosmology over a hundred.

The quaternionic programme

Since about 2010 Arbab's main effort has gone into reformulating physics over the quaternions and biquaternions, with unification as the goal.

Its central result, on his account, is a single universal quantum wave equation from which the Dirac, Klein–Gordon and Schrödinger equations all emerge as special cases, together with the diffusion and quantum heat-transport equations. That paper appeared in EPL in 2010 and is his most-cited quaternionic work. He has developed the same machinery into a quaternionic quantum mechanics and a "Maxwellian" quantum mechanics in which the quantum equations take a Maxwell-like form.

The most heterodox consequence he draws is a set of generalized Maxwell equations which, he argues, violate the Lorenz gauge condition and predict a longitudinal electroscalar wave — a claim with obvious resonance in the Tesla literature, though Arbab reaches it by algebra rather than by experiment. He has applied the framework to the Josephson effect and London superconductivity through a massive electrodynamics, to the fractional quantum Hall effect, to exoplanetary spins and rotation periods, and to galactic rotation curves; and he has proposed a generalized Newtonian law of gravitation as an alternative to general relativity, with gravitomagnetism accounting for planetary and binary-pulsar precession. Recent work extends the quaternionic treatment to acoustic fields.

The electromagnetism–hydrodynamics analogy

The paper catalogued on this wiki, The Analogy between Electromagnetism and Hydrodynamics, appeared in Physics Essays 24(2), 254–259 (2011); the preprint carries the more revealing title "A quaternionic unification of electromagnetism and hydrodynamics". It is an application of the quaternionic programme rather than a separate line of work.

Beginning from a quaternionic form of Newton's law that is Lorentz invariant, Arbab derives fluid equations from Maxwell's equations under an explicit correspondence: the hydroelectric field answers to the local acceleration of the fluid, the hydromagnetic field to its vorticity, the Lorenz gauge condition to the incompressibility condition, and the Lorentz force to the Euler force. From this he obtains Gauss-like, Faraday-like and Ampère-like laws for hydrodynamics, shows that vorticity arises whenever a particle's acceleration is not parallel to its velocity, and argues that pressure contributes to the dynamics in the same positive way that mass does.

Reception

Arbab's reception divides cleanly along the two strands, and the division is instructive.

The cosmology is genuinely part of the mainstream conversation. The variable-G, variable-Λ and bulk-viscosity papers are cited in ordinary journals by researchers working on the same models, and the venues — Physical Review D, Classical and Quantum Gravity, General Relativity and Gravitation, JCAP — are unimpeachable.

The quaternionic work is more mixed. Its strongest results appeared in indexed journals such as EPL, Optik and Symmetry, but much of the programme — particularly the longitudinal-wave and generalized-Newton claims — has gone to Physics Essays, Progress in Physics, the Hadronic Journal and similar venues that mainstream physicists do not read. The electromagnetism–hydrodynamics paper has been picked up modestly by others working on the same analogy, which is a genuinely active if small topic.

What is absent is criticism. No published refutation or critique of the heterodox claims has been located: they have been passed over rather than argued with. One documented point of direct contact is his visit to Towson University in the summer of 2018, where he discussed the quaternionic programme with James Overduin and Richard Henry of Johns Hopkins.

No connection to the Natural Philosophy Alliance or CNPS has been found. His presence in this catalogue runs through Physics Essays and the neighbouring journals rather than through the conferences.

Papers on this wiki

• 2011 – The Analogy between Electromagnetism and Hydrodynamics — Physics Essays 24(2), 254–259.

Selected publications elsewhere

• "Nonsingular cosmology with a time-dependent cosmological term", Physical Review D (1994).
• "Cosmological models with variable cosmological and gravitational 'constants' and bulk viscous models", General Relativity and Gravitation (1997).
• "Cosmic acceleration with a positive cosmological constant", Classical and Quantum Gravity 20, 93 (2003).
• "Cosmological consequences of a built-in cosmological constant model", JCAP 0305, 008 (2003).
• "Derivation of Dirac, Klein-Gordon, Schrödinger, diffusion and quantum heat transport equations from a universal quantum wave equation", EPL 92, 40001 (2010).
• "On the generalized Maxwell equations and their prediction of electroscalar wave", Progress in Physics (2009).

See also

• Cosmology
• Quantum Mechanics
• Dark Energy
• Dark Matter