The Origin of Wave-Particle Duality

John A. T. Bye *

School of Geography, Earth and Atmospheric Sciences, The University of Melbourne, Victoria-3010, Australia.

*Author to whom correspondence should be addressed.


We present a basic model for the formation of a stress-free universe, which shows that its formation gives rise to a wave and particle mass, which together characterize the universe. In this model a decaying exponential expansion rate is responsible for the particle mass (MP) and a growing exponential expansion rate is responsible for the wave mass (MW).  The evolution of the universe is governed by the ratio (α = MP/MW) in which α = Ko/c where Ko is the initial expansion rate and c is the velocity of light. In a stress-free expansion process, 0 ≤ α ≤ ½, the mass ratio, MP/MW = α. The mass of the universe, M = MW + MP, in which it is found from the exponential model that MW = mo c T/ ln (1/α) where T is the age of the universe and mo = c2/G where G is the universal gravitational constant.  Observations of the mass and age of the universe, yield, α = 0.235, and hence MP / M = 0.19. This ratio is very close to the ratio of ordinary matter to dark matter of 0.18 in [1].  Hence, the wave mass, MW, can be interpreted as the dark matter remaining after the formation of the particle matter. The analysis also shows that on temporal scales (to) much less than the age of the universe (T), MP (to) / MW(to) → 1, which is an exact wave-particle duality. 

Keywords: Net-zero stress, evolution of the universe, wave-particle duality

How to Cite

Bye, J. A. T. (2023). The Origin of Wave-Particle Duality. International Astronomy and Astrophysics Research Journal, 5(1), 71–74. Retrieved from


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