## The Origin of Wave-Particle Duality

**Published:**
2023-05-16

**Page:** 71-74

**Issue:**
2023 - Volume 5 [Issue 1]

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.

### Abstract

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 (M_{P}) and a growing exponential expansion rate is responsible for the wave mass (M_{W}). The evolution of the universe is governed by the ratio (α = M_{P}/M_{W}) in which α = K_{o}/c where K_{o} is the initial expansion rate and c is the velocity of light. In a stress-free expansion process, 0 ≤ α ≤ ½, the mass ratio, M_{P}/M_{W} = α. The mass of the universe, M = M_{W} + M_{P}, in which it is found from the exponential model that M_{W} = m_{o} c T/ ln (1/α) where T is the age of the universe and m_{o} = c^{2}/G where G is the universal gravitational constant. Observations of the mass and age of the universe, yield, α = 0.235, and hence M_{P} / 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, M_{W}, can be interpreted as the dark matter remaining after the formation of the particle matter. The analysis also shows that on temporal scales (t_{o}) much less than the age of the universe (T), M_{P }(t_{o}) / M_{W}(t_{o}) → 1, which is an exact wave-particle duality.

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

**How to Cite**

*International Astronomy and Astrophysics Research Journal*,

*5*(1), 71–74. Retrieved from https://journaliaarj.com/index.php/IAARJ/article/view/85

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