Quantum Behavior Arises Because Our Universe is a Fractal

Abstract

To explain the origin of quantum behavior, we propose a fractal calculus to describe the non-local property of the fractal curve [Y. Tao, J. Appl. Math. 2013 (2013) 308691]. This study demonstrates that if the dimension of time axis is slightly less than 1, then Planck’s energy quantum formula will naturally emerge. In this paper, we further show that if the dimension of time axis is less than 1, Heisenberg’s Principle of Uncertainty will emerge as well. Our finding implies that fractal calculus may be an intrinsic way of describing quantum behavior. To test our theory, we also provide an experimental proposal for measuring the dimension of time axis.

Keywords

• Planck’s constant
• fractal calculus
• Heisenberg’s principle of uncertainty
• quantum field theory
• dimensional regularization