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.
Highlights
The quantumeld theory is one of the oldest fundamental and most widely used tools in physics
The starting point of special relativity is the principle of invariant light speed, while the starting point of quantum mechanics is Planck's hypothesis of energy quantum,[1,2] i.e
We provide an experimental proposal for measuring the dimension of time axis
Summary
The quantumeld theory is one of the oldest fundamental and most widely used tools in physics. It is well known that the principle of invariant light speed is an intrinsic requirement for the symmetry of Maxwell electromagnetism equations This is an Open Access article published by World Scientic Publishing Company. We proposed a \fractal calculus"[15] by using fractional calculus, and employed it to verify the validity of Wilson and Svozil's conjectural integral formula.[15] Using such a fractal calculus, we further show that[16] if the dimension of time axis is slightly less than 1, Planck's energy quantum formula (1) will naturally emerge. The main purpose of this paper is to show that if the dimension of time axis is less than 1, by using fractal calculus, Heisenberg's Principle of Uncertainty will naturally emerge.
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