In the mechanical universe we locate an object by its center of mass (CM). The CM is represented by a mathematical point that is dimensionless. Thus, we get the idea of a particle of matter as a dimensionless point in space. We call it a “point particle.”
But, then, we start visualizing all quantum particles, such as, the proton, electron and photon also as “point particles” too. The reality is that they are not point particles. A particle is a ‘physical entity’. It has a size.
For example, according to The Spectrum of Substance, a comparison of wavelengths (or frequencies) shows that
an electron is about 2000 times the size of the proton,
and, a photon of light is more than 200,000 times the size of an electron.
The proton has a radius of about 1 x 10-15 meter. It has a CM, and the laws of mechanics apply to it. Therefore, a proton may be visualized as a point particle both mathematically and visually.
But neither the electron, nor the photon has a CM and the laws of mechanics do not apply to them. Therefore, neither of them may be treated as point particles. Their location in space cannot be calculated mathematically with precision.
Based on the above we reach the following conclusions:
- The notion of physical location is actually the size of the particle of that substance.
- A MATHEMATICAL POINT in space cannot always be equated with a PHYSICAL LOCATION.
- The physical location of quantum particles cannot be determined with precision.
- Space is continuous; whereas, points are discrete.
- In physics, the mathematical space cannot be assumed to be made of mathematical points.
- Calculus assumes the size of the “points” to be uniform. This is not the case in the quantum region.
- The mathematics for Quantum Mechanics is very complex because calculus cannot be applied.
- Calculus may be applied to solve quantum mechanical problems using the relationship among varying particles sizes.
- Thus, it may be possible to simplify the mathematics of Quantum Mechanics.
We may assume particle sizes to be uniform in the mechanical universe as point particles. We cannot apply the same assumption in the quantum universe.
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