onsdag 6 augusti 2025

Mass as Gravitational Mass

Recent posts discuss the concept of mass concluding that gravitational mass appears to be primordial from which inertial mass is derived. The idea is to start with a Universe defined in terms of a gravitational potential $\phi (x,t)$ depending on a Euclidean space coordinate $x$ and a time coordinate $t$ as created in 3 steps:

1. The gravitational potential creates a mass density $\rho (x,t)=\Delta\phi (x,t)$, where $\Delta$ is the Laplacian differential operator acting instantly as a local operation in space. 

2. Mass is subject to free fall according to Newton's equations of motion subject to gravitational force $\nabla\phi (x,t)$. 

3. Redistribution of mass under free fall gives feed-back to gravitational potential.

We thus find a Newtonian Universe determined by gravitational free fall connecting motion of mass in space to gravitational force and so equating inertial mass to gravitational mass. This is a large scale in a sense complete Universe with a precise simple mathematical description, which can be complemented by electromagnetics without interference with gravitation on both macro-scale and atomic micro-scale into the Universe we can see and experience.  

Modern text-books tell another story with mass appearing as (i) gravitational mass, (ii) inertial mass, (iii) rest mass and (iv) Higg's mass, all of different nature, which is is very confusing and lacks reason.  

It seems to be more reasonable to define mass as gravitational mass, which is the operational definition according to SI 2019 standard of units, and then connect other expressions of mass to this standard. 

On the other hand, the formal presence of mass $m$ in the coefficient $\frac{h^2}{2m}$ of the Laplacian in Schrödinger's Equation SE , with the mass of a proton 1836 times that of an electron, is not connected to gravitation and free fall motion.  Instead $m$ here serves as a parameter to determine spatial size, with thus a proton having smaller size than an electron in an atom.  

Different concepts of mass in modern physics.


 

Inga kommentarer:

Skicka en kommentar