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Mass on Earth can be understood as weight in Kg, or units of E/C^2, but what is a viable definition that does not use the words "substance" or "matter" or some other circular term?
I am not sure I completely understand your question. We usually refer to gravitational mass as the one subject to gravitation (giving weight on Earth), and to inertial mass as the one a body "opposes to modifications of its movement". General relativity in particular postulates that those two are equal. Nobody has ever observed that gravitational mass is any different from inertial mass : all bodies "fall at the same rate". Gravitation can thus be described in geometrical terms.Mass on Earth can be understood as weight in Kg, or units of E/C^2, but what is a viable definition that does not use the words "substance" or "matter" or some other circular term?
I am not sure I completely understand your question. We usually refer to gravitational mass as the one subject to gravitation (giving weight on Earth), and to inertial mass as the one a body "opposes to modifications of its movement". General relativity in particular postulates that those two are equal. Nobody has ever observed that gravitational mass is any different from inertial mass : all bodies "fall at the same rate". Gravitation can thus be described in geometrical terms.
Now, E=m is the total energy of a body in its own rest frame, which is just his mass according to this equation. This is valid anywhere (with or without a gravitational field, that is also in "empty vacuum" far away from any measurable source). In an arbitrary referential, the energy has a momentum "component" corresponding to kinetic energy/quantity of movement : [tex]E^{2}=\vec{p}\,^{2}+m^{2}[/tex] (in units such that c=1).
Do you want yet another "equivalent" definition of mass, that is a "third" manifestation of mass, on top of inertial and gravitational ?
Then this discussion will end belonging to GD, not HENPPNo. I do not need another equation.
Mathematics is the only un-ambiguous way to communicate between us human beings.
Well atleast when it comes to physics, the language of physics is math after all.
Please pay attention to what you post. Your logic is completely wrong. Mathematicians create the language of mathematics. Physicists use the language of mathematics to communicate between them. The equations come of course together with text in order to make the communication easier. But essentially, if you can not put your claims into equations, those are completely useless.Does that mean that physicists are simply mathematicians pretending to be scientists?
I don't think you're going to be satisfied. You don't want an equation, and you don't want the words that are commonly used. Fair enough, but I think you'll be disappointed.
Remember, one can take any definition of anything whatsoever and follow up with "But what is it really?" This path doesn't really go anywhere.
Does that mean that physicists are simply mathematicians pretending to be scientists?
A professor at the University of Berkeley and his father had the same philosophy for physics. "Draw a picture of the phenomenon and then we can work out the mathematics." Can you guess who that was?
And it was R Feynman.