# Definition of Mass in Vacuum of Space

## Main Question or Discussion Point

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?

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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.

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 : $$E^{2}=\vec{p}\,^{2}+m^{2}$$ (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 ?

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 : $$E^{2}=\vec{p}\,^{2}+m^{2}$$ (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 ?
No. I do not need another equation. I need a definition in words, not equations of equalities, that explain what mass is. For example: Mass is equal to the attractive-repulsive interactions of one or more atomic particles.

Or, perhaps: Mass is due to the harmonic interaction of one set of atomic particles to another set of atomic particles.

Does that help?

No. I do not need another equation.
Then this discussion will end belonging to GD, not HENPP This is not a joke : words are useful scientifically to communicate only if they can be backed up by an equation. Mathematics is the only un-ambiguous way to communicate between us human beings.

malawi_glenn
Homework Helper
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.

Well atleast when it comes to physics, the language of physics is math after all.
Does that mean that physicists are simply mathematicians pretending to be scientists?

Staff Emeritus
2019 Award
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?
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.

castlegates
Using words to describe what mass is, can be termed (A resistance to being moved due to it's self interaction). In other words .. when you push something it kinda, sorta, pushes back, thusly we have mass, in a kinda sorta way. :-)

malawi_glenn
Homework Helper
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.
yeah, what if we have encountered something fundamental and elementary?

What if I asked the string theorists: "But what is a string made up of? What is it really?" We can go on forever..

malawi_glenn
Homework Helper
Does that mean that physicists are simply mathematicians pretending to be scientists?
What is your definition of science? Science is a quite broad term, http://en.wikipedia.org/wiki/Science

Physical science differs quite much from chemistry, and organic chemistry in perticular. Physical science differs from philosophy, and from archeology and so on.

Physics is an interplay between making theories, models, experiment and interprenting data. The theories are always constraint under some axioms, for instance the requirement of beeing invariant to Lorentz boosts, Gauge invariance etc. No axioms can be prooven, but they can be motivated. This sort of interplay is strongly related to philosophy, that you always must put up axioms that can't be proven in order to formulate a world view. In the old days, physics was called "Natural philosophy" and the foundators of the math we use today (calculus etc) was largely developed by people who where philosophers and experimental 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?

George Jones
Staff Emeritus
Gold Member
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?
No. Who was it?

malawi_glenn
Homework Helper
Well it also depends on the system and the phenomenon. What if drawing a picture is impossible?

And it was R Feynman.

George Jones
Staff Emeritus