# What is matter and what is mass?

In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. (Wiki)

Fair enough, so what is mass?

Mass is the quantity of matter in a physical body. (Wiki)

Ok, these definitions are cyclic. Can someone explain what the two are without relying on the other to explain it? Is matter even something that has a precise definition in physics or is it more like a word to describe some intuitive properties of some things?

• The first one seems ok but mass can be thought of how much matter there is in total. If you have an ice cube and it has a mass of 5 grams, and then you evaporate it, then that water vapor will still have 5 grams of mass (it has not gone away). Commented Jan 30, 2022 at 21:40
• Alternatively, mass can be thought of as a property of matter that creates inertia for matter. Commented Jan 30, 2022 at 21:52
• Similar - What exactly is mass?, Definition of mass Commented Jan 30, 2022 at 22:31
• There is one video on youtube by Royal Institute explaining what is mass..I think this is one of the fundamental question where no one knows answer. Ref. youtube.com/watch?v=HfHjzomqbZc&t=11s Commented Oct 16, 2022 at 10:59

First, there is actually nothing intrinsically wrong with circular definitions, at least they are internally consistent. There will usually be either some circular definitions or some undefined terms. However, in science the basic definitions are usually not circular, they are usually operational. This means that they are defined by some sort of experimental measurement.

This is the case with mass. If you had read the rest of the wiki article you cited then you would have seen that the first sentence which you quoted was intended to be a description, not a definition. The definition was in the section labeled “Definitions” where it says “There are a number of ways mass can be measured or operationally defined:”. It then proceeds to give operational definitions for the various concepts known as mass.

More simply, mass can be operationally defined as the quantity measured by a scale. It can also be theoretically defined as the quantity $$m$$ in the expression $$m^2 c^2=E^2/c^2-p^2$$. This is a nice theoretical definition because it allows you to determine the mass of things that you cannot put on a scale.

• "there is actually nothing intrinsically wrong with circular definitions" If they make no reference to other pieces of math or the world, then... well... then they have no connection to physics or math. Commented Oct 26, 2023 at 2:50
• Luckily, any circular definitions in physics (if there are any) will necessarily make reference to other physics concepts.
– Dale
Commented Oct 26, 2023 at 11:44

In Simple terms this is best definition I can come up with,

"Mass is the ability of not being able to travel at the speed of light"

• The number 3, the color blue, and the idea of a unicorn do not travel at the speed of light (or at any speed for that matter) but I am quite sure that none of them have mass. Commented Oct 26, 2023 at 3:32
• This is kind of true. If you extended it to say that mass is the norm of the four-momentum, and anything travelling at the speed of light has a four momentum with zero norm, then it would be a useful definition. As it is your answer seems like only half an answer. Commented Oct 26, 2023 at 9:00
• A friendly amendment: "mass is the inability of light-speed-travel by something with a physical dimension." @WillO feedback welcome Commented Nov 27, 2023 at 18:19