# What is Mass

#### diverz

For all you physics lovers....

What is Mass? How do you define mass?

Something that is solid and can be felt?

What then is solid? How do you define solid?

Let the debate begin

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#### lethe

not really sure what this has to do with string theory of LQG. perhaps this would look better in the general physics forum?

any physical system can accelerate when a force is exerted on it. the mass is a measure of the inertia of the system, which tells you how strongly it resists acceleration under a given force.

there is a nice alternative definition for elementary particles: mass is a casimir invariant of the Poincar&eacute; group, so it is a quantum number that labels which irrep of the Poincar&eacute; group the particle lives in.

of course, the two definitions coincide for particles at rest.

#### marcus

Gold Member
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Originally posted by lethe
not really sure what this has to do with string theory of LQG. perhaps this would look better in the general physics forum?

any physical system can accelerate when a force is exerted on it. the mass is a measure of the inertia of the system, which tells you how strongly it resists acceleration under a given force.

there is a nice alternative definition for elementary particles: mass is a casimir invariant of the Poincar&eacute; group, so it is a quantum number that labels which irrep of the Poincar&eacute; group the particle lives in.

of course, the two definitions coincide for particles at rest.
this really would look better, as Lethe says, in the general physics forum

Lethe suggests mass is "a measure of inertia" the ratio of the force applied to the acceleration produced.

This is well-defined (independent of the direction of the force) only in case the object to which force is applied is at rest. If an object is moving, then the acceleration produced by a force will depend slightly on the direction in which the force is applied and so the ratio of the two is not well-defined. IIRC Einstein pointed this out in 1905---it may have been he who introduced the terms "transverse inertia" and "longitudinal inertia" for inertia crossways to the object's motion and in line with the motion.

Anyway the simple concept of inertia is only defined for objects at rest. So a photon of light, for example, cannot have inertia because there is no frame in which it is at rest.

I agree with Lethe's choice of a definition of mass as inertia. In my experience it is the most prevalent meaning for the unmodified term "mass". Other concepts need some adjective in front of the word to indicate that a specialized meaning is intended.

the reason I especially like this definition is that it is primitive. It gives an operational non-abstract meaning to the concept, so it can be used as a foundation for building up other ideas, like energy and momentum. It only works for objects at rest, but it is real simple. Force is measurable by the watt balance by electrical means without the use of a standard mass. (one reason metrology is an interesting field these days) (Foundations of physics is also interesting---how basic concepts are defined.)

IIRC Einstein's 1905 paper that introduced E = mc2 was entitled "Does the INERTIA of an object depend on its energy-content?" Evidently for him at that point mass meant inertia and that's good enough for me. It's traditional.

What Lethe says about a particle's (rest) mass also being a parameter of the group representation is cool.

I put "rest" in parens because in modern physics usage it is redundant: not needed in the above sentence. A particle's mass is understood by working physicists to mean its inertia in the rest frame.

#### Mike2

Originally posted by diverz
For all you physics lovers....

What is Mass? How do you define mass?

Something that is solid and can be felt?

What then is solid? How do you define solid?

Let the debate begin
If mass = energy, then there is a mathematical definition of energy, see:

http://mathworld.wolfram.com/DirichletEnergy.html

#### Haelfix

In quantum field theory, mass can be problematic to identify properly. Particularly for composite objects or those subject to containement forces (eg quarks in QCD).

There are notions like bare mass, renormalized mass, being on mass shell. etc

In curved spacetime, field theories can predict results, unfortunately its likely that our intuitive grasp of 'mass' and what it means will have to be altered or abandoned.

I like to think of it as a sort of wavey localization of 'something', subject to the Heisenberg uncertainty principle (for instance, things that decay or which are not perfectly stable have a mass 'width') Thats about as good as we can do.

In curved spacetime, you really have to have a good notion of what 'energy' means, since there is no preferred reference frame. Technically you need timelike killing vectors and asymptotic flatness in order to even begin to talk about things intuitively

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#### S = k log w

Mass is a tangable (or it's mathematical model) that the convention which we call the world, exists. You could chase the many theories until you had reached existentalist angst. You still have to get up in the morning and put on your clothes. They have mass. They do exist. My goodness, so do you.

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