# What is the exact definition of mass?

1. Apr 15, 2006

### mubashirmansoor

I'd be thankfull if someone would help me to figure out what the exact definition of mass is.......:)

The most comfortable idea which gave me a little bit of relief last night was calling mass the intensity of space-time curve but yet not the main definition.

2. Apr 15, 2006

### pmb_phy

I did a lot of work in this area an have placed it on the internet. It will tell you what mass is iin no uncertain terms. Please see

http://www.geocities.com/physics_world/mass_paper.pdf

Pete

3. Apr 15, 2006

### mubashirmansoor

Dear Pete, Unfortunately I can't open the link because at this moment I'm in Iran and geocities.com has been filtered by the government, I'll be really thankfull if anyone would just attach the pdf file to his/her reply
Thankyou once again.

4. Apr 15, 2006

### bobbytkc

I assume you are talking about rest mass. There are other kinds of observable masses resulting from the mass energy equivalence (though equivalence does not necessarily imply energy is mass).

In string theory, the mass of an object depends on the frequency of vibration of the one dimensional string. The higher the frequency, the higher the energy, and energy has a mass equivalance. So in this view, mass is simply the energy of a vibrating one dimensional string.

I do not place too much faith in string theory (though it has potential, i won't hedge my bets on it) I also believe it is not so much that mass is the intensity of the 4- dimensional curvature of space, but rather the curvature of space is the result of a property called mass since mass can not only be measured using gravitational potential, but also through inertial resistance. Of course, this could be a moot point since the two are so inextricably link that the two might as well be the same, similar to the way the electric fields and magnetic fields are now considered one and the same since they are inextricably linked.

To me, I believe that mass is simply another dimension (not a true physical dimension, but a mathematical one) to describe a particle, like how electric charge, spin, position in the x,y,z and t are all just quantities to describe and provide all the possible information of a particle. Of course, this in no way is satisfactory to any physicist since it does not provide an explanation for any behaviour of mass at all.

Last edited: Apr 15, 2006
5. Apr 15, 2006

### pmb_phy

I'd be glad to do it. I think I figured out how. Is this correct?

Basically mass m is a quantity defined such that for all particles in an inertial frame mv is conserved in all elastic collisions. m is called the mass of the particle.

Pete

#### Attached Files:

• ###### Mass Paper V2.3.pdf
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Last edited: Apr 15, 2006
6. Apr 15, 2006

### pervect

Staff Emeritus
That doesn't strike me as being anywhere close to a defintion.

In GR there are at least three commonly used different sorts of mass (Komar mass, ADM mass, Bondi mass) with slightly different exact technical conditions widely used in General relativity.

This beats SR, and Newtonian theory, in terms of sheer numbers, which both have at least two commonly used sorts of mass.

SR defines invariant mass, and (somewhat as a legacy), the so-called relativistic mass, which is a bit of a dead end (IMO) as is not incoroporated into any of the GR concepts of mass that I mentioned.

Newtonian physics has inertial mass and gravitational mass - the distinction between them is not needed in GR anymore, where both of these masses are guaranteed to be the same.

These are too many different concepts to give exact definitions of all of them, therfore a bit of context would be needed in answering your question.

Last edited: Apr 15, 2006
7. Apr 15, 2006

### robphy

As pervect said, the context is important.
In GR, an exact definition in the most general case is an open problem:
for example,
http://relativity.livingreviews.org/open?pubNo=lrr-2004-4&amp;page=articlesu38.html [Broken]

Last edited by a moderator: May 2, 2017
8. Apr 16, 2006

### loopgrav

This is actually a remarkably difficult question. In my opinion, the only term in Newton's second law F=ma that is even vaguely well-definined is the acceleration, and that assumes you believe Newton's "definition" of time. If you take the concept of force as well-defined, then mass is defined as the proportionality constant that relates force and acceleration. On the other hand, you could use the concept of mass to define what you mean by force. You see this is all circular, and I don't think there is a better answer within classical physics. This is also the same mass that is used in non-relativistic QM. In GR, mass is defined in classical (Newtonian) terms, although in a somewhat more general form using the complete stress-energy tensor for the matter under consideration.

The only other definition of mass that I have been able to come up with (and I have thought about this on and off for years) is in QFT. There, one writes down a lagrangian (density) with a (bare) mass parameter. Of course, one still has to worry about "dressing" and the renormalized physical mass, but that just shows you that the entire concept is rather vague even at that level.

9. Apr 17, 2006

### pmb_phy

That's not Newton's law. Newton's law is F = dp/dt. It only reduces to F = ma when the mass is constant.

Pete

10. Apr 17, 2006

### loopgrav

That's completely irrelevant to the issue. It still doesn't let you define force in a manner independently of other terms such as mass (constant or relativistic) or acceleration.

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