Understanding Mass in Relativity Theory: Definitions and Conflicting Views

[Dadface]

It's me again. I refer once more to the relativistic mass equation I mentioned in posts 28 and 36. I am still not clear about the reasons why the equation is out of favour. I see it as being a useful equation in that amongst other things it can be used to calculate the KE of a body.
Can it be used to calculate KE? Does it give the right answers? If so apart from the out of favour terminology used, such as relativistic mass, what's wrong with the equation?

 

[atyy]

It's me again. I refer once more to the relativistic mass equation I mentioned in posts 28 and 36. I am still not clear about the reasons why the equation is out of favour. I see it as being a useful equation in that amongst other things it can be used to calculate the KE of a body.
Can it be used to calculate KE? Does it give the right answers? If so apart from the out of favour terminology used, such as relativistic mass, what's wrong with the equation?

The relativistic mass is not out of favour.

In many treatments, it is confusing to refer to relativistic mass and invariant mass, so the tendency nowadays is to call the former the energy and the latter the mass. However, both usages are useful to know, since one encounters it in introductory treatments like those of Einstein, French, Feynman, Purcell, Rindler, Schutz. Even MTW use the term "mass-energy". (Side note: Often the relativistic mass, which is the same as energy, is identified with the inertial mass. However, photons do not have inertial mass, but they do have energy or relativistic mass.)

Knowing both terms is still necessary in the advanced literature. For example, http://arxiv.org/abs/1001.5429 remarks "Remark 5. In the literature, references are found where the term ADM mass actually refers to this length of the ADM 4-momentum and other references where it refers to its time component, that we have named here as the ADM energy. These differences somehow reflect traditional usages in Special Relativity where the term mass is sometimes reserved to refer to the Poincare invariant (rest-mass) quantity, and in other occasions is used to denote the boost-dependent time component of the energy-momentum."

 

[Dadface]

Thank you very much to all who responded to my particular enquiry. Its good to see some backing for the equation I referred to. My knowledge and understanding of SR is very basic but I have always felt at home with the equation. I think I understand it, it feels right and it seems to work.

 

[Naty1]

I have two texts from Peter Bergmann. No bias against 'relativistic mass' from this student of Einstein!

In both texts, THE RIDDLE OF GRAVITATION [1992], and INTRODUCTION TO RELATIVITY [1976] he discusses definitions and differences between rest mass and relativistic mass without favoring one over the other.

From the first book as an example:

He says: [pg 40]

The mass of a body measured in a Lorentz frame in which it is a rest is called it's rest mass. The rest mass is an intrinsic property of a physical body, whereas the mass that governs its behavior in interactions with other bodies, it's relativistic mass, depends on the relative motion of object and observer as well. The sum of the relativistic masses of several interacting bodies remains unchanged through the interactions, but the rest mass can change.

He then explains as an example the radioactive decay of an atomic nucleus including the relativistic mass of an emitted gamma ray.

This thread leaves a very different impression from several others in these forums regarding 'relativistic mass'. Good to see varied viewpoints.

 

[Bill_K]

I have two texts from Peter Bergmann. No bias against 'relativistic mass' with this student of Einstein! In both texts, THE RIDDLE OF GRAVITATION [1992], and INTRODUCTION TO RELATIVITY [1976] he discusses definitions and differences between rest mass and relativistic mass without favoring one over the other.

The 1976 Dover edition of Peter's book is a reprint of what was the very first textbook on relativity (1942), and it still comes across as a very clear exposition. Plus, there's definite historical interest in what topics were emphasized at that time and how they were presented.

 

[harrylin]

There are some things that concern me about concepts of mass as discussed in threads such as this and I would appreciate it if someone could answer the following :

1. I have the impression that the majority of physicists who use relativity do not favour the equation:

M=MoL (L= Lorentz factor)

. I am a bit familiar with the other equations but is it considered that the above equation is archaic or misleading or incorrect in some way?

. If people reject the equation is it because of the terminology sometimes used? It seems to me that it is accepted that Mo can be referred to as the mass,or invariant mass and sometimes rest mass and that it is unnecessary to use the subscript o.
What doesn't seem to be accepted is that M (or E as it is sometimes written) should be referred to as the total mass where the total mass is the sum of the invariant mass plus the mass equivelent of the kinetic energy .If it is not accepted then what is wrong in calling it total mass and what, if anything, should it be called instead?

. Are there physicists who favour the use of the equation and if so are there examples of where the equation is more useful than any alternatives?
[..]

Hi Dadface,
the Physics FAQ gives a rather good discussion that I think answers all your above questions:

http://math.ucr.edu/home/baez/physic...y/SR/mass.html