0

Is the concept of mass in particle physics relativistic (i.e. mass as described by general relativity) or classical (i.e. mass as described by classical Newtonian physics)?

user132181
  • 569
  • Do you mean special relativity instead of general relativity? – BMS Sep 23 '14 at 16:35
  • @BMS, no, I don't. – user132181 Sep 23 '14 at 16:54
  • 1
    What's the difference you're trying to get at? – David Z Sep 23 '14 at 17:10
  • @DavidZ what exactly do you mean by "difference"? – user132181 Sep 23 '14 at 17:12
  • 1
    Well, I mean, you're asking this question because you have definitions of "GR mass" and "Newtonian mass" in mind which are not the same, right? What's the difference between those two definitions? Or, what are those definitions? – David Z Sep 23 '14 at 17:20
  • There are two conventions for how to define mass in relativity: http://physics.stackexchange.com/questions/133376/why-is-there-a-controversy-on-whether-mass-increases-with-speed . Which one do you have in mind, the obsolete one or the modern one? Using the modern definition, the mass of a material object is exactly the same as the Newtonian mass. –  Sep 23 '14 at 19:14

2 Answers2

1

For the most part, particle physics adhere to the convention of very small lengths. In such lengths, every manifold that is used in general relativity, conforms to Minkowski space-time metric.

As a result it is customary to disregard the overall curvature implied by general relativity and use covariant derivatives that neglect the Christoffel connections.

However, in particle physics, as opposed to Newtonian, the mass term is coupled to the square of the coordinate, as opposed to being a part of the kinetic term.

$$ \mathcal{L}=\frac{1}{2}\left(\partial_\mu\phi\right)^2 + m^2\phi^2 $$

So as to derive the Klein-Gordon equation: $$ P_{\mu}P^{\mu}=m^2 $$

So the answer is: neither.

BeastRaban
  • 812
  • So, mass in particle physics, in a sense, still has its roots in GR? – user132181 Sep 23 '14 at 16:53
  • There is a connection, not sure what you mean as "its roots"... In GR space-time coupled to energy, which partly manifests itself in rest mass. but momentum contributes to the energy as well...

    In particle physics mass has several sources: The elementary constituents of Mesons and Hadrons, as well as electrons, have masses owing to the Higgs mechanism.

    The actual Hadron & Meson masses are almost exclusively a result of the quarks and gluons interacting inside the "bundle" (as they have relativistic velocities, thus higher mass, as well as the interaction forces themselves manifest in energy)

     – BeastRaban Sep 23 '14 at 17:23
  • The weak interacting Bosons have mass owing to the Higgs mechanism as well...

    For a very long time the lepton mass was a conundrum, since they seem to have well-defined chirality, which fly in the face of having mass...

     – BeastRaban Sep 23 '14 at 17:28
0

There are two kinds of mass :

1) the rest mass

i.e. the invariant mass of a system described by a relativistic four vector

inv mass

The invariant mass of elementary particles, which are the foundation stones of the standard model characterizes them uniquely. Composite particles as the proton for example have an invariant mass that comes from the addition of the individual four vectors of the component quarks and gluons.

2) The relativistic mass

the famous E=mc^2

relat mass

This is not very useful for particle physics and has fallen out of use.

In conclusion, the mass used for particle physics is the invariant mass of special relativity, the "length" of the relativistic four momentum vector .

anna v
  • 233,453
  • 3
    I'd rather not even mention relativistic mass — as a try to prevent its propagation through generations of physicists. – Ruslan Sep 23 '14 at 17:22
  • You'll have a hard time with that... Feynman took care of that -> every physicist reading his lecture notes will encounter that – BeastRaban Sep 23 '14 at 17:29
  • @Ruslan we cannotavoid the fact that E=m*c^2 is the most known relativistic mass formula to the general public. – anna v Sep 23 '14 at 17:53