4

Mass and spin are fundamental characteristics of particle. Those quantities are eigenvalues of the Casimir operators of the Poincaré group. My book then writes that $$ p^\mu p_\mu = m_0^2, $$ where $m_0$ is mass of idle and mass $m=\gamma m_0$ is mass of moving (relativistic mass).

If we boost the first equation, we have $$ ({\Lambda_{\nu }^{\mu }}p_{\mu })({\Lambda_{\mu }^{\nu }}p^{\mu })=\gamma^2m_{0}^2=(\Lambda_{\nu }^{\mu }\Lambda_{\mu }^{\nu })p_{\mu }p^{\mu }=1\cdot p_{\mu }p^{\mu } =m_{0}^2, $$ and this is a contradiction! One other author says that exist only mass of idle, and no sense that we speak about mass of moving. Why we hadn't speak about mass of moving?

P.S. Casimir operators are scalar operators, but and $m_0$ is scalar, but it is change as which quantity (scalar, tensor or vector)? This transform as $m=m_0\times gamma$ if we has relativistic mass, but this concept I think that is not valid, it is interpretation.

Emilio Pisanty
  • 132,859
  • 33
  • 351
  • 666
fika97
  • 171
  • 5
    mass doesn't transform under Lorentz transformations. There is no $\gamma m$ "relativistic mass" – FrodCube Nov 26 '19 at 14:32
  • Ok, my main question is why no sense we speak about mass of moving – fika97 Nov 26 '19 at 14:34
  • 1
    Check some papers by Okun https://aapt.scitation.org/doi/10.1119/1.3056168. I had asked a similar question sometime ago. https://physics.stackexchange.com/questions/221224/doppler-effect-of-matter-waves – Chetan Waghela Nov 26 '19 at 15:27
  • 3
    Please do not post formulae as screenshots, but use MathJax instead. I've edited your formulas here, but in future you should do this yourself. – Emilio Pisanty Nov 26 '19 at 16:04
  • The short answer is: $\gamma m_0=p_0$, or energy. So your equation is plain wrong: $({\Lambda_{\nu }^{\mu }}p_{\mu })({\Lambda_{\mu }^{\nu }}p^{\mu }) \neq \gamma^2m_{0}^2$. – Kphysics Nov 26 '19 at 18:23
  • This is an elementary question about a misconception in relativity. It's unfortunate that it's surrounded with fancy talk about Casimir operators, etc. –  Nov 26 '19 at 23:26
  • probably useful reading: https://physics.stackexchange.com/q/133376/25301 – Kyle Kanos Nov 27 '19 at 11:50

1 Answers1

13

The idea that mass changes as speed increases is being phased out of teaching, precisely because it leads to the type of confusion that you're having now. The quantity $\gamma m_0$ has only one name, and that's the total energy of the moving body. Total energy is neither a Lorentz scalar, vector, nor tensor; it changes with the reference frame in a way that is not compatible with any of those concepts. Mass (or, as older textbooks will call it, "rest mass") is a Lorentz scalar, as it doesn't change with reference frame.

probably_someone
  • 35,459