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When we usually talk about elementary particles such as electrons neutrinos etc... we mention their rest mass or their four vector mass which is invariant However how can we associate the "relativistic or inertial" mass that increase with velocity into the rest mass of a particle. Even if a particle is in his inertial frame and he will measure his own rest mass, he should still see a change in his mass if he is going faster because his kinetic energy is increasing as given by the equation

m(rest mass)=Etotal/c^2

So are not relativistic (inertial) mass and rest mass actually two sides of the same coin that we should include in our calculations (the increase of velocity being part of the rest mass too)?

user198045
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  • Does this help in any way? https://profmattstrassler.com/articles-and-posts/particle-physics-basics/mass-energy-matter-etc/more-on-mass/the-two-definitions-of-mass-and-why-i-use-only-one/ –  Jul 10 '18 at 20:39
  • "rest mass" is what they usually called "invariant mass", and as the label implies, it doesn't vary. the $m$ in $$ E = m c^2 $$ can be thought of as "relativistic mass" which is $$ m = \frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}$$ and $m_0$ is your "rest mass". but this way of thinking of it has been deprecated for decades. – robert bristow-johnson Jul 10 '18 at 20:43
  • Yes thank you study study it helped me understand that relativistic mass is unnecessary it just seems weird that we ignore it completely because an electron that is not moving will have a rest mass and we say that when it is moving at has the same rest mass but I Think that if this electron travels near the speed of light he should see an increase in his rest mass obviously – user198045 Jul 10 '18 at 20:59
  • A moving elementary particle gets an increase in its inertial mass, but this is not useful because mass is not a conserved quantity in special relativity and elementary particles as the inertial mass is in classical physics. What is conserved is energy and momentum. see my answers here https://physics.stackexchange.com/questions/390184/relativistic-mass-or-rest-mass/390221#390221 and here https://physics.stackexchange.com/questions/415894/velocity-and-mass-and-particles/415898#415898 – anna v Jul 11 '18 at 07:00
  • the interactions of elementary particles do not depend on the F=ma, m inertial mass, but on energy momentum conservation in and out, exchanging virtual particles that represent the classical forces, but do not follow the classical formula. – anna v Jul 11 '18 at 07:04
  • No electron has kinetic energy in its own frame. – WillO Jul 20 '18 at 05:05

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The mass of a system is its energy ($/c^2$) in its rest frame, so $E_0 = mc^2$. The rest frame is the frame in which the systems momentum is zero. For a photon this only exists in a limiting sense. In any other frame than the rest frame the energy $E^2 = m^2c^4 + p^2c^2$. The concept of relativistic mass has been abandoned as it only creates confusion.

my2cts
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  • Okay so E=mc2 is the equation for rest mass when there is no kinetic energy and the other is relativistic mass but should not the rest mass see an increase in his own mass ? – user198045 Jul 10 '18 at 20:47
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    The concept of relativistic mass has been abandoned as it only creates confusion. – my2cts Jul 10 '18 at 20:50