Exploring the Impact of M = E/c^2 in Modern Physics

[vanhees71]

Indeed, people where confused about the relativistic redefinition of quantities till much later. Particularly thermodynamics and statistical physics was a mess until the late 1960ies, when people realized how to define the phase-space-distribution function as a scalar and following from that the thermodynamic potentials and other quantities like temperature and chemical potential in a consistent relativistic way as scalars. This was particularly due to the raised interest in General Relativity at this time, where you cannot in any way deal with complicated non-covariant quantities like "relativistic mass" or frame-dependent temperatures. All this is far from trivial!

 

[Orodruin]

As I wrote in the Insight (FAQ at the time), one has to be very conscious about what one means with ”mass”. In relativity, ”mass” is related to the invariant norm of the 4-momentum. The term ”relativistic mass” is misapplied in many senses as it is neither related to the classical gravitational mass nor to the actual inertia (which is not a scalar!). To me, the great insight of $E=mc^2$ is that the inertia of an object in its rest frame (which is well defined and can be directly connected to the concept of mass in classical mechanics) is its rest energy.

 

[Mark44]

Relativity still says that $E=mc^2$ is a special case of $E^2=m^2c^4+p^2c^2$

Long before then we are using $E^2=(m_0c^2)+(pc)^2$

I don't think anyone has noticed, or at least commented on, but there's a typo in the first term on the right side. There's a missing exponent that should appear outside of the right parenthesis, as in $(m_0c^2)^2$.

 

[Nugatory]

there's a typo

So there is - thx. Fixed

 

[Vanadium 50]

"relativistic mass" is out of fashion since 1907

Just out of curiosity, why 1907? I though Minkowski was in 1908.

And if there was any doubt that relativistic mass produced nothing but confusion, this thread should remove it.

 

[vanhees71]

I think in the famous review article of 1907, Einstein used $E/c^2$ as a measure of inertia and also argued that it is the "source of the gravitational interaction". It may be that he still called this quantity "relativistic mass", but there was no hint anymore to so confusing concepts as also direction-dependent "relativistic masses". I interpret this as a reaction to the discovery of the correct equations of motion by Planck (1906) and the first development towards a relativistic theory of gravitation, which finally ended up famously with GR in 1915, and it's not only energy but the energy-momentum-stress tensor of all fields except the gravitational field that is the source of the gravitational field.