Kinetic Energy & Relativity: E=mc^2

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The wikipedia article on Kinetic Energy: http://en.wikipedia.org/wiki/Kinetic_energy

"Kinetic energy for single objects is completely frame-dependent (relative). For example, a bullet racing by a non-moving observer has kinetic energy in the reference frame of this observer, but the same bullet has zero kinetic energy in the reference frame which moves with the bullet."

If two people in separate reference frames disagree on the kinetic energy of a bullet, do they also disagree on the mass? (I'm thinking of E=mc^2 here)

 

[HallsofIvy]

Well, yes, of course. If an object has rest mass m₀ (the mass in a frame relative to which it has speed 0), then an observer moving at speed v relative to the object it has mass $m_0/\sqrt{1- v^2/c^2}$- the faster it moves (relatively, of course) the greater the mass.

 

[DrGreg]

The subject of "mass" in relativity crops up regularly in this forum, and it necessary to point out the word has (at least) two different meanings in relativity

1. Relativistic mass includes within it the kinetic energy of the object, and so depends on the relative speed of the object to the observer. Different observers can ascribe different values of relativistic mass to the same object at the same time.
2. Invariant mass, also known as rest mass, excludes kinetic energy, and it a property of the object itself and does not depend on the observer.

Not all authors agree which of these two definitions to use when you say "mass" without further explanation. The modern convention amongst most physicists is to use definition 2, but there are still some people who use definition 1. Neither definition is technically wrong, but one reason 1 is considered unnecessary is because relativistic mass is really just another name for "energy" (via E = mc²). For an object that is stationary relative to the observer, the two definitions give the same answer.

So the answer to your question is "yes" if you mean relativistic mass, but "no" if you mean invariant mass.