By Harrison D.M.
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Extra resources for About Mass-Energy Equivalence
17) Energy E and (inertial) mass m are – except for the factor c2 – just two names for the same thing, E = mc2 = m0 c2 1 − v 2 /c2 . 18) 28 Mechanics of Special Relativity When this was ﬁrst formulated by Einstein, it was a very surprising result, with remarkable consequences, so that the above relation became a trademark of Einstein’s. 18) is that, besides a part due to the motion of the particle, there is an energy m0 c2 due to its rest mass. Kinetic energy can be transformed into other forms of energy, for example into heat, and so it was argued that the same should be the case for the rest energy m0 c2 ; we know nowadays that this is true.
To be precise, let us have a cause at x1 = 0, t1 = 0, and its eﬀect at x2 = L, t2 = T . The velocity of that phenomenon obviously is V = L/T . An observer Σ , moving with velocity v, sees the cause when t1 = 0, and 22 Our world as a Minkowski space the eﬀect when ct2 = (cT − vL/c)/ 1 − v 2 /c2 . e. if vV > c2 . 16) This relation can be true only if at least one of the two velocities exceeds that of light. So to avoid this acausal behaviour, one has to demand: velocities greater than that of light must not and cannot occur.
E. also after a Lorentz transformation has been performed). 21)! 2 Tensor algebra 43 (the middle term of this equation is the rule for calculating the determinant of a matrix). We see that only for proper Lorentz transformations with Ln a = +1 do we get the correct result ε1 2 3 4 = 1; in the general case, we have to add a factor Ln a to the transformation law. 2 Tensor algebra All rules for handling tensors have to guarantee that the results are again tensors. The proof of the tensor property will only occasionally be given in the text – we recommend the reader to ﬁll that gap.
About Mass-Energy Equivalence by Harrison D.M.