I Why is energy not Lorentz invariant?

[Frank Castle]

Yes. As someone said on the previous page, there are unfortunately two different definitions of scalar in use. Basically:

1) a number (i.e., not a vector);

2) a quantity that is invariant and whose value is just a number.

According to the first definition, total energy, kinetic energy, and rest energy are all scalars. According to the second definition, rest energy is a scalar but total energy and kinetic energy aren't.

I guess one needs to be careful then when one stipulates the transformations in which a particular quantity is a scalar with respect to.

Ok cool, I think it's becoming clearer to me now. Thanks for your help, and thanks for the previous post (#29) detailing the relativistic energy derivation.

 

[Traruh Synred]

Apart from technical mathematical cases (tensors) you might just consider 'scalar' to be a real number as opposed to a set of numbers. E.,g., px is a 'scalar' but it makes no sense to ask how it transforms other then in the context of being one element of a 4-vector. Energy is just the same.

Some 'energies' are defined a non-invariant way. E.g.. temperature is given by the average energy of the particles making up a block of stuff. It is defined only in the rest from of the stuff. It would not make sense to say that a object heats up when you run pass it even though the energy of the particles making up your stuff would be higher, this average energy would not be useful in thermo dynamics where the average energy in the rest frame of the stuff is the relevant quantity.

If you were computing the scattering of one blick of stuff with others than it would be relevant to treat the energy contributed by to the total by the 'internal' motion of the particles to the four vector describing the motion of he block. This is, typically, negligible even for very hot objects.