Re: [Phys-L] let's define energy

[John Denker <jsd@av8n.com>]

On 09/29/2015 12:52 PM, Jeffrey Schnick wrote:

> /Physics/ energy is just mass.

I wouldn't have said that.  The equation E=mc^2 is
perhaps the most famous equation in the history of
equations ... but it is widely misinterpreted.  The
E on the LHS is the rest energy, not the total energy.
This is the meaning that Einstein intended in his
original paper, and remains the only reasonable
interpretation.

Energy is conserved.  Mass is not.   [1]

> The usual objection to that is that the kinetic energy of a particle 
> is not its mass.

Indeed.  That is a fatal objection ... perhaps not
quite as fatal as [1], but fatal enough.

> In interactions, what matters is the kinetic energy of the system in
> the reference frame in which the center of mass is at rest.

That is not a viable way of getting around the fatal
objection.  In particular, when watching a baseball
game, I can define "the system" to be bat+ball ... or
define it as bat+ball+earth.  If you insist that there's
only one reference frame in which the energy can be
correctly calculated, all of physics comes to an end.

Not to mention the fact that it violates Galileo's
principle of relativity.

In special relativity, energy is one component of the
[energy, momentum] 4-vector.  In any particular frame,
each component of this 4-vector is separately conserved.
Mass is the invariant norm of this 4-vector.  Oddly
enough, even though it is intimately related to some
conserved quantities, and even though it is Lorentz
invariant, it is not conserved.
  https://www.av8n.com/physics/spacetime-welcome.htm#sec-invariance-conservation
or equivalently
  http://www.av8n.com/physics/spacetime-welcome.htm#sec-invariance-conservation