Andrew Mason said:
I didn't invent the concept of mass-energy equivalence. When you add energy to an electron traveling at 0.9999999999999c the energy goes almost entirely into increasing the mass of the electron.
from the POV of the observer that the electron is whizzing past at 0.9999999999999c.
Andrew, for some reason it has become out of vogue to think in terms of relativistic mass.
E = m c^2 = E_0 + T
makes sense when m is relativistic mass and
E_0 = m_0 c^2
is rest energy (i think this is the equation most people mean when they say " E = mc
2 " and T is kinetic energy (energy which depends on who is watching).
The root of the apparent difference between mass and energy is the distinction that we make between space and time. Einstein showed that space and time are observer dependent and not absolute. So if time and space are equivalent, space^2/time^2 cancel each other and mass=energy.
this equating of dimensions can, in my opinion, eventually lead to madness. so if we equate space and time (there's an arrow of time, but there is no arrow of space outside the event horizon of a black hole) that is effectively setting c = 1. that means (besides that length is the same thing as time), that
E = m c^2
becomes
E = m
and energy is the same thing (or same dimension) as mass.
why stop there? let's do like Planck and set \hbar = 1 and G = 1. so
E = \hbar \omega
becomes
E = \omega
and energy (which is the same as mass) is the same thing as frequency or 1/time. and since time is length, then mass is the same as 1/length. now
E = G \frac{M m}{r}
becomes
E = \frac{M m}{r}
so now energy (the same thing as mass) is the same as mass
2 x length
-1. that says the same thing that mass is the same as length.
so length = 1/length? or time = 1/time? or mass = 1/mass? all this would be true if we say that length (or space), time, or mass are all dimensionless.
so, for my money, either:
1. there is such a thing as different dimensions of physical quantity and mass is not the same as length nor is the same as time. (so energy is
not dimensionally the same thing as mass.) i would also view electric charge as a fundamental dimension, but the
cgs people might not.
or
2. there is no such meaningful thing as dimension of physical quantity and they are just human constructions which no deep physical correspondence.
that's my story and I'm stickin' to it.
.