Originally posted by Gale17
energy is not a physical thing right? or wait, i just confused myself... ok how about, energy isn't matter, that's a good start. ok, energy comes in different ways though ie, light heat sound. ok, is gravity energy? is speed, or wait, do i mean enertia? and as far as potential energy goes, can potential energy be trasformed into any kinds of energy? or i don't know... I'm just terribly confused.
I'm just going to discuss a sliver of what special relativity and quantum theory have to say about energy and in particular, how they differentiate between energy with and without mass known as "matter" and "radiation" respectively. (Note that I'm following the practice in high energy physics of referring to rest mass simply as mass.)
Special relativity:
For matter of mass m traveling at non-relativistic speed v the "mass" increase formula of special relativity may be approximated as m(v) = m(1-v
2/c
2)
-1/2 ≈ m+mv
2/2c
2 = m+KE/c
2 in which the kinetic term indicates that m(v) shouldn't be viewed as mass in the ordinary sense. Next, note that the kinetic energy of matter colliding non-relativistically to form a single mass m at rest is radiated away as the heat of collison U
collison = KE in returning m to the temperature of it's surroundings. By conservation of energy m(v) ≈ m+U
collison/c
2, so heat also contributes to m(v). But then all non-translational energies contribute since they can transmute into heat without changing a body's mass or speed. However, we can't prove that energy must account for
all of m(v): It's logically possible that some strange undiscovered "charge" also contributes to it. Thus - and this is the part that's often misunderstood - mass-energy equivalence at bottom is a
conjecture, which however has never been falsified (though from the more general standpoint of general relativity, it seems impossible that it ever could).
Unlike say classical or quantum mechanics which do not explain but merely invoke and are consistent with energy conservation as an empirical fact, SR has something to say about energy conservation itself, specifically, that it's a consequence of lorentz-invariance. This is an example of the direct correspondence between symmetry and conservation laws established in noether's theorem. Applied to SR, it describes conservation of linear and angular momentum as consequences of translational and rotational invariance respectively. Put another way, conservation of energy-momentum is a consequence of the lorentzian geometry of spacetime. All of this gives rise to the idea that energy and 3-momentum are the time and spatial components of a lorentz 4-vector p
μ = (E,
p), the spacetime 4-momentum, in terms of which p
μp
μ ≡ η
μνp
μp
ν = - m
2 is lorentz-invariant where η = diag(-1,1,1,1) is the minkowski metric. From m(v → c) → ∞ we see why accelerating matter to light speed is forbidden, namely, it would violate energy conservation. On the other hand, radiation always travels at the speed of light.
Quantum theory:
Lorentz-invariance requires that the elementary constituents of matter and radiation (be they described as particles, fields, strings etc), be treated differently with respect to the lorentz group. Specifically, mass and spin indicate how quantum states must transform under lorentz transformations.
In quantum theory we have examples of matter and radiation being completely converted into one another including particle-antiparticle annihilation and creation, various decay or emission mechanisms, as well as scattering processes transmuting particle type.
