Actually, the general relativity (GR) requires a generalization of the straightforward conservation of energy principle that applies to most physical systems of interest. We expand on this issue below, but the short version is that the generalization is the general-relativity energy-momentum conservation equation holds (see also Car-120).
What maintains the structure? Forces.
Note all forms of energy can be changed into all other forms energy. That is why they are all energy. The changes are NOT always easy.
What causes energy transformations? Forces.
Two things:
Q: But there are negative energies, but NO negative masses.
A: There are NO negative masses, but there are negative contributions to mass and that is what negative energies are. If you add up all the contributions to energy in a system, the result is always positive---or so we believe.
Q: Can you elucidate why we ordinarily do NOT notice changes in mass when we change energy: e.g., when we change the heat energy content of a system?
A: Most of those changes in energy create changes in mass that are too small to measure ordinarily. For example, the fiducial minimum food energy needed per day per human is
7.5 MJ = 7.5*10**6 J = (1.7925 ... )*10**6 calories
= (1.7925 ... )*10**3 food calories
= [ (8.344875 ... )*10**(-11) kg ]*c**2
(see Wikipedia:
Food energy: Recommended daily intake).
You can see that this change in
mass
and all others like it are immensely small
by everyday-life standards
and even by ordinary laboratory standards.
So it is NO surprise that the
law of conservation of mass
was thought to absolutely true, rather than just a usually valid approximation
before the introduction of
E=mc**2
with special relativity
in 1905.
Because all energy has an associated mass or vice versa, they are both manifestations of the same thing which we call mass-energy in Relativityspeak. In fact, nowadays people can use energy, mass, and mass-energy as synonyms. The term is used often depends on what aspect of mass-energy is being emphasized.
Usually, heat energy and microscopic forms of binding energy are included in rest mass for macroscopic or bound microscopic composite particles (e.g., atoms and molecules).
However, some truly elementary particles (i.e., those NOT composite of anything smaller) possess (apparently) intrinsic rest mass. Examples include electrons and quarks. Note in modern understanding, the subatomic particles proton and neutron are elementary particles. They are composite particles since they are made up of bound quarks. The composite particles (e.g., molecules) and all macroscopic objects have intrinsic rest mass from their elementary particles, of course, and other kinds of rest mass too as discussed above.
Particles with instrinsic rest mass are massive particles. Particles with NO intrinsic rest mass are massless particles. The photon is the best known example of a massless particle. All massless particles are elementary particles (see Wikipedia: Massless particle).
Note, all massless particle actually have mass since they have energy and E=mc**2 holds. They just do NOT have rest mass because they are NEVER at rest relative to an inertial frame. They always move at vacuum light speed c = 2.99792458*10**8 m/s ≅ 3*10**8 m/s = 3*10**5 km/s ≅ 1 ft/ns relative to all inertial frames. How, they can do this is understood relativistic physics, specifically special relativity. For a full explication of inertial frames, see Mechanics file: frame_basics.html and for the special relativity, frame invariance of the vacuum light speed, see IAL 6: Electromagnetic Radiation: The Fastest Physical Speed.
The three fundamental forms seem to intrinsic rest mass, kinetic energy (i.e., energy of motion) and force field energy (i.e., the energy of the fields that cause forces).
All other forms are, yours truly believes, sub-forms of some degree including forms that are sums of other forms. The forms can overlap: an amount of energy can belong to multiple forms. In fact, forms of energy are often defined just for particular contexts: e.g., sound wave energy for the sum of various other forms that add up to be the total energy of sound waves.
Below is a non-exhaustive list of main energy forms:
You sometimes hear the expression PURE ENERGY, but there is NO such thing in physics. Energy has some form. That said, sometimes people describe electromagnetic radiation (EMR) as PURE ENERGY because it does seem like the closest thing to PURE ENERGY.
For example of energy analysis, the food web illustrated in the figure below (local link / general link: energy_transformation.html) can be analyzed in terms of energy transfers and transformations.
All other measurements are indirect: you measure several quantities that are
characteristics of a body's state that are NOT
energy and calculate
energy from a
formula that contains those quantities.
For example, kinetic energy
is the energy associated with the motion of body and is calculated
in the classical limit
from the formula
KE = (1/2)mv**2, where m is the body mass
and v is the body speed.
Another example is that there is an exact
formula
for the energy density of
electromagnetic fields calculated
from characteristics of the
electromagnetic fields
(see electric field energy
and magnetic field energy).
The formula is pretty simple actually:
Probably it is absolutely true in the limit
of flat spacetime (AKA Minkowski space),
but NOT absolutely in
curved spacetime
which is a spacetime predicted by
general relativity (GR).
This means the
conservation of energy
is probably as valid as we need in most local regions of the
observable universe,
but probably NOT absolutely in intense
gravitational fields
like very near black holes
and NOT in application to the
observable universe as a whole.
The failure of
conservation of energy
to be absolutely valid is disconcerting, but all is NOT lost.
The
energy-momentum conservation equation of
general relativity
is the generalization of
conservation of energy law
and it is absolutely valid in
general relativity.
However, the
energy-momentum conservation equation
is a lot harder to understand and work with than the
conservation of energy law.
See Carroll, 2004, p. 120.
For further discussion of
failure of
conservation of energy
in general relativity, see
Relativity file:
e_mc2.html.
The upshot is that
conservation of energy
is a valid emergent principle
and we usually do NOT want to say more than it is absolutely valid which
saves us from getting into long discussions of
arcana of
general relativity.
energy density = εE**2/2 + B**2/(2μ) ,
where E is the electric field magnitude at a point,
B is the magnetic field magnitude at the point,
and ε and μ are constants.
The formula gives the energy density at the point.