Brutkey

Kaitlyn~Ethylia
@KaitlynEthylia@void.lgbt

@darkwiiplayer@tech.lgbt but how does that make sense, The total amount of energy in the universe is constant but depending on your reference frame that energy is expressed in completely different ways? that seems absurd. If object A and object B are the only things in the universe, and to B, A appears to be moving forward, then to B, A has kinetic energy, but to A, B appears to be moving backwards and so it's the one that has kinetic energy. Like yeah it's still the same amount of energy so conservation of energy still works but surely conservation of energy is an objective thing, so the total energy of the universe is objective but the energy of any individual part of the universe is subjective? but if you have 3 objects in the universe, A, B, and C. A and B appear to me moving forward to C, and C appears to be moving backwards to A and B, then surely from the perspective of A and B, there is half as much total kinetic energy compared to the perspective of C, where both A and B are moving??

Popstar Tourist
@octonion@tech.lgbt

@KaitlynEthylia@void.lgbt @darkwiiplayer@tech.lgbt If we're talking classical (not quantum) mechanics then the issue is that "energy" on it's own is as meaningless as "the z component" of a three dimensional vector. It's going to be completely different based on the choice of coordinates.

One should instead talk about the 4 dimensional energy-momentum vector
(E, p_x, p_y, p_z) and the thing that every observer will agree on is the dot product of this vector with itself in the appropriate metric which works out to

E² - |p|²c² = some constant :)

(where |p| is the usual 3-space vector magnitude). Considering a frame where p=0, taking the square root of both sides and revealing what this mystery constant is gives

E = mc²

Popstar Tourist
@octonion@tech.lgbt

@KaitlynEthylia@void.lgbt @darkwiiplayer@tech.lgbt Another way of looking at it is that in classical mechanics the dynamics of the system are entirely determined by something called the Hamiltonian. In quantum mechanics the Hamiltonian becomes an operator and the eigenvalues of the operator are energy.

(It's time-translation symmetry of the Hamiltonian that gives rise to conservation of energy. The Hamiltonian of the universe does not have this symmetry, because the Universe is expanding, but locally or for closed systems it's a very, very good approximation.)

Kaitlyn~Ethylia
@KaitlynEthylia@void.lgbt

@octonion@tech.lgbt @darkwiiplayer@tech.lgbt These are a lot of words that it will take a lot of googling to figure out but thank you

Popstar Tourist
@octonion@tech.lgbt

@KaitlynEthylia@void.lgbt @darkwiiplayer@tech.lgbt Sorry if that was overwhelming, autistic girl with a Ph.D in the stuff given the chance to infodump :)

I'm happy to clarify anything.

Kaitlyn~Ethylia
@KaitlynEthylia@void.lgbt

@octonion@tech.lgbt @darkwiiplayer@tech.lgbt I'm about to go out but I will probably have many follow-up questions once I've had the chance to go through and read it thoroughly, as well as probably the wikipedia articles for "the Hamiltonian", "eigenvalues", and also try and figure out what was meant by "dot product of this vector with itself in the appropriate metric"