In reply to Dawin123
Talking about proportional responses. Nonetheless, I am going to point out that no pure classical mechanics can solve for a photon fluid, known as the ultraviolet catastrophe. A problem which was solved by Planck's law, which treated each electromagnetic mode as a quantum...
I must say I am intrigued. Those are beautiful descriptions, and they are often sparse in a Thermodynamics book.
Either way I believe solving this problem cannot be by means of Thermodynamics alone, as the temperature of the cosmic background radiation is not due to a fluid, or any classical...
ok there's one detail that I have ignored that may have been what you were looking for. wave mechanics failed to comply with the relativistic energy. at the time dirac solved this by introducing matrices that solved the wave equation if inserted, instead of just the single wave function. for...
i really really think its obvious. for example for the stern-gerlacht experiment, you know the state of the initial particle (spin) as you prepare them in a particular way, and you know the state will change because they will go through the potential, therefore state is time dependant and is...
the mathematician ofcourse, tends to put hard problems in terms of problems that have been solved before. There is a combination of theories that goes behind why you can solve the wave equations in this manner, and going back to the beginning of what I was trying to say, it really boils down to...
I was under the impression, that quantum measurement of the first kind would leave the wave function collapse. clearly that's not the case.
in a quantum non-demolishing experiment you may reverse the change you had done to the system to leave it back in a superposition state. Information taken...
i may have confused cosmic background radiations with vacuum fluctuations. either way even if you manage to get rid of the cosmic radiations, you cannot get rid of the nonzero vacuum fluctuations ground state energy. btw temperature is another measure of the internal energy.
diagonalising a matrix is equivalent to rearranging its eigenbasis such that they are all linearly independent, and thereby equivalent to solving a set of differential equations coefficients to find unique solutions for each one.
for more information you may refer to a mathematical methods for...
I think it is important to know what we know exactly as we do the calculations, rather than simplify them just so that you understand in classical terms, because there is really no alternative. If classical mechanics really explained everything, then there wouldn't be so much success attached to...
The Heisenberg picture is the one that is physically realisable in real experiments. In reality the particle is moving through some potential which leads to changes in it's basis and we can do experiments to find out what that potential looks like. we can make some guesses about what the state...
That's not true. the third law states that zero kelvin is unreachable. Quantum mechanics confirmed this by investigations of the Casimir effect: there's no obligation that you read this obviously, unless you find it interesting:
http://en.wikipedia.org/wiki/Casimir_effect
Essentially the ground...
a rotation in 3 space, is a transformation upon which the length of the initial vector is unchanged.
a Lorentz transformation, is a unique transformation in 4 space that preserves the length of the 4-vector of any line in 4 space, and it necessarily holds if there is a limit to translational...
in the Heisenberg picture, the states are constant in time, and the evolution is carried on by the operators, thereby allowing you to put the equations in tensorial form (matrix), as the gradient of a state tensor is always of the second rank, this simplifies the calculations provided you know...