The uncertainty associated with a superposition state of a certain system isn't related to other systems in any way.Scott Hill said:A particle in a quantum harmonic oscillator can be in a superposition of energy eigenstates, and so the energy is not well-defined. However, energy is still conserved, so if I understand it correctly the "uncertainty" in the superposition's energy must be matched by uncertainty elsewhere in the Universe.
If you don't have a definite energy, energy conservation refers to the expectation value of energy.Scott Hill said:or is there another explanation for how energy conservation works here?
kith said:The uncertainty associated with a superposition state of a certain system isn't related to other systems in any way.
On the other hand, if you have two systems in an entangled state, you cannot assign definite state vectors to the individual systems in the first place. Look up the difference between "pure" and "mixed" states if you are interested in this.If you don't have a definite energy, energy conservation refers to the expectation value of energy.
First of all, bringing your system into contact with a measurement apparatus makes it an open system, so its energy need not be conserved. Naturally, one would try to use a full description including the apparatus and see what happens there. But then, you unfortunately run into all the well-known problems of the foundations of QM.Scott Hill said:OK. Collapsing the wavefunction can cause a dramatic change in the expectation value of the energy, though; how is that energy accounted for?
Energy conservation is the principle that energy can neither be created nor destroyed, but can only be converted from one form to another. This means that the total amount of energy in a closed system remains constant.
In quantum mechanics, superpositions refer to the state of a system being in multiple states at the same time. This is in contrast to classical mechanics, where a system can only be in one state at a time.
Superpositions do not violate the principle of energy conservation, as the total energy in a system remains constant even when the system is in multiple states simultaneously. This is because energy is a conserved quantity and cannot be created or destroyed.
Entanglement is a quantum phenomenon where two or more particles become correlated in such a way that the state of one particle cannot be described independently of the state of the other particles. This means that the particles are inextricably linked, even if they are separated by large distances.
In quantum systems, energy conservation and superpositions can lead to entanglement. When particles are in a superposition of states, their energy states are also in a superposition. This can result in the particles becoming entangled, as their energies are correlated and cannot be described independently. This is an important aspect of quantum mechanics and plays a key role in quantum computing and communication.