Is matter-energy conservation a part of quantum mechanics?

Yes, it is.

In quantum mechanics per se, that is the quantized version of mechanics, energy is conserved the same way as in classical physics - there is a law of conservation consistent with all the laws of motion. For example, in classical physics, the conservation of energy can be derived from the equations of motion, whether they are in the Newtonian, Lagrangian, or Hamiltonian formalism. In quantum mechanics, similarly, the same follows from the Schrödinger equation.

Most people also refer to "quantum mechanics" in a broader sense which covers all things quantum - quantum field theory, for example, which is related to the theory of elementary particles (the standard model). This is the theory of the virtual particle-antiparticle pairs and such. You should note that virtual particles have the property that they can never be observed (all created ones are annihilated again during any event). They can momentarily break the law of energy conservation BUT one can never see that. The particles hitting the detectors always conserve the total energy exactly, at least as far as QFT is concerned.

The black hole evaporation, mentioned by the above answerer, makes a good example of the above: a virtual pair is produced near the event horizon of a black hole. By chance, one particle flies away but its antiparticle falls into the black hole. Interestingly, however, the absorbed particle actually REDUCES the mass of the black hole exactly by the amount of energy carried away by the first particle, which guarantees that the energy is conserved. That's also why this effect is called an evaporation: a black hole loses its mass (= energy) through the escaping particles.

Hope this helps!

these are the questions that MAKE you believe in god !

good one.

this is the disturbing part of quantum mechanics (QM) and what Einstein struggled with.

the greatness in QM is that it is near perfect tool for examining physical reality but its one small flaw gives it away ( the measurement problem ).

the requirement for a "conscious observer" to collapse the wave equations is the dogma for physics.

without the observer there is no reality but only potential realities ( infinite ). the observer is what makes things "real",

but sadly, the workings of consciousness are never explained by any known physical theory. everything in QM rests with the observer but the observer is outside the quantum system ( subject-object paradox ) and not subject to quantum effects ( otherwise the observer himself would have wave equation with multiple possiblities in the state of observation ). the fact is , consciousness chooses one state on observation and that decides the object wave equations collapse.

when you think about it, the very fact that the universe "pops" into existence from nothing is a violation of matter-energy conservation in the grand scheme of things. perhaps our minds will form another "higher" dimensional reality ( superspace ) where this conservation still holds but not in our lower dimensional universe.

the real problem is in our minds. we create solutions which spawn more problems and then find solutions which in turn....etc etc.

the real answer is that it is truly magical that we are all here talking about this when all the forces of physics are stacked enormously against how far we have come ( and will go ).

for those of you who are atheists, the odds of the cosmos self assembling into a human brain ( which is what science says ) is greater than the lifetime of the cosmos ( 14 billion years ) ! ( and much greater like a million trillion to 1 ) . this was done by fred hoyle, the physicst who theorized about nucleosyntheisis.

i see only this.....if the law of mass-energy conservation cannot hold, what good is physics for ?

( other than making atomic bombs )

( although everyone should still study physics its kool ! )

That's a good question. You're right. Matter-energy can indeed pop into and out of existence provided the mass (or its energy equivalent in joules) x the time it exists in seconds = less than or equal to Planck's constant h. h is a very, very small constant equal to 6.67 x 10^- 34 joule-seconds. This physical quantity is called action. This weird result means that matter-energy conservation isn't the last word in physical laws. One important consequence is that if you've got a very large matter-energy contribution, like the Universe, which is balanced by a very large and almost equal negative energy contribution, like its negative energy gravitational binding energy, then it can pop into existence, last for billions of years and then pop out of existence again. So the Cosmos arose out of nothing and is the ultimate free lunch. You don't need a god to make something out of nothing, all you theists. Another interesting result is that of the virtual matter-antimatter particles which pop into existence just outside the event horizon of black holes, one escapes and the other falls in and disappears. Steve Hawkins showed in the 1970s that this means that black holes radiate matter and energy and shrink, eventually disappearing.