Exogen:
Re: delayed choice experiment. I think you're talking about Bell's theorum/Bell's Inequality, quantum entanglement and all that.
Various quantites in physics are "conserved" - which means they can't be created or destroyed. One example is momentum. Eg. If two objects are initally connected together and have zero momentum (they're not moving) and then fly apart, so that they both now have some momentum (they're moving), their momenta must be equal and opposite, and thereby still add up to zero.
Another example is
angular momentum, or spin. This is one of the examples used to illustrate quantum entanglement. Two "connected" particles, initially with zero spin fly apart to an arbitrarily large distance. If you then measure the spin of one of them and find it to be, say, 1 unit, then you've implicitly measured the spin of the other. It has to be -1 units if angular momentum is conserved. That's all fine and unremarkable in the classical world. But in some interpretations of Quantum Mechanics the spin (or other properties) of the particles are deemed, in some sense, not to exist until they are measured. They are thought of as existing in a superposition of all possible states represented by a set of probabilities, expressed mathematically as the famous "wave function". The act of measurement "collapses" this wave function into one of the possible states.
But this seems to imply that the implicit measurement-from-a-distance I mentioned above causes something to happen instantly at a distance, violating the laws of causality. If Quantum Mechanics is right, there are no hidden variables, and the state of the particles' spins before they are measured is truly uncertain, then the act of measuring one causes the other to be instantly determined.
One objection to this is that even if that is so, the information about that act of measurement cannot be transmitted faster than light from the explictly measured particle to the implicitly measured one. So even if the measurer of the first particle now knows with certaintly the state of the other particle, he can't do anything with that information. And it is information, or influence, whose propogation faster than light is prohibed by the theory of relativity.
Anyway, that's a very very brief summary. The whole subject is hugely subtle and complicated. It often sounds, at first glance, all completely ridiculous. (and at second glance.) I remember (vaguely) studying it at University and it's very difficult not to get sucked into the mathematics and start to see it as just a huge convoluted exercise in abstraction with no bearing on reality. You have to remind yourself that QM is completely grounded in empirical observation. It has to be. It could never get away with being so crazy otherwise!
It's very difficult to both understand the maths and be able to step back and look at it philosophically, I think.
Xris:
I know an electron at rest has mass but when it moving it expresses that mass as energy in the form of a wave.
Not quite. Electrons, like all particles with mass, have "rest mass" and they gain mass when they gain kinetic energy - they move. The frequency of an electron (or any other piece of matter) is related to its momentum because the wave represents the uncertainty in its
position. And the uncertainty principle states that there is a fundemental uncertainty in particular
pairs of properties. One such pair is momentum and position.
So electrons, protons, neutrons, atoms, molecules, rocks and buses all have an associated wave function with a frequency which is related to their momentum and energy.