Originally posted by pallidin
A coin is tossed in the air, lands on my hand, quickly covered by my other hand so as not to know if its heads or tails.
Is the coin in some quasi-state of heads/tails existence prior to my lifting the covering hand? Wow, I must, as a human observeratory posses very high powers, and surely the coin must quantum-quiver in some way prior to observational influence, as it is hard-stamped heads/tails.
I simply do not buy into the theory, perhaps because in a very curious way, the theory has NEVER been proven at all beyond mathematical constructs. Am I wrong?
Has this theory EVER been shown to actually exist(not inferred) beyond conjecture?
I think this illustrates why there are major misconceptions on the understanding of the state of superposition in QM. Most people have this kind of impression of the quantum state before measurement - that there IS a definite state the system is in. It is just that our ignorance of it that causes us to put it into some mixture of various outcome. The flipping of a coin is usually an example (of classical probability). When you flip a coin, before you look at it, the coin is EITHER heads OR tails, but not both.
If this were a quantum system, the superposition of the various outcomes (eigenstates) would be interpreted as heads AND tails as in the coin example. The question now is, is this merely a "theory", or mathematical artifact, without any experimental verifications? No, it isn't!
Consider two hydrogen atoms. If they are separated far apart, the energy level of each one is well defined and well-described by the Rydberg states. What happens here is that the electron in each atom can be considered to be localized around each H nucleus. In other words, if you only have 1 electron to share between these two H nucleus, an electron would be at EITHER one OR the other, but not at both simultaneous. The total energy of the system is simply the sum of the individual energy of the two atoms.
Now, let's bring them closer and closer to each other until they feel the presence of each other. In mathematical terms, there are now overlap of the wavefunction due to the distortion of the potential energy field of the individual atom. Something interesting now occurs. You can no longer describe the system as being made up of two individual atoms (no surprise here), but more interestingly, the overlap of the wavefunction seems to imply (if we limit ourselves to the Copenhagen Interpretation) that an electron in the system is SIMULTANEOUSLY spreading itself over BOTH nucleus! The superposition of states here includes the superposition over BOTH locations!
The problem here is that if you try to actually make a measurement of the position of an electron in this system, you will cause a "collapse" of the superposition. The outcome then will only show that the electron is either localized at one, or the other. However, there is more than one way to skin a cat... <pun intended since this is identical to the Schrodinger Cat-type state>
Now, we can test the various consequences of such description. One clearest consequence is that, since the wavefuction has a "phase", you end up having what is known as bonding and antibonding states. What is even more interesting is that there is an energy difference between these two states. (Please remember that the emergence of these two states only occur if the wavefunction contains the superposition described earlier.) Since the energy observable (operator) is non-commuting with the position observable, a measurement of the energy state does NOT collapse the position superposition, i.e. it maintains the scenario where an electron are at BOTH locations simultaneously.
Well, guess what? The energy gap between the bonding and antibonding states in H2 molecule is WELL-KNOWN. In fact, chemists have known about this even way before QM was invented. They just did not have a clear explanation for such phenomena till QM came along. This is simply just one example of the "reality" of quantum superposition. It shows that the strange state of a quantum system isn't merely a reflection of our ignorance of the system - there REALLY is a mixture of various outcomes simultaneously. A particle CAN be in several places at one time (superposition of locations). A photon CAN pass through two slits at one time (superposition of path). And get this, a current can flow in BOTH directions at one time (superpostion of current states), as shown in the various SQUIDS experiments.[1]
These, and many other experimental observations, have shown that such things are more than just "theory".
Zz.
[1] J.R. Friedman et al., Nature v.406, p.43 (2002).
