005b Micro and macroscopic reality (cont.)
The second major difference is that microscopic reality displays degenerate states. One example is different states can have the same energy, and we say that the energy of these states is degenerate. This leads to resonance that also does not exist macroscopically.
Two structures can be different but have the same energy. Quantum mechanics considers that both exist simultaneously as a superposition of the two.
Let’s look at resonance a bit more. In an example is the Zeeman Effect where energy levels of are split in the presence of a magnetic field. For illustrative purposes, let us forget about electronic structure of this atom and consider these are the possible states available to electrons (although we will obey the Pauli Principle).
If we count the states in the presence of a magnetic field, in this case we have 12 distinct levels. If the magnetic field is turned off, then those twelve energy levels all have the same energy.
We say the states are 12-fold degenerate with respect to energy. When the field is on, the degeneracy is lifted and now we can distinguish the 12 states because they have a property, energy, that is different between them.
Degeneracy means we cannot distinguish one state from another on the basis of some property, in this case, energy alone.
It is like gravity. On Earth, there is one way up and depending on your position the force of gravity changes. In space, there is no up or down, and therefore all directions are same, or degenerate.
Let us suppose that there is only one electron available and which occupies one of the 12 states when the field is turned on, we know its state, say it is F=2 and m=2 . But when the magnetic field is turned off, we would not know which of the 12 possible ones it would occupy.
Therefore, in the absence of further evidence, any one of those degenerate states can exist at any instant but we cannot know which one. That is the system is in resonance between them all. In the absence of any other information, the electron on the degenerate side is equally likely to be in any one of the 12 states. When the field is on, it is distinguished by its energy and is in one state labels be, in the example by 2, 2.
At any instant, that one electron on the LHS can be in any one of those degenerate states. It cannot, however, be in all 12 states at the same time. It resonates between all 12. If these are the states of one electron only, then those states must be objectively real.
Quantum Mechanics superposes states
Of course this is not the way quantum mechanics views things. In quantum theory this is called the Superposition principle which treats the electrons as being in all the states with a certain probability. Quantum mechanics cannot distinguish those degenerate states. The reason is clear a state is a statistical ensemble, and the electrons that make up the ensemble can occupy any of the states with a certain probability.
Sub-quantum theory should resolve superposition
This gives us another hint about sub-quantum mechanics:
A sub-quantum theory should resolve, or disentangle, the superposition principle into ontic states. That is the statistical ensembles of quantum mechanics is replaced in a sub-quantum theory by individual ontic particles that make up the ensemble.
Degeneracy and resonance are common at microscopic dimensions and not restricted to energy.
Just because a sub-quantum theory is objectively real does not mean it is “classical” because indistinguishability and resonance lead to new predictions that do not exist in the macroscopic.
We have seen already how such properties account for 90% of the hydrogen molecule’s bond energy. Recall a chemical bond is completely quantum with no classical contributions whatsoever. There is nothing classical about it.
Hence, since these properties must carry over to any successful sub-quantum theory, it could predict new phenomena that can be described by neither classical nor quantum mechanics. Is there anything that cannot be described by either classical or quantum mechanics?
It seems so. I mentioned in my last entry there is one experiment where quantum fails and this is it. “Anomalies in experimental data for the EPR-Bohm experiment: Are both classical and quantum mechancs wrong?” by G. Adenier and A. Khrennikov published in 2008 on the quantum archives. A careful analysis of the data shows that no known theory explains the data.
Even so, in both the micro and the macroscopic, objective reality means that all objects possess exact values of their defining properties. However new properties exist microscopically that cannot exist macroscopically and these properties arise from indistinguishability and resonance.
Up to now I have not given many examples. Over the next few entries, I will discuss the Stern Gerlach experiment and use the objective data it gives to illustrate many of the ideas that we have come across so far.