Firstly thankyou for this clear and informed explanation.
Now I'll explain my notation. If a cat is definitely dead I will denote it: |Dead>. If it is definitely alive then: |Alive>. In Schrodinger’s cat experiment we have that the state is |Dead> + |Alive>. Now my symbols above can contain more information. For instance the state of the Cat being dead and me off in Budapest is:
|Cat is dead and I’m off in Budapest>
Any of these |Insert phrase> things are what may be called a wavefunction.
Each of the |state> terms is the probability of that particular state being the eventual observed state. Is that right? Thus the sum of all the |state> terms = 1 (e.g. |Dead cat> + |Alive cat> = 1). Is that correct?
Would each |state> be a term in the Schrodinger equation? Or are the staes as you have described them independent of time and thus not part of the Schrodinger equation?
Many Worlds:
Quantum Mechanics applies at all levels. This means even large scale objects like you and I can be in superposition. So what happens in this model is that the state of the universe goes from:
|State of World> =
|I haven’t looked at the cat yet and the cat is alive> + | I haven’t looked at the cat yet and the cat is dead>
To
|State of World> =
|The cat is alive and I see him alive> + |The cat is dead and I see him dead>
There is no collapse here because the first state can evolve smoothly into the second in the standard formalism of quantum mechanics. One should also note that Many-Worlds is totally deterministic.
In the case of many worlds dowe consider splitting worlds at the amcroscopic level (i.e. dead cats and alive cats) or the subatomic level or both? Presumably both?
So from any instant in time there are literally as many worlds branching off as ther are posible states for subatomic particles in the universe? Is that correct? If so the number of 'worlds' created at every instant must be vast beyond comprehension even in cosmological terms.
Bayesian interpretation:
The wavefunction only represents our knowledge of the system. Hence collapse is simply when we learn more. That is upon seeing the cat alive, we know the cat is alive and hence there is no probability for anything else. Collapse is therefore not a real event.
Historical Copenhagen/ Bohr Interpretation:
We are classical thinking things. Hence the quantum world makes no sense to us. The formalism of QM is the closest we will get to understanding it. It is a formalism for explaining our big classical world’s interaction with the small quantum world. Collapse is a part of that formalism. Like all of QM though we must not try to understand what it really is/means. That is all.
Are these two not essentially the same? Both suggest that more knowledge/perception is the answer even if they disagree as to how possible that may be in practise.
Modern Copenhagen:
This is actually the only model with collapse in it. Basically we have:
|State of World> =
|I haven’t looked at the cat yet and the cat is alive> + | I haven’t looked at the cat yet and the cat is dead>
Goes to:
|The cat is alive and I see him alive>
Or
|The cat is dead and I see him dead>
With a 50:50 chance of each. This is collapse, because there is no way to go from the first state to either of the second two, in the standard formalism, without an instant jump.
Dynamical collapse:
Basically Modern Copenhagen with attempts at modelling what process causes collapse.
Are there any theories as to what the mechanism of collapse might be?
Do you personally subscribe to any of the interpretations that you have outlined above?
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