I feel as though Demystifier has made tons of claims without any arguments to back them up. I gave a perfectly quantitative explanation of wavefunction collapse (which doesn't go very far beyond the basic postulates of quantum mechanics), and under the assumption that the Schrodinger equation evolves wavefunctions continuously through Hilbert space, it should be obvious that it immediately implies the Quantum Zeno effect. If you disagree that it constitutes a perfectly quantitative demonstration of the Quantum Zeno effect, then I refer you to Griffiths Intro to Quantum Mechanics Section 12.5 (second ed. p 431-433).
So please back up your following claims, which you have merely stated without any support, quantitative or otherwise.
1)
Just the opposite, decoherence is something that can be derived from the Schrodinger equation itself, and in practice it is very difficult to avoid it whenever the system strongly interacts with the environment.
2)
That's true, but a correct QUANTITATIVE description of Quantum Zeno Effect cannot be made without decoherence.
3)
But can we really know that decoherence is really occurring, and not real wavefunction collapse?
In some cases, yes.
4)
Are you saying that it's impossible to get an exact quantitative description of the quantum zeno effect using real wavefunction collapse?
Yes, that's what I am saying. But still, a collapse may often serve as a good approximation.
I have already addressed 2): I think my wavefunction collapse argument is a correct quantitative description, check Griffiths.
I am not so sure about 1). In practice, yes, there is always an environment that interacts with the system, and can be considered to cause "decoherence". However, in standard quantum theory, the entire universe can be considered to be described by a single wavefunction: there is no "environment" that causes decoherence. Please show me quantitatively how it can be derived from the Schrodinger equation without the assumption that there is some external "environment", since that that assumption is NOT one of the standard postulates of quantum theory.
I'd appreciate if you could back up 3) and 4) as well.
I think decoherence is a much more obscure and conceptually elaborate demonstration of the observer effect, whereas wavefunction collapse is one of the basic postulates of quantum mechanics. It seems as though you don't even disagree with wavefunction collapse: if you admit its existence, it's clearly a better example of the observer effect than any "decoherence" phenomena.
Let me ask another question: if decoherence were the definitive explanation for the observer effect, wouldn't Schrodinger's Cat be rendered moot? Based on the various claims you've made, I guess your argument would be something like: "once a quantum system interacts with some macroscopic system, like a cat, it decoheres." As a less philosophical example, let's suppose we put a geiger counter inside a box with a radioactive atom, whereby the geiger counter has two states "Not Decayed" or "Decayed" which correspond to the radioactive element not decaying or decaying. Does the presence of the macroscopic geiger counter inside the box collapse the radioactive element into either the decayed/not decayed state? This is what that argument seems to imply. I argue that's just an interpretation of quantum mechanics: there is an alternate interpretation that states that until the geiger counter is "observed," it too is in a superposition of states. Granted, the "box" is an idealization--no box can shield a system from the environment totally, but the idea of a universal wavefunction ensures that there is at least one system that is shielded from any sort of "environment."
