Posted: Sep 12, 2011 12:09 am
by hackenslash
Let's try a slightly different approach:

First, it's important to outline the precise details of the thought experiment, because that's where the devil resides.

In the experiment, the cat is placed in a box with a vial of poison, which is triggered to release by the decay of a single atom of some suitably radioactive element. Now, the exact moment of decay is an entirely statistically independent event, which cannot be predicted with any accuracy. It may decay as soon as you close the box, or it may not decay for millions of years. Indeed, only when you have sufficient atoms of said element for the law of large numbers to appply can you make any sort of prediction, and that will be a probabilistic one. To simplify this concept, if you have two atoms, then the half-life predicts that one of them will decay in x amount of time, but you can't predict which of the two atoms or when in that time the decay will occur. This is very much an oversimplification, and in reality, it requires far greater numbers of atoms to present enough for statistical applications to have any predictive value.

Under the Copenhagen interpretation, the atom exists in both the decayed and un-decayed states simultaneously, and observations collapses the wavefunction, defining the eigenstate of the atom. Thus, in the thought experiment, the cat is both alive and dead at the same time, because the atom is both decayed and un-decayed, and therefore the poison is both released and unreleased at the same time.

Panderos wrote:Ok so, until I look in the box, the cat might be in the alive state, it might be in the dead state, or it might be in the superposition of dead and alive states.


No. It's always in a superposition of both alive and dead. The reason for this is that the poison is both released and unreleased at the same time.

Then I look and the wavefunction collapses and it will be either dead or alive.


Yep.

But that implies theres something special about humans. That we have the power to make it so just by observing. But I've also heard, in reference to quantum computing, that 'even a passing electron can 'look' and collapse the wavefunction' of some delicate system. I think I've heard this anyway.


Well, this is the nub of the misunderstanding. Anything can constitute an observer, including an electron, a photon, or whatever. In no way does an observer have to be conscious to collapse the wavefunction.

So surely, if electrons can do it, then a passing electron in the cat box will make the wavefunction collapse and I'll have nothing to do with it. So whats the answer?


Well, Darkchilde has given the answer, namely that this thought experiment was erected by Schrödinger to argue against the Copenhagen interpretation, and shouldn't be thought of beyond that. It's somewhat unfortunate that this is employed as an analogy for what actually occurs for this reason. The problem is that it's such a beautiful analogy, and it works.

In reality, the probability of a cat existing in a state of superposition is so extremely low that it has been calculated that it would take longer than the existence of the universe (past and future) before such an event is likely to occur. However, thinking that this means it can't happen commits several fallacies, one of which is elucidated by Cali's exposition of the serial trials fallacy, but can be taken further. What the serial trials fallacy, as demonstrated in Cali's wonderful treatise, doesn't actually tell you is that, even in the presence of a small number of participants, even the most improbable events can happen first time out of the gate, and indeed even in the presence of one try. It may look from his essay that it requires many participants to be involved in order to achieve the goal on the first attempt, but that isn't true, and to assume it is is to commit a different, but related fallacy, namely the gambler's fallacy.

There are no barriers, probabilistically speaking, to a cat existing in a state of superposition. It's extremely unlikely, not least because every particle that comprises the cat constitutes an observer capable of collapsing the wavefunction, but it isn't impossible.

Darkchilde wrote:Twistor, other than energy/time and position/momentum, are there any other pairs of variables that we cannot measure both accurately, as per the Heisenberg Uncertainty Principle?


Field value/rate of change (which are really just expression of position/momentum).

Eric8476 wrote:isn't the entire thought experiment flawed? the variable is the decaying matter, it either decays or not then therefore the cat would be dead or alive, not in limbo.


It isn't in limbo, it's actually both alive and dead. In any event, I've covered this above. It's a thought experiment, and really only analogises the principle of quantum superposition. The decaying atom most definitely can exist in a state of superposition, and this has been experimentally verified. Indeed, the computer you are posting from employs a variation of superposition, in the form of quantum tunnelling, for its operation.