my understanding is that when the cat is in the box, the probability that it is alive equals the probability that it is dead, so the cat is considered to be both dead and alive at the same time. — Kaarlo Tuomi

Probabilities come into play when you apply the Born Rule, and that's the rule you apply when observations are made. While the cat is in the box, it is in a superposition between dead and alive. The state is described as a wavefunction.

we assume the probability that I will pick any given flavour is equal, so that before I pick a flavour, I am assumed to have picked all ten flavours at once. — Kaarlo Tuomi

Having ten flavors does not equate to the probability of each flavor being chosen being 10%.

there is also the multiverse theory, which says that for every choice I make, there is an alternative universe in which I made some other choice. — Kaarlo Tuomi

There's a bit of speculation being applied here that our choices are represented via a wavefunction. QM applies to the mechanics of physical entities. Agents make choices "somehow". But just because agentive choices appear in some fashion to be similar to states in superposition does not mean that an agentive choice is a quantum superposition of possibilities. Perhaps it is, but perhaps it isn't... it would not be inconsistent with quantum mechanics to speculate that your wavefunction could only "reasonably" evolve into your selection of flavor 3, despite the fact that you're mulling over 10 flavors. I think certain philosophers try a bit too hard to link will to QM because they think they need QM like properties for some theory of free will, but I think the latter is mistaken (and QM doesn't quite help explain free will thingies in the way it's usually "needed"), so I would advise proceeding with caution.

so I would advise proceeding with caution — InPitzotl

perhaps not go for the Mint, then.

Kaarlo Tuomi

While the cat is in the box, it is in a superposition between dead and alive. The state is described as a wavefunction. — InPitzotl

I think the cat would disagree with that.

I think the cat would disagree with that. — Olivier5

Which cat? The living one? The dead one? Or the cat wavefunction that Schrodinger sees?

The cat in the box is an observer too. If one really believes that observers collapse wave functions, then any cat can do so, including Schrodinger's.

In fact, even a bacteria does some observing... so I guess bacterias collapse wave functions too... :-)

The cat in the box is an observer too. — Olivier5

Schrodinger still sees a wavefunction. If you posit that the cat is an observer, then there are two cats; a living one, and a dead one. But Schrodinger still only sees one wavefunction (before opening the box). This is part of the core of MWI; the wavefunction that Schrodinger sees is basically a combination of two "worlds", and when Schrodinger observes this, he just entangles with this wavefunction, after which, there's a Schrodinger that sees the dead cat, and a Schrodinger that sees the live cat; both Schrodingers are part of the universal wavefunction.

the wavefunction that Schrodinger sees is basically a combination of two "worlds", and when Schrodinger observes this, he just entangles with this wavefunction, after which, there's a Schrodinger that sees the dead cat, and a Schrodinger that sees the live cat; both Schrodingers are part of the universal wavefunction. — InPitzotl

so when I'm sat in the ice cream parlour there is a single wavefunction, but there are ten "worlds", and when I make a choice from the menu I entangle with the wavefunction and there are then ten of me, each of whom made a different selection from the menu, but there is still only a single wavefunction.

so which one of me tips the waiter?

Kaarlo Tuomi

Schrodinger still sees a wavefunction. — InPitzotl

Actually, in this mind experiment, Schrodinger sees a box. Not a wavefunction for what could potentially be a box.

And Schrodinger only proposed this mind experiment to show how absurd the Copenhagen interpretation is, with its magic thinking about observers.

so which one of me tips the waiter? — Kaarlo Tuomi

Schrodinger only proposed this mind experiment to show how absurd the Copenhagen interpretation is — Olivier5

Here: https://www.youtube.com/watch?v=kTXTPe3wahc
(20 minutes, but worth the watch, and you can play faster if you like)

thank you for that link. actually I've just been reading about the Copenhagen interpretation on Wikipedia, and it seems that if I know where the waiter is I can't tip him anyway!

Kaarlo Tuomi

thank you for that link. actually I've just been reading about the Copenhagen interpretation on Wikipedia, and it seems that if I know where the waiter is I can't tip him anyway! — Kaarlo Tuomi

LOL That's a great theory as long as you don't plan to go back to that restaurant. Although these days none of us may ever go back to any restaurants. How did it all get so strange so fast?

we assume the probability that I will pick any given flavour is equal, so that before I pick a flavour, I am assumed to have picked all ten flavours at once.

there is also the multiverse theory, which says that for every choice I make, there is an alternative universe in which I made some other choice.

so, if I am assumed to have picked all ten flavours at once, how many waiters do I have to tip? — Kaarlo Tuomi

So you can assume ten flavour timmy and a potentially infinite number of multiverses, but you can't figure out where the waiters fit in?! Interesting...

So you can assume ten flavour timmy and a potentially infinite number of multiverses, but you can't figure out where the waiters fit in?! Interesting... — Key

that's because my wavefunction collapsed when I counted out the tip.

Kaarlo Tuomi

that's because my wavefunction collapsed when I counted out the tip. — Kaarlo Tuomi

Or did it?...

my understanding is that when the cat is in the box, the probability that it is alive equals the probability that it is dead, so the cat is considered to be both dead and alive at the same time.

and we do this precisely because the two probabilities are equal. — Kaarlo Tuomi

I think you're misunderstanding the thought experiment. If it was only a matter of probabilities, of which outcome is the likely one, then there would be no problem. The point of the thought experiment is that the cat really is in both states, i.e. alive and dead - which is of course absurd.

'One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter, there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer that shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The first atomic decay would have poisoned it. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.' ~ Schrodinger

https://archive.is/20121204184041/http://www.tuhh.de/rzt/rzt/it/QM/cat.html#sect5

Schrodinger made that point precisely to illustrate the absurdity of quantum physics. He found it perplexing and distressing - he said in a letter to Einstein 'God knows I am no friend of probability theory, I have hated it from the first moment when our dear friend Max Born gave it birth.'

I think, however, that the problem of the live~dead cat has been solved by the development of quantum decoherence. 'Decoherence shows how a macroscopic system interacting with many microscopic systems (e.g. collisions with air molecules or photons) moves from being in a pure quantum state—which in general will be a coherent superposition —to being in an incoherent improper mixture of these states. The weighting of each outcome in the mixture in case of measurement is exactly that which gives the probabilities of the different results of such a measurement' ~ Wikipedia. In other words, it undermines the real possibility of a macroscopic being such as a cat being at once alive and dead (however I believe it doesn't solve the underlying 'measurement problem'.)

But in the spirit of the icecream parlor, you also might enjoy The Multiverse Idea is Rotting Culture.

I just think that "measurement" is nothing an amoeba can't do. All this talk about human measurement determining wave functions is just pre-Darwinian religious talk. All animals process information, cats included. There must be something else that collapses that darn wave function...

There must be something else that collapses that darn wave function... — Olivier5

I think the answer is the Schrödinger-Newton-Equation.

"The regime where the mass is around 10^10 atomic mass units while the width is of the order of micrometers is expected to allow for an experimental test of the Schrödinger–Newton equation in the future."

Wave functions of more heavy parts than 10^10 atomic mass units will catch their own wave function.

Thus the cat is a measuring instrument.