# Schrodinger's Cat Logical Connective

I have heard a lot about Schrodinger's cat.

Let's suppose you have a cat with a flask of poison and a radioactive source in a sealed box.

The box also has a Geiger counter, if it detects radioactivity (due to the decaying of an atom) the flask is shattered, releasing the poison, killing the cat, if it doesn't detect anything, the cat continuous alive.

The Copenhagen interpretation of quantum mechanics implies that after a while, the cat is simultaneously alive AND dead. Yet, when one looks in the box, one sees the cat either alive OR dead, not both alive and dead.

The truth table for conjunction is: $$\mathbf {AND}$$ $$\begin{array} {|r|r|}\hline \mathbf A & \mathbf B & \mathbf {A \land B} \\ \hline 0 & 0 & 0 \\ \hline 0 & 1 & 0 \\ \hline 1 & 0 & 0 \\ \hline 1 & 1 & 1 \\ \hline \end{array}$$

The truth table for disjuntction is: $$\mathbf {OR}$$ $$\begin{array} {|r|r|}\hline \mathbf A & \mathbf B & \mathbf {A \lor B} \\ \hline 0 & 0 & 0 \\ \hline 0 & 1 & 1 \\ \hline 1 & 0 & 1 \\ \hline 1 & 1 & 1 \\ \hline \end{array}$$

Normally, cats cannot be dead and alive at the same time, because that would be a contradiction, this is its truth table: $$\begin{array} {|r|r|}\hline \mathbf A & \mathbf {\lnot A} & \mathbf {A \land \lnot A} \\ \hline 0 & 1 & 0 \\ \hline 1 & 0 & 0 \\ \hline \end{array}$$

but they can be alive or dead: $$\begin{array} {|r|r|}\hline \mathbf A & \mathbf {\lnot A} & \mathbf {A \lor \lnot A} \\ \hline 0 & 1 & 1 \\ \hline 1 & 0 & 1 \\ \hline \end{array}$$

So, in the Schrodinger's cat story, we say that the cat is dead and alive at the same time: $$\begin{array} {|r|r|}\hline \mathbf A & \mathbf {\lnot A} & \mathbf {A \land \lnot A} \\ \hline 0 & 1 & 1 \\ \hline 1 & 0 & 1 \\ \hline \end{array}$$

But this is clearly wrong by definition

My point is, shouldn't we have some kind of new logical connection?, something like a "Quantum Conjunction" with a new symbol different than $$\mathbf {\land}$$ where $$\mathbf{A}$$ and $$\mathbf {\lnot A}$$ is always true, because if not, then logicians are going to be mad

• The quantum set of states is not just dead or alive - there's a continuum of possible superpositions. – Javier Apr 20 at 0:41
• We already do. It is called quantum logic. Ordinary probability theory is also a many valued logic, and adequately describes Schrodinger's cat. – Charles Francis Apr 20 at 15:33
• Is it possible to make the truth table of Schrodinger's cat using this many valued logic? – DieDauphin Apr 20 at 18:02

## 2 Answers

You actually need to be able to express states like “63% chance of being alive and 37% chance of being dead”. The existing math does exactly this, using superpositions of eigenstates. A logical quantum Or does nothing to quantify the state, and physics is all about quantification.

• To add, we can measure and predict such superpositions for smaller-than-cat particles. This is not just theoretical. "Schrödinger's cat" is a thought experiment to see if there's an upper limit to the size of such superpositions. – MSalters Apr 20 at 11:26
• Originally, "Schrödinger's cat" was a thought experiment to show how ridiculous a literal interpretation of quantum mechanics is/was back when Schrödinger was working on his wave equation :P – Marius Ladegård Meyer Apr 20 at 13:21
• @MariusLadegårdMeyer the thing is, many worlds is still going strong while the Copenhagen interpretation is pretty much dead. So... yay? – John Dvorak Apr 20 at 15:46
• Wouldn't be better to say "indeterminate" instead of alive and dead? .. As you mention, the math only expresses the probability of the quantum system collapsing at certain state, it doesn't mean that the cat is "63% alive and 37% dead", it means that those are the probabilities of finding the cat at those states. The interpretetion of what is really happening before the quantum system collapses is another thing. But it doesn't necessarily mean that the cat has to be in two states at the same time, right? – DieDauphin Apr 25 at 6:15

"Quantum logic can be formulated either as a modified version of propositional logic or as a noncommutative and non-associative many-valued (MV) logic".

This a quote from the wikipedia page "Quantum Logic" that gives and entry into the literature.

• Is it possible to make a truth table of Schrodinger's cat using this many valued logic? – DieDauphin Apr 21 at 23:23