# 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