Can something be true and false at the same time?  Can a cat be both alive and dead at the same time?  

Common sense and Thomistic  philosophy would say no.

Nevertheless, some people  argue that science says yes  

because of Quantum Mechanics and the  famous Schrödinger's Cat experiment.

Quantum Mechanics is weird.

It is the most precise theory we have for  describing the atomic and subatomic world  

and it underlies so much of the  technology that we take for granted,  

but many aspects of it are  inherently counterintuitive.

In describing the microscopic  world of particles and atoms  

it refuses to give definite answers  to every question we might ask,  

but often only tells us the probability of  observing various results in our experiments.

Because of this inherent uncertainty,  if physicists want to describe what  

is happening before we actually  observe some microscopic phenomena  

we often use the idea of a superposition.

We might describe a radioactive atom as being in  a superposition of being decayed and not-decayed.

This can very accurately describe the probability  of finding said atom either whole or decayed when  

we actually observe it, but it is hard to get your  head around what a superposition is on its own.

This is the foundation for one of the most  

memorable thought experiments of  Quantum Mechanics: Schrödingers’ Cat.

Erwin Schrödinger, one of the founders of Quantum  Mechanics, suggested that you could place a cat  

in an enclosed box along with a small  sample of radioactive material such that,  

after say one hour, there is a  fifty-fifty chance that either  

no atoms of the sample will  decay or at least one will decay.

This sample could be placed in a Geiger counter  that will detect any radioactive decay and, if  

it does detect that decay, activate a mechanism to  release hydrocyanic acid, sadly killing the cat.

If we have all of that in our box, after waiting  an hour, the nuclei in the radioactive sample  

would each be in a superposition of being decayed  or not-decayed; and, in theory, that means that  

the sample of radioactive material as a  whole would be in an equal superposition  

of having no atoms decayed or  having at least one decayed.

Similarly, the Geiger counter is then in  a superposition of having been triggered  

and not been triggered, the acid is in a  superposition of having been spilled and  

not spilled, and the poor cat seems to be in an  equal superposition of being alive and being dead.

Some people look at this sort of thought  experiment and a whole host of actual (humane)  

quantum mechanical experiments which involve  superpositions and uncertainty about the state  

of things before observation, and argue that  they violate the principle of non-contradiction,  

a fundamental aspect of classical logic and  argue that science has forced us to rethink  

the very way we classify what it is logical.

Aristotle expressed the principle of  non-contradiction as: “It is impossible that  

a thing both belong and not belong to the same  thing at the same time and in the same respect.”

If a cat could be alive and dead at the same time,  or more realistically, if an atom can be both  

decayed and not decayed, then hasn’t this  ancient principle been disproven by physics?  

In truth, Quantum Mechanics implies no actual  contradictions at all. By itself, the mathematics  

of Quantum Mechanics makes no explicit claim  about the cat being in some mixed live/dead state,  

but only gives the probability of our cat having  survived once we open the box to check on her.

No physicist would ever expect to observe a  

“mixed alive and dead cat” or an atom  that is both decayed and not decayed.

Quantum Mechanics alone makes no definitive  statement about what is going on before we  

open the box and further interpretation  is needed to make claims about what the  

“actual” state of the cat  would be before observation,  

and famously there are a whole host of different  interpretations of what a “superposition” is  

actually describing before we observe it. Many  of which fall into three broad categories.

In the first category of interpretation,  the cat is definitely either alive or dead  

in the closed box, because every atom and  every particle everywhere in the universe  

has a definite state at all times, even  if described as being in a superposition,  

because there is some information about  that state that we do not have access to,  

preventing us from knowing those details,  leaving us to deal only in probabilities.

In the second group of interpretations, both the  alive and dead parts of the superposition exist,  

but in different cats. The one live  cat that we put into the box, “evolves”  

or “splits” or “branches” into different cats,  

one for each possible superposition  state of our experiment, and each  

isolated from the others in different branches  of a large infinite dimensional structure.

When we open the box we ourselves are stuck  

on only one of those branches and so  only find one cat, either alive or dead.

In a third class of interpretations, oftenly  coming under the name of the Copenhagen  

interpretation, and historically the most  commonly cited way to describe Quantum Mechanics,  

the cat is neither alive nor dead, but is not  both alive and dead at the same time either.

There is no answer to the question of  what happens before we open the box,  

of what a superposition is “actually” describing.

The only meaningful things that this  interpretations allows us to say about reality  

are rooted in our actual  observations and asking what  

“happens” when we are not  observing is meaningless.

In addition to these categories of interpretations  of what a superposition is in general,  

many thinkers would further reject the idea that  a cat could ever be in a superposition at all.

They argue that the cat or any living  creature would itself be an “observer”,  

it would be the one looking in the box, and so  never properly be described as in a superposition,  

or that the superposition of the  microscopic radioactive atoms would  

break down naturally in some way into a  definite state once it was large enough to  

be a macroscopic sample or interacted  with the macroscopic Geiger counter.

I would argue that some of these interpretations  are hugely problematic for other philosophical  

reasons, and there is very interesting work  being done to develop interpretations of Quantum  

Mechanics that are rooted in Thomistic philosophy,  but for our purposes it is enough to clarify that  

Quantum Mechanics, on its own, does not violate  the principle of non-contradiction, and most,  

if not all, interpretations of Quantum  Mechanics do not imply a contradiction either.

The weird superposition state (whether of  cats, atoms, or electrons) is, at minimum,  

a tool for expressing the probability  of observing various outcomes.

Even when we survey the range of  interpretations of what is actually going on  

in the superposition state, careful consideration  shows that none actually suggest that: “a thing  

both belongs and does not belong to the same  thing at the same time in the same way.”

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