Q: Why is Schrodinger’s cat both dead and alive? Is this not a paradox?

One of the original questions was: A basic rule of logic is that something cannot contradict itself. It is impossible for P to be true and not true. Doesn’t Schrödinger’s cat violate this law and therefore invalidate logic?

The experiment

Schrödinger proposed this thought-experiment to demonstrate how ridiculous quantum super-position is.  Basically the multiple states of a single atom (decayed and not decayed) causes a cat to be in multiple states (living and dead).


Physicist: The resolution to this comes from a careful look at what is meant by the “state” of something.  Turns out, logic is safe from Lil’ Schrödinger’s claws.

There’s a big difference between “reasonable” and “logical”.  To see the difference, find a calm, reasonable person and talk to them, and then (this is more difficult) find a professional logician and try to talk to them.

Talking to professional Logicians: more effective than water-boarding.

Talking to professional Logicians: among the more frustrating conversations you’ll ever have.

It’s pretty reasonable to say that a single thing must be in one state or another, especially if those states are mutually exclusive.  It’s obvious.  It’s common sense.  In fact, it’s so reasonable/obvious/sensible that disagreeing with it would be a good way of being laughed out of every fancy science salon of the 19th century (or at least the occasional salon with sober members).  Logic, on the other hand, has nothing to do with physical reality (neither does being reasonable for that matter).

Logicians start with a big bucket of postulates and symbols and statements, and then run with them.  None of it needs to be “physically motivated” or even remotely intuitive.

Clearly, this reads

Clearly, this reads “P is possibly true if and only if P is not definitely untrue” and also “P is definitely true if and only if it is not possible for P to not be true”.

The statement that things must be one way or another (specifically, that each state is mutually exclusive of the others), is a whole new logical statement on its own.  The statement even has a name: “counterfactual definiteness“.  Overly-complicated terms like that are just made up so that people will think that physicists are wizards-of-smartness.  A better term for things needing to be in a definite state is “realism”.  While realism is “obviously true”, is isn’t necessarily true (not “logically true”), and point of fact: isn’t true.

There’s a famous no-go theorem in quantum physics called “Bell’s theorem” that says that, given the results of a variety of experiments involving entanglement, “local realism” is impossible.  This means that things always being in single states requires the exchange of some kind of faster-than-light signals.  Or conversely, if no effects can travel faster than light, then things must be allowed to be in multiple states.

It’s pretty natural to jump to the conclusion that things are communicating faster than light.  Losing realism is philosophically, even mathematically, a bitter pill to swallow.  Unfortunately, there are a lot of problems with faster than light stuff (like this one!).

It turns out that the universe doesn’t seem to have any problem dropping realism.  Things are perfectly happy being in multiple states at the same time: particles being in multiple positions or energy states, single events happening at multiple times, or (admittedly reaching a little past our grasp) being in multiple states of living and dead.  The last of course has never been observed in the lab (and probably never will be), but this is a well-studied property otherwise.  We’ve seen multiple-stated-ness in every physical system we’re capable of measuring the effect in.  So far, there doesn’t seem to be any limit to the scale at which quantum weirdness shows up.

In short, it does make sense to say that things must be in a single state or another, but it isn’t necessarily “logical”.  The universe couldn’t care less about what makes sense.


Answer gravy: This bit threatened to derail the flow of the post.

Realism is technically a statement that limits the exact nature of what kind of states are allowed.  For example, only the states |living\rangle and |dead\rangle are allowed.  When the cat is both living and dead it’s technically just in multiple states in certain “measurement bases”.  So the cat could be in the single state \frac{1}{\sqrt{2}}\left(|living\rangle+|dead\rangle\right).

We see this all the time in the polarization of light, for example.  A diagonally polarized photon is in a single state, |\nearrow\rangle.  But, if you insist on looking at it (measuring it) in terms of horizontal and vertical polarizations, then you find that it must be in multiple states, |\nearrow\rangle = \frac{1}{\sqrt{2}}\left(|\rightarrow\rangle + |\uparrow\rangle\right).  This moves the problem from being a purely philosophical/logical problem, to one of defining what is meant in detail by the word “state”.

The answer to whether Schrödinger’s cat is in multiple states becomes a resounding “Yes!  Unless some very specific measurement is set up, in which case: no!”.

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22 Responses to Q: Why is Schrodinger’s cat both dead and alive? Is this not a paradox?

  1. Joe says:

    I think it is so cool that two days after this question was answered the question was posted on this site. Also, Schrodinger’s Cat is mindboggling.

  2. Matthew Gill says:

    Would there be any way to observe this in the lab at all?

  3. William says:

    Probably not unless you happen to be located outside of the Universe or are really, really big.

  4. LarryD says:

    The important point about Logicians is that they are interested in Validity and not Truth. Arguments are valid or invalid based on certain assumptions. Obviously it is not true that Unicorns exit (well, here anyway) but that doesn’t stop you making a valid/invalid argument about Unicorns.
    ‘All Unicorns are 4 legged animals; a pig is a 4 legged animal therefore it is a unicorn.’
    Is obviously an INvalid argument but the pattern is important and could be used in real life.
    After Aristotle came the predicate calculus, Modal Logic etc. Then there is 3 valued Logic which attempts such situations that might lay somewhere between ‘yes’ and ‘no’ (1,0). That is to say that you may argue a point where you say ‘No’ but actually be leaning towards ‘yes’. Such a state might be similar to Schrodinger’s Cat and superposition, that is, something lay in between dead, not-dead until the matter becomes trivial.
    One should also not forget ‘fuzzy logic’.

  5. Claudio says:

    Then the real answer is No. A particle can be in as many quantum states as you want at the same time, but the cat will be either alive or dead and nothing in between. This is not as complicated.

  6. theSpleen says:

    hello hello hello

    I just think there is a mistake in the text under the logic symbols. The first statement (I think) should read something like: “P is possibly true if and only if P is not definitely untrue.”

  7. The Physicist The Physicist says:

    That does read a bit smoother.

  8. William says:

    It’s also important to remember that sometimes the right answer to a question really is “Maybe.”

  9. MikeDa says:

    actually G-d and/or Jesus may have something to say about Schrodinger’s cat. the assumption seems to me to be false to begin with, that there is only bi-polar “alive” and “dead” as the possible states of being. reincarnated cat? resurrected cat? are we speaking of physical death or spiritual? what about the soul of the cat, is it alive or dead when the cat dies or has it a separate vector of behavior not governed by logic? what about the consciousness of the cat? is that separate from the soul if there is one? if it is indeed dead do the laws of logic constructs from the world of the living still apply?

  10. Eric says:

    Why is a superposition of two states not considered a third state? If I were making a naive Schodinger cat object in a computer, I’d have a bit for |alive> and one for |dead> for 4 total states. Maybe my question would be answered if you pointed me to the thorough definition of state you mentioned in the answer gravy?

  11. The Physicist The Physicist says:

    It is a new state, but it’s also a combination of the other two. Similarly (very similarly), northeast is a direction different from both north and east, but it’s also a combination of them. A completely new state (a new “orthogonal state”) would not be expressible as a combination of any you’re already working with.

  12. Matt K says:

    If it were a person and not a cat, and for sake of discussion it were just a sleeping gas so the person is asleep or not asleep, what would the person inside the box be experiencing?

  13. The Physicist The Physicist says:

    Nothing unusual at all. Both versions of the unfortunate person would experience the world normally, only one of them would be asleep.

  14. Claudio says:

    Hum. There is only one person and is awake or asleep. People and cats are nott quantum objects.

  15. James says:

    That would depend which interpretation of quantum mechanics is correct.

    The Many Worlds interpretation, which basically follows the reasoning “If all the small bits of the cat follow the laws of quantum mechanics then, in the absence of evidence to the contrary, it is a good guess that the whole cat does as well”. This would imply even things as large as people could be in multiple states. These states would be in separate quantum worlds.

    The Copenhagen interpretation, which boils down to, at a “certain size” all the rules change (the wave function collapses). This would imply, that if people are larger than this “certain size”, they would not behave according to the rules of quantum mechanics even though they are made of things that do. This “certain size” is not defined clearly. Some flavors of this interpretation are worse and grant mystical collapse powers to the “observer”.

    If you want to suffer through less simplified explanations yourself Wikipedia is a reasonable place to start.
    http://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics

  16. Matt K says:

    Theoretically, how long could the superposition state of the cat last? 1 nanosecond, 1 second, 1 day, 100 years, the age of the universe?

    Also, how large could the box be and how many things could be contained inside it?

    Could you have a superposition of a superposition of states? So for instance, a superposition of whether or not you make a measurement of the superposition of states of the cat? Or I’m just sort of curious how complex the superposition states can get. In the case of the cat it’s sort of a binary yes or no, but can it be more than that?

  17. The Physicist The Physicist says:

    Arbitrarily large, for arbitrarily long times. It’s just a question of when you end up entangled with the contents of the box.
    A superposition of superpositions is just a superposition, and yes; there are states a hell of a lot more complicated than binary states. It’s just that, for the purposes of exposition, simpler states are better.

  18. Drew says:

    To “Is this not a paradox?” I can’t help but think about something Feynman said: “The ‘paradox’ is only the difference between reality and what you think reality *should* be.”

  19. mike berneathy says:

    All you have to do is wait a week or so and if the cat is dead you’ll be able to smell it. I you don’t smell it, someone has switched boxes on you while you were in the can.

  20. Eric says:

    @mike berneathy
    After a week without food, the cat is dead. When you smell it, the superposition has decayed.

  21. Morgan Scott says:

    As I remember it right now the concept illustrates the duality of quanta, the cat can therefore be both dead and alive and either dead or alive.

  22. Why do you have to complicate things? Im sorry but i dont see anything mind boggling about this expirement.

    If the observer does not know if the cat is alive or dead. does not change the reality or the outcome of what is about to happen or has already happened.

    To put it in a more simpler explanation. If you dont know who won a basball game last night, It does not change the outcome of the game at all. ( You just dont have that information its that simple).

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