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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40 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.

  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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  24. Banterman says:

    I ‘m going to do the Shrodinger’s cat experiment. OH SHIT I created a parallel universe where I am a mass murdere- oh good it collapsed

  25. Whatudahellu says:

    I don’t understand how this is even a paradox at all. How is the cat alive & dead? Surely it would either be alive, or be dead. Just because we don’t know until we open the box, doesn’t mean the cat could be both athe same time… Right???

  26. Uber Genius says:

    Quantum mechanics simply predicts a significant probability of the system being found in these different states. Thus it is no surprise that we do not see macroscopic “superpositions of live and dead cats” at the same time.

    Paul Dirac states, “When an observation is made on any atomic system that is in a given state, in general the result will not be determinate, i.e., if the experiment is repeated several times under identical conditions several different results may be obtained. It is a law of nature, though, that if the experiment is repeated a large number of times, each particular result will be obtained in a definite fraction of the total number of times, so that there is a definite probability of its being obtained. This probability is what the theory sets out to calculate.”

    (The Principles of Quantum Mechanics, chapter 1, pp.5-14)

    Where physicist seem to err is in assuming that epistemic (how we know something, e.g. Deterministically or indeterministically, and in this case, what knowledge is quantum mechanics providing us about the state of the cat in the box) has something to do with the ontic state of the thing in question. In other words our not knowing to a certainty what state the cat is in (alive or dead) does not somehow magically change the nature of the cat so that he can obtain two mutually exclusive states at time t or the collapse of the wave function.

    So the math is right, but the philosophical underpinnings (philosophy of science) in the case of claims that a cat is now alive and dead, is a category error mixing up ontology with epistemology, and suggests since we can’t determine a probability at a particular moment that all of a sudden mutually exclusive states in beings will obtain.

    This has never been seen in a scientific experiments in the history of science and it won’t. It is a philosophically naive statement. That is what leads to the absurdity.

    For a more detailed discussion see http://www.informationphilosopher.com/solutions/experiments/schrodingerscat/

  27. Gigi says:

    Zombie cat, schrodinger solved, case closed.
    Don’t let it out of the box.

  28. Daryl says:

    Actually, if you consider that the box was empty before and after the experiment, did the observer ever REALLY put the cat into the box or not? Without observing the observer how do we know the cat was ever put into the box in the first place?

  29. Harry Ellis-Cairns says:

    Hi, just a quick question…

    If I go with the classic view of the cat…….
    The cat is randomly going to be killed…
    When I open the box and the cat is shown to be either alive or shown to be dead…
    The randomness is lost and gives way to
    Reality/non randomness…
    So.. after opening the box when does randomness start again “for everybody and everything”? Or …….from that point is everything predetermined..
    Logic says predetermined, which means the whole question “will it be alive or dead” is obselete..Yes? It must be both or there really is no free will……we are being controlled?????

  30. Harry Ellis-Cairns says:

    So, would the classic way of thinking , that the cat could be alive or dead (allowing probability) shoot itself in the foot as from the moment the box is opened , probablity wouldn’t exist, so from this Point onwards we wouldn’t be able to even ask the question.
    I think the cat is alive and dead, I’m leaning towards an undetectable dimension/multiverse existing and that
    Probability doesn’t exist, therefore 1/0’s , yin/yan, yes/no are not opposites but one entity……no positive/negative charges just both…maybe we/I move through other dimensions constantly..

    Btw…. I’m not a scientist lol, just bored at work…with an interest…

  31. Frank Mitchell says:

    re @mike berneathy,

    If you open the box to find the cat dead and smelling, a good forensic scientist might be able to tell you *when* it died from the intensity of the smell, degree of decay, etc. Would that then violate the Uncertainty Principle? Or if the cat is alive and dead until you open the box, will the forensic result on the cat (if it’s dead) always indicate it died at the half-way point between when you shut the box and when you opened it again?

  32. Eric Bourdan says:

    @Francis Lozada

    The difference is that you KNOW someone won the ball game. With the cat, there is no predetermined information to be had because you don’t know if it’s dead or alive. Hence the paradox.

  33. bwise says:

    There are two fundamental misunderstandings here. First, Schrodinger himself stated clearly that the cat would be in one state or another; the puzzle is why. The best answer I know is that it is possible to get weird quantum states, but they are very delicate. For very small, cold objects, they can last – but when connected to a big, warm object (like a cat), the random thermal motion flips them into one state or the other. And this “decoherence” happens extremely quickly – so fast that it was originally thought to be an instantaneous “collapse of the wave function”.
    Second, even when a system is in a “mixture of two states”, it is actually in precisely one state. The entire premise of this article is that “things are perfectly happy being in multiple states at the same time”, but that is just plain incorrect. They are in a single state which can be *described* as the mixture of two others. At a human scale, I can make one sound by mixing two sounds, and there is no paradox: just a single sound which happens to be the mixture of two other sounds. It is amazing that quantum mechanics works this way but it does: the 50/50 mixture of two states is *one* new, completely valid state. It’s a very precise analogy: the wave function of the mixed quantum state is a 50/50 average of the wave functions of the two basis states, just as the sound wave of the mixed sound is the 50/50 mix of the sound waves of the two original sounds.

    The real weirdness is that linear superposition of wave functions actually works, and things like mixed or entangled states are real.

  34. Rick Sparks says:

    The cat is dead! Here’s why; as long as the cat is alive the cat itself can take the measurement ( the cat knows of it’s own existence.) This theory calls for no measurement to be able to be made. In order for that to take place the cat would have to be dead.

  35. Kord Williams says:

    Couldn’t you put the cat,poison,and radioactive source in a glass box to observe the cat without causing the atom to decay or not decay?

  36. Vicky says:

    I’m still snagging on the premise that not being able to predict whether the cat is alive or dead means it is both alive and dead. As others have said, the cat’s experience is one way or the other, isn’t it? Now if you opened up the box and found a long dead cat with a video recording showing it being alive the whole time….

  37. Leo says:

    In Schrodinger’s cat mind experiment the cat is both alive and dead only according to Schrodinger’s specific definition of being-alive-and-dead-at-the-same-time.
    In this definition being alive-and-dead-at-the-same-time in a closed room means the observer is not allowed to check aliveness or deadness of the object.

    So if the cat would die not from radioactive decay of an atom, but from a computer that generates random numbers, the cat would not be alive-and-dead because you can calculate the outcome of the computer random generator from outside the room.

    But let me give you another definition: the cat is alive-and-dead at the same time if you don’t know if it is alive or dead. You don’t know how random computer generator works. You cannot calculate if it has already killed the cat or not. In this definition the cat is alive and dead at the same time.

    I have not read the newspapers today, so I don’t know the USD/EUR rate. For me this rate is spread from 0.5 to 2.5 why not? I am not allowed to check.

    I think Schrodinger’s mind experiment does not add to understanding of physics. Yes, we cannot know exact state of a particle, because if we measure it, we change it. But this is only because we cannot measure the state without changing it. Maybe future scientists will discover some methods which will allow you to measure state of particle without changing it? Maybe there are some fields, currently unknown, that interact with particles and don’t change their state?

  38. Leo says:

    What if we’ve been conveying the Schrodinger’s experiment for one hour and have been keeping saying for one hour: oh, the cat’s half alive half dead, the cat’s half alive half dead. Then we opened the room and found it dead and we conclude: the cat has been half alive half dead for one hour and after that it has been dead. But wait! It turns out someone forgot her smartphone in the room with the camera filming. Now we take a look at the movie and now we say: Hello! The camera show the cat had been alive for 43.5 minutes and the rest of 16.5 minutes it had been dead! So what really happened? Was the cat half-half or not? (If not the camera, we can call for a pathologist and she will make a special test to tell at what minute the cat had died).

  39. SuperSupermario24 says:

    I love how many people in the comments have absolutely no grasp on how quantum mechanics actually works.

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