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Schrödinger’s Cat May Be Dead All Along

Dhan Lord B. Fortela, Ashley P. Mikolajczyk

Published Oct 9, 2023• 1 citation
Publisher

Abstract

By framing the problem of determining the state of Schrodinger’s cat as a problem of searching for Hidden Markov Model (HMM), this work shows that Schrodinger’s cat is dead with stationary probabilities P(Cat = Dead) = 1 and P(Cat = Alive) = 0 consistently in various observation-based modelling of the HMM.
DOI
10.20944/preprints202310.0009.v2

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Modeling the Schrödinger cat by a two state system and assuming that the cat is coupled to the environment we look for the least paradoxical states of the Schrödinger cat in the following way. We require the reduced density matrix of the cat for one of the two states in the superposition to be the same as the one for the total state while distinct from the reduced density matrix of the cat for the other state in the superposition. We then look for the reduced density matrices for which the cat is as alive as possible for the first state (and as dead as possible for the second state). The resulting states are those in which the probability for the cat to be alive (or dead) is 1/2+2/4≈0.8541/2+\sqrt 2/4\approx 0.8541/2+2​/4≈0.854
Abstract Complementarity tells us we cannot know precisely the values of all the properties of a quantum object at the same time: the precise determination of one property implies that the value of some other (complementary) property is undefined. E.g. the precise knowledge of the position of a particle implies that its momentum is undefined. Here we show that a Schrödinger cat has a well defined value of a property that is complementary to its “being dead or alive” property. Then, thanks to complementarity, it has an undefined value of the property “being dead or alive”. In other words, the cat paradox is explained through quantum complementarity: of its many complementary properties, any quantum system, such as a cat, can have a well defined value only of one at a time. Schrödinger’s cat has a definite value of a property which is complementary to “being dead or alive”, so it is neither dead nor alive. Figuratively one can say it is both dead and alive. While this interpretation only uses textbook concepts (the Copenhagen interpretation), apparently it has never explicitly appeared in the literature. We detail how to build an Arduino based simulation of Schrödinger’s experiment based on these concepts for science outreach events.
Schrödinger's cat paradox has persisted for nearly a century as a demonstration of the apparent absurdity of quantum superposition when extended to macroscopic scales. This technical note demonstrates that the paradox dissolves entirely within the CAT'S Theory framework through the triadic invariant Reality = Pattern × Intent × Presence (P × I × Pr). We argue that the cat is neither "both alive and dead" nor the victim of mysterious collapse. Instead, superposition represents a state where Presence (Pr) has not yet instantiated, yielding P × I × 0 = 0 (potential but not actual). Measurement does not "cause" collapse through mysterious observer effects; it provides the Presence component required for actualization. This resolution eliminates the need for Multiple Worlds or hidden variables while maintaining consistency with quantum mechanical predictions.
Schrödinger's Cat is commonly summarized as a cat that is “both alive and dead until observed.” This paper compares that familiar formulation with Schrödinger's original 1935 construction. The original passage contains a radioactive substance, the possibility that one atom decays or none does, the first atomic decay, a Geiger counter, relay, hammer, poison, and a cat inside a steel chamber. Schrödinger then states that the Psi-function of the entire system contains the living and dead cat “mixed or smeared in equal parts,” followed by a warning against naively accepting a “blurred model” as an image of reality. Several ideas commonly associated with the Cat therefore need to be distinguished: the physical state of the cat, the mathematical description of the system, the probabilities assigned to alternatives, and the information available to an outside observer. The popular Cat is a useful shorthand, but it is not identical to Schrödinger's original Cat.
In quantum theory, a particle is allowed to be in a state of coherent superposition among a set of orthogonal states. A vivid picture of this concept is the “Schrödinger cat”: a cat is alive and dead simultaneously. This would be no surprise if one means a large number of an ensemble of cats with 50% alive and 50% dead. But, “Schrödinger cat” is a cat. People are talking about a cat being alive and dead simultaneously. In mathematics, the best word to characterize the relationship between states “alive” and “dead” is perhaps “orthogonal”. In quantum mechanics, the superposition of orthogonal states is used to describe the state of a quantum object, or a particle. The superposition principle is indeed a mystery compared to our everyday classical life experience. Beyond the superposition of orthogonal single-particle states, the superposition of orthogonal multi-particle states represents an even more troubling concept in classical theory.