Originally introduced in Schrödinger's Cat as “a tiny amount,” we generalize this concept and introduce Schrödinger's quantity, a measure of radioactivity from the beginning to the first decay occurrence, or the starting point of radioactive decay. Schrödinger's quantity describes the radioactivity of a given radioactive isotope by the amount, or number of atoms, corresponding to a one-half probability that a decay occurs during one half of the isotope's half-life, whereas half-life measures radioactivity from the beginning to the midpoint of radioactive decay.
Originally introduced in Schrödinger's Cat as “a tiny amount,” we generalize this concept and introduce Schrödinger's quantity, a measure of radioactivity from the beginning to the first decay occurrence, or the starting point of radioactive decay. Schrödinger's quantity describes the radioactivity of a given radioactive isotope by the amount, or number of atoms, corresponding to a one-half probability that a decay occurs during one half of the isotope's half-life, whereas half-life measures radioactivity from the beginning to the midpoint of radioactive decay.
Schrödinger's original Cat explicitly refers to both “one of the atoms decays” and “the first atomic decay.” This paper examines the first decay occurrence of a finite radioactive sample. Let t₁ denote the time of the first atomic decay. Existing quantities such as half-life, decay constant, mean lifetime, and activity describe radioactive decay collectively, whereas t₁ identifies the first actual decay occurrence of a particular sample. Probability theory contains well-developed treatments of first occurrences, including waiting times, first-arrival times, first-passage times, hitting times, and related stochastic processes. Such treatments require information about the underlying process. This raises two distinct questions for radioactive decay: what information determines the probability distribution of t₁, and what information, if any, determines the actual t₁ of a particular finite sample of a given radioactive isotope before the first decay occurs?
“Shut up and calculate” is commonly associated with a pragmatic attitude toward quantum mechanics: instead of debating interpretation, calculate observable predictions. This paper applies that instruction directly to the original Schrödinger's Cat. Schrödinger specified “a tiny amount” of radioactive substance, an equal probability that one of its atoms decays or none does within one hour, and “the first atomic decay” as the decisive occurrence. These statements contain two quantitative questions: What is the amount? What is the probability of the first decay? Using Schrödinger's Quantity and the First Decay time t₁, these become: calculate the number of atoms n satisfying the one-half probability condition, and calculate the probability associated with the first decay occurrence. No interpretation of the cat is required for either question.
Schrödinger's Cat has acquired many descriptions and interpretations since its introduction in 1935. This paper returns to Schrödinger's original text and separates what Schrödinger explicitly constructed from what is inferred from the construction. Schrödinger specified a steel chamber, “a tiny amount” of radioactive substance, a Geiger counter, relay, hammer, poison, a one-hour interval, equal possibilities that one atom decays or none does, and “the first atomic decay” as the decisive occurrence. He then described the wave function of the entire system as containing the living and dead cat “mixed or smeared in equal parts.” However, not knowing which of two mutually exclusive states is true, or being unable to rule out either, does not imply that both are physically true. The distinction involves not only Schrödinger's Cat but also Schrödinger's YOU—the observer outside the steel chamber who lacks information. Moreover, the causal chain from atomic decay to the cat's death contains additional physical and biological conditions. The original construction should therefore distinguish the physical cat, its quantum-mechanical description, and the information available to YOU.
Schrödinger's original Cat places a radioactive substance, Geiger counter, relay, hammer, poison, and cat inside a closed steel chamber and leaves “this entire system” to itself for one hour. The construction is commonly treated as an isolated system. This paper examines what isolation means in the thought experiment. Physical isolation, causal connection, and information available about individual members of a system are different conditions. A comparison with human mortality illustrates the distinction. An actuary may possess individual information such as birthdays and living habits, yet has no probability information about when the first death claim will occur; it may come at any time and at any probability. For radioactive atoms, the standard description supplies no comparable individual information and treats atoms of the same isotope as identical or dismisses their differences for radioactive decay. Schrödinger's Cat therefore raises a question beyond the physical isolation of the steel box: what information about individual radioactive atoms is available to determine the first decay?
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.
Following the spirit of the Turing Test, we propose Schrödinger’s Test using the original text of Schrödinger’s Cat thought experiment as a test of logical reasoning and independent thinking in artificial intelligence. For a radioactive isotope, we introduce its Schrödinger’s Amount, the weight or quantity of its atoms equal to “a tiny amount” in the original text, and it is put in the steel box with the cat of the thought experiment. The test consists of a machine reading the text and answering several test questions. A higher level of the test is to have it write a report to see how many answers to the questions it contains. As a starting set, our questions are designed to dissect Schrödinger’s Cat part by part and step by step, a few of which are original, not yet available on the internet, unknown to current artificial intelligence programs, and can therefore serve as test questions. For example, why must the box be open? Are atoms identical? Is Schrödinger’s Cat repeatable? For each question, two answers are presented: a conventional or known answer reflecting standard interpretations in physics available on the internet, and an unconventional answer derived through facts and logic not yet available on the internet. Since Schrödinger’s Cat was introduced in 1935, with Einstein’s involvement, it has been extensively studied, taught, and wrote for nearly 100 years, Schrödinger’s Test represents an extremely high-level of human intelligence.