Atoms are different (not identical), and a complete reading of Schrödinger’s Cat

1. The original thought experiment: Schrödinger’s cat.
   Schrödinger, in 1935, wrote:
   "One can contrive even completely burlesque [farcical] cases. A cat is put in a steel chamber along with the following infernal device (which must be secured against direct interference by the cat): in a Geiger counter, there is a tiny amount of radioactive substance, so tiny that in the course of an hour one of the atoms will perhaps decay, but also, with equal probability, that none of them will; if it does happen, the counter tube will discharge and through a relay release a hammer that will shatter a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would tell oneself that the cat is still alive if no atom has decayed in the meantime. Even a single atomic decay would have poisoned it. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or spread out in equal parts.
   It is typical of these cases that an indeterminacy originally restricted to the atomic domain turns into a sensually observable [macroscopic] indeterminacy, which can then be resolved by direct observation. This prevents us from so naïvely accepting a "blurred model" as representative of reality. Per se, it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks."
   Observation 0 — A sealed box couples a radioactive source to a lethal mechanism and a cat. First decay detection in the experiment, or the experiment of detecting the first atom to decay. The "first atom" suggests that the atoms are not the same. Therefore, only one Geiger counter is needed, and it's counted or not counted, replacing whether the cat is alive or dead.
2. Einstein’s version of the original Schrödinger’s cat.
   Einstein, in 1950, wrote:
   "You are the only contemporary physicist, besides Laue, who sees that one cannot get around the assumption of reality, if only one is honest. Most of them simply do not see what sort of risky game they are playing with reality—reality as something independent of what is experimentally established. Their interpretation is, however, refuted most elegantly by your system of radioactive atom + amplifier + charge of gun powder + cat in a box, in which the psi-function of the system contains both the cat alive and blown to bits. Nobody really doubts that the presence or absence of the cat is something independent of the act of observation."
   Observation 1 — Forfeited information. The box is non-transparent and soundproof. “Alive & dead” appears only if we choose not to observe until the end. That’s an information rule, not a seen fact. Schrödinger’s cat is a Blind and Deaf physicist’s cat.
   Observation 2 — Visual and auditory cues matter. In Einstein’s explosion variant, light and sound highlight the process before we get to the cat. The cat becomes unnecessary: even before “alive or dead” is a question, we can ask whether the Geiger counter is counting, the hammer is falling, the flask is breaking, or the dynamite explodes. One counter is sufficient.
3. Blind and Deaf physicist’s Geiger counter.
   Observation 3 — Feasible, therefore not a pure thought experiment. Without exotic assumptions (like a train at light speed), the “blind & deaf” Geiger setup is doable. No animal need be involved or harmed.
4. The “50%” only makes sense after the start time and window are fixed.
   Physicists have two ways of describing radioactivity: decay rate and half-life. The former describes the deterministic and continuous decay of a radioactive element; the latter describes the deterministic and continuous decay of half the total amount, though this half can be discrete when the number of atoms is even. Both indicate that the larger the amount of radioactive material, the sooner the first decay occurs—perhaps, according to Schrödinger's theory, within an hour. However, physicists do not know or can calculate the probability of the first decay occurring within a certain period of time, whether or not within an hour.
   Observation 4 — Since the experiment is detecting the first decay, the probability of 1/2 is of the occurrence of the first decay in a one-hour time window. The original classic line—“so tiny that in an hour one atom perhaps decays, and with equal probability, none”—is ill-defined unless we fix a clear start (t₀) and window (T). Otherwise, even “50%” has no footing, especially when in a continuous model the atoms are indistinguishable, identical, or even completely identical.
5. Schrödinger’s cat is about the first radioactive decay (or its detection).
   Observation 5 — The ‘tiny amount’ premise is logically sloppy. Preparing many atoms and then reasoning “more atoms ⇒ higher chance within an hour” changes the object of study. The chain really keys off the first decay event. Assuming uranium-238 is used, based on its 4.47 billion-year half-life, 12,000 atoms decay per second in a one-gram sample. No physicist, including Schrödinger himself and Einstein, could calculate the tiny amount required for Schrödinger's cat thought experiment, not even in theory.
6. The third version of Schrödinger’s cat: use only one radioactive atom.
   With a single radioactive atom in the box, the experiment must start on this atom's birthday.
   Observation 6 — Now it is a thought experiment, but the thought misfires. With a single atom the time may be long—fine for thought experiments. But we do not know how long the trial lasts if we do not know when the atom was created or when the trial starts. Without t₀, the trial could last “forever.”
7. The correct version: the Actuary’s cat.
   With a single cat and nothing else in the box, without opening the box, you still don't know whether the cat is alive or dead, because the cat itself may die or is capable of dying on its own.
   Observation 7 — Human mortality, life tables, and life insurance companies. Insurance policies are controlled experiments: policyholder birthdays are known; each policy has a clear start date; one claim means little, but many policies (many trials) yield stable statistics. That, not a single sealed box, is how to reason about rare events.
8. Schrödinger’s cat vs. Actuary’s cat.
   Observation 8 — As Schrödinger’s cat is the cat of the first decay, Actuary’s cat should be the cat of the first claim of a lifepolicy or the death of policyholders. Insurance company and Actuarys know the birthdays of their policyholder, while Schrödinger and physicists, blind or deaf or both, they know nothing about the birthdays of radioavtive atoms, therefore, first devay is lack of control compare to the first death. In fact, the first claim is not contralable, so, the first decay of a tiny amount of radioactive material or a number of atom is completely unkown, i.e., the probability for first decay and death are not defined. In conclusion, borrow from Schrödinger’s words, there is not a tiny amount of radioactive substance, so tiny that in the course of an hour one of the atoms will perhaps decay, but also, with equal probability, that none of them will.
9. “You can’t step in the same river twice.”
   Just like every cat, including every human, has been on the road to death since birth, and every radioactive atom has been on the road to decay since its birth.
   Observation 9 — What repeatable should mean. Exact repeat (same nucleus + same micro-history) is impossible. Repeat the procedure for comparable statistics; do not pretend identical micro-states.
10. Atoms of the same isotope are not identical.
    Observation 10 — Non-identity is the central theme. Even with the same counts of protons and neutrons, atoms differ (at least logically, and often physically). Treating many atoms as one smooth object smears these differences and wipes out their individual electromagnetic fields. Since the number of atoms is finite, “identical” is a modeling convenience, not a fact.
11. Practical Implications of the same isotope's atoms being not identical.
    If atoms of the same isotope are not identical, this insight could have significant practical consequences—especially in fields that implicitly assume atomic uniformity.
    Observation 11 — One major area is nuclear fusion. Current approaches treat all hydrogen atoms as equivalent fuel. But if some are more “fusion-able” than others, distinguishing them could help initiate and sustain fusion more efficiently—much like choosing dry wood over wet wood to start and maintain a fire.