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Based on the idea of quantum mechanics, Erwin Schrödinger proposed his famous "Schrödinger's cat" idea, which is a cat that is both alive and dead until observed.
Is Schrödinger's cat inscribed for a year of Life and Death, and then subsequently erased from one of those books once observed?
And is there an Issur of Shochet to observe the cat on Shabbos or Yom Tov?
א"ר כרוספדאי א"ר יוחנן שלשה ספרים נפתחין בר"ה אחד של רשעים גמורין ואחד של צדיקים גמורין ואחד של בינוניים צדיקים גמורין נכתבין ונחתמין לאלתר לחיים רשעים גמורין נכתבין ונחתמין לאלתר למיתה בינוניים תלויין ועומדין מר"ה ועד יוה"כ זכו נכתבין לחיים לא זכו נכתבין למיתה
(Gemara Rosh HaShanah 16b)
"Rabbi Kruspedai said that Rabbi Yoḥanan said: Three books are opened on Rosh HaShana (before the Holy One, Blessed be He:) One of the completely wicked people, and one of the completely righteous people, and one of middling people (whose good and bad deeds are equally balanced). Wholly righteous people are immediately written and sealed for life; wholly wicked people are immediately written and sealed for death; and middling people are left with their judgment suspended from Rosh HaShana until Yom Kippur, (their fate remaining undecided). If they merit, (through the good deeds and mitzvot that they perform during this period,) they are written for life; if they do not so merit, they are written for death."
(from Sefaria's translation)
Question #1
"Schrödinger's cat", is (on erev R"HaShannah, hidden from sight) living in both the state of life and death. Therefore, it cannot be considered "completely" or "wholly" righteous or wicked, since it is neither completely or wholly one thing or the other at this point.
Therefore, on R"H, it cannot be inscribed in the Book of Life or Death. However, since it is considered as having aspects of both life and death at the same time, then it is a "Beinoni" by definition (middle group).
So the cat has its judgment suspended until Yom Kippur.
But, since no matter how estranged or how non-religious a Jew may unfortunately be.... it is well known that EVERY JEW is OBSERVANT on Yom Kippur!
Therefore, by Yom Kippur, the cat will be observed. At that point it will be inscribed into its proper book.
Question #2
The cat (before being observed) is both in a potential state of life and death at the same time. This is a Halachic "Safek" (doubt) #1.
Opening the box on Shabbos, will either determine that the cat is now dead or alive. But we do not know which will be. This is Halachic "Safek" (doubt) #2.
Since before opening the box, the cat may be considered possibly dead, and now opening the box merely causes potential taking of life... then the whole act of opening the box is merely a S'fek S'fekah and is permitted on Shabbos.
Is the cat awake or asleep?
If he is awake, the odds are even that he will be alive or dead upon observation and the matter is entirely in the hands of Heaven.
But if he is asleep, we must remember that the Talmud says that sleep is 1/60 of death, so upon observation there is a 31/60 chance he will be dead, and only a 29/60 chance he will be alive. This means we must consider him dead for practical purposes.
Since Hashem knows exactly what will happen, then we can considered that Hashem (or even the Malach Hamaves) is already observing the cat. Thus, Hashem knows what state the cat is in and will have already written it into the correct book. Also, since the book of life and the book of death are based on the decree that Hashem has given for each person on Rosh Hashanah, then it would still be written in the correct book.
