Schrodinger's Cat Box (シュレディンガーの猫箱, Shuredingā no Neko-bako), often simply referred to as the Cat Box, is a reasoning technique which asserts that multiple truths about an event can exist in parallel when the event itself has not been observed. It is a loose metaphorical application of the real life quantum physics thought experiment Schrödinger's cat.
Schrödinger proposed the thought experiment as a challenge to the Copenhagen interpretation by showing that it would lead to absurdity when applied to the macroscopic world. In the thought experiment, a cat is placed inside a sealed box with a source of radioactivity and a radioactivity detector hooked up to shatter a flask of poison. Because radioactivity is the result of quantum processes, this would in effect make the life-or-death status of the cat dependent on a probabilistic quantum process. While the common sense view of the scenario would suggest that the cat is either alive or dead, the Copenhagen interpretation would assert that the cat can simultaneously be both alive and dead.
In Umineko, Schrodinger's cat box is used to describe the state of Rokkenjima from October 4 to 5, 1986. The physics of the original thought experiment has little bearing on its use as a metaphor; what is important is the idea of an unobserved entity with multiple possible states. Because Eva, the survivor of the Rokkenjima Mass Murders, refused to disclose the truth of what happened on the island, and because no evidence was found on the island to establish any events that transpired, the events of the two days are said to be "shut within the cat box". Multiple explanations of what happened on the two days were made, some of which were presented in the discovered message bottles, and others which were born out of public speculation in the aftermath of the incident. However, without an authoritative way of establishing the actual events of the two days, all of the narratives are allowed to coexist as individual truths.
In the story, Schrodinger's cat box was first introduced by Virgilia in a conversation with Battler. Virgilia used the example of Braun tubes, suggesting that unless one takes apart a Braun tube to look inside, it is impossible to disprove her magical explanation that gremlins in the tubes are what allows television images to be displayed. While the cat box was first mentioned only in the narration, Beatrice and Ronove recognized Battler's subsequent argument as a use of this reasoning technique.
The key insight of the cat box in Battler's game against Beatrice is that it allowed him to recognize that the events that he observed of the game board from Purgatorio are Beatrice's narrative of what happened, not the actual events that occurred. This allowed him to avoid being overwhelmed by Beatrice's grandiose displays of magic and distracted by the search for an explanation for them. He would thus be able to focus on getting Beatrice to establish the facts by using the red truth.
Another key feature of the cat box, as pointed out by Bernkastel and Ange in Alliance of the Golden Witch, is that the true status of the "cat" can be established by opening the "box". In Twilight of the Golden Witch, this idea is explored in the existence of and conflict over Eva's diary, a locked diary where Eva had written and sealed away the true events of the Rokkenjima Mass Murders. When one has both the diary and the key to it, the "lid" of the cat box can be opened, allowing one to view its contents and establish a single truth over all other narratives. The issue of whether or not the diary should be revealed to the public or even opened at all by Ange serves as the central conflict of the story arc.