A Two-Sided Ontological Solution to the Sleeping Beauty Problem

I describe in this paper an ontological solution to the Sleeping Beauty problem. I begin with describing the Entanglement urn experiment. I restate first the Sleeping Beauty problem from a wider perspective than the usual opposition between halfers and thirders. I also argue that the Sleeping Beauty experiment is best modelled with the Entanglement urn. I draw then the consequences of considering that some balls in the Entanglement urn have ontologically different properties form normal ones. In this context, considering a Monday-waking (drawing a red ball) leads to two different situations that are assigned each a different probability. This leads to a two-sided account of the Sleeping Beauty problem. On the one hand, the first situation is handled by the argument for 1/3. On the other hand, the second situation corresponds to a reasoning that echoes the argument for 1/2 but that leads however, to different conclusions. 1. The Entanglement urn Let us consider the following experiment. In front of you is an urn. The experimenter asks you to study very carefully the properties of the balls that are in the urn. You go up then to the urn and begin to examine its content carefully. You note first that the urn contains only red or green balls. By curiosity, you decide to take a sample of a red ball in the urn. Surprisingly, you notice that while you catch this red ball, another ball, but of green colour, also moves simultaneously. You decide then to replace the red ball in the urn and you notice that immediately, the latter green ball also springs back in the urn. Intrigued, you decide then to catch this green ball. You note then that the red ball also goes out of the urn at the same time. Furthermore, while you replace the green ball in the urn, the red ball also springs back at the same time at its initial position in the urn. You decide then to withdraw another red ball from the urn. But while it goes out of the urn, nothing else occurs. Taken aback, you decide then to undertake a systematic and rigorous study of all the balls in the urn. At the end of several hours of a meticulous examination, you are now capable of describing precisely the properties of the balls present in the urn. The latter contains in total 1000 red balls and 500 green balls. Among the red balls, 500 are completely normal balls. But 500 other red balls have completely astonishing properties. Indeed, each of them is linked to a different green ball. When you take away one of these red balls, the green ball which is associated with it also goes out at the same time of the urn, as though it was linked to the red ball by a magnetic force. The red ball and the green ball which is linked to it behave then as one single object. Indeed, if you take away the red ball from the urn, the linked green ball is also extracted instantly. And conversely, if you withdraw from the urn one of the green balls, the red ball which is linked to it goes out immediately of the urn. You even tried to destroy one of the balls of a linked pair of balls, and you noticed that in such case, the ball of the other colour which is indissociably linked to it was also destroyed instantaneously. Indeed, it appears to you that these pairs of balls behave as one single object. The functioning of this urn leaves you somewhat perplexed. In particular, your are intrigued by the properties of the pairs of correlated balls. After reflection, you tell yourself that the properties of the pairs of correlated balls are finally in all respects identical to those of two entangled quantum objects. The entanglement (Aspect & al. 1982) is indeed the phenomenon which links up two photons, for example, so that when one modifies the quantum state of one of the entangled photons, the quantum state of the other one is instantly modified accordingly, whatever the distance where it is situated. Indeed, the pair of entangled photons really behave as one and the same object. You decide to call “Entanglement urn” this urn with its astonishing properties. After reflection, what appears peculiar