The idea that we live in the sum of all possible universes, where anything is possible, is a concept found in certain interpretations of quantum mechanics, such as the many-worlds interpretation. According to this view, all possible outcomes of a quantum event actually occur in separate parallel universes.
Richard Feynman's path integral formulation is a powerful mathematical tool used in quantum mechanics to calculate the probability amplitudes of different paths that a particle can take between two points in space and time. It provides a consistent mathematical framework for understanding quantum phenomena, including the double-slit experiment.
In the double-slit experiment, when particles like electrons or photons are sent through a barrier with two slits, they exhibit wave-like behavior and create an interference pattern on a screen behind the barrier. This phenomenon can be explained using the mathematical formalism of quantum mechanics, including the path integral approach.
The path integral formulation of quantum mechanics does not necessarily imply that universes are only probable rather than certain. It deals with the calculation of probabilities and allows us to determine the likelihood of different outcomes. It provides a mathematical framework to understand the behavior of quantum systems and make predictions about their observable properties.
However, it's important to note that the many-worlds interpretation and other similar interpretations are just that—interpretations. They are attempts to make sense of the mathematical formalism and provide a conceptual framework for understanding quantum mechanics. While these interpretations can be mathematically consistent and provide useful insights, they are still subject to ongoing debate and are not universally accepted by all physicists.
In summary, Feynman's path integral formulation is a powerful tool in quantum mechanics that can explain the behavior observed in the double-slit experiment. It does not necessarily imply that universes are only probable, but rather provides a mathematical framework for understanding the probabilities associated with different outcomes in quantum systems. The nature of reality and the interpretation of quantum mechanics continue to be topics of active research and discussion in the scientific community.