In both quantum mechanics and M-theory (which is an extension of string theory), the concept of randomness and determinism is a subject of ongoing debate and interpretation.
In quantum mechanics, the prevailing interpretation is that certain phenomena, such as the measurement outcomes of certain observables, exhibit inherent randomness. This is captured by the probabilistic nature of quantum mechanics, where the outcomes of measurements are described by probability distributions. However, it's important to note that quantum mechanics is a mathematical framework that provides predictions for experimental results, and there are different interpretations about the underlying nature of the randomness, such as the Copenhagen interpretation, many-worlds interpretation, and others.
In the context of M-theory and string theory, which aim to provide a unified framework for describing fundamental physics, the question of determinism and randomness is complex. These theories propose that the fundamental building blocks of the universe are tiny vibrating strings or higher-dimensional objects. While M-theory encompasses quantum mechanics within its framework, it also includes additional dimensions and incorporates gravity.
The nature of determinism and randomness in M-theory is still an active area of research and debate. Some researchers argue that the apparent randomness observed at lower dimensions might emerge from deterministic and highly organized processes in higher dimensions. This perspective suggests that what appears random in our observable universe is a manifestation of deeper underlying deterministic laws in higher-dimensional physics.
However, it's important to note that the precise details and implications of M-theory are not yet fully understood, and many aspects of the theory remain speculative. The question of determinism and randomness in the context of M-theory is still an open topic of investigation, and researchers continue to explore and develop different ideas and interpretations.