In M-theory, the behavior of microscopic particles in higher dimensions is indeed influenced by their vibration modes in those extra dimensions. However, it is important to note that M-theory does not necessarily imply that determinism in higher dimensions directly translates to randomness in lower dimensions.
Determinism refers to the concept that given the initial conditions and the laws of nature, the future state of a system can be uniquely determined. In the context of M-theory, the behavior of particles in higher dimensions is governed by the vibrational patterns of extended objects, such as strings or membranes, in those dimensions. These vibrational patterns, known as modes, dictate the particle properties we observe in our three-dimensional world.
While it is true that the behavior of these particles in higher dimensions can be complex and may exhibit properties that appear random to us, it does not necessarily imply that determinism in those higher dimensions translates to randomness in our lower-dimensional reality. The apparent randomness in our three-dimensional world arises due to our limited ability to perceive and access the full information of the higher-dimensional physics.
It's important to recognize that our understanding of M-theory and its implications is still a subject of ongoing research and development. Therefore, the precise relationship between determinism in higher dimensions and the observed randomness in our lower-dimensional reality is an active area of investigation within theoretical physics.