In quantum mechanics, particles are described by wave functions, which are mathematical objects that contain information about the probabilities of finding particles in different states. The wave function provides a set of possible outcomes for measurements of observables, such as position or momentum.
The uncertainty principle, a fundamental principle in quantum mechanics, states that certain pairs of physical properties, such as position and momentum, cannot be precisely measured simultaneously. This means that the more precisely one property is known, the less precisely the other can be known. This is not due to limitations in measurement techniques but is an inherent property of quantum systems.
The assumption of a definite position or speed is not required in quantum mechanics. Instead, the wave function describes the probability distribution of finding a particle in different positions or having different speeds. When a measurement is made, the wave function "collapses" to a specific value corresponding to the outcome of the measurement.
The probabilistic nature of quantum mechanics arises from the wave-particle duality, which suggests that particles can exhibit both wave-like and particle-like behaviors. This duality is supported by experimental evidence, such as the famous double-slit experiment, where particles exhibit interference patterns similar to waves.
The mathematical framework of quantum mechanics has been remarkably successful in describing the behavior of microscopic particles and their interactions. It provides a consistent and accurate description of phenomena that classical mechanics cannot explain. While the probabilistic nature of quantum mechanics might seem counterintuitive from a classical perspective, it has been extensively validated by experimental observations and is an essential aspect of our understanding of the microscopic world.