According to our current understanding of quantum mechanics, the future cannot be predicted with certainty, even if we know the exact initial conditions. This is due to the inherent probabilistic nature of quantum systems.
Quantum mechanics describes the behavior of particles and systems at the microscopic level, and it introduces fundamental uncertainties in the form of wave-particle duality and the Heisenberg uncertainty principle. These principles state that certain properties of particles, such as their position and momentum, cannot be simultaneously known with arbitrary precision.
In addition to these uncertainties, quantum mechanics introduces the concept of wavefunction collapse. When a measurement is made on a quantum system, its wavefunction "collapses" to a particular state, and the outcome of the measurement is probabilistic. This means that even if we have precise knowledge of the initial conditions of a quantum system, we cannot predict with certainty the outcome of future measurements or the precise evolution of the system.
However, quantum mechanics provides us with probabilistic predictions. We can calculate the probabilities of different outcomes based on the system's initial conditions and the mathematical framework of quantum mechanics. These probabilities allow us to make statistical predictions about the behavior of quantum systems and the likelihood of different measurement outcomes.
It's important to note that at the macroscopic level, where classical mechanics dominates, the probabilistic nature of quantum mechanics typically becomes less noticeable. The behavior of large-scale systems, such as everyday objects, can often be described using classical physics and deterministic equations. But at the quantum level, when dealing with individual particles or small systems, the probabilistic nature of quantum mechanics is essential to our understanding.
In summary, while quantum mechanics provides probabilistic predictions about the behavior of quantum systems, it does not allow for deterministic predictions of the future, even with complete knowledge of the initial conditions.