Question

In classical mechanics, it is postulated that in principle the position and velocity of particles are perfectly determined and can be perfectly known. And it is by using such determined properties that the evolution of classical systems can be predicted and computed (at least in principle).

In quantum mechanics, on the contrary, positions and velocities are not perfectly determined together. More precisely, the description of the states of systems are based on wave functions, and indeterminacy such as the one between velocities and positions are embedded in the expressions of the wave functions.

But then, does quantum mechanics postulate that wave functions themselves are perfectly determined, and if so, can they be (at least in principle) perfectly known/knowable? Or are there on the contrary fundamental limits imposed by the theory on what can be known/knowable about a wave function?

Answer 1

Quantum mechanics relies on wave functions to probabilistically describe particle behavior, with Heisenberg's uncertainty principle restricting the precision of simultaneous position and momentum measurements. While wave functions in quantum mechanics are mathematically precise, the knowledge we can gain about the system is fundamentally limited by its probabilistic nature and the effects of measurement.

Step-by-step explanation:

In quantum mechanics, the concept of perfect determinacy, as assumed in classical mechanics, is replaced by probabilistic descriptions encompassed by wave functions. While a wave function can be mathematically expressed with precision, according to the Heisenberg Uncertainty Principle, there are intrinsic limits to the precision with which certain pairs of physical properties, such as position and momentum, can be known. This principle declares that the act of measurement affects the system and introduces an element of indeterminacy, preventing the simultaneous knowledge of both position and momentum to arbitrary precision.

The wave-particle duality underscores the inherent limitations of the classical description and affirms that neither a purely classical particle nor wave theory can entirely explain quantum phenomena. At the quantum level, objects exhibit both wave and particle characteristics, which introduces the probabilistic nature of measurement in quantum mechanics. This dual nature is leveraged in practical applications like digital imaging sensors and electron microscopy.

Despite the fundamentally probabilistic interpretation of wave functions, quantum mechanics aligns with classical mechanics at macroscopic scales. This agreement is known as the correspondence principle, indicating that quantum effects are negligible for large-scale systems, and classical descriptions suffice. Therefore, although the wave function provides a perfectly determined framework in quantum mechanics, what can be known about the system it represents is limited by probabilistic interpretations and measurement effects.