The Bohmian interpretation, also known as the pilot wave theory or de Broglie-Bohm theory, is an alternative interpretation of quantum mechanics that introduces the concept of pilot waves guiding particles. In this interpretation, particles are considered to have well-defined positions and trajectories determined by the interaction with a guiding wave.
On the other hand, the standard interpretation of quantum mechanics describes particles in terms of probability waves or wave functions. These waves describe the probability distribution of finding a particle in different states or locations, but they do not correspond to physical waves in space. Instead, they are mathematical entities used to calculate probabilities.
In terms of mathematical formalism, the Bohmian interpretation is compatible with the standard mathematical framework of quantum mechanics. It provides a way to explain the observed statistical behavior of quantum systems while introducing additional variables, such as the particle positions and the guiding wave.
The key difference between the Bohmian interpretation and the standard interpretation lies in the ontological assumptions they make about the nature of particles and their behavior. The standard interpretation treats particles as inherently indeterminate until a measurement is made, where the wave function collapses to a specific state. In contrast, the Bohmian interpretation assumes that particles have well-defined positions and trajectories at all times, guided by the pilot wave.
While the Bohmian interpretation provides a deterministic picture of particle motion, it comes at the cost of introducing nonlocality, where the position of a particle can instantaneously influence its behavior at a distant location. This aspect is often seen as a challenge to the Bohmian interpretation, as it conflicts with some aspects of relativity theory.
It's important to note that both interpretations—Bohmian and standard—can reproduce the same experimental predictions and are mathematically consistent with quantum mechanics. The choice between these interpretations often comes down to philosophical or interpretational preferences, as they offer different conceptual frameworks for understanding the nature of quantum systems.