Bohmian mechanics
Introduction
Bohmian mechanics, also known as the de Broglie-Bohm theory, pilot-wave theory, or the causal interpretation, is an interpretation of quantum mechanics. It is named after physicist David Bohm who revived it in the 1950s, and Louis de Broglie who originally proposed it in 1927. Unlike many other interpretations of quantum mechanics, Bohmian mechanics provides a realist description of quantum phenomena.
Historical Background
Bohmian mechanics was first proposed by Louis de Broglie in 1927 during the Solvay Conference. However, it was not widely accepted due to the success of the Copenhagen interpretation and the lack of experimental evidence to distinguish between the two. It was later rediscovered and extended by David Bohm in 1952, who provided a more detailed mathematical formulation and addressed some of the criticisms of de Broglie's original proposal.
Theoretical Framework
Bohmian mechanics is a deterministic and non-local hidden variable theory. The theory postulates that particles have definite positions at all times, guided by a wave function that evolves according to the Schrödinger equation. This is in contrast to the probabilistic nature of the wave function in the Copenhagen interpretation.
Wave Function
In Bohmian mechanics, the wave function is not a complete description of a quantum system. Instead, it is supplemented by the actual positions of particles. The wave function guides the motion of these particles in such a way that the probability distribution of the positions of the particles is given by the square of the absolute value of the wave function, known as the Born rule.
Particle Trajectories
The trajectories of particles in Bohmian mechanics are determined by the guidance equation, also known as the Bohmian equation of motion. This equation describes how the velocity of a particle is influenced by the wave function. The trajectories are deterministic, meaning that the future positions of the particles are completely determined by their initial positions and the wave function.
Non-locality
Bohmian mechanics is explicitly non-local, meaning that the velocity of a particle can depend on the positions of other particles, even if they are far apart. This is a consequence of the entanglement phenomenon in quantum mechanics, and is in line with the predictions of Bell's theorem.
Comparison with Other Interpretations
Bohmian mechanics is one of many interpretations of quantum mechanics, each with its own strengths and weaknesses. It is often compared with the Copenhagen interpretation, the many-worlds interpretation, and the transactional interpretation, among others.
Copenhagen Interpretation
The Copenhagen interpretation is the most widely accepted interpretation of quantum mechanics. It postulates that the wave function provides a complete description of a quantum system and that it collapses upon measurement. In contrast, Bohmian mechanics maintains that particles have definite positions at all times and that the wave function does not collapse.
Many-Worlds Interpretation
The many-worlds interpretation postulates that all possible outcomes of quantum measurements are realized in some "world" or universe. In contrast, Bohmian mechanics maintains that there is only one actual outcome, determined by the initial positions of the particles and the wave function.
Transactional Interpretation
The transactional interpretation proposes that quantum processes involve a backward-in-time aspect. In contrast, Bohmian mechanics is a time-symmetric theory, meaning that the laws of physics are the same in both forward and backward time directions.
Experimental Tests and Predictions
Although Bohmian mechanics is deterministic, it is empirically equivalent to standard quantum mechanics for all practical purposes. This is because the initial positions of the particles, which determine the outcomes of measurements in Bohmian mechanics, are not accessible to experiment. However, there are some subtle differences in the predictions of the two theories that could, in principle, be tested.
Criticisms and Controversies
Bohmian mechanics has been the subject of much debate and controversy since its inception. Critics often point to its non-local nature, the role of the wave function, and the lack of experimental evidence distinguishing it from standard quantum mechanics. However, proponents argue that it provides a clear and intuitive understanding of quantum phenomena.
Conclusion
Bohmian mechanics provides a unique perspective on quantum mechanics, offering a deterministic and realist interpretation of quantum phenomena. While it has not been widely accepted by the physics community, it continues to be a topic of active research and discussion.