Discussion Overview
The discussion revolves around Bohmian trajectories, particularly their behavior in relation to intersections and implications in the context of Young's experiments. Participants explore the nature of these trajectories, their representation in space-time, and the conditions under which they may or may not intersect.
Discussion Character
- Exploratory
- Technical explanation
- Debate/contested
Main Points Raised
- Some participants assert that a Bohmian trajectory cannot intersect itself due to the dependence of speed on position, particularly in the context of a particle trapped by a potential.
- There is a distinction made between intersections in space-time versus 3-space, with some arguing that crossing the same spatial point at different times does not constitute an intersection in space-time.
- One participant questions whether two trajectories can be very close without intersecting and whether there is a force that repels them, drawing a parallel to the Fermi exclusion principle.
- Another participant notes that the inability for trajectories to intersect is not unique to Bohmian mechanics but applies to any well-behaved initial-value problem in differential equations.
- There is a mention of geodesics being able to meet, contrasting with Bohmian trajectories, and a reference to Bohm's writings regarding boundary conditions in equations of motion.
- Participants discuss the possibility of two points in a small neighborhood having orthogonal momentums, with some suggesting that if the neighborhood is not of zero size, there are no inherent restrictions.
- Questions arise about specific momentum configurations at time t = 0, with one participant proposing a scenario that is met with a definitive "no" from another.
Areas of Agreement / Disagreement
Participants express differing views on the nature of intersections of Bohmian trajectories, with some asserting that they cannot intersect while others explore the conditions under which they might be close without intersecting. The discussion remains unresolved regarding the implications of these trajectories in specific scenarios.
Contextual Notes
Participants reference various theoretical concepts and principles, such as boundary conditions and the Fermi exclusion principle, which may introduce limitations or assumptions that are not fully explored in the discussion.