- #1
StevieTNZ
- 1,934
- 883
Can you consider the particles in Bohmian Mechanics mixtures?
StevieTNZ said:Can you consider the particles in Bohmian Mechanics mixtures?
Yes, it can influence the motion of other particles. Moreover, it can do it even more "strongly" than classical particles can, in the sense that it can do it nonlocally, with a strong influence at an arbitrarily large distance distance. In fact, many people dislike that theory not because a particle cannot influence other particles, but because it can influence them "too strongly" in the sense above.Delta Kilo said:Can actual particle position (the one that comes out of the guiding equation) be observed/measured or even influence anything at all? If yes, how?
Ok, the trajectory of a particle influences and is influenced by all other particles in the universe. But these trajectories cannot be observed/measured directly, they can only be inferred from the results of a measurement (which again strictly speaking depends on the position of all particles in the universe and not just the particle we want to measure).Demystifier said:Yes, it can influence the motion of other particles.
Yes, very good.Delta Kilo said:Ok, the trajectory of a particle influences and is influenced by all other particles in the universe. But these trajectories cannot be observed/measured directly, they can only be inferred from the results of a measurement (which again strictly speaking depends on the position of all particles in the universe and not just the particle we want to measure).
If we knew the entire initial state we could predict the evolution at any arbitrary moment of time and the uncertainty principle would not have applied. But since we do not know the initial state, the numbers are out of our reach. And we cannot increase our knowledge through experiments because every time we do a measurement we gain some knowledge but at the same time we introduce more unknowns through the degrees of freedom of measuring apparatus. In fact we cannot learn enough of it to increase out predictive power beyond the capabilities provided by wavefunction alone (w/o guiding equation).
Does this all make sense? Is this a fair summary?
Pointing to be unable to see the point is a good point.Delta Kilo said:To be honest, I sort of see how it all works but I still don't see a point.
If that was a good analogy, then it would be a good argument against Bohmian trajectories. But the analogy fails because in the quantum case there is no analog of the magnetic field. In particular, the wave function is NOT analogous to the magnetic field. Namely, the magnetic field can easily be interpreted as an objectively existing entity, while the wave function cannot (due to its probabilistic interpretation, or problems with collapse, or problems with the Born rule in MWI, depending on which interpretation you prefer). So if the wave function does not objectively exist, then what does? When we observe, WHAT do we observe? THAT is the question which the Bohmian interpretation tries to answer. THAT is the point of it.Delta Kilo said:All these definite trajectories sound like an attempt to describe magnetic field of a permanent magnet by postulating the existence of invisible metal shavings that line up along the field lines
I'm not prepared to debate the exact meaning of "objectively existing". However in order to predict anything in QM one needs to know the wavefunction but not the definite trajectories. This gives an indication which one is more objective.Demystifier said:Namely, the magnetic field can easily be interpreted as an objectively existing entity, while the wave function cannot.
Well, that's what I'm trying to figure out. One thing we do NOT observe are the famed deterministic trajectories. What we do observe instead are macroscopic pointer states which correspond to the trajectories but in a strange roundabout ways. Not to mention [STRIKE]white elephant in the room[/STRIKE] decoherence, einselection and the like which always [STRIKE]muddy the water[/STRIKE] accompany the process of observation.When we observe, WHAT do we observe?
If the only objective of quantum mechanics (or of science in general) is to PREDICT, then you are right - at the moment there is no much use of trajectories. But many scientists wouldn't agree that that's all what science is supposed to do. Many scientists want EXPLANATIONS, and that's where Bohmian trajectories may be useful and more powerfull than standard form of QM.Delta Kilo said:However in order to predict anything in QM one needs to know the wavefunction but not the definite trajectories. This gives an indication which one is more objective.
I agree, it may be helpful, but there is nothing that requires it. But at least it is a logical possibility worthwile to explore, isn't it?Delta Kilo said:The equation certainly makes sense, it helps visualise the flow of probability, I guess it can be handy in monte-carlo simulations etc.
But there is nothing in it that requires coordinates to have definite values at all times. They might as well be distributions.
Bohmian Mechanics is a theory of quantum mechanics that was developed by physicist David Bohm in the 1950s. It proposes that particles have definite positions and trajectories, rather than existing in a state of superposition as described by traditional quantum mechanics.
Traditional quantum mechanics describes particles as existing in a state of superposition, meaning they have multiple possible states or positions until they are observed. Bohmian Mechanics, on the other hand, proposes that particles have definite positions and trajectories at all times, even when they are not being observed.
In Bohmian Mechanics, the wave function is seen as a guiding equation that determines the behavior and movement of particles. It is not just a mathematical representation of probabilities, as it is in traditional quantum mechanics.
One implication of Bohmian Mechanics is the idea of non-locality, which suggests that particles can influence each other instantaneously regardless of distance. This challenges the concept of locality in traditional quantum mechanics.
Bohmian Mechanics is still a controversial theory and is not widely accepted in the scientific community. However, there are ongoing experiments and studies being conducted to test its predictions and implications. Some potential applications of Bohmian Mechanics include developing new technologies based on the understanding of particle behavior and exploring the concept of non-locality in quantum communication.