Quantum mechanics had many interpretations for ages. The most accepted ones are the ones most experimentally proven ones. Bohmian mechanics is one of the less probabilistic and more conventional deterministic approach towards quantum mechanics. Bohmian theories can be formulated by introducing a privileged foliation of space-time. This introduction of a completely new foliation of space-time would contradict with the theory of relativity,this is the reason of Bohmian mechanics not being so wide-spread or worked on. My research would be to work on Bohmian mechanics,trying to show a relativistic approach can be made to work for all inertial reference frames and pilot-wave theory can help solving the age long debate of the difference between Macroscopic and Microscopic world and if the spooky actions of the microscopic world is completely random or seems random because of the ignorance of pre-existing local variables.
Bohmian mechanics or pilot wave theory is based upon trajectory,it doesn't have that same randomness like relativistic quantum mechanics. Bohmian mechanics is based on precise calculation where there is an initial position,and it's velocity vector is dependent on the wave function.Observations and measurements in the microscopic world have no effect on the head of the velocity vector. So,to sum up,in relativistic quantum mechanics, an initial position of a particle can be a among every a huge range of possibilities because measurements affect it's state and position,and it's velocity vector is considered to be among all the possible vectors in that reference frame until it's measured. Whereas in Bohmian mechanics, a slight change in object's initial position can cause a direct change to the entire velocity vector,and it can be predicted by using trajectory using the Schrodinger wave equation (only for spinless non-relativistic particles) .
Equation 1.1
Although it abides by the Schrodinger's equation the trajectory is actually found by the guidance formula.
Equation 1.2
Here Ψt, the universal wave function, is a complex-valued function on the 3N-dimensional configuration space of the N particles.The argument still stands,as this universal wave function is for spinless non-relativistic particles,but still the velocity vector of each particle is being described in terms of the wave function and even if we replace that first equation with a more relativistic equation like the dirac's equation,the second function which is the guiding function is still being evaluated using the derivatives of the wave in the exact initial point of the entire system.
Another argument ( or maybe I should say question,as all I have right now is questions) about ignorance of pre-existing variables in a reference frame,for a very generic example.If I flip a coin,there is no certain deterministic answer to what the outcome would be,so we express it as a probability of two different outcomes,in a fraction. But in theory,if we know the coin's initial position,initial state of heads or tails,and the forces surrounding that object,we can know the outcome. I think what Bohmian mechanics uses is the same deterministic outlook of things.
For a visual explanation of what I am trying to say can be modeled by the picture below.
Figure 1.1
As we can see the results are certainly different if the initial position is changed even in he slightest of manner,and because of the initial positions are not always completely certain in relativistic quantum mechanics,the results might seem random,just we saw in the flipping coin experiment. And this still agrees with the phenomenon of particles making an interference pattern where the wavefunction is big because in pilot wave theory we still are using the wave function in equation 1.2,the guidance equation.
Now let's take a look at another example where the ignorance of local variables might cause difference in results.
figure 1.2
in figure 1.2,we block one way where the particles can go through,this rejects the interference pattern and the particles go through the way we expect them in a singular wave pattern.
figure 1.3
But as we can see in figure 1.3, because of just opening up the other slit recreates the interference of waves,and it creates an interference patterns in the places where the wave function is high,so it still adheres to the laws of quantum mechanics.
What I am saying is if we treat that block on the slit as a hidden variable,the block being there or not being there completely changes the outcome of that velocity vector,so it seems random but isn't quite random indeed.
Quantum mechanics just might be like Brownian motion,in where Einstein pointed out in 1905, that the the erratic random movement of microscopic particles in a fluid, was a result of continuous bombardment from molecules of the surrounding medium and if we knew the behaviours of the surrounding medium,the random movement of microscopic particles in a fluid,wouldn't be random anymore.
Saikanam Siam
Sophomore
Brooklyn Technical High School (Present)
Natore Govt. Boys' High School,Natore,Bangladesh ( Former)
References and further Reading
References
Dürr, Detlef, et al. “Can Bohmian Mechanics Be Made Relativistic?” [1307.1714] Can Bohmian Mechanics Be Made Relativistic?, ArXiv, 24 Dec. 2013, arxiv.org/abs/
Dürr, Detlef, et al. “Can Bohmian Mechanics Be Made Relativistic?” Proceedings. Mathematical, Physical, and Engineering Sciences / The Royal Society, The Royal Society Publishing, 8 Feb. 2014, www.ncbi.nlm.nih.gov/pmc/articles/PMC3896068/.
Further Reading
https://plato.stanford.edu/entries/qm-bohm/
There's reference to other sources in this link,and also an interesting observation is that they put Bohmian mechanics in the category of philosophy,instead of modern physics.
this cured my cancer tbh
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