Quote:
Originally Posted by David Sklansky
Why does the double slit experiment results depend on whether there is an observer?
There is an "intuitive" interpretation of Quantum Mechanics, assuming having a particle with a position and momentum at all times is intuitive to you, called Bohmian Mechanics or de Broglie–Bohm theory. I'm going to assume you're most familiar with the Newton's laws version of classical mechanics, in which one could roughly summarize a particle's trajectory by saying it follows a straight line path, i.e. it's velocity is a constant, unless acted on by a force which can be modeled, in many cases, as a potential energy field, e.g. the gravitational potential, or electric potential:
x = x(t); V = V(x), m = mass.
m * d^2(x)/dt^2 = -dV/dx,
I.e. the particle accelerates proportional to how steeply the potential energy field is sloped. It's as though this field is guiding the particle's acceleration.
In contrast, in Bohmian mechanics, the particle's velocity, not it's acceleration, is guided by the "steepness" of a field (See the Overview section of
https://en.wikipedia.org/wiki/De_Bro...ory#Overview):
W = W(x, t), h = constant, Im[ Z ] = the imaginary part of a complex variable Z.
m * dx/dt = h * Im[ (dW(x, t)/dx) / W(x, t) ],
where I wrote h instead of h_bar = h/(2*pi) to save space, and W(x,t) is the standard Quantum Mechanics wavefunction which obeys the Schrodinger equation:
i * h * dW/dt = -(h^2/(2 * m)) * d^2W/dx^2 + V*W,
where V = V(x) is the same potential as in classical physics.
For the difference between the single and double slit experiments within Bohmian mechanics, see section 2 "Example: The Double-Slit Experiment":
https://arxiv.org/pdf/1704.08017.pdf...%20is%20shown.
For the case when there are two slits and a detector is placed at one, the momentum transferred from the detector to the particle behaves in part as if the slit was partially blocked, depending on how much momentum is transferred, which also effects how accurately you measure the particle's position. See the answer to this post:
https://physics.stackexchange.com/qu...he-double-slit
The Derivations section of the Wikipedia article has more perspectives on connections between classical and Bohmian mechanics:
https://en.wikipedia.org/wiki/De_Bro...ry#Derivations.
The method which shows the complex Schodinger equation to be two real equations, one for conservation of probability, and the other a version of the Hamilton-Jacobi equation with an extra Potential function, the "Quantum Potential", is especially interesting, though it depends on how intuitive the Hamilton-Jacobi formulation of classical mechanics is for you.