Pilot Wave theory (Bohmian mechanics), Penrose & Transactional Interpretation explained simply

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In the Copenhagen interpretation, which is what is typically taught to undergraduate students, particles are in superposition. What is superposition? In quantum mechanics, there is no equation that states exactly what some properties of a particle are. They are expressed in a wave function which is part of the Schrodinger equation. This describes the shape of what looks like a wave.

But this wave-particle duality doesn’t fit with our observations. So Bohr and Heisenberg interpreted the mathematics to mean that particles really are waves until they are measured. This state of multiple properties at once is called superposition.

In this interpretation, the wave is not a physical wave, but a mathematical way to figure out the probability of finding a particle in a certain state. This is in contrast to DeBroglie-Bohm or pilot wave theory, named after Louis de Broglie and David Bohm, also known as Bohmian mechanics. This theory describes the wave function as real physical waves that push real particles around. They are just being guided by the wave function which evolves according to the Schrodinger equation.

This theory is completely deterministic. The wave provides a set of potential trajectories, but the particle takes only one trajectory.

No measurement problem and no collapse occurs because there is no superposition.

How the wave guides the particle is described by a new equation that is introduced to accompany the standard Schrödinger equation - the Guiding Equation. This describes the configuration over time of the particle even when unobserved. This equation has the wave function in it, so it is not completely new.

In this scenario, the trajectory of a particle only appears random because we don’t know its initial starting point. But if we did, we could predict where the particle would be at all times, and where it will end up. So the uncertainty in this scenario is due to our inability to measure the particle’s initial state, not because the particle’s position is unknowable.

Bell’s inequality is not violated because this is a Non-local hidden variable theory because Its position and velocity depends on the configuration given by the wave function, which extends to all of space. The hidden variables are distributed throughout the entire universe, not just at the particle.

This is a problem because it means that the wave function in a distant parts of the universe can simultaneously affect each other. This instant communication violates special relativity, and is not compatible with quantum field theory.

In addition, simultaneity doesn’t really exist in relativity, because it depends on your choice of coordinates.

Another problem is that real waves push real particles, but they don’t push back which violates Newton's third law.

Pilot wave theory explains the double slit experiment by showing that measuring instrument interfere with the pilot waves and ruin their quantum behavior. Results from this theory are the same as with standard QM.

Another theory by 2020 Nobel laureate Roger Penrose, is called induced collapse, where he proposes a relationship between quantum mechanics and general relativity. He say that large mass particles cannot sustain superposition in two places because too much energy is required to bend space-time. So one Planck mass and heavier particles revert to one position.

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One of the craziest theories, imo, is called the transactional interpretation, by John Cramer in 1986. It is non-local and treats waves as being physically real. In it, future events can have a retro-causal link explaining the correlation between the particle properties and the measurements yet to be performed on them. This means that later events can cause earlier events—that causation can operate backwards in time as well as forwards in time.

If you extrapolate this idea to the entire universe, and all of time, you can argue that all backward traveling and forward traveling waves evolve to a single reality that we experience in the present. But this interpretation doesn’t generate any new predictions, so is not testable.