## A Gentle Introduction to Bohmian mechanics

This page is intended to be a gentle introduction to both Bohmian mechanics and quantum mechanics. It is written for the curious minded, but not necessarily for those with a mathematical or physics. It is hoped that this could be read and understood by anyone.

#### Why the Quantum

In classical mechanics, we had particles moving about under the application of forces. The forces affected the acceleration of the particles. For example, when one uses the accelerator in a car, the speed of the car changes based on the pedal, but it is not directly set by the pedal. If you push the pedal to the floor, your speed does not instantly change to 60 mph, but it does get there fairly quickly. More quickly, in fact, then if the pedal is half of the way to the floor.

That is Newtonian mechanics. It is a second-order theory. The forces we saw were mainly electro-magnetic and gravitational. Other forces were effective, such as friction being the result of electrostatic contact between surfaces. At first, they were instantaneous actions. But overtime, the actions were seen to be propagated. Gravity, under the theory of relativity, was actually about the bending of space-time. There ceased to be a definite “now”. My “now” is different than your “now” though in our world, they are essentially indistinguishable except under very sensitive testing conditions.

All was good. Well, not quite good. Not everything was explained, not even in principle. The spectrum of atoms, for example. Why did they have these sharp lines? The photovoltaic effect was also a little odd and suggested that light might be discrete particles, not waves.

The most pressing theoretical problem was the stability of atoms. Moving charges radiate energy and opposite charges attract. So why did protons and electrons not collapse into other? There was no explanation for that.

Bohr postulated that there were only certain “orbits” that electrons could occupy in the atom. A transition from orbit to another would release or absorb energy. That energy would be light energy of a certain frequency. Hence the well-defined spectrum we see. The why of this was not yet known.

As the quantum theory developed, it was postulated by Louis de Broglie that just as light waves led to particles, perhaps matter particles led to waves. And shortly after that, it was discovered that electrons did diffract, a feature of waves.

Those waves gave some credence to Bohr’s theory. The orbits correspond to the standing waves, that is, the waves that fit exactly around. More or less.

The question then became are these particles? Are these waves?

#### Particle and Wave

The resolution the quantum founding fathers chose was that it was sometimes a particle, sometimes a wave. What it was and what it did depended on whether a human being, presumably with a PhD, was looking at the system. They thought this was reasonable.

de Broglie had the idea that the waves were guiding the particles. He presented that idea at the same time the current quantum formalism was gaining acceptance. But it was rejected on the basis of a poorly understood thought experiment. See Quantum Theory at the Crossroads for a discussion and the original writings.

de Broglie abandoned the idea and it was later rediscovered by David Bohm.

More to come…