Modern Quantum Theory

I think I can safely say that nobody understands quantum mechanics.

--R. Feynman

Particle Wave Duality

If one sends water waves through an opening, they spread out. This is called diffraction. If one sends water waves through two openings, the wave splits into two pieces which then spread out. As they spread out, they interfere with each other causing an interference pattern. This works with all waves, in fact such as those of light. This is part of the compelling evidence for the theory of light as a wave.

However, as noted previously, Einstein's explaination of the photoelectric effect indicated that light is made up of discrete particles called photons. If you throw baseballs through two holes, they aren't going to interfere with each other as they move away from the holes.

This dual nature of light was accepted as fact by 1920, even though there was no theoretical basis for it. Scientists would use whichever version of light was more convenient at the time.

In 1924, a graduate student named Louis de Broglie, a member of a French aristorcratic family, developed a theory about the wave nature of matter. He figured that if a light wave could be a particle, then a particle could also be a wave. In his doctoral dissertaion, de Broglie proposed that a particle of mass m traveling with a speed v should have associated with it a wavelength l, given by

l = h/mv = h/p

This allows a different view of the orbits in the Bohr atom. They can be thought of as standing waves around the atom. Each fundamental quantum number, n, is the number of wavelengths contained in the orbit.

The de Broglie wavelength for a baseball is around 10-30 m. Much to small do be detected by any means of obsevation. The de Broglie wavelength for an electron, however, is around 10-10 m, or one angstrom, the size of atomic radii. It is thus possible, through advanced laboratory techniques to detect the wave motion of electrons.

By passing electrons through a double slit, it is seen that an interference pattern is indeed produced.

Defining Particles

(Caution: this section is extremely simplifed. Gross assumtions have been assumed.) We define particles as localized in space and time. If we consider particles to be waves, such a localized wave is called a pulse. A pulse is the combination (constructive and destructive inerference) of a several waves. We can group these waves together in what is called a wave packet.

particles are groups of waves called wave packets

The more localized that we wish to make our particles the more waves we have to add to the packet. This causes a problem in that the more waves that are added to the packet, the less certain is the motion of the packet. This gives rise to a limiting condition:

Dk Dx ~ 1

Dw Dt ~ 1

Heisenberg Uncertainty Relations

In 1927 Werner Heisenberg developed a theory based on the previous discussion: The Heisenberg Uncertainty Principle states:

It is not possible to determine both the position and the momentum of a particle with unlimited precision.

A more formal way to write this is:

Dp Dx ~ h/2p

DE Dt ~ h/2p

These relations have been demonstrated by single slit experiments and by high energy particle experiments.

These relations imply that the universe is unknowable to some degree. One way to think of the uncertainty relations is that the act of observing changes the motion of the particle. But there is more to it than that. Particles exist everywhere at the same time but by our observation we narrow it down to a particular regin. Do we influence reality by observing it? Does our very conciousness affect our reality? In his later years, Heisenberg speculated on these and other questions. He believed that the next great advance (paradigm shift) in physics would be discovering the realtion between conciousness and reality.