Paradoxes in Quantum Mechanics

Relativity and quantum mechanics both emerged more than a century ago. While relativity is strange, quantum mechanics is even stranger. One hundred years later, aspects of this field continue to baffle the world’s leading physicists, and no relief is in sight!

One of the first paradoxes that triggered the advent of quantum mechanics was the problem of blackbody radiation. If you consider radiation emitted from a box, the classical picture is that at a temperature , each mode has energy where is the Boltzmann’s constant, according to statistical mechanics. But there are infinitely many harmonic modes for radiation waves in a box, so the energy should be infinite. This is similar to the issue of infinite intensity that we discussed in the context of the night sky being dark rather than overwhelmingly bright. Planck resolved this dilemma by suggesting that energy is quantized in multiples of , where is the frequency of the radiation. He showed that this assumption alone was sufficient to resolve the paradox. Basically what happens is that for frequencies where they will not be produced and thus we have effectively a finite number of frequency modes for radiation.

This insight was an important step toward the development of quantum mechanics, which comprises some of the most counter-intuitive portions of our physical laws as we know them today. The unintuitive aspects start with the very postulates of quantum mechanics: particles are like waves, and we cannot ascertain physical phenomena with certainty, but only probabilistically. There is a probability density function (which is the square of the particle’s wave function) for determining a particle’s position. So the uncertainty in position is not due simply to the inadequacy of our measurement apparatus, but is instead an inherent aspect of the particle. In fact, the result of an experiment depends on what you measure: measurement thus becomes an important part of the theory.