Pauli, Heisenberg, and all That

Most recent answer: 10/22/2007

Q:
What is the appeal of the exclusion principle of Pauli to the physicists, so much so that they have accepted it as an inviolable "principle"? Same question regarding Heisenberg’s principle of uncertainty? In other words, how did Pauli and Heisenberg originally became aware of such effects, and why did they assume these effects to hold in every situation? Although, conservation of momentum is easy to visualize (i.e., the more mass and the more velocity of an object, the more mass and velocity you expect from an opposing object to stop it; or from a stationary object after it has been struk), however, conservation of enery is not that intuitive, i.e., half-mass and velocity-squared or force-and-distance do not present anything that we feel urged to conserve! Why is then, the law of conservation of energy?
- Mehran (age 53)
Lisle, Illinois
A:
To answer your questions one by one:

First:
There are multiple lines of evidence supporting the exclusion principle, the principle that there cannot be more than one fermion particle in any given quantum state.

1. It obviously works empirically in explaining why the electrons in atoms occupy the states that they do, rather than all piling up into low-energy states.

2. There is a deep theorem, called the spin-statistics theorem, which shows that in any quantum theory consistent with special relativity the exclusion principle has to hold for all particles whose spin is a half-integral number of units. Of course, the fermions are precisely these particles, so the formal theorem matches perfectly with observed behaviors.

3. There are countless other experimental and theoretical developments linking quantum mechanics, special relativity, and the behavior of all sorts of particles. Breaking the exclusion principle would require destroying all of this intricate and highly successful structure.

However, even with the most compelling principles, there is always the possibility that in some future physics the whole framework will have changed and the current principle will be seen merely as an approximation. Usually it’s best to keep that possibility far to the back of your mind.

Second:

Again, Heisenberg’s uncertainty principle is a direct consequence of the whole structure of quantum mechanics. Quantum mechanics has been a spectacularly successful way of predicting the behavior of everything on a small to medium scale. We don’t have any alternative theory that is even close to being able to describe the microscopic behavior of things. At any rate, the most troubling aspects of the uncertainty relation are confirmed by experiments showing that nature violates the Bell inequalities, which would be obeyed by any processes which have definite values for measurable quantities. So even if we someday transcend our current quantum mechanics, it seems that something like the uncertainty relations will have to be a permanent part of physics.

Third:

Heisenberg tried to write a formal mathematical description of atomic behavior, and the uncertainty relation popped right out of the math. Schroedinger wrote a very different looking wave description of atomic phenomena, and the same relations emerged from it. The two descriptions turned out to be mathematically equivalent.

Pauli initially was trying to account both for atomic spectra and for the effects of magnetic fields on these spectra. Later, he went back to confirm his picture by proving the spin-statistics theorem.

Fourth:
There are many forms of energy, of which the classical kinetic term you mention is just one. In quantum mechanics, energy is really another word for frequency, and the basic rules for how things change in time do not allow for it to change. The fundamental theorem here, due to Emmy Noether, is that so long as the same laws of physics apply at all times, the variable (frequency or energy) describing how things change in time must itself be conserved. As for how the classical kinetic energy term arises, it pops up as an approximation for the relativistic expression for the net energy. The fact that the same laws of physics apply in all different parts of space gives, via Noether’s theorem, the conservation of momentum.

Mike W.

p.s. We’re still working on your deep question about why electron clouds don’t self-repel. It’s hard.

(published on 10/22/2007)