My son, Matt, tells me that all of quantum mechanics can be written down on a half-sheet of paper. In fact, he did it, and here it is:
- The state of a system is entirely represented by its wave function, which is a unit vector of any number of dimensions (including infinite) existing in Hilbert space. The wave function can be calculated from the Schrodinger equation.
- Observable quantities (like position, momentum) are represented by hermitian operators, which function as linear transformations that operate on the wave function.
- The expectation value (in a statistical sense) of an observable quantity is the inner product of the wave function with the wave function after being operated on by the observable’s hermitian operator.
- Determinate states, or states of a system that correspond to a constant observed value, are eigenstates of the observable’s hermitian operator, while the observed value is the eigenvalue. (ex. energy levels that give rise to discrete atomic spectra are eigenvalues corresponding to energy determinate states.)
- All determinate states are orthogonal and all possible states can be expressed as a linear combination of determinate states.
- When a measurement is made, the probability of getting a certain value is the square root of the inner product of that value’s determinate state with the wave function.
- Upon measurement, the wave function “collapses”, becoming the determinate state corresponding to the value that was measured.
I know it all sounds complicated, but Matt assures me that as a body of scientific discovery, it’s all quite elegant and conceptually simple. A person need not be a physicist to understand the laws. Physics undergrads are required to master them before they graduate.
People who seek common ground between science and religion often say that God works through (or at one time defined) the physical laws that we observe in nature. If that’s the case, why didn’t He take the opportunity to jot down the half-page in Genesis? Why did He water down the truth by claiming the world was created by “His word”?
If you’re a religious person, you’re likely to answer what is obvious—that, in short, people weren’t prepared to hear about such laws at the time Genesis was written. Given the scientific advances our world has experienced recently, we can all relate to the notion. Furthermore, our interactions with kids, too, teach us that due to human limitations the facts can’t always be apprehended. As I’ve mentioned before, we seldom divulge the full truth on any topic to children and this isn’t because we’re devious. If a three year-old boy asks why the sky is blue, for example, do we explain the nature of light—how it travels in waves, with each wave length corresponding to a color? No, that would be too much information for him. Whatever answer we do provide won’t be a complete reckoning, because the child isn’t prepared for it.
Now, despite what my son says, I think the majority of people today—and that includes me—are ill-prepared to understand the physical concepts he has described above. Yet, can’t the same be said regarding a range of topics that continuously advance beyond general understanding? For this reason, I think of the gospel as something more akin to a compass than a roadmap. Though ultimately we may want to head in a specific direction, a compass will sometimes point us to impassable terrain, around which we must detour. Christ’s gospel says precious little about how we should love our neighbors, only that we must. Though circumstances may cause us to meander, compassion is the true north that establishes our orientation.
That, however, begs a question: Why didn’t Christ offer a roadmap instead of a compass? The Mosaic Law, after all, was an attempt to answer any and all questions about correct and moral behavior, and it would seem logical that Jesus would attempt to accomplish the same. Perhaps the reason is due to the fact that the world changes and the terrain of our lives morph constantly in terms of complexity and degree of difficulty. The problem with a map is that it’s static and doesn’t account for washed out bridges and pathways that are subject to redevelopment. If you happen to be in a new city and need directions to get around, will you refer to a map commissioned by the city’s founders? It would be better just to know an ultimate heading and improvise a way there.
For this reason, I’m not impressed by assertions that God commands this or that. In my mind, there are two rules of thumb that, if followed objectively and sincerely, will invariably lead to what is decent and lovely, albeit with some allowance for meandering.
Of course, you know what those rules are.