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Approximations

January 29, 2014

einstein quotes 1

Today, I have a Christianity/quantum mechanics post for y’all. I know, weird combo. I won’t go into gory details of what I am studying, don’t worry. I will make a point to be pretty general for people not familiar with anything past high-school physics. I know not all of my followers are Christians, but those that are might be interested. I welcome comments from all of my followers though, Christian or not.

This all started when I was sitting in my time-dependent quantum dynamics class, and something the professor said hit me in a weird way.

He said (truthfully) that everything I had learned previously in quantum mechanics classes (of which I have had four in graduate school so far) was completely wrong in most instances. It was all done time-independently, which of course means that it is an approximation, as it doesn’t take an expert in quantum mechanics to realize that we need to take into account how things change with time eventually. Everything I had learned was correct only in a limited sense, in a particular application. If I am looking at a snapshot of reality where time is removed from consideration, then the quantum mechanics I had learned will work. Otherwise, which is most cases, I need a different, more advanced, and more general theory.

What is fascinating to me is where I have been before now, and how much of what I have learned is actually an approximation. An approximation is a way of limiting some very difficult aspect of a concept to make it more accessible or more applicable to a certain situation. Rounding numbers is an example of an approximation that we deal with every day. It would be impractical to pay exactly $21.639175 for a $19.99 item with Texas’ 8.25% sales tax. So we approximate.

What influence has this had on my studies of science?

Approximations in science

Well, I learned in high-school physics that you can plot the trajectory of a particle or a football, and predict where it was going to be, based on Newton’s Laws of Motion.

Except that, according to quantum mechanics, it is impossible to know the position and momentum simultaneously at the subatomic level. This is called the Heisenberg Uncertainty Principle [1]. Therefore, we cannot know where a particle is going to be in the future based on initial conditions, only the probability of it being in certain places.

heisenberg

Newton’s Laws were part of the “classical realm,” which has continuous positions and energies. It would be like saying the energy could be 1.01 or 1.011 or 1.012 or 1.013 or any decimal in between, versus the quantum realm which says the energy might be 1, 2, 3, 4, but not anything between those numbers (hence quantized).

So I was a good little student, and I learned all about quantum mechanics, the particle in a box [2], the hydrogen atom, etc. Then we shattered those concepts and piled on new information about the actual workings of quantum mechanics, and I learned about Hartree-Fock electronic structure theory, which was replaced with more accurate Møller-Plesset perturbation theory, which is then improved with Coupled Cluster theory. More and more concepts, all improving on each other, relaxing approximations, but all of which are still limited by something called the Born-Oppenheimer approximation [3], which basically says that we can solve the nuclei’s math separately from the electrons’ math. Also, all of this was done time-independently.

Then I learned that the way I had studied thermodynamics was limited as well. I found this out in my statistical mechanics class. For example, as an undergraduate, we treated a lot of things as constant that actually vary with temperature, and this changed a remarkable number of things. Undergraduate thermodynamics was yet another approximation. Ironically, statistical mechanics was also done time-independently, i.e. it was also an approximation and only correct in certain instances.

So now, it comes as no surprise to me that I am once again putting aside my preconceived notions of how science works. I am learning a new way to think of things as I go deeper.

But does that mean that everything I learned is wrong? I think not.

In science, we approximate because in most situations, certain parts of science don’t apply. For example, there is no need to take into account the random probabilistic fluctuations of the quantum soup that is empty space when, in general, “empty” space has no net energy or mass at the macroscopic level. The fluctuations all cancel out, leaving no trace of them even occurring. It looks empty to the naked eye.

Undergraduate thermodynamics works in combustion engines; the classical Newtonian Laws work to keep an airplane in the air; Hartree-Fock is used all the time to gain a basic understanding of chemical systems. The methods work within their own approximations. A violinist doesn’t need to know how friction works. They just need to know how to use the concept of friction to play their violin strings with their bow.

My point draws nigh.

Approximations in Christianity

In Christianity, Christians often prove things with the Bible. Not saying that this is wrong, but I am disturbed at times by the way we do this. We form an opinion, then look for evidence in the Bible to back it up. We find evidence, then point to it and say, “Look! God says I’m right and you’re wrong!”

I think Christians often approach the Bible the same way scientists approached something like Newton’s Laws. Things that have been said about both would include,

  • “Everything that we need to know is here.”
  • “This is the way the universe works.”
  • “It is self-contained.”

I would argue that these things are not true. At least, not generally. I think that the Bible should be treated as an approximation, just like Newton’s Laws. Now hang with me here while I explain what I mean by the seemingly blasphemous thing I just said.

The key to my reasoning here is that something can be both true and approximate. Christians would generally agree with me, I think, if I said that God is big. Really, REALLY big. I would argue, he is bigger than whatever box we could possibly put him in with our puny minds. That includes something like the Bible. It is written human words. Nothing about that can possibly transmit everything God is as a Being that created space and time. He is outside of our sphere of reason and intellect. What we think we understand, we cannot logically assume to be the whole picture.

With that said, I view the Bible as an approximation, albeit a good approximation, of who God is. It works for our situation, applies to our circumstances, but it is inherently limited by the confines of our physical reality. It is trying to show us a non-corporeal Being through corporeal means. It just won’t be the full picture. Science can’t show us the full picture either, though. As Einstein once said, “science can only ascertain what is, but not what should be, and outside of its domain value judgments of all kinds remain necessary” [4].

When we take passages out of context, or try to read too much between the lines, we can bring our own imperfections into the picture. We color the facts with our judgement, and we lose the accuracy of the approximation when we pretend that such confines don’t exist. That doesn’t mean we can’t try to find implications of what we read, we just have to take the terms of our approximation into account, sort of like ground rules that influence how we read everything else.

This means that it is okay that we don’t know certain things. It also means that we shouldn’t pretend to have all the answers. Both of these things are prebuilt into the idea of an approximation.

Relaxing the approximation

 
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I think the reality of quantum mechanics is probably a lot more simple than we realize. I think someday, we will discover some nice, neat mathematical form that will incorporate all of the special cases into one simple law or something. All of the weird caveats will be gone, and it will all be connected succinctly.

I think that the reality of God is also probably a lot more simple than we realize. Who knows, when we meet Him face-to-face (which I believe we will), we may discover that the Bible is much more simple than we realize. It might boil down to two simple Laws [5],

  • Love the Lord your God with all your heart and with all your soul and with all your mind.
  • Love your neighbor as yourself.

You might say everything hangs on these two things.

 

References:

[1]: http://en.wikipedia.org/wiki/Uncertainty_principle (back to text ↑)

[2]: http://en.wikipedia.org/wiki/Particle_in_a_box (back to text ↑)

[3]: http://en.wikipedia.org/wiki/Born-Oppenheimer_approximation (back to text ↑)

[4]: The conference on Science, Philosophy and Religion in Their Relation to the Democratic Way of Life, New York, 1941. Source: Boğaziçi University (Turkey) (back to text ↑)

[5]: Matthew 22:37-40 (back to text ↑)

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