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What’s the difference between the following two sentences?

Two billiard balls, rolling along a table, crash into each other.

Two planets, traveling through space, crash into each other.

The difference is the scale. Two billiard balls rolling into each other on a pool table may just be the highlight of a high schooler’s Saturday evening. Two asteroids striking each other, however, would certainly be catastrophic to life on either of those planets, or anything within range of the destruction.

It’s hard to believe, but physics works the same way, whether things are big or small. The two collisions described above follow the same laws of physics. The two collisions would never be EXACTLY identical, because the collision of any two objects is very complex. However, the laws of physics as we understand them are the exact same for the billiard balls as for the planets. In fact, the same rules apply to galaxies colliding as well as cars or bowling pins or bacteria.

Around 1900, something strange happened — this wasn’t true anymore. A series of then-unsolved problems led to the idea that maybe this wasn’t true. As the solutions to those problems trickled in, it became clear that for really small scales, things get weird. This is because, ultimately, of the theory of the atom. Atoms together create bulk material. But when you try to move around things as tiny as atoms, the forces between the atoms can change quite radically with the distance that separates them, and so the old rules no longer apply.

In physics there are really two different scales of distance which have their own rules. The larger distance scale comprises the world of more than a few atoms at a time. This is the “macroscopic” world. The branch of physics that seeks to describe the motion of macroscopic objects is called Newtonian mechanics, after Sir Isaac Newton. As far as we all knew in the late nineteenth-century, Newtonian mechanics was all there was. In the first few decades of the twentieth century, what became known as quantum mechanics sought to describe the motion of very small objects. Quantum mechanics has some pretty strange rules. Particles can only spin in certain units. You can’t exactly tell where anything really is and know how fast it’s going at the same time. Symmetries which seem to be obvious break down.

Fortunately, in 1900 the entire body of Newtonian mechanics didn’t have to be thrown out. Science is based on observation, and the realization that things got weird when distance scales were small didn’t change the observations on the scale of our everyday life. Quantum mechanics must always “reduce” to Newtonian mechanics as the distance scale increases. So, still one set of laws, just two different parts.

Thankfully there are only two different scales in nature. Due to the fairly limited size of the world’s particle accelerators, we can only observe down to about the proton’s scale (about 0.000000000000001 m, or 10^-15 m). What if there are entirely new laws of physics at a scale one-trillionth of the size of a proton? We would have no idea. For now, our two sets of physical laws are presenting us with enough trouble as it is.

Tags: complete course, quantum mechanics

This entry was posted on Tuesday, June 5th, 2007 at 5:15 pm and is filed under Physics Is Phun. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.