The Big Mo

I think I need to get the Ayn Rand Institute cooties out of my head, so how about a cosmic ray tangent?

Cosmic rays are pretty interesting, highly energetic charged particles from space. Most are protons, but there's about a 9% component of helium nuclei, and there are even some heavy nuclei like iron in the mix. Prior to the creation of really big particle accelerators, cosmic rays were the only way to study particles having energies of above a GeV. The energy spectrum decreases with increasing energy, but some cosmic rays are way above a mere billion electron volts.

On October 15, 1991 a cosmic ray event was observed with an energy of 3 x 10^20 eletron volts, i.e. 300 billion, billion electron volts, or about 50 joules. There have been a number of similar observations since, confirming the existence of particles so energetic that they must be of recent origin (in the astronomical sense). Otherwise, they would lose energy by interacting with the cosmic microwave background left over from the big bang. The first such particle discovered was dubbed the "Oh-My-God" particle, a joking reference to the nickname of the Higgs particle as "The God Particle."

All very cool, but that's not precisely what this essay is about. No, this essay is about energy and momentum.

Every article that I've ever seen compares the energy of Ultra High Energy Cosmic Rays (as they are called) to some macroscopic object, traveling at a fairly low velocities. Science magazine writers are particularly fond of comparing UHECRs to a strongly hit golf ball. The Wikipedia article on them compares the energy to a baseball thrown at 60 miles per hour.

The thing is, people do not interact with macroscopic objects via their energy content. An object's momentum is what produces force when it encounters another object. If you are hit by a golf ball, and it bounces off you elastically, there need not be a lot of energy transfer, but the momentum transfer (and damage) can be substantial.

Once, on the inevitable science fiction convention panel, during the Q&A, we were asked what we considered to be the greatest scientific error common among the general public. My answer was "the confusion of energy and momentum."

Think of a movie like the Schwarzenegger vehicle Eraser, where the MacGuffin is an ultra-high velocity rail-gun rifle. The gun is shown as knocking people backwards, using the old "stunt wire" trick that movies love so much. The problem is that such a weapon would transfer very little momentum to the target (and would have very little recoil). What would happen is that the projectile would basically explode on contact with an interacting mass. To a lesser degree, that is what happens with high velocity rifle shells. Similarly, Hollywood used the stunt wire for practically all gun shots, often giving the impression that a handgun is really a "momentum pistol," like the one seen in Fritz Lieber's The Wanderer.

Meteor Crater in Arizona was originally thought to be of volcanic origin, in part because it was circular, and it was believed that a meteor would almost certainly come down at an angle, producing an elliptical crater. Eventually, experiments with high velocity projectiles confirmed that they produce circular craters from almost any angle.

A fellow on the old Compuserve Science Forum explained it by analogy to throwing a hand grenade. The grenade carries so much explosive energy that it overwhelms the momentum, so if you throw one into a sand box, it will create a circular crater, no matter what the angle it hits. In fact, the ratio of energy to momentum for a meteor is considerably higher than for a thrown grenade.

If you really want to get a feel for the energy of an Oh-My-God Particle, you should compare it to things in ordinary experience where the energy is important. Thus, the energy from such a particle would light a 50 watt bulb for one second. Or it would power a single flash from a mid-size photoflash, perhaps ten from a small flash attachment.

Fifty joules will raise the temperature of one gram of water about 12 degree C, about 22 degrees F.

Or, if you want to stay with the moving mass analogy, how about propelling a mid-size automobile at a speed of a quarter of a mile per hour, assuming you have a friction free environment and some perfect method of converting cosmic ray energy into the motion of a motor vehicle, and, these days, who doesn't have those lying around?