The End of the Beginning #10

by Whabby

Have we reached the tortured end? No more scientific nonsense on Wednesdays? Yep, we have (at least for the moment…. hehehehe). But before I leave you, I’d like to finish by tackling time dilation as it exists in the real world, as opposed to the imaginary world of Einstein-style thought experiments with vaguely vagina-shaped spacecraft carrying excited naked male passengers.

Did you know that, every second of every day, subatomic particles, mostly protons, strike our atmosphere? You may have heard them referred to as cosmic rays. They are most definitely not rays, though; protons are bona fide particles with bona fide masses. And despite the name, cosmic ray, they’re hardly exotic; there are one or more protons inside every atom in your body, and inside every atom in the universe.

As cosmic rays, though, protons travel to us over phenomenal distances, having been spun up by black holes at the centers of other galaxies to about 0.99 of the speed of light. When these naked protons (by naked, I mean they’re not part of an atom) strike the gas molecules in our upper atmosphere, about 15 kilometers above the ground, they immediately decay, creating a particle called a muon. The muon continues through the atmosphere in roughly the same path as the originating proton at roughly that same high rate of speed. Now, the thing is, muons are very short-lived particles. They take an average of just two-millionths of a second to decay into other particles. That’s just an average, mind you. Some muons survive for a little more time than two-millionths of a second, while others survive for a little less. Since the muons are traveling at about 0.99 the speed of light, or 297,000 kilometers per second, how far do they travel through the atmosphere before they expire?

Distance equals speed multiplied by time. In the muon’s frame of reference, 297,000 kilometers per second (their speed) multiplied by two-millionths of a second (their average time of existence) is roughly 0.6 of a kilometer. This means that the average muon doesn’t come close to covering the distance between the top of the atmosphere, where it was created, and the ground, before it passes out of existence. Even the muons that beat the average, and exist for a little longer than two-millionths of a second, don’t last long enough to travel all the way to the surface.

Or do they? The discussion so far has been all in the muon’s frame of reference. In your (the Earth’s) world (which is stationary compared to the muon), we’ve got to factor in the extra distance that the muon is going to cover due to that now familiar time dilation phenomenon, whereby extra cycles of time/space creation occur for items, like muons, that move very fast compared to you. In the specific case of a muon traveling at 0.99 the speed of light, time is stretched by a factor of about four. In our frame of reference, therefore, instead of existing (and moving) for about two-millionths of a second, the average muon exists for about eight-millionths of a second. That is enough time for the average muon to travel about five kilometers of Earth-coordinate space before decaying, or about a third of the distance to the Earth’s surface.

But that’s just the average muon. For some of the muons that decay more slowly, the time dilation is enough for them to reach the surface, or all the way to you and I (actually, only about four muons out of every hundred last long enough for the combination of their relative longevity, compared to other muons, and time dilation, to allow them to make it).

Of course, you’ll recall that, for the object traveling quickly, time is locally the same as it is for you, and the phenomenon of time dilation turns into a phenomenon of space compression. From he perspective of the muon, it lasts exactly as long as it should, which is never much more than two millionths of a second. The muon manages to make it all the way through the atmosphere, not because it gets a longer period of time in which to move, but because the surface of the Earth lies in the direction of the muon’s motion, so the surface is about four times closer to the top of the atmosphere than it is in our framework. Stated another way, from the muon’s perspective, the distance from where the muon is created to the surface of the Earth is about four times smaller than it is from our Earthly perspective.

Actually, you could verify the presence of muons near the surface with a simple Geiger counter. Muons are radioactive, and many of the clicks you would hear when you turned on the counter would be in response to their presence. If you climbed a mountain and turned the counter on, you would hear more frequent clicks, because more muons get that far.

Well, owls, that’s kind of a wrap! We’ve reached the inevitable point where I need to “close the circle” with Karl, my friend and motivation to research and write these blogs. Frankly, that connection is kind of a downer. Being radioactive, muons are actually kind of nasty. The ones that make it, and hit the surface, also hit us, and become potential cancer-causing agents. I’ve had four different surgeries in the last year for skin cancer, with another biopsy just this afternoon. I wonder if I would be cancer free were it not for time dilation? And Karl died of complications due to surgery necessitated by the strong suspicion that he had colon cancer. I wonder if he would be alive today, without time dilation.

Ah, well. Time dilation is built into the very fabric of our reality, so there’s no point in wishing that it didn’t exist. I hope you’ve enjoyed finding out what it’s all about, owls. I know Karl would have!