The End of the Beginning

Have we reached the tortured end? Yep, almost (at least for the moment…. hehehehe).  But before I leave the topic of time dilation and special relativity, I’d like to address time dilation in the real world, as opposed to the imaginary world of Einstein-style thought experiments featuring vaguely vagina-shaped spacecraft carrying excited male celebrities. 

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 often after being spun up by black holes 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.  One of the byproducts of proton decay is a particle called a muon, which continues through the atmosphere in roughly the same path as the originating proton at roughly that same high rate of speed.  Now, one thing about muons is that they’re 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. 

At a velocity of about 0.99 the speed of light, or 297,000 kilometers per second, how far do muons travel through the atmosphere before they decay?

Distance equals speed multiplied by time.  In the muon’s frame of reference, 297,000 kilometers multiplied by two-millionths of a second (their average time of existence) yields roughly 0.6 of a kilometer.  This means that the average muon doesn’t even come close to covering the distance between the top of the atmosphere, where it was created, and the ground, before it decays.  Even the muons that beat the average, and survive for a little longer than two-millionths of a second, don’t make it.

That’s a good thing, because muons are radioactive.  Exposure to them can cause cancer.  But, is it really the case that muons never travel far enough to cause us any harm?  So far, our discussion about how long a muon exists, and how far it travels through the atmosphere, has been from the muon’s frame of reference.  In our (the Earth’s) frame of reference, which is at rest compared to the muons, we’ve got to factor in the extra distance that the muon is going to cover due to time dilation.  For a muon traveling at 0.99 light speed, time is stretched by a factor of about four.  In our frame of reference, therefore, instead of existing (and traveling) for about two-millionths of a second, the average muon exists for about eight-millionths of a second.  That is enough time to traverse about two and a half kilometers before decaying.

But that’s just the average muon.  For muons that decay more slowly than average, time dilation makes just enough of a difference that they do manage to reach the surface, and maybe even hit you or I.  It’s not a lot of muons; statistically, only about four out of every hundred last long enough for the combination of their relative longevity, compared to other muons, and time dilation, to make it all the way down.

From our earlier discussions, 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 is manifest as space compression.  In the muon’s frame of reference, it lasts exactly as long as it should (on average, only two-millionths of a second).  Thus, the (statistically) most durable muons manage to make it all the way through the atmosphere, not because time dilation extends their lifetime, but because the distance between the top of the atmosphere and the ground is compressed by a factor of four.  

 

You could verify the presence of muons reaching the surface with a simple Geiger counter.  Being radioactive little beasties, some 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 Geiger counter on up there, you would hear more frequent clicks, because more muons make it that far.

The bottom line: Time dilation is real, influencing real events in our real lives. And that’s a wrap on the topic, at least for now.  I just have to “close the loop” between time dilation and my late friend Karl, my original motivation to research and write these blogs.  Frankly, the connection is kind of a downer.  I’ve had four different surgeries in the last couple of years for skin cancer.  Would I have escaped the cancer scourge if not for time dilation?  I don’t know.  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, too, if the phenomenon didn’t exist.

Ah, well.  Time dilation is built into the very fabric of our reality, so there’s no point in wishing.  I just hope you’ve enjoyed finding out what it’s all about.  I know Karl would have!