|I’m not pompous; I’m pedantic.|
|There’s a difference.|
|—The Calligraphic Button Catalogue|
Just about a year ago, a team of scientists reported that Betelgeuse—the bright red star in Orion’s shoulder—appears to have shrunk by about 15% since 1993. That would mean the diameter’s been shrinking at about 1200 miles an hour for all that time.
Such shrinkage—if it’s really happening (it’s hard to be sure)—could be the precursor to a supernova explosion, which would be way cool. The mathematician John Baez computes that a supernova Betelgeuse might be roughly as bright as the full moon, or maybe up to three times as bright.
Surprisingly, it took almost a year for this information to be widely reported on the Internet, but in the past few weeks, a number of sites have cropped up touting the upcoming supernova, and, as you might expect, a few prophecying doom. You can ignore the doomsayers; at a distance of 600 light years, Betelgeuse is too far away to hurt us.
Browsing the various science forums (such as Discover‘s), I’m struck by how often the following simple question comes up: Given that Betelgeuse is 600 light years away, is it or is it not true that it would it would take 600 years for us to notice any explosion? Or to put this another way: If the sky lights up with a new moonlike object tomorrow night, does that mean the explosion took place 600 years ago?
A pretty good answer—and the one that’s being given on all those science forums—is “yes”. But that can’t be exactly right, at least not for all of us, because at any given moment some of us are sitting in our living rooms while others are driving on the Interstates. Relativity tells us that if we’re moving relative to each other, then we must disagree about the times of distant events.
How much do we have to disagree? By about a half an hour, if I’ve done my arithmetic right. If you, standing on a street corner, say the explosion took place at noon on June 9th of the year 1410, then the driver of the car who has just run over your toes at 70 miles per hour (heading in the general direction of Betelgeuse) must say the explosion took place at 11:30AM on the same day. A half hour is not a lot (though it’s more than the few fractions of a second most of my friends have guessed), but here at the Big Questions, we aim to be precise in every detail.
Edited to add: It’s clear from the comments that I should have been clearer about what I’m assuming. My assumption (which I’d thought I’d stated but now see that I didn’t) is that you (and your friend) see the explosion at the exact moment when he’s running over your toe. You then each calculate how long ago the explosion must have taken place. Your conclusions will differ by half an hour.