Remember when “going viral” didn’t mean hospitalization and possible death? (Obviously if we go back even further to the original meaning, it did.) I had an old post go briefly and mildly viral last week. Big traffic spike with a very rapid tail-off. Most bemusing.
I’ll tell you about that, and about a spike on another post, this one weirdly seasonal — huge spike ever September for three years now. I have no idea what’s going on there. Most puzzling.
There is also a book about the friendship and conflict between Albert Einstein and Erwin Schrödinger that I thoroughly enjoyed despite it not being my typical sort of reading (I’ve never gone in much for either history or biography).
Back in 2015, to celebrate Albert Einstein’s birthday, I wrote a month-long series of posts about Special Relativity. I still regard it as one of my better efforts here. The series oriented on explaining to novices why faster-than-light travel (FTL) is not possible (short answer: it breaks reality).
So no warp drive. No wormholes or ansibles, either, because any FTL communication opens a path to the past. When I wrote the series, I speculated an ansible might work within an inertial frame. A smarter person set me straight; nope, it breaks reality. (See: Sorry, No FTL Radio)
Then Dr Sabine Hossenfelder seemed to suggest it was possible.
I hadn’t really planned to, but it’s both Pi Day and Albert Einstein. As a fan of both the number and the man, it seems like I should post something.
But I’ve written a lot about pi and Einstein, so — especially not having planned anything — I don’t have anything to say about either right now. In any event, I’m more inclined to celebrate Tau Day when we double the pi(e). I do have something that’s maybe kind vaguely of pi-ish. It’s something I was going to mention when I wrote about Well World.
It’s just a little thing about hexagons.
I was gonna give us all the day off today, honestly, I was! My Minnesota Twins start their second game in about an hour, and I really planned to just kick back, watch the game, have a couple of beers, and enjoy the day. And since tomorrow’s March wrap-up post is done and queued, more of the same tomorrow.
But this is too relevant to the posts just posted, and it’s about Special Relativity, which is a March thing to me (because Einstein), so it kinda has to go here. Now or never, so to speak. And it’ll be brief, I think. Just one more reason I’m so taken with matrix math recently; it’s providing all kinds of answers for me.
Last night I realized how to use matrix transforms on spacetime diagrams!
In the March Mathness post I mentioned that one reason I love March is that it contains the Vernal Equinox, the official astronomical start of Spring. More importantly to me, it means six months of more daylight than darkness, and as much as I’m a night person, I prefer long, sunny days.
Well, today is the day! The equinox happened at 21:58 UTC (two minutes before 5:00 PM locally). What’s better is that, after all the miserable bitter cold and all that snow in February and into March, the weather is indeed finally turning. Deeply embedded in our mythologies is the idea of spring rebirth; New Year’s parties aside, this, today, is the true new year.
And the forecast is for muon showers!
Speaking of Special Relativity, back when I wrote the SR series, one topic I left along the wayside was the concept of the spacetime interval. It wasn’t necessary for the goals of the series, and there’s only so much one can fit in. (And back then, the diagrams I wanted to make would have been a challenge with the tool I was using.)
But now that we’re basking in the warm, friendly glow of March Mathness and reflecting on Special Relativity anyway, it seems like a good time to loop back and catch up on the spacetime interval, because it’s an important concept in SR.
It concerns what is invariant to all observers when both time and space measurements depend on relative motion.
Earlier, in the March Mathness post, I mentioned Albert Einstein was born on March 14th. That’s also Pi Day, which deserved its own pi post (about pizza pi), so old Al had to wait for me to address a topic I’ve needed to address for several months.
To wit: Some guy was wrong on the internet.
That guy was me.
Back in 2015 (also celebrating Einstein’s birthday), I wrote a series of posts exploring Special Relativity. Near the end of the series, writing about FTL radio, I said (assuming an “ansible” existed) I wasn’t convinced it violated causality if the frames of reference were matched.
Time for math!
I have a special fondness for the month of March. For one thing, it contains the Vernal Equinox — one of my favorite days, because it heralds six months of light. (As a Minnesotan, Spring has much more impact than it did when I lived in Los Angeles.)
March is when the weather elves begin preparing for the April Showers that create May Flowers. It’s when baseball Spring Training is in full swing with the regular season looming (lately, even at the end of the month; this year on the 28th).
It also contains some important birthdays: Albert Einstein (3/14) and Emmy Noether (3/23), to name two, and in their honor I have myriad math posts planned!
It took almost exactly 100 years. In 1905, über-geek hero Albert Einstein presented four papers of major significance to the world. One of those was about Special Relativity. It took Einstein ten more years to figure out the General theory of Relativity. He presented that work in November of 1915.
One of the predictions of General Relativity is that gravity warps space, creating gravity waves (which move at the speed of light). And while many other predictions of GR have been tested and confirmed (to very high precision), we’ve never quite managed to detect gravity waves.
Until September 14th of 2015!
We sometimes say that dogs are living in the now. Sometimes we say that of people who live in the moment and don’t think much about the future (or about the consequences). Whether we mean that as a compliment — as we generally do with dogs — or as an oblique implication of shallowness depends on the point we’re making.
There is the tale of the ant and grasshopper; it divides people into workers who plan for the future and players who live in the now. The former, of course, are the social role models the tale holds heroic. The grasshopper is a shifty lay-about, a ne’er do well, a loafer and a moocher, but that’s not the point.
The point is our sense of «now» and of time.