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.
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.
We’re finally sliding into home plate in this series (it’s baseball season, so I get to use baseball metaphors now). After spending a lot of time looking into how Special Relativity works, we’re able to at last explore how it applies to the idea of faster-the-light travel.
Last time we saw that FTL radio seems hopeless — at least at communicating between frames of reference in motion with regard to each other. It’s possible there might be a loophole for FTL communication between matched frames. (If nothing else, it may be fertile background for some science fiction.)
Today we examine the idea of FTL motion — of “warp drive!”
Over the last five weeks I’ve tried to explain and explore Einstein’s Theory of Special Relativity. We’ve seen that motion, velocity, simultaneity, length, and even time, are all relative to your frame of reference and that motion changes the perceptions of those things for observers outside your frame.
All along I’ve teased the idea that the things I’m showing you demonstrate how the dream of faster-than-light (FTL) travel is (almost certainly) impossible. Despite a lot of science fiction, there probably isn’t any warp drive in our futures.
Now it’s (finally) time to find out just exactly why that is.
This week I’ve focused on the relativity of time under motion, and we’ve seen that moving very fast allows “time travel” into the future. Very handy if you don’t mind the one-way trip. What’s more, a spaceship capable of such a flight is physically possible, so it’s a “time machine” we know works!
On Monday I described how fast-moving, but short-lived, muons created high in the atmosphere live long enough to reach the ground due to time dilation. That’s just one place we see Special Relativity actually working exactly as Einstein described. For another, fast-moving particles at CERN have decay times showing they, too, have slow clocks.
As we’ll see today, light’s behavior requires time appear to run slower!
Last time we saw that Em non-paradoxically time-travels over three years into Al’s future by flying 12 light years at half the speed of light for just over two decades. Her journey completed, Em has aged only 20.8 years while Al has aged 24.
That may not seem like much of a gain, but Em was only moving really fast — not really, really fast. If she travels at 99% of light-speed, her round trip shortens to 1.7 years while Al doesn’t wait much longer than it takes light to make the six light-year round trip: 12.12 years! And at 99.9% c, Em’s whole trip takes her only half a year!
Today we break down dime tilation. I mean, time dilation!