Tag Archives: Einstein

SR #X4: Matrix Spacetime

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!

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SR #X3: Spacetime Interval

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.

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SR #X2: Sorry, No FTL Radio

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.

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Low-Mass Thoughtinos

I’m torn over today’s topic. I’m tired (for the moment) of nattering about work (got some thanks, but no thanks messages today, and that makes me disinclined to discuss the distress; nepenthe beckons, I’ll answer the call, now 94 bottles of beer on the wall). And I’ve spent some time in the blogsphere, which is endlessly fascinating, but time-consuming and a bit draining. After reading about the struggles of others, mine own seem pale and pointless.

So it’s time for something light and refreshing. I realized I haven’t bored anyone with science recently, so, as the good The Doctor would say, “Run!”

Still here?  Well, don’t say I didn’t warn you. Alons-y!

An old game begins with the question, “Animal, mineral or vegetable?” The idea is that everything in the world falls into one of those three giant bins. [For bonus points, try to think of things that don’t.] In all three cases, things are made of smaller things, and those are made of tinier things, and those are made of miniscule things, and at some point it’s all down to chemistry and compounds.

And even that’s all made of  mind-bogglingly small things, called atoms, and it turns out the Greeks were totally wrong! You can cut atoms into smaller bits, called electrons and neutrons and protons. The electrons are the end of the line (as far as we can tell), but the neutrons and protons turn out to be made of quarks (and gluons).

Toss in the photons and neutrinos, and we’ve more or less (less, really) covered the parts of interest in a domain known as particle physics.  As far as we know, these “particles” (and we call them “particles” for lack of a better term) are the basic building blocks of everything.  They are points with properties, pico-Legos that build a universe.

One of the more elusive members of the menagerie is the fleeting neutrino, a feather-weight “particle” that’s almost impossible to catch. Like a tiny minnow, they slip through almost any net.  You may have heard of them recently. A science experiment over in Italy, associated (but not directly connected) with the Large Hadron Collider (LHC) at CERN, thought they’d discovered a new and supposedly impossible fact. It appeared that neutrinos were going faster than light speed.

If they’d been correct, Einstein would have spun in his grave, since back in 1905 he laid down the universal speed limit. 186,000 Miles Per Second… not just a good idea, it’s The Law (to be said in Judge Dredd voice).  If you try to break that law, no cops stop you, the math stops you.  In fact, you can only get so, so close; you can never quite get there (another Greek, Zeno, was spot on about that one).

Those neutrinos give it a good run for the money, though. They’re so light-weight and slippery that they get closer to light speed than anyone.  But the idea that they not only get there, but go faster… that would have been a problem.  Turns out the folks in Italy, the operators at OPERA, had a loose wire. Literally. Screwed that sucker down tight, and physics turned out to be same old, same old, once again.  Got some folks excited for a while, there, though!

Well, some folks got excited. Most of us just waited for them to find their error. If Eric is Music God, Albert is Light Speed God (also Gravity God, but that’s another article). And, as we all expected, Albert was right again (gods, after all, are infallible).  So all’s right, or at least normal, with the Universe again.

Here’s a fun neutrino fact: our local star, the Sun, produces craploads of neutrinos all the time. To them, the planets don’t really exist, except as a vague thin smoke. They just blast on through it all and out into the universe. The fun fact is this: every second, in every square centimeter of your body, 65,000,000,000 neutrinos are passing through! You don’t notice them, and they don’t notice you! Neutrinos are the most aloof of the aloof.

My thoughts feel like that today. Speeding fast as light (nearly) and yet they are without mass or traction. The bubble chamber of my mind isn’t detecting their tracks; they leave no trace as they zip off into the Void.  (There have been a few semi-sleepless nights the last three, and that makes the thought particles even more fleeting and sleeting.)

They are thoughtinos! Low-mass ones, at that.

Maybe if I absorb more beer particles it will slow them down…