Category Archives: Science
Last week I introduced you to the idea of relative motion between frames of reference. We’ve explored this form of relativity scientifically since Galileo, and it bears his name: Galilean Relativity (or Invariance). Moving objects within a (relatively) moving frame move differently according to those outside that frame.
I also introduced you to the idea that light doesn’t follow that rule; that light moves the same way to all observers. This is what makes Special Relativity different. It turns out that, if a frame is (relatively) moving fast enough, some bizarre things happen.
Time-space diagrams will help us explore that.
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2 Comments | tags: 1D, 2D, 3D, diagrams, dimensions, Edwin Abbott, Emmy Noether, Flatland, maps, motion, Special Relativity, time, time-space, time-space diagram | posted in Physics
It’s Friday, and I’m sure you’re thinking about the weekend, so today will be just a review and some more details about the speed of light.
And speaking of light, today is the Vernal Equinox. For the next six months (for those of us in the northern hemisphere), our days will be longer than our nights. No doubt the combination of spring, the Equinox, and the weekend, have you wondering what you’re doing at your computer reading about Special Relativity.
I’ll try to be very brief…
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8 Comments | tags: Albert Einstein, equinox, Galilean invariance, Galileo Galilei, light, light speed, light year, moon, Special Relativity, spring equinox, Sun, vernal equinox | posted in Physics
Throwing like a girl!
I’ve introduced the idea of an inertial frame of reference. This is when we, and objects in our frame, are either standing still or moving with constant (straight-line) motion. In this situation, we can’t tell if we’re really moving or standing still relative to some other frame of reference. In fact, the question is meaningless.
I’ve also introduced the idea that objects moving within our frame — moving (or standing still) along with us, but also moving from our perspective — move differently from the perspective of other frames. Specifically, the speed appears different.
Now I’ll dig deeper into that and introduce a crucial exception.
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11 Comments | tags: Albert Einstein, Emmy Noether, Galilean invariance, Galileo Galilei, Mo'ne Davis, motion, scalars, Special Relativity, speed, vectors, velocity | posted in Physics
In the last two posts I’ve explained how Special Relativity concerns relative motion between two frames of reference, and that the motion involved is constant, straight-line motion that allows us to view either frame as the “moving” one or the “standing still” one.
Today I’m going to dig a little bit deeper into the idea of relative motion and what that involves for actions within a constantly moving frame of reference versus what observers in a different frame perceive. In other words: trains, planes, and automobiles.
(Warning: this gets a little math-y, but you can ignore those bits.)
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25 Comments | tags: Albert Einstein, bowling ball, Emmy Noether, frame of reference, Galileo Galilei, James Maxwell, motion, relative motion, relativity, Special Relativity | posted in Physics
A fun way to feel acceleration!
Last time I introduced some of the foundation concepts required for our exploration of Special Relativity. In particular, that the word “special” in this case refers to a specific kind of motion: constant motion in a straight line.
Which may have caused some of you to wonder: Okay, what about motion that isn’t constant (and what’s that business about “in a straight line” — why keep mentioning that)? As it turns out, when motion involves speeding up, or slowing down, or going along a curve (or even just changing direction), that changes the situation in very significant ways!
That’s what I’m going to discuss today.
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3 Comments | tags: acceleration, Albert Einstein, constant motion, cubit, deceleration, fortnight, furlong, General Relativity, jiffy, motion, slowing down, Special Relativity, speeding up | posted in Physics
Okay, if you’ll all take your seats and quiet down, we can begin. I’ll keep this very short today because I know it’s Spring and many of you are eager to get out there and walk Frisbees and throw dogs… I mean — well you know what I mean.
The point is, that in keeping with spring, I’m aiming to keep these posts light and breezy. Unfortunately, I have terrible aim, so we’ll see how that goes. I never met a paragraph I couldn’t make longer!
Ready? Let’s go…
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24 Comments | tags: Albert Einstein, constant motion, frame of reference, motion, Special Relativity | posted in Physics
Okay. I’ve been teasing doubly special Saturday and (especially this year) since last Monday (and planting hints along the way). If you haven’t figured it out by now, today is Albert Einstein’s birthday. It’s also pi day, and how cool is it that a guy like Al was born on pi day?
So: Happy Birthday Albert! The (especially this year) part is because it’s extra-special pi day (3/14/15) and because this year I’m finally going to do what I’ve been wanting to do here to commemorate Einstein’s birthday since I started this blog back in ought-eleven.
I’m going to write — at length — about Special Relativity!
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8 Comments | tags: Albert Einstein, Emmy Noether, faster than light, FTL, Happy Birthday, light speed, pi day, Special Relativity | posted in Math, Physics
It’s pi day! Be irrational!
Earlier this week I mentioned that “this coming Saturday is a doubly special date (especially this year).” One of the things that makes it special is that it is Pi Day — 3/14 (at least for those who put the month before the day). What makes it extra-special this year is that it’s 3/14/15— a pi day that comes around only once per century. (Super-duper extra-special pi day, which happens only once in a given calendar, happened way back on 3/14/1529.)
I’ve written before about the magical pi, and I’m not going to get into it, as such, today. I’m more of a tau-ist, anyway; pi is only half as interesting. (Unfortunately, extra-special Tau Day isn’t until 6/28/31, and the super-duper extra-special day isn’t until 6/28/3185!)
What I do want to talk about is a fascinating property of pi.
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148 Comments | tags: cake, Carl Sagan, Contact (book), Ellie Arroway, irrational numbers, Magnum Pi, normal sequence, numbers, pi, pi day, pie, real numbers, tau, tau day, transcendental numbers | posted in Math
Computing…
I’ve written here before about chaos theory and how it prevents us from calculating certain physical models effectively. It’s not that these models don’t accurately reflect the physics involved; it’s that any attempt to use actual numbers introduces tiny errors into the process. These cause the result to drift more and more as the calculation extends into the future.
This is why tomorrow’s weather prediction is fairly accurate but a prediction for a year from now is entirely guesswork. (We could make a rough guess based on past seasons.) Yet the Earth itself is a computer — an analog computer — that tells us exactly what the weather is a year from now.
The thing is: it runs in real-time and takes a year to give us an answer!
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3 Comments | tags: analog, analog computer, chaos theory, digital, Information Technology, mathematics, orbital mechanics, Pluto, Pluto is a planet, solar system, three-body problem, weather, weather prediction | posted in Math
You couldn’t know this, but my blogging workspace is littered with balls of virtual crumpled paper. The ones writers make when they rip failed writing attempts from their typewriter, smush them up in disgust, and toss them disdainfully over their shoulder. This post — which has been in my mental queue for well over a year — has the strongest resistance to being written that I’ve ever encountered.
I wrote the note you see here somewhere back in 2013. It seemed like exactly the sort of thought chain that would make an interesting post. Many of the items in that chain (consciousness, art, science) are things that fascinate me and are even areas this blog tries to discuss.
So why is a post about it so dang hard to write?
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18 Comments | tags: art, consciousness, experience, Isaac Newton, language, questions, relaxation oscillation, technology, Vitruvian Man | posted in Philosophy, Science
Logos con carne 