The last two posts introduced and explored the concept of time-space diagrams. This time I’ll complete that exploration by using them to consider motion from two points of view. This will be an exercise in application of our diagrams.
I’m going to connect that application with something I stressed last week: that motion has a symmetrical component. It’s perfectly valid to think of the world moving past the train as it is to think of the train moving through the world.
It happens that here our dueling points of view are resolved by something else I discussed last week. See if you spot it before I mention it.
3D holograms! Me want!!
Last time I introduced you to the idea of a time-space diagram, which is a kind of map used to describe motion. As with many maps and diagrams, we choose to use a flat, two-dimensional representation. Someday hologram technology may advance to casual use of three-dimensional images, but so long as we use paper and display screens, we’re stuck with two.
Motion is movement in both space and time, so we want to use one of our two dimensions to represent time. That leaves us with only one remaining dimension for space, so our diagrams exist in a reduced one-dimensional world.
Today I’ll explore that world in more detail.
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.
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.
In the last two posts I’ve explained how Special Relativity is about 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.)
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.
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…