The main topic this week was how simultaneity is relative to your frame of reference. How there are (virtual) lines of simultaneity where all points on some line — at all distances from you — share the same moment in time. For any instant you pick, that instant — that snapshot — includes all points in your space.
A line of simultaneity freezes the relative positions of objects at a given moment — which enables distance measurements. Simple example: When their watches both read 12 noon, Al and Em were 30 miles apart. A more mathematical example uses x, y, & z (& t), but it amounts to the same thing: a coordinate system.
The gotcha is that simultaneity and coordinate systems are relative when motion is involved!
A couple of readers have asked about the diagrams in this series of Special Relativity posts. I created them with the freeware 3D ray tracing application, POV-Ray. The diagrams are actually three-dimensional “scenes” designed to be viewed as flat pieces. If some of the “dots” look more like little spheres, that’s because they are!
I wrote some introductory posts a while ago (here, here, and here). You can read those if you want more details about the application.
For a little (optional!) Friday fun, I thought I’d share some POV-Ray images that have a bit more “dimension” to them.
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.