#
Tag Archives: 1D

Four years ago I started pondering the **tesseract** and four-dimensional space. I first learned about them back in grade school in a science fiction short story I’d read. (A large fraction of my very early science education came from SF books.)

Greg Egan touched on tesseracts in his novel *Diaspora*, which got me thinking about them and inspired the post *Hunting Tesseracti*. That led to a general exploration of multi-dimensional spaces and rotation within those spaces, but I continued to focus on trying to truly understand the tesseract.

Today we’re going to visit the 4D space *inside* a tesseract.

Continue reading

4 Comments | tags: 1D, 2D, 3D, 4D, cube, dimensions, square, tesseract | posted in Math, Sideband

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!

Continue reading

5 Comments | tags: 1D, 2D, 3D, Albert Einstein, Emmy Noether, frame of reference, Galilean invariance, light, light clock, light cone, light speed, line of simultaneity, simultaneity, simultaneous events, space-time, Special Relativity, surface of simultaneity, time-space | posted in Physics

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.

Continue reading

6 Comments | tags: 1D, 2D, 3D, 3D images, distance, Emmy Noether, light, light speed, POV-Ray, ray tracing, space, space-time, Special Relativity, time, time-space, time-space diagram | posted in Physics

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.

Continue reading

7 Comments | tags: 1D, 2D, 3D, diagrams, dimensions, maps, motion, space, Special Relativity, time, time-space, time-space diagram | posted in Physics

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.

Continue reading

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