For the last week or so, on a physics blog I follow, I’ve been part of a debate about the nature of time. It’s been interesting and fun, but the conversation has reached that point where folks are mainly maintaining their positions, and it seems that the matter has stalled.
Some of the on-going assertions bemused me so much, that I was about to tender one more rebuttal comment… When I remembered what a wiser person, “back in the day” (before the web), said about online debates: State your view. Support it further if you need to address points raised. But once you’ve covered it well enough, just stop. After that, you’re just wasting your time; it’s rare that anyone changes their mind on the internet. Including yours.
Fair enough. I can natter on about it to myself on my own blog, though…
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!
Last time our friend Al used lasers and timers to create a regular grid-like map of the space and time near him. The map allowed him to assign space-time coordinates to events in his frame of reference (even if it takes time for him to see light from those events).
An important concept is the idea of simultaneity — of events in different locations happening at the same moment according to some observer (who has to wait for the event’s light to reach their eye).
So far the events weren’t moving relative to us. What if we — or the events, same thing — are moving (and moving fast)? It turns out, this changes the picture!
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.
My Special Relativity “icon”!
This week I’ve introduced you to time-space diagrams. They’re the foundation of everything that follows in this series, so I hope you’re feeling very comfortable with them.
I also introduced you to space-time events, and I apologize for any confusion in calling the diagrams “time-space” and the events “space-time.” Six of one, half-dozen of the other. I wanted to stress the time component of the diagrams, whereas space-time is the more usual general term.
Today we wrap up the week with some important diagram details.
Last time I introduced you to the idea of a space-time event. In physics, an “event” has the same meaning as when Hollywood blares out about a “major motion picture event” — that is to say, nothing at all special — just something that happens at a specified location and time.
If you attend a social event, it has a location and a time. When we talk about space-time events, all we mean is a specific location and a specific time (hence the name, space-time event).
Today we’ll explore some interesting aspects of such events.
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.