To describe how space could be flat, finite, and yet unbounded, science writers sometimes use an analogy involving the surface of a torus (the mathematical abstraction of the doughnut shape). Such a surface has no boundary — no edge. And despite being embedded in three-dimensional space, the torus surface, if seen in terms of compensating surface metric, is indeed flat.
Yet a natural issue people have is that the three-dimensional embedding is clearly curved, not flat. It’s easy to see how wrapping a flat 2D sheet into a cylinder doesn’t distort it, but hard to see why wrapping a cylinder around a torus doesn’t stretch the outside and compress the inside.
In fact it does, but there are ways to eat our cake (doughnut).
If you keep an eye on the night sky you may have noticed two bright “stars” to the south just around midnight. (To be precise: Jupiter is dead south at 11:02 pm; Saturn is dead south at 11:37 pm. By midnight they’ve moved slightly to the west.)
If you’re the type to keep an eye on the night sky, you likely already know those “stars” are Saturn (on the left) and Jupiter (on the right). What you may not know — and certainly can’t see — is that almost right smack dab between them is the former planet Pluto. All three just happen to be lined up nicely right now.
The New Horizons spacecraft is also out there, well beyond Pluto.
There comes a time when words fail, and all you can do is stare in amazement. The Friday press conference from the New Horizons team had that effect on many of us. (I’m not the only one who wept with sheer joy.)
From behind the planet, the Sun illuminates Pluto’s 100 mi layer of haze.
They say pictures are worth thousands of words, so I’ll let the pictures do most of the talking (click on any image to go to the source)…
Hot off the press! Check out Pluto’s first close up:
Those mountains are up to 11,000 feet high! And the surface looks to be roughly 100 million years old — extremely young compared to the four-and-a-half billion year age of the solar system (and not a crater in sight!).
Pluto… like no one has ever seen it before!
(At least no one on Earth!)
Oh, my! I mentioned last time that the Minnesota Twins, after a surprisingly good month of May, cooled down big time in June. Fans held their breath wondering how far the team would fall from the height reached in May. Now, with June behind us and July well under way, we can start breathing normally again.
The Twins lost ground in June, but remained above the .500 mark (by five games!) by month’s end. But July seems to have brought an end to the ice-cold bats. The Twins are 8-4 in July as we begin the All-Star break.
But more importantly: It’s Pluto Day!
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.