TAG SEP 1999: Spacetime for Campers

Read Instructions Below First!

There are a number of good Web sites given below. It is not absolutely required that you take them in the order that they are given, but it may help. For each one, read any text that may go with the link first before going down the link. You may wander far from my site as long as you stick to math, science and certain mathematical art; do not go outside these bounds.

We have not discussed in class every technical term you will see in these pages. Please feel free to poke around on the Web trying to find definitions for words that you do not understand. You may also ask me while we are still in the lab, or when we are back in class.

If you have any other questions, ask me. The "Go" menu on the top toolbar will let you jump directly back to most places that you have already been, unless you have been to too many places since then. If anything like a movie has trouble loading, let me know. Warning: the Ed Tech lab computers may not have all the software required to view and/or listen to certain files. And yes, this page will remain up on my Website indefinitely, in case you want to look at it again in a few months. It was too much work for me to just throw it away! :-)

Please read my *entire* page first, even if you do not get a chance to go to all the Websites. Also, I will be asking you where you went, so it might be a good idea to take some notes.

Read Instructions Above First!

A Note

Einstein actually proposed two theories. The first one is called Special Relativity (1905) and deals with cases where there is no acceleration and no gravity. The second theory, which has harder math in it, deals with non-inertial reference frames (that is, ones involving acceleration), gravity and the bending of space. It's called General Relativity (proposed in 1915), and it is the one where black holes come in. This chart will help remind you when to use Galilean relativity (the author says "Newton's laws" but he means the same thing), when to use Special Relativity, and when to use General Relativity.

A good starter site for Special Relativity

This site does a nice job of illustrating many of the same Special Relativity ideas that we discussed in class. If it starts to load a sound or midi file, please stop it before it finishes loading! Thank you.

"Suppose I do not really understand inertial reference frames?"

This professor's site has more equations, but it also has more pictures.

"OK, maybe I understand inertial reference frames, but I did not understand what you were doing with Minkowski diagrams in class."

All the diagrams on this page are Minkowski diagrams, and this page has far more explanations than I would have time to give in class, plus moving pictures. For those who like algebra, this page even gives a nice geometrical derivation of the full Lorentz transformations, another thing that I did not have time to go over in this course.

So you want to see animated pictures of what is happening, using objects from real life?

This site has a number of still pictures and small movies illustrating Special Relativity. Be sure to read the text about the pictures, because the authors made some modifications to make certain relativistic effects more visible than they are in daily life.

"But what about gravity?"

As long as we stick to Special Relativity, all we are doing is imposing a new geometry on space and time. This is hard enough to fully understand. This new geometry is controlled by our friend g (this is gamma, often called by physicists the Lorentz factor). Einstein's second postulate, the invariance of the speed of light, allows us to trade off between space and time, thus unifying them into a new four-dimensional thing called spacetime.

But, as long as we stick to Special Relativity, spacetime is still . . . flat. As soon as we permit gravity and acceleration, then spacetime is allowed to warp.

Now we are in the General Theory of Relativity, in which mass does not cause the force of gravity, mass warps space and it looks to us like a force called gravity. This is a bit more difficult.

"I want to see more equations and geometrical diagrams to help me understand what is going on!"

"But what does all this talk have to do with stars and black holes and stuff? I thought that this class was going to be about space!!"

Ah, but it is about space. The study of the universe as a whole is called cosmology, and in order to understand many of the things we see in space, we need relativity.
Now, this is less true about G-type stars like Sol (our sun) and "Class M" planets like Earth. We are fairly used to those. But even there, we need relativity to explain things like the precession of Mercury's orbit about the Sun. (Heck, after two or three years of calculus, you might even understand the equations for this.)

While some other subjects in astronomy and cosmology do not really require you to understand relativity in order for you to appreciate them (like the constellations), many of the more exotic topics do need relativity for a full comprehension of their workings. Here is a short list:

So you want to see *more* animated pictures of the topics we cover in this course?

This site has a huge number of good pages on Special Relativity, black holes, wormholes, and more.

SETI: the Search for Extra-Terrestrial Intelligence

Humanity is indeed even now searching this vast universe for signs of (other) intelligent life. What it might be like if this search ever found something is described in the movie "Contact".

"This is still not enough Websites to suit me!"

No problem. There are more relativity Websites and lots of pretty pictures of stars, nebulae, planets and other objects in the universe.

And finally, a little bit of humor from the Sun's point of view.

(Last updated 7/10/99)