Is spacetime the surface of a 5 dimensional ball.

[Spinnor]

At one time it was thought(still is?) that we live in a closed universe?

So if we live in a closed universe we might try to get a picture of this space by thinking of the space S^3? remember,

S^1 surface of a 2 dimensional ball,
S^2 surface of a 3 dimensional ball,
S^3 surface of a 4 dimensional ball,
S^4 surface of a 5 dimensional ball.

Let us not forget time. In a closed big bang universe can time be thought of as a big circle if we identify beginning and end points? If so can spacetime of a closed universe be thought of as the surface of a 5 dimensional ball?

Thank you for any thoughts.

 

[Peeter]

In chapter 7, "Unification and the Quantum Challange" of Michio Kaku's book "Einstein's Cosmos", a popular science book which I happen to be reading at the moment, such an idea is mentioned.

Theodr Kaluza, in 1921, extended GR to a five dimensional space, and in doing so was able to find that Maxwell's equations "fall out" of such a treatment. I don't know the details behind this, as the book does contain any mathematics, but it sounds like this is the root idea behind much of string theory.

 

[NWH]

Would you mind defining "fall out?"

 

[Peeter]

No, I can't really define it. Like I said, I don't know the details, although it sounded much like the Spinnor's description. The Kaku book, which I happened on at the public library, doesn't have any math, also just descriptive:

"Then, in a few lines, Kuluza showed that if the fifth dimension is separated from the other four, Einstein's equations emerged, along with Maxwell's equations!"

If you want more detail, google finds stuff like:

http://en.wikipedia.org/wiki/Kaluza-Klein_theory

... I personally can't make much sense of that without first studying GR, something that I don't have any intention of trying without first getting much more SR under my belt;)