# Are wormholes evidence for traversal of a higher dimension?

Wormholes in GR do not require higher dimensions. It easier to imagine curved spacetime as being embedded in higher dimensions, but the usual mathematical description of curved spaces does not require that.

Sadly I do not really understand everything you said. But I can comment on this

wormholes that can connect different points in space time

The thing is, that all you really need to know is exactly which points are connected or "next to each other". You do not need any higher dimensional space for this.

Take for example 6 points called P1, P2, ..., P6. I will use notation A<->B to say, that A and B are connected.

To represent line, the information required is that P1<->P2, P2<->P3, ...,P5<->P6

To represent circle you have P1<->P2, P2<->P3, ...,P5<->P6 and P1<->P6, which connects the end points together.

On this "space" you can form a "wormhole" by connecting P2 to P4.

The thing is, that these connections require no knowledge of some higher dimensional space. All the information is encoded using the points of the space you have.

If you wish to read more about the topic, the mathematical structure that encodes this information is called topology.

Agree to Rd Basha. Embedding spaces are only necessary for the mathematical constructions. They don't necesserily have physical reality.

Like the mathematics of a 2-sphere is easier if it's embedded into a 3-dimensional Euclidean space. But the 2-sphere happily exists without a third physical dimension.