Are wormholes evidence for traversal of a higher dimension?

Question

Warning, pop science coming.. please correct what I’m getting wrong. Einstein’s equations of relativity showed the potential for existence of wormholes that can connect different points in space time. I understand the mechanisms for their practical implementation are nothing near feasible. However, based on the equations of gravitational “tunneling”, I can traverse back and forth between times and locations. Wouldn’t this require a higher dimension than 4d space time?

That is, we’re moving from a point that we would think of as the present to another point we would think of as the present. If this were feasible, Would These “presents” need to be on a traversable continuum?

To my lay brain, This seems as though there are points along a higher dimension where what we would consider the future is currently present, and what we consider the past is also present. That the world we see is determined and laid out as slices in a higher dimension that would be traversed with a wormhole, and that we normally traverse in a single direction.

Answer 1

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.

Answer 2

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.

Answer 3

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.

Answer 4

I guess so. At least according to the illustrations/analogies of folding paper. However there is nothing in Einstein's equations that require an existence of a higher dimension unlike in string theory. But if wormholes are proven to exist, then yes this could prove the possibility of higher dimensions since there is no other way for wormholes to work.