# Surface waves on a balloon and our possible extra dimensions.

• Spinnor
In summary: Thanks for your help.That idea (geometrodynamics) is still being pursued under different guises: spin foams, 'pregeometry', loop quantum gravity.As I understand it, our universe is thought to be finite in size but unbounded. Wouldn't this imply that it is folded over a 4th spatial dimension to allow it to 'wrap around'? Aren't there many different shapes we have proposed (i.e. saddle, horn, sphere, etc.)?Thanks for your help!Many different shapes have been proposed, but I don't think that's what the question is asking.The question seems to be, if the fields of the Standard Model correspond to various curvatures of our 4 dimensional
Spinnor
Gold Member
Think about the dimensionality of a balloon with surface waves. Say these waves are of small amplitude compared with the radius of the balloon. Two coordinates label points on the balloon and a third labels radial position. Creatures who lived on the surface could make measurements that determined the curvature of their space. Let us say they would also be able to detect the waves that went about their space. They would say their space is two dimensional but they needed a real field to describe the waves on their surface. To we who live in 3 space dimensions we would say, what field, they live on a two dimensional surface that can vibrate. They need three coordinates to describe their world.

Giving our spacetime extra dimensions seems natural even if wrong.

Thanks for any thoughts, and apologies if this post is in the wrong place.

While what you say is a common conceptual device, it's important to remember that (in GR anyway), the 4 spacetime dimensions are not embedded in a Euclidean 5-dimensional manifold.

Andy Resnick said:
While what you say is a common conceptual device, it's important to remember that (in GR anyway), the 4 spacetime dimensions are not embedded in a Euclidean 5-dimensional manifold.

I'm not sure that changes anything I said.

Thanks.

Andy Resnick said:
While what you say is a common conceptual device, it's important to remember that (in GR anyway), the 4 spacetime dimensions are not embedded in a Euclidean 5-dimensional manifold.

In my simple example it seems there are two ways map this surface,

Radial distance as a function of theta and phi, or

A metric that describes curvature of the surface as a function of theta and phi.

Maybe 4D Theorists think in terms of intrinsic curvature and > than 4D Theorists think in terms of extrinsic curvature, two ways of thinking of different aspects of the same system?

Last edited:
Spinnor said:
In my simple example it seems there are two ways map this surface,

Radial distance as a function of theta and phi, or

A metric that describes curvature of the surface as a function of theta and phi.

Maybe 4D Theorists think in terms of intrinsic curvature and > than 4D Theorists think in terms of extrinsic curvature, two ways of thinking of different aspects of the same system?

In this simple example if it makes sense for a two dimensional creature to describe waves on the surface of his two dimensional world as a field (when in fact his two dimensional manifold is curved on both large and small scales) can the fields of the Standard Model correspond to various curvatures of our 4 dimensional spacetime manifold, thus eliminating the need for extra dimensions? This is what Einstein was after, all of physics in terms of geometry? Why does it not work if it doesn't work or is it more simple to think in terms of extra dimensions? Leave out quantum physics for the time being, that makes things messy and real, real messy?

If I am understanding you, then yes- IIRC, Yang-Mills theory was an attempt to 'geometrize' electromagnetism by postulating a 5th dimension corresponding to charge. This led to the idea of 'wormholes' connecting positive and negative charges and a whole lot of extra complexity. Because of the huge increase in complexity and not much increase in understanding, that program was dropped.

That idea (geometrodynamics) is still being pursued under different guises: spin foams, 'pregeometry', loop quantum gravity.

As I understand it, our universe is thought to be finite in size but unbounded. Wouldn't this imply that it is folded over a 4th spatial dimension to allow it to 'wrap around'? Aren't there many different shapes we have proposed (i.e. saddle, horn, sphere, etc.)?

## 1. What are surface waves on a balloon?

Surface waves on a balloon refer to the undulations or ripples that form on the surface of a balloon when it is inflated. This phenomenon is caused by the stretching and tension of the balloon's surface as it is filled with air.

## 2. How are surface waves on a balloon related to extra dimensions?

Surface waves on a balloon are often used as a visual representation to explain the concept of extra dimensions. Just as the surface of a balloon can stretch and ripple, scientists believe that our universe may have additional dimensions that are folded and hidden from our perception.

## 3. What is the significance of studying surface waves on a balloon?

Studying surface waves on a balloon can provide insight into the properties of extra dimensions and how they may interact with our observable universe. It can also help scientists develop new theories and models to better understand the nature of our reality.

## 4. Can surface waves on a balloon be observed in our everyday lives?

Yes, surface waves on a balloon can be observed in our everyday lives when we blow up a balloon or observe ripples on the surface of water. However, these waves are microscopic and cannot be seen with the naked eye, which is why they are used as a metaphor for extra dimensions.

## 5. Are there any practical applications of studying surface waves on a balloon?

While the direct practical applications of studying surface waves on a balloon may be limited, the research and understanding gained from this study can have implications in fields such as cosmology, physics, and engineering. It can also help us better understand the fundamental laws of nature and our place in the universe.

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