Why should we expect to be able to "see" extra dimensions assuming they exist?

[Qdogsman]

I think that the idea of the existence of real extra dimensions should be taken more seriously by scientists. The idea was suggested at least as early as Kaluza's letter to Einstein. Except for string theorists, and now dark matter researchers, the idea is usually dismissed for one of two reasons.

 

First, the claim is that if extra dimensions exist we should be able to "see" them or detect them with our instruments. Second, the claim is that the familiar inverse square laws would instead be inverse cube, or higher, laws.

 

To overcome the first of these "strawmen" objections, Klein suggested that the extra dimensions are rolled, or curled up so tightly that they become smaller than anything we can see. I understand that there are active scientific investigations to see if maybe some inverse square laws become inverse cube laws at extremely small scales.

 

My position is that large, relatively flat, extra dimensions do exist, but that our 4D spacetime is a manifold embedded in that higher-dimensional space. This would mean that all structures involved in our "seeing" or otherwise detecting real existing structures, including eyes, EM radiation, and the very structures we are trying to "see", are 3D structures existing in the manifold. As such, they cannot interact with higher-dimensional structures, and thus there can be no detection of the higher-dimensional structures.

 

Dropping down a dimension, this is equivalent to the existence of 2D structures on a sheet of paper, which in reality, is a 2D manifold in 3D space. The 2D structures cannot rise off the paper and interact with 3-dimensional objects in the room.

 

This interpretation not only explains why we can't "see" the extra dimensions, but also why the inverse square laws hold.

 

Does anyone disagree with my arguments against these two objections, or does anyone know of another reason the idea of large extra dimensions should not be taken seriously?

[Doctordick]

This interpretation not only explains why we can't "see" the extra dimensions, but also why the inverse square laws hold.

If you look at your arguments, they are essentially circular: "we can't see the extra dimensions because we can't see the extra dimensions. You have not defined the term "see" but have presumed it is what you do when you experience a three dimensional universe.

Does anyone disagree with my arguments against these two objections, or does anyone know of another reason the idea of large extra dimensions should not be taken seriously?

I think the idea should be taken very seriously and that is exactly what I have done in my analysis.

[Qdogsman]

I don't agree that my argument is circular. Here's how I see it:

 

Mathematically, I am saying that if our universe is an embedded manifold, then we can't see the extra dimensions. I do not claim that the converse is true. That is, if we can't see extra dimensions then the universe is an embedded manifold with extant extra dimensions. It could be that such extra dimensions don't exist, or that we can't see them for some other reason.

 

Empirically, all we can say is that we can't see extra dimensions. That fact, however, does not imply that extra dimensions don't exist.

 

My position is to assume that 1. extra dimensions do exist, and 2. that our universe is an embedded manifold, and then explore the implications of those assumptions. One such implication is that we would not be able to "see" the extra dimensions. I suspect that other implications could be deduced that could explain some of the outstanding mysteries such as quantum non-locality, dark matter, dark energy, etc.

 

That is why I asked you to solve your equation in four dimensions just to see if any enlightening implications pop out. Your response was that solving it for n dimensions was adequate. I disagree because in that general case, important implications might not be easily noticed.

 

What I think we should look for are possibilities for higher-dimensional interactions that generate 3D effects in our manifold. We could then predict and test for these effects. For example, my suspicion is that the orthogonal aspects of the components of electromagnetism have orthogonal counterparts in higher dimensions, and that there may be additional, as yet unobserved, manifestations of electromagnetism in our 3D world.

 

I think that if scientists would abandon the, to my mind silly, requirement that any additional dimensions must be "curled up", they would have a much better chance of discovering the true nature of reality.

 

Thanks for your comments, Dick.