Are 10 dimensions related to the tensor of 3d

In summary, the conversation discusses the number of components in a tensor of order ##k## over a three-dimensional vector space. It is stated that none of the tensors will have ten components, as three does not divide ten. However, symmetries in the type of tensor being considered can reduce the number of unique components and result in ten components. The conversation also mentions string theory and its relation to vector spaces with more dimensions, such as eleven. It is clarified that the metric tensor in 3+1 dimensions and the concept of spacetime dimensions in string theory have different origins. Additionally, it is noted that the metric tensor in general relativity has 16 components, but due to symmetry, it reduces to 10 independent components.
  • #1
Pjpic
235
1
I think I've read the the tensor in three dimensions has 10 elements in its matrix(?). Is this related to the 10 dimensions in some forms of string theory?
 
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  • #2
There is more than one tensor over three-dimensional vector spaces. The tensor of order ##k## has ##3^k## components. None of the tensors will have ten components, as three does not divide ten. However, if there are symmetries in the type of tensor you are considering, that will reduce the number of unique components, as some will be the same as others, and you may get ten that way.
This has nothing to do with string theory though, which seems to be about vector spaces with many more dimensions, eg eleven.
 
  • #3
None of the tensors will have ten components, as three does not divide ten.
I was thinking 9 plus 1 (zero).

eg eleven
I was thinking 10 spatial plus 1 (time).

But if they aren't related they aren't. Thanks
 
  • #4
Maybe you mean the metric tensor in 3+1 dimensions? The number of spacetime dimensions in string theory has a different origin :)
 
  • #5
andrewkirk said:
There is more than one tensor over three-dimensional vector spaces. The tensor of order ##k## has ##3^k## components. None of the tensors will have ten components, as three does not divide ten. However, if there are symmetries in the type of tensor you are considering, that will reduce the number of unique components, as some will be the same as others, and you may get ten that way.
This has nothing to do with string theory though, which seems to be about vector spaces with many more dimensions, eg eleven.

This is the case with the metric tensor of GR. It has 16 components but being symmetric it reduces to 10 independent components.
 

1. Are there really 10 dimensions in our universe?

According to string theory, there are 10 dimensions in our universe. However, these dimensions are not perceivable in our everyday experience, as they are thought to be curled up and exist on a microscopic scale.

2. How are the 10 dimensions related to the tensor of 3D?

The tensor of 3D, also known as the metric tensor, describes the geometry of our 3-dimensional space. The remaining 7 dimensions in string theory are thought to be compactified and influence the shape and curvature of our 3-dimensional space.

3. Can humans visualize or understand 10 dimensions?

Humans have evolved to perceive and understand the world in 3 dimensions, so it is difficult for us to visualize or understand 10 dimensions. However, mathematical models and simulations can help us better understand these dimensions.

4. What is the purpose of having 10 dimensions?

The additional dimensions in string theory are necessary to reconcile inconsistencies between quantum mechanics and general relativity. They also play a role in explaining the fundamental forces and particles in our universe.

5. Is there any evidence for the existence of 10 dimensions?

Currently, there is no direct evidence for the existence of 10 dimensions. However, some theories, such as the holographic principle, suggest that our 3-dimensional reality may be a projection of a higher-dimensional space. Further research and experiments are needed to confirm the existence of these dimensions.

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