Understanding Tensors & General Relativity

In summary, the conversation discusses a video about tensors and their role in understanding general relativity. The speaker recommends the video to anyone seeking to understand the concept, and suggests fast forwarding through repetitive parts and approaching it from a beginner's perspective. They also mention the power of the association between basis vectors and components in understanding tensors and how it can help shift one's thinking from a vector as an arrow to a more generalized association. This is seen as a good conceptual definition of a tensor and a helpful way to approach further exploration of the topic.
  • #1
jmatt
23
1
I enjoyed this video about tensors very much. I would recommend it to anyone seeking to understand the concept in general and general relativity specifically.

https://vimeo.com/32413024

You can fast forward through the repetitive parts and try to place yourself in the role of beginner as you watch.

Do you think anything essential is missing in this presentation?
 
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  • #2
I forgot to mention I found the emphasis on the association between basis vectors and components to be powerful. It leads to moving beyond thinking of a vector as an arrow to thinking of it as one of many possible associations between basis vectors and components. This generalized association is a good conceptual definition of a tensor in my opinion. It's a good way to find your footing as you explore.
 

Related to Understanding Tensors & General Relativity

1. What are tensors and why are they important in understanding general relativity?

Tensors are mathematical objects that describe the relationships between different physical quantities in a space. In general relativity, tensors are used to represent the curvature of spacetime and the distribution of matter and energy. They are important because they allow us to understand the effects of gravity on the behavior of matter and light.

2. How does the concept of spacetime curvature relate to general relativity?

In general relativity, gravity is not seen as a force between masses, but rather as a curvature of spacetime caused by the presence of mass and energy. This curvature affects the paths of objects and the passage of time, and is described by the equations of general relativity using tensors.

3. Can you give an example of how tensors are used in general relativity?

One example is the stress-energy tensor, which describes the distribution of mass, energy, and momentum in a given region of spacetime. This tensor is used to calculate the curvature of spacetime and the gravitational effects of a particular distribution of matter and energy.

4. What is the difference between tensors and other mathematical objects, such as vectors and scalars?

Vectors and scalars represent physical quantities such as speed, force, or energy, while tensors represent relationships between these quantities. Tensors have multiple components and can change depending on the coordinate system used, while vectors and scalars have fixed values in any coordinate system.

5. Is it necessary to have a deep understanding of tensors in order to understand general relativity?

While a basic understanding of tensors is helpful in understanding general relativity, it is not necessary for a complete understanding. Many concepts in general relativity can be explained without using tensors, although they provide a more precise and comprehensive mathematical description of the theory.

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