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## Summary:

- In the book Gravitation by Wheeler, they say any tensor can be completely antisymmetrized. Does this mean we can then convert any Tensor to differential form notation?

I read in the book Gravitation by Wheeler that "

And in Topology, Geometry and Physics by Michio Nakahara, on page 52 definition 5.4.1, it says a differential r-form (differential form of order r) is a totally antisymmetric tensor of type (0,r).

Putting these facts together, does this mean that we can always convert a tensor into a differential form by the following process; Tensor -> Antisymmetrize the Tensor -> Differential Form Notation.

Maybe I am reading this wrong and hopeful someone can clarify. I ask this question because many authors suggest that tensors are in fact more general than differential forms, but if you can always turn tensor into a differential form, I just see these as equivalent but different notations.

My follow-up question would be the following; given the Tensor form of the laws of physics, why would anyone want to rewrite them in the notation of differential forms anyway? I read that differential forms simplify higher dimensional calculations compared to tensors where we have to carry around all the indices, and they generalize many theorems such as stokes to higher dimensions, they unify and simplify some laws of physics such as Maxwell equations. Why then would we rather use differential forms as opposed to the Tensor case and would it just cause more headaches doing Tensor -> Antisymmetrize the Tensor -> Write in Differential Form notation.

I hope that someone with enough experience can clarify all of this. Very confusing. Thank you.

**Any**tensor can be completely symmetrized or antisymmetrized with an appropriate linear combination of itself and it's transpose (see page 83; also this is an exercise on page 86 Exercise 3.12).And in Topology, Geometry and Physics by Michio Nakahara, on page 52 definition 5.4.1, it says a differential r-form (differential form of order r) is a totally antisymmetric tensor of type (0,r).

Putting these facts together, does this mean that we can always convert a tensor into a differential form by the following process; Tensor -> Antisymmetrize the Tensor -> Differential Form Notation.

Maybe I am reading this wrong and hopeful someone can clarify. I ask this question because many authors suggest that tensors are in fact more general than differential forms, but if you can always turn tensor into a differential form, I just see these as equivalent but different notations.

My follow-up question would be the following; given the Tensor form of the laws of physics, why would anyone want to rewrite them in the notation of differential forms anyway? I read that differential forms simplify higher dimensional calculations compared to tensors where we have to carry around all the indices, and they generalize many theorems such as stokes to higher dimensions, they unify and simplify some laws of physics such as Maxwell equations. Why then would we rather use differential forms as opposed to the Tensor case and would it just cause more headaches doing Tensor -> Antisymmetrize the Tensor -> Write in Differential Form notation.

I hope that someone with enough experience can clarify all of this. Very confusing. Thank you.