Faraday Tensor Conflicts: MTW vs. Wikipedia

In summary, there are various sign conventions and definitions used in relativity, including the signature of the metric, the ordering of indices, and the notation for covariant derivatives. However, all sources should ultimately describe the same physics, so it is important to consider the relationships among these conventions. The Faraday Tensor with both indices down has a different sign convention in MTW Gravitation book compared to Wikipedia, and this may depend on the signature of the metric. Sources may also differ in their notation for forming the electric field. It may be helpful to refer to a table of different sign conventions and their relative results in order to better understand these relationships.
  • #1
Cesarth
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Hello, I've found that the Faraday Tensor with both indeces down has in the first line, in MTW Gravitation book (pg 74, eq 3.7), minus the electrical field, while in Wikipedia we find that it is plus the electrical field.
Which one is right?
Does it depend on the signature of the metric?
 
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  • #2
Unfortunately, there are numerous sign conventions in relativity.

The signature sign convention is one: [itex]+---[/itex] , [itex]-+++[/itex] (using the "0" convention for the time coordinate)
...so there is also the ordering of indices: is the time coordinate "0" or "4"?

There is also the definition of the Faraday tensor in terms of how covariant derivatives are notated... [itex]\nabla_{[a} A_{b]}[/itex]? [itex]A_{[b;a]}[/itex]?
Which index is used to form the electric field? [itex]u^{a}F_{ab}[/itex]? [itex]u^{b}F_{ab}[/itex]?

In the end, all sources should be describing the same physics... so one might look there to unravel the relationships among the conventions.
 
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  • #3
If I do not misremember, there should be a table of different sign conventions and their relative results listed in MTW. I might have confused it with some other book though.
 

1. What are Faraday Tensor Conflicts?

Faraday Tensor Conflicts refer to discrepancies between two different interpretations of the Faraday tensor, a mathematical object used to describe and calculate electromagnetic fields. These conflicts have been observed between the textbook "Gravitation" by Misner, Thorne, and Wheeler (MTW) and the online encyclopedia Wikipedia.

2. Why do these conflicts exist?

The conflicts arise due to differences in notation and conventions used by MTW and Wikipedia when defining and using the Faraday tensor. These differences can lead to different results and interpretations of the same physical phenomenon.

3. Which interpretation is correct?

Both interpretations are correct in their respective contexts. MTW uses a more traditional and widely accepted notation, while Wikipedia uses a more modern and concise notation. Both approaches have their advantages and are useful for different purposes.

4. How can these conflicts be resolved?

The conflicts can be resolved by carefully examining and understanding the differences in notation and conventions used by MTW and Wikipedia. It is important to recognize that both interpretations are valid and to choose the most appropriate approach for a given problem.

5. Why is it important for scientists to be aware of these conflicts?

Being aware of these conflicts is important for scientists because it highlights the importance of clear and consistent notation and conventions in scientific communication. It also encourages critical thinking and evaluation of different approaches to problem-solving and interpretation of mathematical objects.

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