Tensor Manipulation in Spacetime and Geometry

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Discussion Overview

The discussion centers around the tensor form of the Lorentz force law as presented in Sean Carroll's book 'Spacetime and Geometry'. Participants are exploring a specific equation (1.106) and the discrepancies encountered when attempting to verify it, particularly regarding the presence of an extra negative sign.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant reports difficulty in verifying the tensor form of the Lorentz force law due to an extra negative sign appearing in their calculations.
  • Another participant questions whether an erratum related to the equation applies, indicating they do not have access to the text for confirmation.
  • A later reply confirms that the erratum does indicate a minus sign should be present in the equation, suggesting a potential source of the discrepancy.

Areas of Agreement / Disagreement

There appears to be some agreement regarding the existence of a minus sign in the equation, as indicated by the erratum, but the initial participant's confusion about the extra negative remains unresolved.

Contextual Notes

Participants have not resolved the underlying assumptions or calculations leading to the discrepancy, and the discussion relies on the erratum for clarification.

bdm000
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I am self-studying GR and have run into a problem. In Sean Carroll's book 'Spacetime and Geometry', he states what the tensor form of the Lorentz force law is in Equation 1.106. However, whenever I try to verify the equation, I keep getting an extra negative. Has anyone worked this problem or does anyone have any suggestions?

Thanks!
 
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I'm assuming http://preposterousuniverse.com/spacetimeandgeometry/errata.html doesn't apply?

I don't actually have access to the text.
 
Last edited by a moderator:
lbrits said:
I'm assuming http://preposterousuniverse.com/spacetimeandgeometry/errata.html doesn't apply?

I don't actually have access to the text.

Good catch! Indeed, from the link provided by lbrits:

p. 32: (1.106) should have a minus sign. [11/28/03.]
 
Last edited by a moderator:
Thanks!
 

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