Is this just a typo in Schutz' book on General Relativity?

In summary, the conversation discusses a confusion regarding the meaning of a non-zero component in the momentarily comoving inertial frame. The book is correct in stating that the time component of the four-acceleration is zero in this frame. However, the statement that only one component of ##\tilde{U}## is non-zero is misleading. It would be clearer to say that ##\tilde{U}## only has a non-zero time component. This is a common issue in Schutz's writing, as the physics is sound but the explanations can be confusing.
  • #1
Ahmed1029
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I'm wondering is I'm missing something, or this should be " a non-zero component"?
Screenshot_2022-12-06-19-25-32-84_e2d5b3f32b79de1d45acd1fad96fbb0f.jpg
 
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  • #2
The book is correct. In the momentarily comoving inertial frame the time component of the four-acceleration is indeed 0.
 
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  • #3
No, it means that in the MCRF the only non-zero component of ##\tilde{U}## is the zeroth one (because the three velocity is zero by definition in that frame). Hence the four acceleration (which he's just proved is orthogonal to ##\tilde{U}##) must take the form given.

I agree it's not particularly clearly written - it would be better if he'd said "##\tilde{U}## has only a ##{\tilde{U}}^0## component".
 
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  • #4
Ah yes, it's clear now. I thought he meant that it had only one component taking the value zero, which didn't make sense.
 
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  • #5
I must say this isn't the only thing I've found confusing in Schutz. The physics is sound enough, but I do feel like he really needed a better editor.
 
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FAQ: Is this just a typo in Schutz' book on General Relativity?

1. Is it common for there to be typos in scientific books?

Yes, it is not uncommon for there to be typos in scientific books. Despite rigorous editing and proofreading processes, errors can still occur due to the complex and technical nature of the subject matter.

2. How do typos in scientific books affect the validity of the information presented?

Typos in scientific books do not necessarily affect the validity of the information presented. However, they can lead to confusion or misunderstandings for readers. It is important for authors and publishers to correct any typos in subsequent editions to ensure accuracy.

3. How can I determine if a typo in a scientific book is significant or not?

Determining the significance of a typo in a scientific book depends on the context and the extent of the error. It is always best to consult with other sources and experts in the field to verify information and clarify any discrepancies.

4. Are typos more common in certain fields of science?

There is no evidence to suggest that typos are more common in certain fields of science compared to others. However, some fields, such as mathematics and physics, may have more complex equations and formulas that are prone to typos if not carefully checked.

5. What should I do if I find a typo in a scientific book?

If you find a typo in a scientific book, you can report it to the author or publisher for correction in future editions. It is also helpful to bring it to the attention of other readers or experts in the field to prevent any misunderstandings or confusion.

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