Question on general principle of relativity

[Ronald_Ku]

I want to ask about the two statements.
1) Physics laws remain unchange at any Gauss' coordinates.
2) Physical laws are the same in all reference frames -- inertial or non-inertial.

Why is 1st statement better than the second statement in representing the general principle of relativity?

What's the importance of including the Gauss; coordinates?

I know this may be simple question but i am really struggling about it.

 

[tiny-tim]

Welcome to PF!

Hi Ronald_Ku! Welcome to PF!

I want to ask about the two statements.
1) Physics laws remain unchange at any Gauss' coordinates.
2) Physical laws are the same in all reference frames -- inertial or non-inertial.

Why is 1st statement better than the second statement in representing the general principle of relativity?

What's the importance of including the Gauss; coordinates?

Well, I think the 2nd statement is better …

Gaussian coordinates (synchronous coordinates) aren't covariant.

(see http://en.wikipedia.org/wiki/Coordinate_conditions#Synchronous_coordinates)

 

[altonhare]

The first one is a bit more mathematical and the second one is a bit more intuitive or physical.

Do you have a reason to think the first statement is "better" than the second?

 

[Ronald_Ku]

Well, I found the 1st statement better from the book " Relativity: The Special and the General Theory".

 

[tiny-tim]

Einstein's book?

Well, I found the 1st statement better from the book " Relativity: The Special and the General Theory".

ah … you mean Einstein's book?

Einstein wrote the book a long time ago, when "Gaussian coordinates" had a different meaning.

Then, they meant any curvilinear coordinates, now they mean synchronous coordinates.

I assumed you meant synchronous coordinates.

If they mean any coordinates, I don't see much difference between the statements, except that, as altonhare says, the first is slightly more mathematically expressed.

Are you using Lawson's English translation in the 2002 http://books.google.com/books?id=f_...lativity:+The+Special+and+the+General+Theory"? If so, which page is it on?

 

[Ronald_Ku]

No I'm a chinese. I'm using the edition translated to chinese.
I just translate all the words I read to english.
Besides I still don't see what you mean.