Question on general principle of relativity

In summary, the first statement is more mathematically expressed and the second statement is more intuitive and physical. However, the first statement is better in representing the general principle of relativity because Gaussian coordinates are not covariant, while the second statement does not specify the type of coordinates being referred to. The inclusion of Gaussian coordinates is important because they have a specific meaning in the context of relativity and their use can impact the interpretation of physical laws. This is discussed in Einstein's book "Relativity: The Special and the General Theory."
  • #1
Ronald_Ku
17
0
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.
 
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  • #2
Welcome to PF!

Hi Ronald_Ku! Welcome to PF! :smile:
Ronald_Ku said:
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)
 
  • #3
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?
 
  • #4
Well, I found the 1st statement better from the book " Relativity: The Special and the General Theory".
 
  • #5
Einstein's book?

Ronald_Ku said:
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 :smile: 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?
 
Last edited by a moderator:
  • #6
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.
 

FAQ: Question on general principle of relativity

What is the general principle of relativity?

The general principle of relativity is a theory proposed by Albert Einstein in 1915 that describes the relationship between gravity and the motion of objects in space. It states that the laws of physics are the same for all observers in any inertial frame of reference, and that the effects of gravity can be explained as the curvature of space and time caused by massive objects.

How does the general principle of relativity differ from Newton's theory of gravity?

In Newton's theory of gravity, gravity is seen as a force acting between objects with mass. This force is described by a mathematical equation and is instantaneous. In contrast, the general principle of relativity describes gravity as a curvature in the fabric of space and time, with the effects of gravity being felt as objects move through this curved space. It also takes into account the effects of high speeds and strong gravitational fields, which Newton's theory does not.

What evidence supports the general principle of relativity?

There is a significant amount of evidence that supports the general principle of relativity. One of the most famous examples is the bending of light near massive objects, known as gravitational lensing. This effect was observed during a solar eclipse in 1919 and confirmed Einstein's theory. Other evidence includes the precession of Mercury's orbit, the gravitational redshift of light, and the time dilation of clocks in strong gravitational fields.

How does the general principle of relativity impact our understanding of the universe?

The general principle of relativity has had a profound impact on our understanding of the universe. It has led to the development of theories such as the Big Bang theory and the theory of black holes. It also plays a crucial role in modern cosmology and our understanding of the structure and evolution of the universe.

Are there any limitations or challenges to the general principle of relativity?

While the general principle of relativity has been extensively tested and confirmed, there are still some limitations and challenges to the theory. One of the major challenges is the difficulty in reconciling it with quantum mechanics, which describes the behavior of particles on a very small scale. Another limitation is that it does not provide a complete explanation for the behavior of the universe at very high energies, such as during the Big Bang. Scientists are still working towards a unified theory that can encompass both general relativity and quantum mechanics.

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