[parakorn (OP)]

   I have read many book about The General Relativity. Einstein started with the equivalence between Acceleration and Gravity. And almost of the book jump to the space time curvature . I don't understand it how did Einstein find the path way from the equivalence principle to The spacetime curvature. Who know about it please explain me  

[PmbPhy]

I have read many book about The General Relativity. Einstein started with the equivalence between Acceleration and Gravity.

That part is most certainly correct. However when this is explained in that way then rrrrrrit's only valid locally is withheld. It's only later, if at in in fact, that it only applies locally, i.e. within a limited region of space for a limited amount of time.

And almost of the book jump to the space time curvature.

Those correct but most don't explain why or they don't do if very well.

I don't understand it how did Einstein find the path way from the equivalence principle to The spacetime curvature.

Because Einstein had to be able to explain arbitrary gravitational fields and not merely those which are locally equivalent.

Who know about it please explain me

Sure. I'll contact a friend in that field and as him for some references for you to year. Also, I recommend that you read my article on this subject which is online at http://xxx.lanl.gov/abs/physics/0204044

[parakorn (OP)]

I have read many book about The General Relativity. Einstein started with the equivalence between Acceleration and Gravity.

That part is most certainly correct. However when this is explained like that the fact that it's only valid locally is withheld. It's only later reveled, if at all, that it only applies locally, i.e. within a limited region of space for a limited amount of time.

And almost of the book jump to the space time curvature.

That too is often correct but most don't explain why or they don't do if very well.

I don't understand it how did Einstein find the path way from the equivalence principle to The spacetime curvature.

Because Einstein had to be able to explain the arbitrary gravitational field and not merely those which are locally equivalent.

Who know about it please explain me

Sure. I'll contact a friend in that field and as him for some references for you to year. Also read my article on this subject at
http://xxx.lanl.gov/abs/physics/0204044 [nofollow]

Thank you for your answer. My answer that I want to know is How does Einstein think about space time curvature . In many book that I have read must start with Equivalence principle in year 1907 and then they both go to spacetime curvature without explained How einstein got this idea from .

[PmbPhy]

Thank you for your answer. My answer that I want to know is How does Einstein think about space time curvature . In many book that I have read must start with Equivalence principle in year 1907 and then they both go to spacetime curvature without explained How einstein got this idea from .

That's a great question. In actuality I've never actuality seen him use that term. Let me do some background on this.

[PmbPhy]

Thank you for your answer. My answer that I want to know is How does Einstein think about space time curvature . In many book that I have read must start with Equivalence principle in year 1907 and then they both go to spacetime curvature without explained How einstein got this idea from .

That's a great question. In actuality I've never actuality seen him use that term. Let me do some background on this.

I got a response back from my friend John Stachel on these. He said

As for the transition from the equivalence principle to the metric tensor, I discuss this in detail in "The First Two Acts" included in pp. 261-292 of my book Einstein from 'B' to 'Z'.

Regarding the rest of your questions he sent me two other papers. Since they're too large to upload to the forum how can I get them to you?

[David Cooper]

Get yourself a dropbox account and you can simply upload the two files to a folder in the cloud and then post a link here to that folder so that anyone who wants to can access them. They won't be able to access any other folders that you might want to keep there because people can only get into a folder if they have the link to it. (You'll also be able to keep shared folders in the cloud which allows you to put files straight into a friend's machine and to receive files from them straight onto yours, as well as having them backed up to the cloud along the way - saves a lot of time wrestling with email attachments.)

[PmbPhy]

Get yourself a dropbox account and you can simply upload the two files to a folder in the cloud and then post a link here to that folder so that anyone who wants to can access them. They won't be able to access any other folders that you might want to keep there because people can only get into a folder if they have the link to it. (You'll also be able to keep shared folders in the cloud which allows you to put files straight into a friend's machine and to receive files from them straight onto yours, as well as having them backed up to the cloud along the way - saves a lot of time wrestling with email attachments.)

I'm sure that's a very simple thing to figure out, much like it was so easy for me to figure out how to program my VCR when they came out but my mother couldn't. Now I'm in my mother's place and you're in my place thinking "It's just so easy if you just sit down for a moment and think about it." But I don't want to sit down for a moment. And I rarely, if ever, have to do this. In the future this won't be a problem anyway.

[David Cooper]

Well, it would actually be easier for you if Parakorn simply sends you his/her email address in a PM, but I was thinking about other people reading the thread who might benefit from accessing the same files, unless there are legal reasons (e.g. copyright) for not making them more widely available.

[PmbPhy]

Well, it would actually be easier for you if Parakorn simply sends you his/her email address in a PM, ..

He already did and I already e-mailed it to him.

..but I was thinking about other people reading the thread who might benefit from accessing the same files, unless there are legal reasons (e.g. copyright) for not making them more widely available.

It actually is illegal to do that but it's never stopped me in the past.