- #1

aeroboyo

- 70

- 0

hey,

i'm just trying to learn about special and general relativity and i figure a good place to start is with minkowski space since that is the basis of special relativity. I have a few questions though, i hope you forgive me because these questions will sound rather ignorant and silly i guess but please understand that I've never seen tensor calculus or anything like this before.

The first thing I'm confused about is this concept of a Minkowski metric. You can see on page 3 of this pdf what I'm referring to exactly in the rest of this post:

http://preposterousuniverse.com/grnotes/grtinypdf.pdf

I don't understand what this metric is... what is a metric? Or why is the signature of this metric (-1,1,1,1). So as you can see i have a total lack of basic understanding.

Also, the dot product of this metric confuses me. The two vectors are A and B, which i gather are two fixed vectors in this minkowski space right... and the dot product is given as

A . B = n(uv)A^uB^v = -A^0B^0 + A^1B^1 + A^2B^2+A^3B^3+A^4B^4

Well that's messy and I'm sorry, i hope you understand what i am trying to write there. I can see that signature in there with the (-,+,+,+,+) pattern, and if I'm not mistaken the negative term is the time coordinate right? I really need some help to understand the basics of this! It doesn't make sense why A.B equals NuvA^uB^v what does A^u and B^v mean anyway? Thankyou.

i'm just trying to learn about special and general relativity and i figure a good place to start is with minkowski space since that is the basis of special relativity. I have a few questions though, i hope you forgive me because these questions will sound rather ignorant and silly i guess but please understand that I've never seen tensor calculus or anything like this before.

The first thing I'm confused about is this concept of a Minkowski metric. You can see on page 3 of this pdf what I'm referring to exactly in the rest of this post:

http://preposterousuniverse.com/grnotes/grtinypdf.pdf

I don't understand what this metric is... what is a metric? Or why is the signature of this metric (-1,1,1,1). So as you can see i have a total lack of basic understanding.

Also, the dot product of this metric confuses me. The two vectors are A and B, which i gather are two fixed vectors in this minkowski space right... and the dot product is given as

A . B = n(uv)A^uB^v = -A^0B^0 + A^1B^1 + A^2B^2+A^3B^3+A^4B^4

Well that's messy and I'm sorry, i hope you understand what i am trying to write there. I can see that signature in there with the (-,+,+,+,+) pattern, and if I'm not mistaken the negative term is the time coordinate right? I really need some help to understand the basics of this! It doesn't make sense why A.B equals NuvA^uB^v what does A^u and B^v mean anyway? Thankyou.

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