A few questions about the Einstein field equations?

[zeromodz]

1) What exactly does the metric tensor expand into? Since it describes general space-time, shouldn't it be more like a vector like

R = √(x^2+y^2+z^2)

Why even should we use tensors in relativity when we can just stick with vectors?

2) Are the equations all theoretical? Have they been proven? Can they calculate anything physical calculations like exactly to what angle or degree space and time are curved?


3) Why do all the equations and math attempt to look so confusing? I have been doing a lot of research on the equations recently, and I am deducing that theoretical physicists use redundant notations just to make everything seem too complex for an average person to understand?

Thank you!

 

[espen180]

1) GR deals with curved 4-dimensional psuedo-riemannian manifolds. Do some reading on those, then see if you can avoid using tensor quantities when expressing genereal expressions.

2) Einstein's equation can be used to calculate extremely accurately any orbit, as well as gives very accurate predictions of time dilations. Read about how a GPS system works. It uses GR to function properly.

 

[fzero]

1) What exactly does the metric tensor expand into? Since it describes general space-time, shouldn't it be more like a vector like

R = √(x^2+y^2+z^2)

Why even should we use tensors in relativity when we can just stick with vectors?

In simple terms, a metric generalizes the dot product of two vectors to the case where space(time) is curved. If $$\vec{r} = (x,y,z)$$, then

$$|\vec{r}| = \sqrt{ g_{ij} r^i r^j}.$$

In flat space where $$g_{ij} = \delta_{ij}$$, this reduces to the formula that you quoted.

2) Are the equations all theoretical? Have they been proven? Can they calculate anything physical calculations like exactly to what angle or degree space and time are curved?

Einstein's equations have been proven to be valid in many situations. Perhaps the most down to Earth application is to the GPS system. General relativity is required to obtain correct positions from the satellite references.

3) Why do all the equations and math attempt to look so confusing? I have been doing a lot of research on the equations recently, and I am deducing that theoretical physicists use redundant notations just to make everything seem too complex for an average person to understand?

Examples? Scientific notation is generally chosen to make it easier for scientists to do calculations, not to make it easier for lay people to understand.