Clocks, rulers... and an issue for relativity

[Mordred]

There is a commonly used expression.

"mass tells space how to curve, space tells matter how to move."

Its not completely accurate in so far as flux and vorticity can also influence curvature. Mass is only one contributor.

A more accurate statement. "the stress tensor tells space how to curve..."

 

If you take a free falling particle the geometric relations of spacetime determine the path. It does so without applying any force. A freefalling particle will choose the path of least action. Action being the sum of kinetic energy vs potential energy.

 

This is a non relativistic derivitave.

[latex]Action=S=\int_{t_0}^{t_1}[\frac{1}{2}m (\frac{dx}{dt})^2+-mgx]dt [/latex]

Edited September 29, 2016 by Mordred

[swansont]

 

Is the aproach stating that gravity is curvature of spacetime really correct? Gravity seems to be the consequence of spacetime curvature or at least one of the implications of mass effecting spacetime seems to be that of gravity but is that equivalent to your statement?

 

 

I don't see much of a distinction between these. The geometry dictates how things move, as Mordred says. We interpret that as gravity.

[koti]

There is a commonly used expression.

"mass tells space how to curve, space tells matter how to move."

Its not completely accurate in so far as flux and vorticity can also influence curvature. Mass is only one contributor.

A more accurate statement. "the stress tensor tells space how to curve..."

 

If you take a free falling particle the geometric relations of spacetime determine the path. It does so without applying any force. A freefalling particle will choose the path of least action. Action being the sum of kinetic energy vs potential energy.

 

This is a non relativistic derivitave.

[latex]Action=S=\int_{t_0}^{t_1}[\frac{1}{2}m (\frac{dx}{dt})^2+-mgx]dt [/latex]

 

This seems pretty clear to me (excluding the math unfortunately) I still feel that I'm missing something though.

If I understand correctly there is no vorticity nor stress tensors to describe (one is a vector field and the other is kind of a vector if I'm not mistaken?) when there is no curvature/when no mass is affecting spacetime.

 

 

 

I don't see much of a distinction between these. The geometry dictates how things move, as Mordred says. We interpret that as gravity.

 

I will have to take your word for it for now as I'm missing the math tool :/

[swansont]

 

This seems pretty clear to me (excluding the math unfortunately) I still feel that I'm missing something though.

If I understand correctly there is no vorticity nor stress tensors to describe (one is a vector field and the other is kind of a vector if I'm not mistaken?) when there is no curvature/when no mass is affecting spacetime.

 

 

 

When all that's missing there is no gravity.

[Celeritas]

Is the aproach stating that gravity is curvature of spacetime really correct? Gravity seems to be the consequence of spacetime curvature or at least one of the implications of mass effecting spacetime seems to be that of gravity but is that equivalent to your statement?

 

I would say it this way ...

 

The gravitational-field is curved-spacetime. The effect of gravity, is the effect of directed inertial motion.

 

Best regards,

Celeritas

[robinpike]

I think my original question was incorrect - as my concerns are probably with explanations of relativity (such as space-time etc) and not relativity itself.

 

Since it would be incorrect to now re-direct this thread along those lines (and there are a couple of space-time threads currently on-going anyway), I would just like to conclude by thanking everyone for their help on this discussion.