Ok, so my acceleration is constant. So I can say that the frame of reference made by the walls of house is a constantly accelerated frame. Then can I say I am in Rindler coordinates?
I think he simply said that in a 1-dimensional vector space every vector is a multiple of the other ones. Right. But aren't we reasoning in 4 dimensions?
About the whole "differential-derivative" stuff I think I'm figuring it out, thanks everyone for the help.
I have no idea. Is a scale an accelerometer? If yes, then when I stand on a scale I see constantly the same weight.
And the other question now is: if a is different than zero, what is its cause? It must be some non-gravitational interaction, right? Is it the reaction of the floor under my feet?
Thanks, I am still studying, I was not sure of what I wrote. I am just trying to fix some concepts in my head, so when I read "earth-not-inertial" I was scared of not understanding once again.
This really surprises me. I thought the Earth was inertial, because it moves on a geodesic around the sun. How can a planet, a body which undergoes only gravitational interaction, accelerate?
Hello,
I am wondering,
if I am sitting on my chair, here at home, planet Earth, am I accelerating (in GR)?
Does the tangent four-vector u to my worldline obey the equation
\nabla_{u} u = a
or instead
\nabla_{u} u = 0
??
and if the first one is correct, is the four-vector a constant?
This seems reasonable, but as you know tensors can be represented by matrices, so are you saying that if a matrix equals a scalar multiplied by another matrix then it implies that the quotient of those matrices is a scalar?
M = a N \Rightarrow M/N = a ?
My only problem is that the...
It's conceptually the same thing only if u is constant I think. If the world line of the particle is not straight I don't think it's correct to use the transformations without the d's.
And those must be 1-forms, since Lorentz transformations leave the metric invariant:
\text{d}t^2 -...
Hello
I am studying some differential geometry. I think I have understood the meaning of "differential" of a function:
\text{d}f (V) = V(f)
It is a 1-form, an operator that takes a vector and outputs a real number.
But how is it related to the operation of "total derivative" ?
For...
I have some problems using this definition, maybe because it's not valid in every coordinate system:
T^{\mu\nu} = (\epsilon + p) \frac{dx^{\mu}}{ds} \frac{dx^{\nu}}{ds} -p g^{\mu\nu}
since in cylindrical coordinates
x^0 =t \qquad x^1 =\rho \qquad x^2 = \phi \qquad x^3 =z
using weyl metric...
Thanks a lot bcromwell, you have been extremely helpful. I'll read all of the articles you suggested and probably come up with another question, but it's going to take me some time to study the subject.
By the way, Weinberg wrote that book about forty years ago, thing may have changed in the...
Thanks for explaining Landau and Lifgarbagez, it's still mysterious why they never mentioned gravitational potential energy in defining their gravitational mass defect (nor they mentioned anything else, actually) but you convinced me.
This is the passage in Steven Weinberg's book which troubles...
It was a sort of milestone to me too. Gravitational mass equals inertial mass.
Until two weeks ago, when my professor asked me to review the concept. He pointed me to some papers like this:
http://arxiv.org/abs/gr-qc/0606077
in which the author clearly states that inertial mass is different...
I really don't know, I'm having huge problems understanding the concept of gravitational mass defect. Is it related to the gravitational binding energy?
From the formulas above, can we deduce that for a spherical body of perfect fluid the inertial mass is different from the gravitational mass...