- #1
Buzz Bloom
Gold Member
- 2,519
- 467
In another thread
I was amazed to learn the following from a post by bcrowell:
Obviously for small volumes, like in a laboratory,
If this is plausible, then a question might be:
To calculate the first nonlinear term one needs to know both its exponent and the coefficient.
If the following simplification would be useful, it would be OK to assume spherical volumes with all with the same uniform distribution of dust particles per unit volume.
Does anyone know if such a calculation, or a similar one, has been published somewhere? If not, can someone post the equation(s) that need to be solved in order to make this calculation?
I would much appreciate any help anyone can offer.
Regards,
Buzz
I was amazed to learn the following from a post by bcrowell:
"You can't get the total mass of the system by adding up the masses of all its parts."
The reason for this is that the GR equations regarding mass are nonlinear.Obviously for small volumes, like in a laboratory,
M = V × ρ
works just fine. The first question that occurs to me is how big does the volume have to be before the nonlinear aspects of mass makes this equation noticeably false. That is, if the above equation is only a linear approximation, perhaps the actual mass in a given volume might have a power series representation, maybe something like the following:Mlinear = V × ρ
M = Σ (i = 1 to ∞) ci Mlineari
where c1 = 1.M = Σ (i = 1 to ∞) ci Mlineari
If this is plausible, then a question might be:
which terms in the summation have non-zero coefficients?
That is, are all powers present in the summation, or perhaps only odd powers, like the sine? To calculate the first nonlinear term one needs to know both its exponent and the coefficient.
If the following simplification would be useful, it would be OK to assume spherical volumes with all with the same uniform distribution of dust particles per unit volume.
Does anyone know if such a calculation, or a similar one, has been published somewhere? If not, can someone post the equation(s) that need to be solved in order to make this calculation?
I would much appreciate any help anyone can offer.
Regards,
Buzz