On 12/22/2017 3:43 AM, [email protected] wrote:
On Friday, December 22, 2017 at 7:45:42 AM UTC, Brent wrote:
On 12/21/2017 11:06 PM, [email protected] <javascript:> wrote:
On Friday, December 22, 2017 at 4:46:10 AM UTC, Brent wrote:
On 12/21/2017 4:22 PM, [email protected] wrote:
On Thursday, December 21, 2017 at 11:03:53 PM UTC, Brent wrote:
On 12/21/2017 2:04 PM, [email protected] wrote:
On Tuesday, December 19, 2017 at 8:51:51 PM UTC, Brent
wrote:
On 12/18/2017 11:44 PM, [email protected] wrote:
Invariants are always the important things in
physics because they are what we can have
intersubjective agreement on.
Brent
*IIUC, the field equations are covariant, which
means coordinate system independent. *
Right. Covariant means that something that changes
in such a way that invariant things remain the
same. So vectors components transform covariantly
so that they keep the vector physically the same.
*Isn't Newton's Law of Gravitation also coordinate
independent? That is, if we use Newton to
calculate the planetary orbits, won't we get the
same results in different coordinate systems? *
Right.
*
If Newton's Law of Gravitation is covariant -- that is,
coordinate frame independent -- I'd expect it to to be
invariant between inertial frames, but I don't believe
it is. That is, I don't think a LT between inertial
frames will leave the form of the law unchanged. How do
you resolve this problem? TIA, AG
*
Don't use a Lorentz transform between frames in a
Galilean invariant theory.
*OK, So why didn't Einstein do what he did for classical
mechanics which is not Lorentz invariant, and directly
modify Newton's Law of Gravitation? AG*
(a) I don't read minds, and especially not Einstein's and
(b) I don't know what "directly modify" means.
Brent
*He changed (= directly modified) the laws of mechanics to make
them Lorentz invariant. So why can't that be done for Newton's
Law of Gravitation? Does that law work for any inertial frame? AG*
Newton's gravity is a field theory. It implies an infinite speed
of changes in the gravitational field. That wasn't consistent
with relativity. What you're calling "directly modified" was just
local mechanics, not fields.
Brent
*When you think about it, it's apriori highly improbable that
Newtonian gravity would work as well as it does, say for planetary
orbits, given the substantial light times between the Sun and the
planets, and between the planets. AG
*
It's an interesting point that if you just take Newton's theory and
allow for the finite travel time of gravitational fields, so each body
is attracted toward the point another body was in past, the theory
doesn't work at all.
Brent
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