Re: Simple Question About GR And Uniform Acceleration


Ken S. Tucker wrote:
> Tom Roberts wrote:
> > Ken S. Tucker wrote:
> > > mathexpert@xxxxxxxxxxxxx wrote:
> > >>[accelerated observer] Can we address this simple type
> > >>of problem
> > >>outside of the umbrella of GR?
> > >
> > > Yes if you put square pegs in round holes.
> > > But the answer is NO to your question, GR is required,
> > > and was invented for that reason.
> >
> > Nonsense. The references I gave all describe this perfectly well in SR,
> > and are explicit counterexamples to your claim.
>
> Tom SR does NOT exist, except as a SPECIAL CASE in GR
> where UNIFORM VELOCITY is specified, it's kook bait as you
> demonstrate.
>
> See Eq(2) and read it this time. <shrug>.
> Ken

Perhaps this is wishful thinking, but with reference to the original
post of this thread,
I am wonderfully if SR could be generalized just one step up to apply
to UNIFORM
ACCELERATION outside of the umbrella of GR. For velocities << c and for
regions
of space-time whose 4D volume can be measured in "quartic" light
seconds (as opposed
to quartic light years), Newtonian Mechanics can be used to plot the
orbits of satellites.
For Newtonian Kinematics in one spatial dimension we have for uniformly
accelerated motion

x''' = 0
eq.(1)

where x' = dx/dt

whose general solution is

x = 1/2*at^2 + vt + d eq(2)

where d, v and a are constants that denote initial displacement,
velocity and acceleration respectively.

I understand, as was quoted above, that GR reduces to SR in the
special case of UNIFORM VELOCITY. I for one am very appreciative
of the symmetry, elegance and the invariance properties that are
associated with the Lorentz Transformations in which the expression

x - vt

makes an appearance. Can someone tell me what does GR reduce to
in the special case of UNIFORM ACCELERATION and what is the
counterpart of the Lorentz Transformations (for that case) that should
be
expected to contain an expression of the form

x - 1/2*at^2

Are we going to allow institutional inertia
to prevent us from calmly examining the old
in preparation for what is new?
Or will we be bold and put the inertia on hold
until we find what is true?

This could be the dawning of a new age of discovery. What better way to
celebrate the 100th anniversary of the 1905 paper and ush in the new
Millennium than a critical and calm search for the next realm of truth?

.

Relevant Pages

  • Re: How can this work in relativity?
    ... > that as long as you do your calculations in a single frame, ... >>> uniform acceleration by applying the appropriate compensating ... >From the moving FoR that includes the rod, ...
    (sci.physics.relativity)
  • Re: How can this work in relativity?
    ... but the acceleration would not be uniform. ... >> Then the acceleration would not be uniform[along the length of the rod, ... > thing as the rod's "own frame of reference" while it is ...
    (sci.physics.relativity)
  • Re: How can this work in relativity?
    ... but the acceleration would not be uniform. ... Uniform acceleration (in the original frame) means that the ... But our rod obeys Hooke's law, ...
    (sci.physics.relativity)
  • Re: How can this work in relativity?
    ... >> that as long as you do your calculations in a single frame, ... the same at all points of the rod. ... >> Uniform acceleration means that the ...
    (sci.physics.relativity)
  • Re: How can this work in relativity?
    ... but the acceleration would not be uniform. ... > Then the acceleration would not be uniform[along the length of the rod, ... >>> and not when looked at from its own frame of reference, ...
    (sci.physics.relativity)
Quantcast