On 12/18/2017 6:54 PM, agrayson2...@gmail.com wrote:
On Tuesday, December 19, 2017 at 2:36:32 AM UTC, agrays...@gmail.com
wrote:
On Monday, December 18, 2017 at 8:48:08 PM UTC, Brent wrote:
On 12/18/2017 12:19 AM, agrays...@gmail.com wrote:
On Sunday, December 17, 2017 at 10:39:18 PM UTC,
agrays...@gmail.com wrote:
On Sunday, December 17, 2017 at 12:21:27 AM UTC, Brent
wrote:
On 12/16/2017 2:59 PM, agrays...@gmail.com wrote:
There's a problem applying SR in this situation
because neither the ground or orbiting clock is an
inertial frame.AG
An orbiting clock is in an inertial frame. An
inertial frame is just one in which no forces are
acting (and gravity is not a force) so that it moves
with constant momentum along a geodesic. Although
it's convenient for engineering calculations, from a
fundamental veiwpoint there is no separate special
relativity and general relativity and no separate
clock corrections. General is just special
relativity in curved spacetime. So clocks measure
the 4-space interval along their path - whether that
path is geodesic (i.e. inertial) or accelerated.
*Interesting way to look at it. So free falling in a
gravity field is an extension of SR. But the thing I find
puzzling is that in GR the curvature of space-time is
caused by the presence of mass, yet I can draw the path
of an accelerated body as _necessarily_ a curve in a
space-time diagram. I am having trouble resolving these
different sources of curvature. AG*
*Einstein must have figured that since gravity produces an
acceleration field, and accelerating test particles move
along curved paths in space-time, he could replace
acceleration by inertial paths in a space-time curved by the
presence of mass-energy. But now, when comparing test
particles moving along different paths in space-time, he
couldn't use the Lorentz transformation because the relative
velocities of the frames are not necessarily constant. So how
did he propose to find the correct transformation equations,
and what are they? And what were the laws of physics, in this
case gravity, that had to be invariant? AG*
What's invariant is the measure along a path in spacetime -
it's what an ideal clock measures. The relation between the
measure along two different paths obviously depends on the
lumpiness of the spacetime through which they travel. It's as
if I headed north thru the Sierras while you sailed up the
coast. There's no simple relation between our path lengths
even if we travel between the same two points.
*So what's invariant along along two paths with the same
endpoints? Not clear from what you write. But whatever it is, why
is that deemed to be invariant? Shouldn't it be the laws of
physics, in this case gravity, and hence the field equations? AG *
*I think you mean the dS^2 value is invariant along two paths with the
same endpoints, but not the path length of the spatial coordinates.
Correct? *
Right.*
*
*But why is this particular invariant so important, and perhaps used
as a guide to Einstein? AG*
Invariants are always the important things in physics because they are
what we can have intersubjective agreement on.
Brent
The Lorentz transformation is just the simple limiting case of
flat, smooth spacetime. It's useful because in a sufficiently
small local region spacetime is going to be flat and smooth.
Brent
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