On 7/12/2020 12:37 AM, Alan Grayson wrote:
On Saturday, July 11, 2020 at 10:30:21 PM UTC-6, Alan Grayson wrote:
On Saturday, July 11, 2020 at 10:20:54 PM UTC-6, Brent wrote:
On 7/11/2020 9:00 PM, Alan Grayson wrote:
On Saturday, July 11, 2020 at 9:49:31 PM UTC-6, Brent wrote:
On 7/11/2020 8:07 PM, Alan Grayson wrote:
On Saturday, July 11, 2020 at 8:41:21 PM UTC-6, Brent
wrote:
On 7/11/2020 4:29 PM, Alan Grayson wrote:
On Saturday, July 11, 2020 at 5:05:02 PM UTC-6,
Brent wrote:
On 7/11/2020 12:54 AM, Alan Grayson wrote:
On Tuesday, July 7, 2020 at 10:06:44 PM UTC-6,
Alan Grayson wrote:
On Tuesday, July 7, 2020 at 8:50:50 PM
UTC-6, Alan Grayson wrote:
On Tuesday, July 7, 2020 at 8:05:28 PM
UTC-6, Bruce wrote:
On Wed, Jul 1, 2020 at 4:18 PM
Alan Grayson <[email protected]>
wrote:
How, exactly, is the Principle
of Equivalence used by
Einstein to develop GR? TIA, AG
This lecture by Sean Carroll
should answer all your questions:
URL: https://wp.me/p2WMeM-3vl
Bruce
I'll watch it tonight, but I think
I've figured it out; specifically, the
EP implies space-time is curved by the
presence of mass/energy (and this is
independent of the need to express the
laws of physics in a coordinate
independent way via tensors). AG
Here's my reasoning regarding the EP; if
an observer is in a box subject to uniform
acceleration, a beam of light starting on
the extreme left side (moving transverse
or perpendicular to the acceleration
vector), will hit a lower point on the
right side, showing that uniform
acceleration results in curved paths in
space-time. But if this result is
identical to gravity, locally, it means
that curved paths in space-time are
produced by, or are equivalent to gravity.
That makes no sense. You're saying that
because curved paths can be produced two
different ways then they must always be
produced the second way.
BUT gravity is only observed in the
presence of mass/energy. ERGO, the EP
implies mass/energy curves space-time. AG
And that's not even true. Gravitational waves
can propagate thru the vacuum. The
Schwarzschild solution is for empty space. De
Sitter space is an empty cosmos.
Light can propagate through empty space, but it
can't arise from nothing. Same presumably for
gravitational waves. AG
Are you going to say the same thing about matter?
electric charge?
Brent
I'm not sure what your point is. All I was saying above
is that mass/energy causes curvature of space-time as
per the EP. A gravitational wave moving through empty
space seems no different in principle than light moving
through empty space. In both cases there is a
mathematical solution for the wave motion, with the
source of the wave left undefined. But every wave motion
must has a source. AG
And every source must have an origin? There is nothing
in the equations that says there must be a source.
Brent
Can EM waves exist if there are no charges and currents? If
you affirm, has this ever been observed? This result, if it
is a result, is likely an artifact of the mathematics which
has no basis in physical reality. Anyway, are you claiming
that spacetime curvature can exist in the absence of
matter/energy? Is this what the EP says? AG
It's what the equations say. So if waves only exist due to
matter sources that's a separate fact, not part of the
theory. It seems just as plausible to me that fields existed
first and "stuff" appeared as quantized waves in the fields.
Brent
What do you find erroneous in my interpretation of the EP? I never
heard it interpreted to mean that curvature of space-time is NOT
caused by gravity. AG
Are you claiming that because there are gravitational wave solutions
to GR in the absence of matter/energy, curvature of space-time isn't
caused by, or is equivalent to gravity? But how can there be curvature
of space-time in the absence of matter/energy
There can be because it's consistent with the equations. A black hole
doesn't include any matter. General relativity is non-linear, that's
why there can be non-flat cosmologies that contain no matter. Of course
there may be some different, better theory in which spacetime can't be
curved without matter...but it seems unlikely since we have good
evidence that gravitational waves exist.
Brent
since, in this case, we're dealing with SR, wherein space-time has no
curvature? AG
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