=R4C= IS THE "SMALL WORLD" A CONFORMAL METRIC ?

[George Hammond]

On Mon, 14 May 2012 14:23:43 CST, "Ken S. Tucker"
<dyna...@rocketmail.com> wrote:

[George Hammond]
NOTE...
.Pursuant to a hunt for the scientific explanation of the
age old phemomena of "God", the author has discovered that
human perception of reality (aka space-time) during
childhood growth can be described subjectively as if the
person remained the same size and intelligence (mental
speed) all his life, and it was the "world" that actually
got smaller and slower rather than the person simply getting
bigger and faster.
This leads the author to believe that it would
perceptually APPEAR as if the World (Universe) was
undergoing a CONFORMAL CONTRACTION according the the well
known conformal-metric of Standard Cosmology:

ds^2 = a(t) [dt^2 - dR^2] FLRW Conformal Metric

where in this case a(t) = 1/g(t) where g(t) is simply the
Human Growth Curve well known to testbook Biology.
Note that there is NO REAL physical contraction of real
spacetime... the contraction (and slowing down) of
space-time is only APPARENT, OR VISUAL OR PERCEPTUAL ...
EVEN "VIRTUAL" IF YOU WILL. So this is a "PSYCHOLOGICAL
METRIC" not a real physical metric... terefore the metric
does not have to obey:

1.. Einstein's Field Equations
2. Conservation of energy
3. Special Relativity
4. Hubble redshift

NEVERTHELESS.... the metric is of overwhelming importance
to the theory of "God" because there is reason to belive
that the "contraction of the Universe" which is supposed to
fall to a(t) = 1 at age 18 (adulthood) never actually gets
there, dropping to about only 1.25 for the average person
leaving the world permanently, terminally 25% "bigger and
faster" than it should be.... and that this biological,
perceptual, indeed Relativistic fact... EXPLAINS THE AGE OLD
PNENOMENA OF "GOD".

IF ANY READER KNOWLEGEABLE OF THE FLRW CONFORMAL METRIC
OR "WEYL GAUGE TRANFORMATIONS" HAS ANY INTUITION ON THIS
SUSPICION YOUR COMMENTS WOULD BE OF CONSIDERABLE INTEREST

>
>[Ken S. Tucker]
>George, make sure you're cognizant of H. Weyls efforts on
>gauge variation that is regarded as mathematical genius was
>difficult physically in reality, I spent a few years sniffing
>his "lambda" to vary invariants, and is apparently an unnecessary
>departure from reality.
>Regards
>Ken S. Tucker
>
>
[George Hammond]
Hi Ken, sorry I didn't recognize the significance of your
post the first time around.
However exactly as you said, Weyl's 1920 "Gauge Theory"
may have significance for my scientific problem.
I am investigating an FLRW type of conformal metric:

ds^2 = a(t) [dt^2 - dR^2] "FLRW Conformal Metric"

where dR^2 = [dx^2 + dy^2 + dz^2]

note that unlike FLRW, a(t) in this "conformal metric" now
multiplies not only the spatial part dR, but also the time
part dt. This makes it similar to a "Weyl Gauge
Transformation" type of metric.... g' ----> Lambda g
Weyl’s Conformal Factor "Lambda" of course was not merely
a function of t as it is in this Conformal Metric, but was
also a function of xyz which made it "path dependant" and
ultimately led to the denouement of his theory. Obviously
with a(t) being only a function of time the Conformal Metric
does not have that problem.
This Conformal Metric is in fact well known to standard
Cosmology where it crops up if a time scale substitution
n=a(t) t is inserted into the standard FLRW metric. While
this is merely a change of time coordinate and physically
meaningless; what I am talking about is a space-time
manifold where the Conformal Metric is actually physically
real. (and that incidentally is what Weyl was talking about
also).
Obviously if the Conformal Metric were real, it cannot be
describing real space-time, since the Conformal Metric,
unlike the FLRW, is not a solution to Einstein's Field
Equations.... in fact I don't know if it even obeys SR,
never mind GR !
But anyway.... in view of Weyl’s famous theory, there
must be a lot known about "conformal Metrics" of the type:

a(t) [ dt^2 - dR^2]

and since you said you investigated Weyl's theory can I ask
you a few questions about this particular metric:

1. We know that if a(t) is a positive increasing function
of time, that a(t) multiplying dR causes a physically
"expanding" universe (e.g. the Hubble expansion).
My question then is, am I right that this same
a(t) multiplying dt will then describe a universe
where any peculiar local activity, if any, will
appear to be "speeded up" as a(t) increases?
I assume that this is true because for instance
a decreasing factor in the Schwarzschild metric
multiplying dt is well known to make an atronought
appear to "slow down" as he approaches the
Schwarzschild radius of a Black Hole.
IOW, am I CORRECT when I assume that the
Conformal Metric causes the Universe to get
"bigger and faster" as a(t) increases, and conversely
"smaller and slower" as a(t) decreases ?
It would be nice if someone could confirm that
I have the right metric ?

2. Are there any books or papers connected with Weyl’s
work which discuss the metrical properties of a
Conformal Metric as regards it's effect on a space and
time dilation as I have described.
And in particular: Does the Conformal Metric obey
SR.... i.e..... ds is obviously zero for a light ray
since the metric simply says that the speed of light
is always 1 irregardless of a(t) just as it is in the
simple Lorentz Metric. But does the Lorentz
transformation still hold in the case of a Conformal
Metric such as:
a(t) [ dt^2 - dR^2] ?

Thanks in advance for your comments.

George Hammond