I think I've constructed a numerical system that places a value on most every unit of measurement and those values change as the universe ages. I call it "The System of Universal Angles" and it goes like this:
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1) Every number in this system represents the A angle of a triangle, the A point represents a hypothetical "location" for the Big Bang and the a side represents the observed measurement between points B and C.
2) I assumed that the age of the universe (visible horizon) was equal to 180 degrees - a.k.a., a line.
3) I assumed that anything that can be observed has a value greater than (<) 0 degrees - 0 degrees being a point or line.
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If we assume that the age of the universe is percisely 13.7Gyrs old then:
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One billion light years will equal 13.13868613 deg. (uA1Gly)).
One second will equal 4.166250042e-16 deg (uA1(sec)).
One mile will equal 2.236523745e-21 deg (uA1(mi))
One meter will equal 1.389711426e-24 deg (uA1(m)).
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These values can be expressed as:
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180/uA1(Gly)=13.7Gly old/long
180/uA1(sec)=4.320432e+17 seconds old
180/uA1(m)=1.295232928e+26 meters long
uA1(sec)/uA1(m)=299,792,458 m/s
uA1(sec)/uA1(mi)=186,282.397 mi/s
uA1(mi)/uA1(m)=1,609.344 m/mi
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What this does is give a ratio that shows the relationship between like units but, like I said before, these numbers also change with time.
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If you were looking at an object 1Gly away then you would be observing our universe as it was one billion years ago. The ratio between the uAs of that timeframe (180=12.7Gly) and our current timeframe (180=13.7Gly) can be used to determine the recession velocity and cosmological red-shift of that observed object.
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2(a/x)^1/2-2=Z
c/(a/r)=H
1-1/(Z+2/2)^2a=r
1-1/(Z+2/2)^2c=H
a/x=past uA1/equivalent future uA1
a/r=1/1-(x/a)
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Where:
a=distance to observers visible horizon
r=distance to observed object
x=a-r
c=speed of light
Z=Cosmological red-shift
H=Hubble's constant
.
1) Every number in this system represents the A angle of a triangle, the A point represents a hypothetical "location" for the Big Bang and the a side represents the observed measurement between points B and C.
2) I assumed that the age of the universe (visible horizon) was equal to 180 degrees - a.k.a., a line.
3) I assumed that anything that can be observed has a value greater than (<) 0 degrees - 0 degrees being a point or line.
.
If we assume that the age of the universe is percisely 13.7Gyrs old then:
.
One billion light years will equal 13.13868613 deg. (uA1Gly)).
One second will equal 4.166250042e-16 deg (uA1(sec)).
One mile will equal 2.236523745e-21 deg (uA1(mi))
One meter will equal 1.389711426e-24 deg (uA1(m)).
.
These values can be expressed as:
.
180/uA1(Gly)=13.7Gly old/long
180/uA1(sec)=4.320432e+17 seconds old
180/uA1(m)=1.295232928e+26 meters long
uA1(sec)/uA1(m)=299,792,458 m/s
uA1(sec)/uA1(mi)=186,282.397 mi/s
uA1(mi)/uA1(m)=1,609.344 m/mi
.
What this does is give a ratio that shows the relationship between like units but, like I said before, these numbers also change with time.
.
If you were looking at an object 1Gly away then you would be observing our universe as it was one billion years ago. The ratio between the uAs of that timeframe (180=12.7Gly) and our current timeframe (180=13.7Gly) can be used to determine the recession velocity and cosmological red-shift of that observed object.
.
2(a/x)^1/2-2=Z
c/(a/r)=H
1-1/(Z+2/2)^2a=r
1-1/(Z+2/2)^2c=H
a/x=past uA1/equivalent future uA1
a/r=1/1-(x/a)
.
Where:
a=distance to observers visible horizon
r=distance to observed object
x=a-r
c=speed of light
Z=Cosmological red-shift
H=Hubble's constant
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