Einsteins field equation

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syhprum

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Einsteins field equation
« on: 04/01/2013 21:28:16 »
The complexities of special relativity are way beyond me but it seems it can be simplified to one special equation 8*pi*G/c^4 that can be further simplified by setting G=c=1 hence it becomes 8*pi, what is this telling us about the real universe ?

Correction
I meant General relativity of course I can just about get my head around special
« Last Edit: 05/01/2013 20:30:43 by syhprum »
syhprum

Pmb

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Re: Einsteins field equation
« Reply #1 on: 04/01/2013 22:25:26 »
The complexities of special relativity are way beyond me but it seems it can be simplified to one special equation 8*pi*G/c^4 that can be further simplified by setting G=c=1 hence it becomes 8*pi, what is this telling us about the real universe ?

I'm not sure what you mean by "telling us about the real universe" since that's quite a metaphysical thing to say. All Einstein's field equiations do is relate matter to spacetime curvature.

CliffordK

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Re: Einsteins field equation
« Reply #2 on: 05/01/2013 00:00:12 »
This seems better suited to new theories.

c, of course, is a constant, 299,792,458 m/s = 3.00 x 108 m/s
G is also a constant, but much smaller.  6.67 x 10-11 $$\frac{m^3}{kgs^2}$$
$$\pi$$ is also a constant, 3.14159....

You can certainly change your base to whatever you wish.  However, you can't magically do a change of base that would make them all the same.

You could, of course, create a new constant, call it Syhprum's constant,
S = $$\frac{8\pi G}{c^4}$$ = $$\frac{8 x 3.14 x 6.67 x 10^{-11}}{(3 x 10^8)^4}$$ = 2.077 x 10-43

Which is a very small number.  You could then transform all your math to be base 2.077 x 10-43, but no doubt some previously simple tasks such as counting from 1 to 10 become far more complicated.

Pmb

• Neilep Level Member
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Re: Einsteins field equation
« Reply #3 on: 05/01/2013 02:18:31 »
This seems better suited to new theories.

c, of course, is a constant, 299,792,458 m/s = 3.00 x 108 m/s
G is also a constant, but much smaller.  6.67 x 10-11 $$\frac{m^3}{kgs^2}$$
$$\pi$$ is also a constant, 3.14159....

You can certainly change your base to whatever you wish.  However, you can't magically do a change of base that would make them all the same.

You could, of course, create a new constant, call it Syhprum's constant,
S = $$\frac{8\pi G}{c^4}$$ = $$\frac{8 x 3.14 x 6.67 x 10^{-11}}{(3 x 10^8)^4}$$ = 2.077 x 10-43

Which is a very small number.  You could then transform all your math to be base 2.077 x 10-43, but no doubt some previously simple tasks such as counting from 1 to 10 become far more complicated.
I don't understand what you mean by the term "base". Please explain. syhprum was refering to the system of units which is often used in relativity in which Einstein's field equations reads

G = 8piT

What point were you trying to make?

CliffordK

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Re: Einsteins field equation
« Reply #4 on: 05/01/2013 02:43:53 »
Perhaps I'm missing something, but G & c are both typically constants, so they can't be just set to be equal to 1.

Typically we count in base 10 (numbers 0,1,2,3,4,5,6,7,8,9,10,...)
Computers work in binary (base 2) and various conversion schemes (0,1,10,11,100,101,110,111,1000,1001...)
One can also count in octal (0,1,2,3,4,5,6,7,10,11,12,13,14,15,16,17,20,...)
Or hexidecimal (0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F,10,11,12,13,14,15,16,17,18,19,1A,1B,1C,...)

Technically the base can be any number one wants, although the conversion to an irrational number would be tricky, but not technically impossible.

Distance is often written in many different units.  Don't like one, try another.

Angstrom
microns, nm, mm, cm, meters, km, etc.
AU
light year

and etc.

Changing your units, and you can simplify things, as long as you don't get too confused with the units.

For example, if you wished to know the area of the circle inscribed by Earth's orbit, πr2 (assuming a circular orbit).  If you do the calculations in meters, one gets a really big number.

However, in AU, it is simply π(1AU)2 = πAU2

I suppose since c is expressed in meters and seconds.
and G is expressed in kg, meters, and seconds.

Then one could transform it so one now expresses c in a new unit, say CM which is defined as 3x108m, so the speed of light is now 1 CM/s.

Then you define G in terms of your new CM unit, time, and some funky weight unit.

But, of course, you have to always maintain the units as part of your equation, and the calculations come out the same.
« Last Edit: 05/01/2013 09:50:09 by CliffordK »

Spacetectonics

• Full Member
• 85
Re: Einsteins field equation
« Reply #5 on: 05/01/2013 08:27:30 »
This seems better suited to new theories.

c, of course, is a constant, 299,792,458 m/s = 3.00 x 108 m/s
G is also a constant, but much smaller.  6.67 x 10-11 $$\frac{m^3}{kgs^2}$$
$$\pi$$ is also a constant, 3.14159....

You can certainly change your base to whatever you wish.  However, you can't magically do a change of base that would make them all the same.

You could, of course, create a new constant, call it Syhprum's constant,
S = $$\frac{8\pi G}{c^4}$$ = $$\frac{8 x 3.14 x 6.67 x 10^{-11}}{(3 x 10^8)^4}$$ = 2.077 x 10-43

Which is a very small number.  You could then transform all your math to be base 2.077 x 10-43, but no doubt some previously simple tasks such as counting from 1 to 10 become far more complicated.
I don't understand what you mean by the term "base". Please explain. syhprum was refering to the system of units which is often used in relativity in which Einstein's field equations reads

G = 8piT

What point were you trying to make?

I think syhprum is looking for a numeric system like this(for the base):

A= 0,A = 1,A = 2,A =3,A=4,A=5,A=6,A=7,A=8,A=9 ,A = Infinity when A0 to A9 are equal and IF Degree of “A” spin between 0-360 Degrees in X,Y,Z plane, Clockwise and counterclockwise respectively."A" will be equal to infinity(and Time) when it heads outside any of these planes regardless of its direction.

How this system fits into your equation?!

Regards

JP

• Neilep Level Member
• 3366
Re: Einsteins field equation
« Reply #6 on: 05/01/2013 15:46:34 »
Perhaps I'm missing something, but G & c are both typically constants, so they can't be just set to be equal to 1.

But as you noted, you can change units to set both equal to one.  I suspect that's what Simplified was pointing out, and its what Pmb noted in the equation he posted above.

Pmb

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• Physicist
Re: Einsteins field equation
« Reply #7 on: 05/01/2013 20:13:54 »
Perhaps I'm missing something, but G & c are both typically constants, so they can't be just set to be equal to 1.
Its always possible to choose a system of units such that c = 1 and G = 1. Relativists use this system of units.

Measures time in seconds . Measure distance in light-seconds where 1 light-second is the distance light travels in 1 second. It then follows that c = 1. A similar argument holds for G.

Such a system of units in which G = c = 1 is called "geometerized units".

http://en.wikipedia.org/wiki/Geometrized_unit_system

Here is an example of a gravitational field with zero spacetime curvature
http://home.comcast.net/~peter.m.brown/gr/grav_cavity.htm

Since the field inside the cavity is uniform there are no tidal forces and since there are no tidal forces there is no spacetime curvature.

syhprum

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Re: Einsteins field equation
« Reply #8 on: 06/01/2013 10:29:51 »
Many thanks for the links I can just about 1% of general relativity now!
syhprum