[Ethos]

I believe the following equation has some merit, what do you folks think?

[(hbar*c/e^2)^3]*[(hbar*c/G^3)^3] = (pi^3 * 10^20)

[DoctorBeaver]

erm...

[JP]

Uh.... I think your units are off to say the least.

[Ethos]

Uh.... I think your units are off to say the least.

Please point out which units sir. This equation is balanced and dimensionless and is satisfied both in cgs and SI units. If you have a mind, please solve for G and tell me what your results are...........Ethos

[JP]

I'm assuming e is the electron charge.  The constants hbar, c and G don't have units of charge to cancel that out.

[Ethos]

Yes, e stands for the electron charge. However, hbar times c divided by e squared is the fine structure constant to the minus 1.

(hbar * c/e^2)= approx. 137
(hbar * c/e^2)raised to the third power equals: 2.57338006 E6

[(hbar * c/e^2)]^3 * [(hbar * c/G^3)]^3 = (pi^3 * 10^20)

moving (pi^3 * 10^20) to the left denominator and G^9 to the right numerator,

we have: [(hbar * c/e^2)]^3 times [(hbar * c * pi-1)^3]/10^20] = G^9

         [2.57338006 E+6]  X  [1.019159191E-71] = 2.6226839407 E-65

taking 2.6226839407E-65 to the ninth root we get: 6.6727538776 E-8 in cgs units

Because (hbar * c/e^2) is dimensionless and,
because (hbar * c/G^3) is dimensionless,

this equation works just as well when done in SI units.

6.6727538776 E-8 in cgs units and 6.6727538776 E-11 in SI units agrees very closely with NIST figures.

[Ethos]

I'm assuming e is the electron charge.  The constants hbar, c and G don't have units of charge to cancel that out.

Understanding so little about gravity, how can we be sure that the graviton has no significant charge. Charged particles bend space time because they posess magnetic fields. Even though gravity does not bend space time to the same extent per supposed particle, gravity does bend it. That being said, are we being premature in judging gravity to have no charge?

Understanding that there is no space empty of field, and the bending of space time is accomplished by both the electromagnetic and gravitational forces, I suspect that to assume gravity to have no charge is short sighted. We must honestly ask ourselves these question:

What is charge anyway?
And if magnetism and gravity both bend space-time, why should they be considered so different? Maybe it's only a question of magnitude and local stimuli....................Ethos

[JP]

Ok.  If you're working in the proper units, you can write the fine structure constant in that way.  If that's the case, the second term needs to also be dimensionless.  I'm confused as to how it gets so.  Let's just check it in SI:

hbar ~ J-s = kg m²s^-1
c ~ m s^-1
G^-3 ~ m^-9kg³s⁶,

so:
hbar c G^-3 = (kg m²s^-1)( m s^-1)(m^-9kg³s⁶)=(kg s)⁴m^-6,

which isn't dimensionless.

[Ethos]

Wouldn't hbar ~ J-s = Kg m²s^-2

[JP]

J-s means J*s, which is the units for hbar, and I'm using * to denote multiplication.  1 Joule is 1 kg m²s^-2, so 1 J*s= kg m²s^-1

[syhprum]

erm  []

[Ethos]

Yes, e stands for the electron charge. However, hbar times c divided by e squared is the fine structure constant to the minus 1.

(hbar * c/e^2)= approx. 137
(hbar * c/e^2)raised to the third power equals: 2.57338006 E6

[(hbar * c/e^2)]^3 * [(hbar * c/G^3)]^3 = (pi^3 * 10^20)

moving (pi^3 * 10^20) to the left denominator and G^9 to the right numerator,

we have: [(hbar * c/e^2)]^3 times [(hbar * c * pi-1)^3]/10^20] = G^9

         [2.57338006 E+6]  X  [1.019159191E-71] = 2.6226839407 E-65

taking 2.6226839407E-65 to the ninth root we get: 6.6727538776 E-8 in cgs units

Because (hbar * c/e^2) is dimensionless and,
because (hbar * c/G^3) is dimensionless,

this equation works just as well when done in SI units.

6.6727538776 E-8 in cgs units and 6.6727538776 E-11 in SI units agrees very closely with NIST figures.

Remembering that (hbar * c/e^2) is dimensionless, the first part of the equation will remain the same whether figured in cgs or SI units. Now plug in the values in the second part of the equation with SI values and you'll find the answer for G will also be registered in SI values. This should prove that (hbar * c/G^3) is also dimensionless. Be my guest and do the math yourself.

If this interests you, I have something even more interesting to share........Ethos

[Ethos]

An even easier exersize would be to figure (hbar * c/G^3) using both cgs units and SI units. If both computations are equal, then this equation is dimensionless.

Let's try in cgs: (1.054572669 E-27 * 2.99792458 E10/(6.67275E-8)^3 = 1.064098E5

Now in SI: (1.054572669E-34 * 2.99792458E8/(6.67275E-11)^3 = 1.064098E5

Looks like a dimensionless relationship to me....................Ethos

[Vern]

Very interesting Ethos; I'm assuming your maths correct; what is the implication? Have you shown a relationship that was not previously known? Are you showing a new relationship between gravity and the electromagnetic field?

[lightarrow]

Remembering that (hbar * c/e^2) is dimensionless, the first part of the equation will remain the same whether figured in cgs or SI units.

No, hc/e² is dimensionless in c.g.s. only. In M.K.S. the dimensionless expression is 4πε₀hc/e².

Now plug in the values in the second part of the equation with SI values and you'll find the answer for G will also be registered in SI values. This should prove that (hbar * c/G^3) is also dimensionless.

No, that expression is not dimensionless neither in c.g.s. nor in M.K.S.

[Ethos]

Remembering that (hbar * c/e^2) is dimensionless, the first part of the equation will remain the same whether figured in cgs or SI units.

No, hc/e² is dimensionless in c.g.s. only. In M.K.S. the dimensionless expression is 4πε₀hc/e².

Now plug in the values in the second part of the equation with SI values and you'll find the answer for G will also be registered in SI values. This should prove that (hbar * c/G^3) is also dimensionless.

No, that expression is not dimensionless neither in c.g.s. nor in M.K.S.

Dimensionless is a term equal to a ratio, and when changing from cgs to SI, if the ratio does not change, then the equation is dimensionless. If you'll do the math, you'll find that the results are approiate for both cgs and SI units. Whether you agree that these initial terms are dimensionless or not, math does not lie and the ratio stays the same.

[lightarrow]

Dimensionless is a term equal to a ratio, and when changing from cgs to SI, if the ratio does not change

Who told you that it doesn't change? hc/e² ≈ 137 in c.g.s. while it's ≈ 1.24*10¹² J*m*C^-2 = 1.24*10¹² kg*m³*A^-2*s^-4 in M.K.S..

[Ethos]

Dimensionless is a term equal to a ratio, and when changing from cgs to SI, if the ratio does not change

Who told you that it doesn't change? hc/e² ≈ 137 in c.g.s. while it's ≈ 1.24*10¹² J*m*C^-2 = 1.24*10¹² kg*m³*A^-2*s^-4 in M.K.S..

I'll grant you that, but I'm referring to (hbar c/G^3) not changing. All three values have their cgs and SI counterparts. Now for those that don't like me using (hbar c/e^2) in this equation, let's use this equation instead: (hbar c/(re me c^2)) All values in this equation have their cgs and SI counterparts.

[hbar c/(re, me, c^2)]^3 * [hbar c/G^3]^3 = pi^3 *10^20

All values in the above formula have their cgs and SI counterparts. If you'll do the math, using cgs units wil produces G in cgs. Likewise, using SI units will produces G in SI.

[Ethos]

Very interesting Ethos; I'm assuming your maths correct; what is the implication? Have you shown a relationship that was not previously known? Are you showing a new relationship between gravity and the electromagnetic field?

Yes, but untill we can reach an understanding about the equation I'm using, it would be of little use to expound upon it. Thanks for the interest..................Ethos

[JP]

Now for those that don't like me using (hbar c/e^2) in this equation, let's use this equation instead: (hbar c/(re me c^2))

Why don't you just call that first term α^-1, the inverse of the fine structure constant, which is dimensionless?  But even if you do that, it doesn't change the fact that the second term has the wrong units and is not dimensionless.  Having the same value in c.g.s. and SI does not mean something is dimensionless.  Any quantity with units of mass²/distance³ will have the same value in c.g.s. and SI, but it has dimensions.  Take for example:
1 kg²/m³=1 g²/cm³=10⁶g²/m³=10^-6kg²/cm³