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by **FrediFizzx** » Thu Feb 26, 2015 12:22 am

Yablon wrote:
FrediFizzx wrote:...There is one thing we are certain of in CE is that k_e/k_m = c^2. ... So for the force of electric charge quantum we have,

$F = k_{e} e^2/r^2,$

and for the force between hypothetical magnetic charge quantums,

$F = k_{m} g^2/r^2.$ Fred

Fred,

Why not just give k_e and k_m the same dimensionality k_e/k_m = 1 and then e and g have the same dimensionality? And then g is just the magnetic charge $\mu$ in the DQC.

Well in H-L units, you still have k_e = 1/4pi = k_m if you do that. But if you set c = 1 then e = g so that is OK. But magnetic charge ends up being,

$g = 2\mu \alpha/n$

So magnetic charge, g, does end up with the same dimensions as magnetic flux $,\mu,$ in that case. And if $\hbar = \epsilon_{0} = 1$ also, then g, mu and e are all dimensionless but it doesn't mean they are all the same thing.

Fred

by **Yablon** » Wed Feb 25, 2015 9:05 pm

FrediFizzx wrote:...There is one thing we are certain of in CE is that k_e/k_m = c^2. ... So for the force of electric charge quantum we have,

$F = k_{e} e^2/r^2,$

and for the force between hypothetical magnetic charge quantums,

$F = k_{m} g^2/r^2.$ Fred

Fred,

Why not just give k_e and k_m the same dimensionality k_e/k_m = 1 and then e and g have the same dimensionality? And then g is just the magnetic charge $\mu$ in the DQC.

Jay

by **FrediFizzx** » Wed Feb 25, 2015 8:54 pm

Hi Jay,

Well, in classical electrodynamics it is actually g = q*c but with q = e, the electric charge quantum, we should get the hypothetical magnetic charge quantum. There is one thing we are certain of in CE is that k_e/k_m = c^2. IOW, the electric constant divided by the magnetic constant is equal to c^2. So for the force of electric charge quantum we have,

$F = k_{e} e^2/r^2,$

and for the force between hypothetical magnetic charge quanta,

$F = k_{m} g^2/r^2.$

Now in H-L units, k_e = 1/4pi and k_m = k_e/c^2 = 1/4pi c^2. So make those replacements and set the two equations equal and you get,

$e^2 = g^2/c^2$ --> $e c = g$

I suppose a question here would be why are the two force equations equal? No particular reason; we are forcing them to be equal so that g will be in terms of e and c. It has nothing at all to do with fields.

Fred

by **Yablon** » Wed Feb 25, 2015 8:08 pm

FrediFizzx wrote:... I showed earlier in this thread that magnetic charge is g = ec in CGS units.

Fred,

You did say that, but please explain or provide a reference as to why $g=ec$ . (Magnetic) charge = (electric) flux times velocity (of light). That is what I am not seeing or not familiar with.

Is this somehow related to the field strength bivector:

$cF^{\mu \nu } =\left(\begin{array}{cccc} {0} & {-E_{x} } & {-E_{y} } & {-E_{z} } \\ {E_{x} } & {0} & {-cB_{z} } & {cB_{y} } \\ {E_{y} } & {cB_{z} } & {0} & {-cB_{x} } \\ {E_{z} } & {-cB_{y} } & {cB_{x} } & {0} \end{array}\right)$ ?

If so, how?

I also found a neat 6x6 table at http://en.wikipedia.org/wiki/Dimensiona ... anck_units, but I do not see (Magnetic) charge = (electric) flux times velocity (of light) there.

Jay

by **FrediFizzx** » Wed Feb 25, 2015 7:01 pm

Hi Jay,

Oops sorry, I think I put the n in the wrong place on the LHS so it is messed up.

Ok, referring to Dirac's paper on page 68, he shows for magnetic flux,

$\mu = n \hbar c/2 e.$

He is using Gaussian-CGS units where $\alpha = e^2/\hbar c$ not your Heaviside-Lorentz (H-L, another commonly used unit system) units of $\alpha = e^2/4\pi \hbar c.$ I showed earlier in this thread that magnetic charge is g = ec in CGS units. So rearranging the above equation,

$2 \mu e/n \hbar = c$

Then multiply both sides by e,

$2 \mu e^2/n \hbar = e c$

Gives us,

$g = 2 \mu e^2/n \hbar = e c$ in CGS units or in CGS natural units $ng = 2 \mu e^2 = n e.$

So now to convert to your H-L units. g is still equal to ec in H-L units so going thru the same procedure as we did for CGS units above,

$g = \mu e^2/n 2\pi \hbar = 2 \mu \alpha c/n = e c$

Then multiply thru by n/c,

$\mu e^2/ 2\pi \hbar c =2 \mu \alpha = ne = n g/c.$ In your H-L units which you have correct.

Fred

by **Yablon** » Wed Feb 25, 2015 3:00 pm

FrediFizzx wrote:... Magnetic charge is,

$g = 2 n \mu e^2 = 8\pi n \mu\alpha = n e$ .

Fred,

The bottom line calculation I get for $ne$ with $\hbar$ and $c$ included is:

$\mu e^{2} /2\pi \hbar c=2\mu \alpha =ne$

I have been scratching my head as to how you equate this to magnetic charge.

Jay

by **FrediFizzx** » Wed Feb 25, 2015 2:12 pm

Hi Jay,

I don't ever use that SI units (weber convention). Don't know what it is really. I have my MathCad program setup for regular SI units or Gaussian-CGS units as they are the most common for physics besides natural units of $\hbar = c = 1$ or $\hbar = c = \epsilon_{0}=1.$ The last one is the natural units you use in your paper since you specify $\alpha = {e^2}/{4\pi \hbar c}.$ or in your natural units $\alpha = {e^2}/4\pi.$

So in your natural units magnetic flux is,

$\Phi_{B} = \mu = 2\pi n /e$

Magnetic charge is,

$g = 2 n \mu e^2 = 8\pi n \mu\alpha = n e$ This is wrong; see below.
.

by **Yablon** » Wed Feb 25, 2015 1:26 pm

FrediFizzx wrote:Hi Jay,

That can't be right. Magnetic flux in CGS units has the same dimensions as electric charge, cm^1.5 gm^0.5 sec^-1. Your mistake is in eq. (2). $\mu$ is magnetic flux. It should be,

$\Phi_{B}=\mu=\frac{2\pi n \hbar c}{e}$

Which we can see the units are right since hbar*c is charge^2 divided by charge gives units of charge.

Fred,

I agree something is amiss. Go to http://en.wikipedia.org/wiki/Magnetic_m ... antization, middle box, SI Weber. That is what I used for flux because it removes the $c$ from the denominator as you did with your derivation. There must be something hidden in that which I do not see. This is why I just stick with natural units all the time to avoid the arcane details of different systems of units.

Jay

by **FrediFizzx** » Wed Feb 25, 2015 12:34 pm

Hi Jay,

That can't be right. Magnetic flux in CGS units has the same dimensions as electric charge, cm^1.5 gm^0.5 sec^-1. Your mistake is in eq. (2). $\mu$ is magnetic flux. It should be,

$\Phi_{B}=\mu=\frac{2\pi n \hbar c}{e}$

Which we can see the units are right since hbar*c is charge^2 divided by charge gives units of charge.

by **Yablon** » Wed Feb 25, 2015 7:51 am

FrediFizzx wrote:Hi Jay,

Putting magnetic charge in terms of the magnetic flux quantum we have,

$g=\frac{2\mu e^{2}}{\hbar}=2\mu c \alpha=e c.$

So I think the DQC is relativistic as can be seen when we go to the fine structure constant in the formula. And even though the magnetic flux quantum seems to be stronger in relation to a quantum of electic charge, magnetic charge quantum is equal to electric charge quantum when $\hbar = c =1.$

Hi Fred,

This is how I would do your calculation:

Start with the DQC in SI units:

$e\mu =2\pi n\hbar c$ (1)

Divide through to isolate $nc$ on the right, which puts everything into units of magnetic flux (Weber) denoted $\Phi _{B}$ :

$\Phi _{B} =\frac{e\mu }{2\pi \hbar } =nc$ (2)

Multiply through by $e$ to obtain:

$\Phi _{B} e=\frac{\mu e^{2} }{2\pi \hbar } =nce$ (3)

The squared electric charge is related to the dimensionless fine structure number $\alpha$ (1/137.036 at low probe) by:

$4\pi \hbar c\alpha =e^{2}$ (4)

Use this in (3) to finally obtain:

$g=\Phi _{B} e=2\mu c\alpha =\frac{\mu e^{2} }{2\pi \hbar } =nce$ (5)

This gives us your $g=\Phi _{B} e$ which is a magnetic flux times the electric charge strength. I am not sure of your interpretation of this in relation to $ce$ all the way on the right. The main thing I read out of (5) after dividing out $e$ is:

$g/e=\Phi _{B}=nc$ (5)

which tells me that the magnetic flux is an integer times the speed of light.

Jay

by **FrediFizzx** » Wed Feb 25, 2015 12:08 am

Of course in our non-relativistic world, since magnetic charge is electric charge cranked up by the speed of light, then maybe Dirac was right. Magnetic poles are too hard to separate. :-)

by **FrediFizzx** » Sun Feb 22, 2015 3:12 pm

Hi Jay,

Putting magnetic charge in terms of the magnetic flux quantum we have,

$g=\frac{2\mu e^{2}}{\hbar}=2\mu c \alpha=e c.$

So I think the DQC is relativistic as can be seen when we go to the fine structure constant in the formula. And even though the magnetic flux quantum seems to be stronger in relation to a quantum of electic charge, magnetic charge quantum is equal to electric charge quantum when $\hbar = c =1.$
.

by **Yablon** » Sun Feb 22, 2015 7:45 am

FrediFizzx wrote:So... the DQC does not ruin what I originally thought about magnetic charge. A photon sees electric charge as magnetic charge since g = q*c. Magnetism is a relativistic effect. Now... how does this relate to the DQC?

Fred,

I would think of the DQC as a nonrelativistic form of magnetism which emerges out of the fact that charge is quantized. Keep in mind, Maxwell's equations contain no net magnetic flux through any closed surface. But neither do they require that charge be quantized.so the quantization of charge goes hand-in-hand with the existence of monopoles, if you take the DQC strictly at face value. My own work refines that view somewhat, because under all conditions where the DQC is not actually observed, which is to say when the temperature is not near absolute zero, the charge quantum number of the DQC turns into the principal quantum number for electrons in atomic shells and goes from representing charge quantization to representing energy quantization.

Jay

by **FrediFizzx** » Sun Feb 22, 2015 12:07 am

So... the DQC does not ruin what I originally thought about magnetic charge. A photon sees electric charge as magnetic charge since g = q*c. Magnetism is a relativistic effect. Now... how does this relate to the DQC?

by **FrediFizzx** » Sat Feb 21, 2015 12:29 am

Thanks Jay,

OK, problem solved. Mu is not magnetic charge; it is magnetic flux in the CGS units that Dirac is using. And that is what he says it is in the paper on page 68. It just so happens that in CGS units magnetic flux and electric charge have the same dimensions. Easy to see since hbar*c = (electric charge)^2 so hbar*c/e = electric charge. Or... in this case magnetic flux.

by **Yablon** » Fri Feb 20, 2015 8:12 pm

FrediFizzx wrote:Hi Jay,

That doesn't really help. In the limit of hbar --> 0, we should be able to recover the classical electrodynamic result of magnetic charge being electric charge times the speed of light. Do you happen to have Dirac's original derivation for the DQC that you could email me? Thanks.

Hi Fred:

Actually, Dirac's paper is posted online at http://rspa.royalsocietypublishing.org/ ... l.pdf+html. As it happens, I have been very closely re-studying this paper over the last week and am going to add a new section to my paper which very carefully relates Dirac's original work to where I have moved it in the present day. I should have something to share early to middle of this coming week.

I tend to think of the classical limit as the $n=0$ rather than $\hbar=0$ limit of $e\mu =2\pi n\hbar c$ , but the main result either way is that you then get $\mu=0$ (no monopoles) and e remains undetermined. You will see from Dirac that the undetermined nature of e is a major facet (and in his words, disappointment) of his paper. He started out trying to explain the fine structure number 1/137.036 and instead all he got was the lousy t-shirt, er, I mean, this DQC. :lol:

To this day people are still at it on the 137 number.

Jay

PS: If you look at surveys of the top theoretical physicists of the 20th century, of course Einstein is in the #1 slot, but #2 can be very contested. I absolutely put Dirac in that position, ahead of Bohr and Heisenberg and other usual suspects. And what he did with monopoles is a significant part of that because I believe that the road to theoretical unification is paved with monopoles and he started that.

by **FrediFizzx** » Fri Feb 20, 2015 4:07 pm

In classical electrodynamics, there is no hbar. I probably should have written, "in the classical limit of hbar --> 0".

by **Ben6993** » Fri Feb 20, 2015 3:40 pm

Hi Fred

hbar is a constant http://en.wikipedia.org/wiki/Planck_constant
How can it tend to nought?
Am I missing something?

by **FrediFizzx** » Fri Feb 20, 2015 3:04 pm

Hi Jay,

That doesn't really help. In the limit of hbar --> 0, we should be able to recover the classical electrodynamic result of magnetic charge being electric charge times the speed of light. Do you happen to have Dirac's original derivation for the DQC that you could email me? Thanks.

by **Yablon** » Wed Feb 18, 2015 8:01 pm

FrediFizzx wrote:...So with n = 1, I don't see how to get to the DQC q*g = 2pi in the unit system you are using of hbar = c = eps0 = 1?

Hi Fred,

With the fundamental constants restored, the DQC for n=1 is $e\mu =2\pi \hbar c$ . If you are having trouble with length-time-mass dimensionality, think of two Planck masses $m_{P}$ put into the numerator of Newton's law with a gravitational coupling G. Those masses are defined as $\sqrt{G} m_{P} \sqrt{G} m_{P} \equiv \hbar c$ . So $e\propto \sqrt{G} m$ , i.e. it has the same dimensionality as mass time the square root of a coupling constant; same with $\mu$ .

Jay

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