h c

I have been pottering around with the physics again for the last 3 or 4 years and I think its time to step up, put my head above the parapet, and finally publish a post about what I really think, this, is that post.

If you wondering why it is title hc, well it should really be

$ \hbar c$

$\hbar$ is reduced Planck's constant
$c$ is speed of light

I think this is pretty much core to the whole of physics, again, more posts on this later.

Right, lets start with some ground rules;

1) everything that I put in the post I will attempt to justify, when necessary, in later posts.
2) if I claim something that someone else has already laid claim to, I will update this post as soon as I become aware of it.
3) if I think of any other ground rules I will add them later

Ok, here we go;

1) Force is quantised.

Energy is quantised, we have Planck's equation

$ E = h \nu $ ...(1)

$\nu$ - frequency of photon.

now multiply top and bottom by $\lambda$, wavelength and use relationship $ c = \nu \lambda$ and you have

$ E = $ $\frac {hc} {\lambda} $ ... (2)

now divide each side by $\lambda$ and you have

$ \frac {E} {\lambda} = \frac {hc} {\lambda^2} =$ $ F $ ...(3)

where F is force. There are a number of different ways of deriving equation (3), but the point is that just as energy can be quantised, so can force. It also means that a photon as an intrinsic force who's value is given by (3).


2) Energy is accelerated when photons are created. I've covered this in a previous post. The upshot is that the acceleration is proportional to the frequency of the photon created, given by

$ g = \nu c $ ...(4)

or

$ g \lambda = c^2 $ ....(5)

note: I also covered this one here.

3) There is only one force and this is defined by

$ F = $ $ \frac {k \hbar c} {r^2} $ ... (6)

k - unitless coupling constant

Gravity, the electrostatic, weak and strong force are all different manifestations of the same force given in equation (6). Each having its own version of k. I think it goes further than this though. I think they are exactly the same force. We currently have the 4 different coupling constants, because we have failed to grasp the significance of equation (6). I think we can use this to bridge quantum mechanics and general relativity, but more on that later.


4) There are other maximums in the universe besides the speed of light. Planck units define the borders of the universe, eg

Planck Force - maximum force that can be exerted
Planck Energy density, the maximum energy that can be compressed into a given volume.
Planck length - smallest meaningful length.
etc


5) From the proposition in (4) the following results can be inferred

a) Singularities within Black Holes do not exist.
b) black holes behave like superconductors at the event horizon
c) Space-time is quantised
d) Dark matter / dark energy do not exist - actually, I'm beginning to rethink this in light of something Max said.

I'll go into the detail of this one later.

6) Space-time has surface tension, curvature of space time is related to this surface tension. The value of the surface tension is given by the following equation

$ k_t r^3 = \hbar c $    ...(7)

$k_t$ - surface tension of space time
$r$ - radius of curvature

7) The equivalence principle extends way beyond acceleration and gravity, for example, energy density and pressure have the same units, they are the same thing.

and last and by no means least


8) Gravity & Coulombs constant.... Save this one for later :)


Right so that is it. I've covered or discussed a few of these in the past mostly around October 2013, when I had a month off work and messed around with some equations. This time round I'll see if I can go through them a little more methodically with some justifications.

bye for now.

Speed of light, squared

It's been a while since I managed to post anything, mostly because I have been going round and round in circles!

This post is actually two posts! This post is on one of the more commonly known constants in physics, the speed of light, or rather the speed of light squared. In the first part I am going to derive a couple of equations and in the second I will discuss them in a little more detail.

The most common version of $C^2$ as got to be Einstein's very famous equation,

$ E = mc^2 ... (1)$

E - energy
m - mass

probably the most famous equation in the world. There a a fair number of others, from Maxwell's equations we have

$ \frac {\delta E} {\delta t}$ $= c^2 \bigtriangledown$ x $ B  ... (2) $

E - Electric field
B - Magnetic field

from General relativity we have the Schwarzschild radius

$ 2GM = r_s c^2 ...(3) $

G - gravitational constant
M - mass
$r_s$ - Schwarszchild radius

If you have a play with the Planck Units you can derived a whole bunch, here are a couple of them

$\sqrt {F_p G} = c^2 ... (4) $

$F_p$ - Planck Force
G - gravitational constant

$\frac {v_p q_p} {m_p}$ $= c^2 ...(5) $

$v_p$ - Planck voltage
$q_p$ - Planck charge
$m_p$ - Planck mass

From equation (2) though there is another version that prompted this post, it is this

$ c^2 =$  $\frac {1} {\epsilon_0 \mu_0}$ $ ...(6) $

$\epsilon_0$ - permittivity of free space
$\mu_0$ - permeability of free space = $4\pi . 10^{-7} \ kg \ m \ q^{-2}$

So, a while back I did an introductory post on the idea of Planck units. These are values for mass, length, force, energy etc based on five constants of nature. See my earlier post for more details. The 5 constants are

c - speed of light
G - Gravitational constant
$\hbar$ - reduced Planck's constant
$4 \pi \epsilon_0$ - Coulomb's constant
$k_b$ - Boltzmann's constant

The $\epsilon_0$ in Coulomb's constant and the $\epsilon_0$ in equation 6 are the same, which got me thinking, are there similar equations for the other 3 natural constants? ie,

$c^2=$ $\frac {1} {\hbar \mu_\hbar}$ $ ...(7) $
$c^2=$ $\frac {1} {G \mu_G} $ $ ...(8) $
$c^2=$ $\frac {1} {k_b \mu_{k_b}} $ $ ... (9) $

$\mu_\hbar, \mu_G, \mu_{k_b}$ - something to be determined.

Let's start with equation (7) $\hbar$ is the reduced Planck's constant, but what is $\mu_\hbar$? is there anything that corresponds to this? Rearranging (7) and multiplying by $4\pi^2$ we get

$\frac {4\pi^2} {\mu_\hbar} $ $= 2 \pi h c^2   ...(10)$

note that the $\hbar$ is now h - Planck's constant.  In physics there is something called the first radiation constant ($c_1$) which has the value

$c_1 = 2\pi h c^2  ...(11) $

with a little substitution from (10) & (11) and some minor rejigging we have

$\mu_\hbar = $ $\frac {4 \pi^2} {c_1}$  $ = 1.055073 . 10^{17} \ s^3 \ kg^{-1} \ m^{-4}...(12)$

That's a good start, and is probably to be expected. There is a very close relationship between h and c that we will explore else where, but what about (8) and (9)? Repeating the rearranging we did for (7) we get

$\mu_G =$ $\frac {1} {G c^2}$ $ = 1.66718.10^{-7} \ kg  \ s^4  \ m^{-5} ...(13) $

$\mu_{k_b} =$ $\frac {1} {k_b c^2} $ $ = 805,889 \ K \ s^4 \ kg^{-1} \ m^{-4} ...(14)$

It looks like we have drawn a blank here. (13) and (14) do not appear to have any recognised physical significance. I shall pick this up in a later post. For now dividing  $\mu_0$ by (13) gives

$\frac {\mu_0} {\mu_G} = \frac {G} {\epsilon_0} $ $=$ $\frac {4 \pi .10^{-7}} {1.66718 .10^{-7}} $ $\approx 2.4 \pi \ m^6 \ q^{-2} \ s^{-4} ... (15) $

and,

$\frac {G} {4 \pi \epsilon_0} $ $\approx 0.6    ...(16)$

and also

$\frac {\mu_G} {\epsilon_0} $ $=$ $\frac {\mu_0} {G}$ $\approx 6000 \pi \ kg^2 \ s^2 \ q^{-2} \ m^{-2}  ...(17)$

Finally, taking

$z_0 = \sqrt {\frac {\mu_0} {\epsilon_0}} $ 

and

$z_G = \sqrt {\frac {\mu_G}{G}} $ $\approx 50 $

$\frac {z_0} {z_G} $ $\approx 2.4 \pi$, as expected

So, just to summarise this post. We have shown that equation 7 is actually something already known, the first radiation constant. For (8) and (9) we do not yet have a clear understanding, but it has been shown that in the case of G, the gravitational constant and $4 \pi \epsilon_0$, the values are very similar.

More on this in the next post.