Magnetic Permeability and Electric Permittivity effects on atomic clocks

[kmarinas86]

Speed of Light

 

[math]c= \frac {1} {\sqrt{\varepsilon_0\mu_0}}[/math]

 

Phase Velocity

 

[math]v= \frac {1} {\sqrt{\varepsilon\mu}}[/math]

 

Electric Permittivity of Free Space

 

[math] \varepsilon_0 = 10^{7}/4\pi c^2 \quad \mathrm{(in~ A^2\, s^4\, kg^{-1}\, m^{-3}, \, or \, F \, m^{-1})}[/math]

 

Magnetic Permeability of Free Space

 

[math] \mu_0 = 4\,\pi\, 10^{-7} \quad \mathrm{(in~ kg\, m\, s^{-2}\, A^{-2}, \, or \, N \, A^{-2})}[/math].

 

The meter is a function of the speed of light in a vacuum, simply put, it is the distance light travels in a vacuum in 1/299,792,458th of a second which is equivalent to the duration of 9,192,631,770/299,792,458 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom. If we call these "cesium periods", we have:

 

[math]\frac{1\ meter}{30.66\ cesium\ periods}=\frac {1} {\sqrt{\varepsilon_0\mu_0}}[/math]

 

[math]constant=1\ meter=\frac {30.66\ cesium\ periods} {\sqrt{\varepsilon_0\mu_0}}[/math]

 

What if for instance the cesium atoms were undergoing time dilation due to an accelerated reference frame? The cesium period itself would be enlongated due to the time dilation. Then we would have the following:

 

[math]constant=1\ meter=\frac {30.66\ cesium\ periods} {\sqrt{\varepsilon\mu}}[/math]

 

If the meter is constant, this implies that [math]30.66\ cesium\ periods\propto {\sqrt{\varepsilon\mu}\propto Time\ Dilation}[/math]

 

This would imply that the cause of time dilation is the square root of the product of electric permittivity and magnetic permeability. In the case of infinite time dilation, that would imply that at least either electric permittivity or magnetic permeability is infinite at the region of infinite time dilation, but we know electric permittivity and magnetic permeability cannot be infinite, so what are we left with? Have we disproven the possibility of inifinitely time dilated cesium atoms? If such were the case, we would have proven that cesium atoms cannot exist at the event horizon, and whatever is at the event horizon would have to be subject to an infinite product of electric permittivity and magnetic permeability, where in the phase velocity would have to be 0, provided that the meter does not expand infinitely at this region.

 

If the event horizon is a pure vacuum, where light travels at c, then we would be left with the conclusion that a meter elongates to infinite length. Could we really have that?

 

Could it be that either something is wrong with the way time is defined, or that there is new physics involved at black hole celestial objects?

 

Can an accelerated reference frame exist in a vacuum? If not, then it would follow that accelerated reference frames do not exist in the vacuums surrounding black holes, but we know that this is false, and that all celestial objects have in them accelerated reference frames. Some would say that an accelerated reference frame requires space-time curvature. Isn't space time curvature manifested by the influence of pressure and energy density? Isn't pressure and energy density manifested by propogation velocities less than c? Isn't then, gravity caused by the influence of electric permittivity and magnetic permeability of the background vacuum, provided that these influences also control the time dilation of cesium atoms and thus determines the duration of 30.66 cesium periods in an atomic clock, and hence, the second itself, which later lead to perceived constant values for electric permittivity and magnetic permeability in free space?

 

[math]constant=1\ meter=\frac {30.66\ cesium\ periods} {\sqrt{\frac{henries}{1\ meter}\frac{farads}{1\ meter}}}[/math]

 

[math]1=\frac {30.66\ cesium\ periods} {\sqrt{henries*farads}}[/math]

 

[math]1=\frac {30.66\ cesium\ periods} {\sqrt{inductance*capacitance}}[/math]

[IDMclean]

Here's something to concider.

 

Permittivity and Permeability are seperate properties. They are essentially equal at ground state (that is freespace). If one changes one or the other than the velocity changes. c is a velcity which is equal to: 299792458 m/s.

 

Mass has non-ground state values for it's Permittivity and Permeability, and therefore non-luminal speeds.

 

I like what your doing here, keep it up. I'll check back in when I have my head straightened out.

[kmarinas86]

I didn't go all the way through...but aren't you implying that length is a Lorentz invariant? Besides, relative permeabilities and dielectric constants are meterial properties defined in the rest frame of the material.

 

I am assuming that the objects (mediums) are still with respect to an observer, therefore, I assume no length contraction as a result of velocity. I am also assuming that gravity does not cause length contraction for an object with 0 radial velocity. However, if there is a factor by which the length decreases as a result of gravitational influence, we would have the following:

 

[math]\frac{1\ meter_{default}}{Time Dilation}=\frac {30.66\ cesium\ periods_{default}*Time Dilation} {\sqrt{\frac{henries*Time Dilation}{1\ meter_{default}}*\frac{farads*Time Dilation}{1\ meter_{default}}}}[/math]

 

[math]\frac{1\ meter_{default}}{Time Dilation}=\frac {30.66\ cesium\ periods_{default}*Time Dilation} {\sqrt{\frac{henries}{1\ meter_{default}}*\frac{farads}{1\ meter_{default}}}*Time Dilation}[/math]

 

[math]constant=1\ meter_{default}=\frac {30.66\ cesium\ periods_{default}*Time Dilation} {\sqrt{\frac{henries}{1\ meter_{default}}*\frac{farads}{1\ meter_{default}}}}[/math]

 

[math]1=\frac {30.66\ cesium\ periods_{default}*Time Dilation} {\sqrt{henries*farads}}[/math]

 

[math]1=\frac {30.66\ cesium\ periods_{default}*Time Dilation} {\sqrt{inductance*capacitance}}[/math]

 

Where:

 

[math]1\ meter_{default}[/math] is the length of the medium without length contraction.

[math]30.66\ cesium\ periods_{default}[/math] the length of the 30.66 cesium periods without time dilation.

 

Therefore, the existence of gravitational length contraction makes no difference, and time dilation would still be a function of inductance and capacitance.

 

Magnetic Permeability and Electric Permeability are also causes, except now, since [math]1\ meter_{default}[/math] is constant, this implies that.

 

[math]constant=1\ meter_{default}=\frac {30.66\ cesium\ periods_{default}*Time Dilation^2} {\sqrt{\varepsilon\mu}[/math]

 

Therefore, [math]30.66\ cesium\ periods_{default}*Time Dilation^2 \propto \sqrt{\varepsilon\mu}[/math].

[UncleAl]

Speed of Light

 

[math]c= \frac {1} {\sqrt{\varepsilon_0\mu_0}}[/math]

 

If you define lightspeed in such a manner, how do you account for normal dispersion on one side and anomalous dispersion on the other side of an optical transition? How can materials be birefringent (e.g., single crystal alumina)? If you make a window out of white sapphire, you'd better be looking through it parallel to the crystallogrphic c-axis or you get double images.

 

What of lightspeed within a Casmir etalon or Rabi cavity and causality thereform? Scharnhorst effect,

 

http://arXiv.org/abs/gr-qc/0107091

http://arXiv.org/abs/quant-ph/0010055

Phys. Lett. B236 354 (1990)

Phys. Lett. B250 133 (1990)

J Phys A26 2037 (1993)

 

What then happens to lightspeed and information propagation inside metamaterials?

 

http://focus.aps.org/story/v9/st23

http://www.photonics.com/content/spectra/2004/June/research/77504.aspx

http://physics.ucsd.edu/~drs/left_home.htm

http://nam.epfl.ch/res10.en.html

http://rsphy2.anu.edu.au/nonlinear/research/lhm/

 

What happens to lightspeed hard by an atomic nucleus with atomic number near the Fine Structure Contant reciprocal? What happens to lightspeed at magnetars or deeply relativsitic gold nuclei collisions when magnetic field is sufficiently intense to render the vacuum birefringent?

 

Questions like that. Interface between theoretical prediction and empirical observation.

[kmarinas86]

As for why the value of mu and epsilon are what they are, at least in a vacuum: well, they're "fundamental constants"...so we don't know why, they just are. As for why a medium has a particular value, its the way the material retards and interferes with EM waves by the presence of the charged atomic particles.

 

If you want a butt easy answer to this question first you must assume the speed of light is c in all mediums. To do the fix, assume that when the speed of light slows down that it's actually "time dilation" so that a refractive index of 2 corresponds to a time dilation of 2. Then time dilation is simply 1/(v*sqrt(mu*epsilon)), where v is the velocity of light using our units of time (as if we possessed the coordinate time frame). In this case, you assume that time runs at different speeds inside different mediums (e.g. time would run slower in diamond than it would in glass). As for force in netwons, being in units of kg m/s^2, it would increase with the square of the time dilation (i.e. the forces just look weaker than they really are due to time dilation making them "slow motion"), and with energy (gravitational potential energy, kinetic energy, etc.) - still the square of the time dilation. kg*m/C^2 (i.e. permeability) would remain the same, whereas permittivity ((C^2*s^2)/(kg*m)) it would be inversely proportional to second power of the time dilation (i.e. this would mean that permittivity is overestimated by a factor equal to the second power of the time dilation) such that sqrt(permittivity*permeability) is overestimated by the factor for time dilation.

 

As for the values of mu and epsilon, they're like the constant G, that is, they depend on the units we use to define them. If we use different units we (in just about all cases) will get a different "magnitude".

 

See also: http://academia.wikia.com/wiki/Unification_of_Fundamental_Forces

[IDMclean]

I'm no expert, but are you sure about the index of refraction thing?

Where:

[math]n = \sqrt{\epsilon_r\mu_r}[/math]

 

My physics text has it as:

[math]n = \frac{c}{v} = \sqrt{{\epsilon_0\mu_0}{\epsilon\mu}}[/math]

 

The last portion is derived. but the c over v is not. c is the speed of light through vacuum and v is the speed of light through a medium.

[kmarinas86]

I'm no expert, but are you sure about the index of refraction thing?

Where:

[math]n = \sqrt{\epsilon_r\mu_r}[/math]

 

My physics text has it as:

[math]n = \frac{c}{v} = \sqrt{\frac{\epsilon\mu}{\epsilon_0\mu_0}}[/math]

 

The last portion is derived. but the c over v is not. c is the speed of light through vacuum and v is the speed of light through a medium.

 

[math]\epsilon_r=\frac{\epsilon}{\epsilon_0}[/math]

 

http://scienceworld.wolfram.com/physics/RelativePermittivity.html

 

[math]\mu_r=\frac{\mu}{\mu_0}[/math]

 

http://scienceworld.wolfram.com/physics/RelativePermeability.html

[IDMclean]

Index of refraction

 

I'm confused now, and what's worse is this computer won't display proper latex renders, so I can't read most of the math posted.