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

Phase Velocity

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

Electric Permittivity of Free Space

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

Magnetic Permeability of Free Space

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

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:

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

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

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:

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

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

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?

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

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

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

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# Magnetic Permeability and Electric Permittivity effects on atomic clocks

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