Magnetic Permeability and Electric Permittivity effects on atomic clocks

[kmarinas86]

Speed of Light

$c= \frac {1} {\sqrt{\varepsilon_0\mu_0}}$

Phase Velocity

$v= \frac {1} {\sqrt{\varepsilon\mu}}$

Electric Permittivity of Free Space

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

Magnetic Permeability of Free Space

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

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:

$\frac{1\ meter}{30.66\ cesium\ periods}=\frac {1} {\sqrt{\varepsilon_0\mu_0}}$

$constant=1\ meter=\frac {30.66\ cesium\ periods} {\sqrt{\varepsilon_0\mu_0}}$

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:

$constant=1\ meter=\frac {30.66\ cesium\ periods} {\sqrt{\varepsilon\mu}}$

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

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?

$constant=1\ meter=\frac {30.66\ cesium\ periods} {\sqrt{\frac{henries}{1\ meter}\frac{farads}{1\ meter}}}$

$1=\frac {30.66\ cesium\ periods} {\sqrt{henries*farads}}$

$1=\frac {30.66\ cesium\ periods} {\sqrt{inductance*capacitance}}$

 

[Gokul43201]

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.

 

[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:

$\frac{1\ meter_{default}}{Time Dilation}=\frac {30.66\ cesium\ periods_{default}*Time Dilation} {\sqrt{\frac{henries*Time Dilation}{1\ meter_{default}}*\frac{farads*Time Dilation}{1\ meter_{default}}}}$

$\frac{1\ meter_{default}}{Time Dilation}=\frac {30.66\ cesium\ periods_{default}*Time Dilation} {\sqrt{\frac{henries}{1\ meter_{default}}*\frac{farads}{1\ meter_{default}}}*Time Dilation}$

$constant=1\ meter_{default}=\frac {30.66\ cesium\ periods_{default}*Time Dilation} {\sqrt{\frac{henries}{1\ meter_{default}}*\frac{farads}{1\ meter_{default}}}}$

$1=\frac {30.66\ cesium\ periods_{default}*Time Dilation} {\sqrt{henries*farads}}$

$1=\frac {30.66\ cesium\ periods_{default}*Time Dilation} {\sqrt{inductance*capacitance}}$

Where:

$1\ meter_{default}$ is the length of the medium without length contraction.
$30.66\ cesium\ periods_{default}$ 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 $1\ meter_{default}$ is constant, this implies that.

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

Therefore, $30.66\ cesium\ periods_{default}*Time Dilation^2 \propto \sqrt{\varepsilon\mu}$.

 

[BoTemp]

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

No, it isn't. You have assumed that lengths do not change in the presence of either increased velocity (in the first post) or gravitational field (in the second post). Neither of those things are true. What I'm about to say applies qualitatively to the gravitational case as well, but it's easier to explain for constant velocity.

c is constant in any inertial frame, so let's say that's where you are observing from. A cesium atom is doing it's thing, in a spaceship moving at constant velocity relative to you, and you measure it's oscillations. You will measure the oscillations as longer than they would be measured in a rest frame, giving you a second which is longer than is defined nowadays. This would in turn give you definition of the meter which is longer, keeping the definition of c the same.

The meter isn't a constant; that's where the hangup above comes from. You'd measure it differently. As long as the observer and the cesium atom are at rest relative to each other, the above definitions work fine. If they aren't, then time dilation/length contraction needs to be taken into account.

I didn't understand most of the rest of what you said. If by "accelerated frame" you mean one frame having a relative velocity/acceleration with respect to another, yes, those can exist in a vacuum, and do. Even the event horizon of a black hole is locally flat. If you were to do the experiment described above in a sufficiently small amount of time, and you were close enough to the cesium atom, you'd get the same results as an observer in a complete vacuum. Time dilation is not a fuction of permittivity and permeability; you're assuming things constant where they aren't.

 

[kmarinas86]

No, it isn't. You have assumed that lengths do not change in the presence of either increased velocity (in the first post)

I didn't deal with velocity in the first post. By accelerated reference frame, what I really meant was that the object was sitting in a gravitational field, not that it was accelerating in a rocket.

or gravitational field (in the second post).

False! What analysis you deduced from this, does not apply, see:

However, if there is a factor by which the length decreases as a result of gravitational influence, we would have the following:

The second half of the my second post takes this into account, and the result is the same.

Because of your misinterpretation of some, not all, of what I said, the following comments is not relevant, but nonetheless correct:

Neither of those things are true. What I'm about to say applies qualitatively to the gravitational case as well, but it's easier to explain for constant velocity.

c is constant in any inertial frame

True, because c is the speed of light in a vacuum, and that does not change.

so let's say that's where you are observing from. A cesium atom is doing it's thing, in a spaceship moving at constant velocity relative to you, and you measure it's oscillations. You will measure the oscillations as longer than they would be measured in a rest frame

That is true, but remember that I am assuming the the observer and the atomic clock are stationary with respect to each other, therefore, what you say here is not something I described in this thread.

giving you a second which is longer than is defined nowadays. This would in turn give you definition of the meter which is longer, keeping the definition of c the same.

Just because the space shuttle travels fast, does that really mean that meter is longer? I know that the space shuttle undergoes a length contraction, this also makes stationary destinations appear closer for people on the space shuttle. But this is the case for objects moving relative to each other, not the same as what I talked about earlier.

The meter isn't a constant; that's where the hangup above comes from.

I unclearly dealt with the hang up in the second half of the second post.

However, if there is a factor by which the length decreases as a result of gravitational influence, we would have the following:

You'd measure it differently. As long as the observer and the cesium atom are at rest relative to each other, the above definitions work fine. If they aren't, then time dilation/length contraction needs to be taken into account.

True.

I didn't understand most of the rest of what you said. If by "accelerated frame" you mean one frame having a relative velocity/acceleration with respect to another, yes, those can exist in a vacuum, and do. Even the event horizon of a black hole is locally flat. If you were to do the experiment described above in a sufficiently small amount of time, and you were close enough to the cesium atom, you'd get the same results as an observer in a complete vacuum.

True.

 

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