Light Trajectory

Discussion in 'Pseudoscience Archive' started by CheskiChips, May 16, 2010.

  1. CheskiChips Banned Banned

    Messages:
    3,538
    I've posted this in pseudo science to save someone time.

    I recall using \(c^{-1} = sqrt(\epsilon_0 \mu_0)\) in my university electromagnetism course, I assume it still holds roughly true in modern physics.

    I look at contour maps at constant pressures everyday, constant pressure is chosen because winds flow at a constant pressure rather than height...I was curious as to whether or not there was a parallel in electromagnetism.

    1. Does the value of \(\epsilon_0 \mu_0\) vary over space?

    2. If so; does light have a preferential path? For example:
    \(\epsilon_0 \mu_0 = K\)

    The following 2D scalar field is a value of a in an equation a*K
    Emboldened are values where a=1

    0.90 .092 0.94 0.96 0.98 1.00 1.02 1.04 1.06 1.08
    0.88 0.90 .092 0.94 0.96 0.98 1.00 1.02 1.04 1.06
    0.86 0.88 0.90 .092 0.94 0.96 0.98 1.00 1.02 1.04
    0.84 0.86 0.88 0.90 .092 0.94 0.96 0.98 1.00 1.02

    Does the trajectory of light become influenced by these values even if it's not a direct imposition on it.


    If so...(and I will await an answer before proposing further insane ideas)...I have an idea about planetary development.
     
  2. Google AdSense Guest Advertisement



    to hide all adverts.
  3. AlphaNumeric Fully ionized Registered Senior Member

    Messages:
    6,702
    The direct physical property which is easily measured is c, the factorisation into \(\epsilon_{0}\) and \(\mu_{0}\) is not of any real relevance beyond nice notation in the equations of motion (ie \(\nabla \cdot E = \frac{\rho}{\epsilon_{0}}\) etc. If you always work in c=1 natural units you can largely ignore it.

    Depends who you ask and how theoretical you want to be. Special relativity has the postulate that the speed of light is seen by two inertial observers in relative motion to be the same but this is not to say it doesn't vary of space and time. If you don't get what I mean just say, its just the explanation isn't terribly relevant at the moment. Non-inertial observers and the complications relating to extending SR to GR allows for light to appear to be moving at speeds other than c but this is not the same as it actually going faster to a local observer. Space and time varying c has been considered, as it has implications for physical processes, though its also important to be careful there as, despite what you might guess, changing the values of 'constant's which have units is not going to change your physics, only dimensionless constants have physical meaning. There's a thread started by Ben around somewhere (about 3 months ago?) and a related paper on ArXiv.

    You can't just put in c(x) instead of c into known results/equations because much of the mathematics done to obtain those results assumes c is constant in space and time. For instance, consider Maxwell's equations (2 of them at least) :

    \(\nabla \cdot E = \partial_{i}E_{i} = \frac{\rho}{\epsilon_{0}}\) and \(\nabla \times B - \mu_{0}\epsilon_{0}\frac{\partial E}{\partial t} = \mu_{0}J\).

    Applying \(\nabla \cdot\) to the second and using \(\nabla \cdot (\nabla \times B) = 0\) gives

    \(- \nabla \cdot (\mu_{0}\epsilon_{0} \frac{\partial E}{\partial t} ) = \nabla \cdot (\mu_{0} J)\)

    If \(\mu_{0}\) or \(\epsilon_{0}\) are position and time dependent (even if they still give a constant c) then you cannot pull them through the derivatives and if you can't do that you can't use the first expression for \(nabla \cdot E\) and thus E (and by the same method, B) doesn't satisfy the wave equation. If you weren't considering a vacuum but some kind of conductive medium then you can make them position or time dependent. In such cases you absorb them into the electromagnetic fields to define new ones, as done in http://en.wikipedia.org/wiki/Maxwell's_equations in the first table.

    Suffice to say that all experiments done so far to look for deviations in various constants from their measured values here and now on Earth have come up empty.

    I believe so. I vaguely remember an exam question I once did which involved light moving through a material of varying density and you have to use Lagrangian multipliers or the Euler-Lagrange equations to obtain the curved path. Things like a mirage on a hot day are due to the light path being bend by variable density air so if you were to regard \(\mu_{0}\) and \(\epsilon_{0}\) as some kind of dielectric quantities for space-time (though it makes it sound like an aether) you'd get a clearer view.

    I'd write down a Lagrangian and work it out from there.

    What has it got to do with variable c?
     
  4. Google AdSense Guest Advertisement



    to hide all adverts.
  5. James R Just this guy, you know? Staff Member

    Messages:
    39,397
    The zero subscripts indicate that those are the values for the vacuum. In any non-vacuum material, you replace them with the values for the material. For example, in glass both the permittivity \(\epsilon\) and permeability \(\mu\) are larger than in vacuum, so the speed of light in glass is less than in vacuum.

    Yes. This is how refraction of light comes about. Light follows the path of least time between two points in any medium. Since it changes speed in crossing from one medium to another, the light also bends (refracts) at the boundary (unless it hits the boundary at normal incidence).
     
  6. Google AdSense Guest Advertisement



    to hide all adverts.
  7. prometheus viva voce! Registered Senior Member

    Messages:
    2,045
    It is possible for 1 loop quantum effects to change the refractive index, and therefore the speed of light, in curved space. Originally it was thought that the speed of light would be greater than c for all frequencies (guessed really) creating a big problem for causality, however that has been resolved in a series of papers here.
     
  8. CheskiChips Banned Banned

    Messages:
    3,538
    Thanks for your explanations these two in particular were useful:
    Continuing with the parallel to Meteorology, an Explaining it's application on planetary development:
    wind:\(\mu\)
    density : \(\rho\)
    In Meteorology you use the circulation function of momentum flux to determine atmospheric vorticity. Keep in mind in this application it's done at a constant Z because usually vertical motion is minimal in comparison. Thus the momentum flux vector is two dimensional.
    \(\nabla \times \mu\rho\)

    The lagrangian is essentially approximated from a scalar field in independently interpolated wind values and density values. If that scalar field has a field such that the magnitude of its vector field is an enclosed contour it's considered a closed low. There are also other types of closed lows, this is just one.
    \(||< b(y)\le C*sin(t),a(x) \le -C*cos(x)>|| = C\)

    If either one of them has a vector gradient less than the above stated values then the low is likely contracting. This implies increased densities and typically a convergence of different air masses occur from the periphery to the center of the low. The accumulation of this mass creates a very low temperatures in the center with high density and/or pressure. In the case of the atmosphere the increased mass typically increases in the secondary circulation by contracting the updraft zone and in the primary circulation by having increased chaotic flow (increased eddie genesis)...eventually the horizontal pressure gradient attenuates as compared to the centrifugal force and the system dissipates.

    It's this last step which doesn't seem likely to occur in "space weather". The steps preceding it seem entirely plausible in cosmology. That is to say...
    a scalar field of \(\epsilon\mu\) {I mistakenly earlier typed their 'not' values, thanks James R} such that it would result in a closed circulation, albeit a large circulation. If the principals have parallels in space then the circulation would contract eventually perhaps creating radiative winds and circulations which might in time influence small mass particles to collect at the center of the low. Or perhaps circulations of (and I am overstepping my bounds here a little) the electromagnetic fields expounded upon by AlphaNumeric in his explanation of Maxwell's equations.
     

Share This Page