Plasma Theory of 'Gravitational Lensing' of Light

The bending of light around massive astronomical objects is generally thought to be a gravitational effect and considered as a proof for Einstein's General Relativity. Examples for 'gravitational lensing' range from the apparent shift of star positions close to the sun to the lensing effects observed around clusters of galaxies.
General Relativity describes this phenomenon through the concept of a distorted space around the object rather than a physical interaction with the light wave. This view can however be discounted as logically inconsistent (see On the other hand, it is unreasonable to assume that immaterial and massless objects like light can be in any way subject to a gravitational interaction.
It is therefore much more likely that the propagation of electromagnetic waves is, by their very nature, only affected by electromagnetic fields. I have already suggested in connection with the Hubble- redshift of galaxies that the latter is caused by the small scale electric field due to the plasma charges in intergalactic space. In that case, the average electric field is actually zero due to its random nature and the homogeneity of the plasma, and thus there is no systematic deflection of light associated with the redshift, but only a (very small) random blurring. Now the point is that inhomogeneous plasmas (as practically present around all massive astronomical objects) must be associated with a non-zero static electric polarization field due to the different ion and electron velocities: in an isothermal plasma, the electrons have a velocity about √1800=42 times higher than protons due to their mass being 1/1800 times smaller, and thus they will tend to escape from the plasma, setting up a plasma polarization field in the process which prevents further electrons from escaping on their own. Applied to the sun, this simply means that it effectively becomes positively charged by an amount corresponding to the original kinetic energy of the electrons. This energy is given by the gravitational energy of the sun and corresponds to about 1 keV (see Eq.(3) on my page regarding Coronal Heating) i.e. the sun is at a potential of 1 kV (with the corresponding electric field decreasing outward like 1/r2). Now this electric field is, in contrast to the random field of a homogeneous plasma, static in space and time and thus could deflect light in a systematic manner. The deflection will obviously also be proportional to the length of the light path, which, at an impact radius r is also of order r, i.e. we have

(1)       αSun ~ M/r2.r ~ M/r

where, M the mass of the object (which enters into the equation because the electric field is proportional to the gravitational energy and hence M), and r the (average) distance of the of the light ray from the object. Note that this is exactly the same dependence the gravitational lensing theory predicts and which is indeed observed.

In order to obtain a numerical value for α with this interpretation, one would have to know, from theoretical arguments or laboratory data, how strongly light is deflected by a given electric field, which unfortunately is not the case. However, assuming that the Hubble- Redshift of Galaxies is also related to the same interaction of light with an electric field, one can use this as a reference measurement here. In order to compare the two cases, one has to make a more general consideration as done above though. First of all, it is reasonable to assume that the redshift (as well as the angular deflection) is not only proportional to the electric field, but also to the wavelength as the potential difference between two wave crests is proportional to it. Furthermore, one has to take into account that the field gradient (i.e. the finite size of the field region) should lead to a diffraction effect which can be expected to result in a reduction of the redshift/deflection i.e. in an inversely proportional dependence on wavelength. Overall there should thus not be an wavelength dependence (as observed). However, due to the diffraction there is now an additional dependence on the scale of the field region, so in general the redshift is given by

(2)       z ~ E.rE .s

where E is the electric field strength, rE the average scale of the electric field variation and s the total path of the light ray. Now for the intergalactic redshift one can assume values of E=4.10-9 V/m (corresponding to a plasma density of the order of 1m-3), rE=1m and s=1026m (for z=1). The corresponding values for the solar case are E=1.4.10-6 V/m (103V/7.108m) near the edge of the sun, rE=7.108m and s=7.108m. According to (2), the solar redshift is thus given by the ratio of the products of these values, which results in

(3)       zSun = 1.7.10-6

which, given the approximations and uncertainties in the above derivation, is consistent with the observed value for the 'gravitational redshift' of solar lines (see Reference).

Assuming that a light pulse which has suffered a redshift of z=1 would be associated with a bending through 360 deg in a homogeneous field (which of course is actually not the case for the intergalactic redshift as the plasma microfield is merely of a stochastic nature), this results then in a deflection near the edge of the sun by

(4)       αSun = 1.7.10-6 .360o = 2.2"

which again is consistent with the observed value of 1.75" given the the crude nature of the above estimate.

It is worth noting that in order to achieve the same redshift or deflection as by the sun in a lab experiment of the size of the order of 1m, the field would (according to Eq.(2) for rE=s=r) have to be (7.108m/1m)2= 5.1017 times stronger than the solar one i.e. almost 1012 V/m which would be about the same as the inner-atomic electric field. It is therefore not further surprising that the effect has not been discovered yet in the laboratory and only becomes apparent over astronomical distances.

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Thomas Smid (M.Sc. Physics, Ph.D. Astronomy)