Aether drag hypothesis

The aether drag hypothesis was an early attempt to explain the way experiments such as Arago's experiment showed that the speed of light is constant.^{[citation needed]} The aether drag hypothesis has been considered for some time to be incorrect by most mainstream science.^{[citation needed]}

According to the aether drag hypothesis light propagates in a special medium, the aether, that remains attached to things as they move. If this is the case then, no matter how fast the earth moves around the sun or rotates on its axis, light on the surface of the earth would travel at a constant velocity, as observed.

The primary reason the aether drag hypothesis was considered invalid wass because of the occurrence of stellar aberration. In stellar aberration the position of a star when viewed with a telescope swings each side of a central position by about 20.5 seconds of arc every six months. This amount of swing is the amount expected when considering the speed of earth's travel in its orbit. In 1871 Airy demonstrated that stellar aberration occurs even when a telescope is filled with water. It seemed that if the aether drag hypothesis were true then stellar aberration would not occur because the light would be travelling in the aether which would be moving along with the telescope. A corrected analysis of stellar abberation came later^[1]^[2]

If you visualize a bucket on a train about to enter a tunnel and a drop of water drips from the tunnel entrance into the bucket at the very center, the drop will not hit the center at the bottom of the bucket. The bucket is the tube of a telescope, the drop is a photon and the train is the earth. If aether is dragged then the droplet would be traveling with the train when it is dropped and would hit the center of bucket at the bottom. However, a drop of water from the ceiling of the carriage would hit the centre, as the train is an inertial system with mass, so it's own dragged field.

Modified versions of the hypothesis are held by SR dissidents who argue that aether drag happens on a global (or larger) scale and the aberration is merely transferred into the entrained "bubble" around the earth which then faithfully carries the modified angle of incidence directly to the observer. This larger entrainment effect was believed by some scientists such as Dayton Miller who continued the search for aether many years after the widespread acceptance of relativity.

The amount of stellar aberration, $\alpha$ , is given by:

$\tan(\alpha )={\frac {v\delta t}{c\delta t}}$

So:

$\tan(\alpha )={\frac {v}{c}}$

The speed at which the earth goes round the sun, v = 30 km/s, and the speed of light is c = 299,792,458 m/s which gives $\alpha$ = 20.5 seconds of arc every six months. This amount of aberration is observed and this was seen to contradict the aether drag hypothesis.

In 1818 Fresnel introduced a modification to the aether drag hypothesis that applies to the interface between media. This explained the Sagnac effect and was accepted and developed during much of the nineteenth century including by George Stokes, and Heaviside. Stellar aberration was still not understaood at that time and the theory waned. It was replaced by the special theory of relativity (see below).

Historical importance

The aether drag hypothesis is historically important because it was one of the reasons why Newton's corpuscular theory of light was replaced by the wave theory and it is used in early explanations of light propagation without relativity theory. It originated as a result of early attempts to measure the speed of light.

In 1810 François Arago realised that variations in the refractive index of a substance predicted by the corpuscular theory would provide a useful method for measuring the velocity of light. These predictions arose because the refractive index of a substance such as glass depends on the ratio of the velocities of light in air and in the glass. Arago attempted to measure the extent to which corpuscles of light would be refracted by a glass prism at the front of a telescope. He expected that there would be a range of different angles of refraction due to the variety of different velocities of the stars and the motion of the earth at different times of the day and year. Contrary to this expectation he found that that there was no difference in refraction between stars, between times of day or between seasons. All Arago observed was ordinary stellar aberration.

In 1818 Augustin Jean Fresnel examined Arago's results using a wave theory of light. He realised that even if light were transmitted as waves the refractive index of the glass-air interface should have varied as the glass moved through the aether to strike the incoming waves at different velocities when the earth rotated and the seasons changed.

Fresnel proposed that the glass prism would carry some of the aether along with it so that "..the aether is in excess inside the prism". He realised that the velocity of propagation of waves depends on the density of the medium so proposed that the velocity of light in the prism would need to be adjusted by an amount of 'drag'.

The velocity of light $v_{n}$ in the glass without any adjustment is given by:

$v_{n}={\frac {c}{n}}$

The drag adjustment $v_{d}$ is given by:

$v_{d}=v(1-{\frac {\rho _{e}}{\rho _{g}}})$

Where $\rho _{e}$ is the aether density in the environment, $\rho _{g}$ is the aether density in the glass and $v$ is the velocity of the prism with respect to the aether.

The factor $(1-{\frac {\rho _{e}}{\rho _{g}}})$ can be written as $(1-{\frac {1}{n^{2}}})$ because the refractive index, n, would be dependent on the density of the aether. This is known as the Fresnel drag coefficient.

The velocity of light in the glass is then given by:

$V={\frac {c}{n}}+v(1-{\frac {1}{n^{2}}})$

This correction was successful in explaining the null result of Arago's experiment. It introduces the concept of a largely stationary aether that is dragged by substances such as glass but not by air. Its success favoured the wave theory of light over the previous corpuscular theory.

The Fresnel drag coefficient was confirmed by an interferometer experiment performed by Fizeau. Water was passed at high speed along two glass tubes that formed the optical paths of the interferometer and it was found that the fringe shifts were as predicted by the drag coefficient, light propagating at 'c' with respect to the medium in relative motion. This was later confirmed by fibre optic and other interferometers, including longitudinally by Wang et al.^[3]

The special theory of relativity predicts the result of the Fizeau experiment from the velocity addition theorem without any need for an aether. In his generalisation of the theory Einstein did however require an aether field and said as early as his 1920 Leiden adress; "..space without aether is unthinkable",^[4] and in trying to find a unified field theory in 1952; "There is no such thing as an empty space, i.e. a space without field."

If $V$ is the velocity of light relative to the Fizeau apparatus and $U$ is the velocity of light relative to the water and $v$ is the velocity of the water:

$U={\frac {c}{n}}$

$V={\frac {c/n+v}{1+v/nc}}$

which, if v/c is small can be expanded using the binomial expansion to become:

$V={\frac {c}{n}}+v(1-{\frac {1}{n^{2}}})$

This is identical to Fresnel's equation.

It appears as if Fresnel's analysis can be substituted for the relativistic approach, however, more recent work indicates that Fresnel's assumptions may lead to different amount of aether drag for different frequencies of light and violate Snell's law (see Ferraro and Sforza (2005)).

The aether drag hypothesis was one of the arguments used in an attempt to explain the Michelson-Morley experiment before the widespread acceptance of the special theory of relativity.

NASA Laser Lunar Ranging

Analysis of the lunar ranging experiment in 2009 by D Gezari ^[5] ^[6] prove the Sagnac effect as first order, and suggest either 'c' non-constant or a quantum field 'ether' dragged by the planet. To resolve Einsteins unified field dilemma this may be possible with the Discrete Field Model (DFM) adjustment to SR, working within the postulates and suggesting how each inertial frame, or set of co-ordinates, may have a quantum physical counterpart. This predicted the Lunar Ranging results^[7] and claims to resolve some astrophysical anomalies^[8]. It is the present version of Aether drag, so far matching observation of phenomina from space exploration and particle accelerators without paradox but it has not yet been proven or conclusively tested experimentally.

Bibliography and References

^ Stellar Aberration. James Bradley 1727. www.mathpages.com/rr/s2-05/2-05.htm
^ Does Stellar Aberration contradict ether drag. H Ansari. http://vixra.org/abs/0908.0064
^ http://arxiv.org/ftp/physics/papers/0609/0609235.pdf Wang et al. Generalised Sagnac Effect 2004nsert footnote text here
^ Ether and the Theory of Relativity. AEinstein. Leiden 1920. http://www-groups.dcs.st-and.ac.uk/~history/Extras/Einstein_ether.html
^ http://arxiv.org/abs/0912.3818v2 Experimental Basis for Special Relativity in the Photon Sector. 18 Dec '09. Daniel Y. Gezari
^ http://arxiv.org/abs/0912.3934v2 Lunar Laser Ranging Test of the Invariance of c. D Gezari. NASA. Dec '09.
^ http://vixra.org/abs/1001.0010 Relativistic GPS Evidence and Quantum Gravity Architecture of the Discrete Field Model. Peter Jackson. Dec. 09.
^ http://vixra.org/abs/0912.0041 Lensing and Galactic Mass Anomaly Solution From DFM Shock Model. Peter A Jackson 19 Dec '09.

Wikibooks: Special Relativity
Resnick, Robert, Basic Concepts in Relativity and Early Quantum Theory, 1972, John Wiley and Sons Inc.
Rafael Ferraro and Daniel M Sforza 2005. Arago (1810): the first experimental result against the ether Eur. J. Phys. 26 195-204

Historical importance

NASA Laser Lunar Ranging

Bibliography and References

See also