Brane Space

Tuesday, February 19, 2019

Einstein's Deflected Starlight Test Of General Relativity - As Momentous Now As It Was 100 Years Ago.

Related image
Einstein soon after publication of his paper on special relativity

One hundred years ago one of the most astounding tests of a physical theory (the general theory of relativity) was carried out, and its audacity still echoes through the decades.   The experiment entailed making a prime test: measuring the deflection of distant starlight during a total eclipse, with the light having passed by the Sun (and being influenced by its gravitational field).

But how can light - radiant energy - be affected by a gravity field? To find out one must adopt the view that light consists of particles which we call photons.  And although photons have zero rest mass there is still a way to tweak the equations of motion peculiar to general relativity to be able to fashion meaningful results. Remember also that Einstein received the Nobel Prize specifically for his work on the photoelectric effect which showed light can behave as particles.

The effect was first observed by Heinrich Hertz in 1887, but it was left for Einstein to explain (and for which he won the Nobel Prize) in 1905. The effect at the time, was most directly observed when a + charged zinc plate (in a Braun -type electroscope) was exposed to x-rays or ultraviolet radiation which caused an increased deflection of the electroscope leaf.  Conversely, a negatively charged plate exposed to the same high frequency radiation caused a decreased deflection showing a loss of potential. Hertz demonstrated the effect using an apparatus such as shown below:

Image result for brane space, deflected starlight


Here, an evacuated tube contained two electrodes connected to an external circuit with the anode being the metal plate on which the radiation was incident. The photo-electrons emerging from the surface thus had sufficient kinetic energy to reach the cathode despite its negative potential. These electrons formed the current (photo-current) measured by the ammeter. 

To measure the maximum kinetic energy of the photo-electrons one applies a retarding voltage V, gradually increasing it until the most energetic photo-electrons are stopped so the photo-current becomes zero.



At this point::  eVs = K max=  ½ mv max2

According to Einstein's explanation a beam of radiation consists of bundles of energy of size hf called “photons”. When such photons collide with electrons at or on a metal surface, they transfer an energy hf. The electrons on the metal surface either get all of this energy or none at all. In leaving the surface, electrons lose an amount of energy f which is the work function of the surface. The maximum energy with which an electron can emerge is:

(Energy gained from work function) – (work function)

In Einstein's general relativity paper, ‘On the Influence of Gravitation on the Propagation of Light’   he computed a deflection of only 1.7 seconds of arc.  This is a tiny amount indeed, and some idea can be grasped that the angular diameter of the full Moon or 1/2 degree, and one arcminute is 1/30 the width of the full Moon, and one arcsecond is 1/60th of an arcminute.

The basic concept illustrating deflection of starlight is given below:
Image result for brane space, deflected starlight

Here the light from a star at an actual position S2 is seen to deflect by some angle a    thereby altering the image position to that seen at S1. This is a direct result of the effect of the gravitational field of the Sun on the light rays. The true direction is thus alone the ray ES2 while the deflected position is along the ray ES1.

Theoretically and quantitatively, one get obtain an estimate of the magnitude of deflection by incorporating another parameter – call it b   ("impact parameter") as shown in the diagram below:

Image result for brane space, deflected starlight
Then we obtain for the deflection angle, a:


 a  = - 4 GM/ b   or (in cgs units): 


 a       = - 4 GM/ b c2  

The backstory to the experimental test validating at least one prediction of the general theory (though some nitpickers remain unconvinced because of measurement errors) is itself interesting.  We learn, for example, that in the midst of World War I in 1917, one of the astronomers involved (Frank Dyson - Astronomer Royal),  persuaded the British government to budget   £ 1,000 for a team of 4 astronomers - led by Sir Arthur Eddington of Cambridge - to make the critical observations during a total solar eclipse on May 29, 1919. 

As a sidenote, Eddington's book, 'Space, Time and Gravitation', remains one of the most readable accounts including the tie in to general relativity. It is also available as a pdf book online for those interested, e.g.

[PDF]

Space, Time and Gravitation


Anyway, one team of two astronomers was stationed at Principle, an island off the coast of West Africa, and the other team of two went to Sobral, a city in northeast Brazil.   As Eddington recorded in his diary:

"The first ten photographs show practically no stars.  The last six show a few images which I hope will give us what we need, but it is very disappointing."

Disappointed though he was, once back in England Eddington developed four more Principe plates. He detected in them Einstein's value for the deflection of starlight though within a rather large margin of error. Fortunately, the Sobral plates provided conclusive support for Einstein's theory. 

 Ciufolini and Wheeler, in their (1995) Princeton monograph 'Gravitation and Inertia (p. 120) note that the Eddington- Dyson measurements "confirmed the general relativistic predictions with about 30 percent accuracy".  However, since then (p. 121): "Long baseline interferometry and very long baseline interferometry "have dramatically improved the accuracy of photon deflection measurements" .   The amount of enhancement in accuracy is on the order of 50 times using VLBI instruments. 

In November, 1919 Sir Arthur presented his conclusions to a joint meeting of the Royal Society and the Royal Astronomical Society in London.  The greatest personage then involved in British physics - J.J. Thomson, declared:

"This is the most important result obtained in connection with the theory of gravitation since Newton's day. If it is sustained....it is the result of one of the highest achievements of human thought."

Most recently (last June) Dr. Thomas Collett of the Institute of Cosmology and Gravitation at the  University of Portsmouth, along with an international team of astronomers,  conducted what they say was the first test of general relativity on a large astronomical scale. The paper entitled:  A Precise Extragalactic Test of General Relativity,  was published in the journal Science and found that gravity’s behavior in distant galaxies reflects that way gravity behaves in our solar system, just as Einstein’s theory predicted.  

So far, Einstein's general theory is indeed one of the highest achievements of the human mind.


See also:



Brane Space: Select Questions-Answers From All Experts Astronomy ...


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Posted by Copernicus at 7:47 AM
Labels: deflection of starlight, Frank Dyson, General Relativity, Heinrich Hertz, impact parameter, photoelectric effect, Sir Arthur Eddington

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About Me

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Copernicus
Specialized in space physics and solar physics, developed first astronomy curriculum for Caribbean secondary schools, has written seventeen books - the most recent: Essays In Brane Space. Also: The Oswald Option, Advanced Topics In Mathematical Physics, Fundamentals of Solar Physics, Modern Physics: Notes, Problems and Solutions;:'Beyond Atheism, Beyond God', Astronomy & Astrophysics: Notes, Problems and Solutions', 'Physics Notes for Advanced Level&#39, Mathematical Excursions in Brane Space, Selected Analyses in Solar Flare Plasma Dynamics; and 'A History of Caribbean Secondary School Astronomy'. It details the background to my development and implementation of the first ever astronomy curriculum for secondary schools in the Caribbean.
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