Newtonian Gravity Vs General Relativity

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General relativity & Gravity by stevebd1 Youtube


Warping of space around the sun

GETTING A GRIP ON GRAVITY  Einstein’s general theory of relativity explains gravity as a distortion of space (or more precisely, spacetime) caused by the presence of matter or energy. A massive object generates a gravitational field by warping the geometry of the surrounding spacetime.


If a light ray happens to pass close to a massive object such as a star, it will be forced to bend in order to follow the curved space around it.

Notice that in the above figure, the star at position at location “Real” can only be seen at position “Observed” from the earth if the light bends as shown. If the light did not bend, you would not see the star because it will be blocked by the sun shown in the middle.

The picture above shows how the direction of light will be affected by the  curved space around the sun. Light emanating from the “Real” position will curve around the outermost fringe of the curved space around the sun, and then, once out of the curved space, will travel in a straight line to the earth. From the earth, it will appear like the star is at the “observed” position when, it actually is at the “Real” position.

bending-of-light-03

bending-of-light-02

Newton first computed the angle of the bending light as 0.87 arc second, Einstein in 1915 modified it to be the double of that which is 1.75 arc second. From the angle of bend, the physicists computed the weight of light.

When the sun is not anywhere close to the path between the earth and the star, you could see the star at the “Real” position because the light will travel in a straight line to the earth.


Gravitational Lensing

Gravitational_lens-full

Gravitational lensing was first observed in 1979, but Einstein had suspected its possibility in 1912, even before his theory had been completed.

The bending of light by gravity can lead to the phenomenon of gravitational lensing, in which multiple images of the same distant astronomical object are visible in the sky.

This diagram shows how light from a distant galaxy bends around a massive object in the foreground, perhaps a neutron star or a black hole. The orange arrows show the apparent position of the background galaxy. A duplicate or multiple image can be observed from Earth. The white arrows show the path of light from the true position of the source.


Angle of the bending light

Einstein  in 1911 obtained a deflection angle of (radians) = 0.87 arc second,  which is the Newtonian value.

About four years after his first paper in 1911, Einstein had developed the General Theory of Relativity (1915) which prompted him to modify the above Newtonian value by adding the effect of curved space thus doubling the bending angle resulting in a new value of 1.75 arc seconds (1.7505395 arc second). The new result was published by Einstein on November 18, (1915) and was experimentally verified by Crommelin and Eddington during the solar eclipse expeditions of May 29, 1919.


Any large mass distorts the geometry of space around it (Note the word “around”), for instance making parallel light rays diverge or converge. One consequence, described by Einstein’s general theory of relativity is that objects behind a body such as the Sun may look magnified or distorted as the optical path of light goes through the region of warped space.

The bending of light in gravitational fields is much better explained by Snell’s law of refraction (see Fig. 1) which was experimentally established by Willebrod Snell and theoretically by René Descartes over three hundred years ago.


Bending Light
The first prediction put to test was the apparent bending of light as it passes near a massive body. This effect was conclusively observed during the solar eclipse of 1919, when the Sun was silhouetted against the Hyades star cluster, for which the positi ons were well known.

Sir Arthur Eddington stationed himself on an island off the western coast of Africa and sent another group of British scientists to Brazil. Their measurements of several of the stars in the cluster showed that the light from these stars was indeed bent as it grazed the Sun, by the exact amount of Einstein’s predictions. Einstein became a celebrity overnight when the results were announced.

The apparent displacement of light results from the warping of space in the vicinity of the massive object through which light travels. The light never changes course, but merely follows the curvature of space. Astronomers now refer to this displacement o f light as gravitational lensing.


Important Historical Anecdote: The solar eclipse of 1919 

Albert Einstein’s prediction of the bending of light by the gravity of the Sun, one of the components of his general theory of relativity, can be tested during a solar eclipse, when stars with apparent position near the sun become visible.

Two expeditions were made to measure positions of stars during this eclipse. The first was led by Sir Frank Watson Dyson and Sir Arthur Eddington to the island of Principe (off the west coast of Africa), the second by Andrew Claude de la Cherois Crommelin and Charles Davidson to Sobral in Brazil.

The expedition to observe the eclipse proved to be one of those infrequent, but recurring, moments when astronomical observations have overthrown the foundations of physics. In this case it helped replace Newton’s Law of Gravity with Einstein’s theory of General Relativity as the generally accepted fundamental theory of gravity.

Following were the three possibilities: There might be no deflection at all; that is to say, light might not be subject to gravitation. There might be a `half-deflection’, signifying that light was subject to gravitation, as Newton had suggested, and obeyed the simple Newtonian law. Or there might be a `full deflection’, confirming Einstein’s instead of Newton’s law.


The nice thing about using mass instead of mass is that mass is a property that all observers agree on, whereas mass is not. There aren’t that many properties of an object that are like this.  Take the speed of an object; different observers won’t agree on what it is.  For instance, there goes a car; how fast is it moving? Well, from your point of view, standing by the road, perhaps it is moving at 80 kilometers per hour.  But from the point of view of the car’s driver, the car isn’t moving at all; you’removing.  And from the point of view of someone in a car going the other direction, the first car may be moving at, say, 150 kilometers per hour.  The bottom line?  Speed is a relative quantity; you cannot ask, what is the speed of the car, because it has no answer.  Instead you must ask, what is the object’s speed relative to a particular observer.  Every observer has an equal right to make the measurement, but different observers will get different answers.  Galileo’s principle of relativity (long before Einstein’s principle of relativity, which involved adjusting Galileo’s principle)  already incorporated this idea.

This dependence on the observer also applies to energy, and to momentum.  And it applies to relativistic mass.  That’s because relativistic mass is simply the same as energy, divided by a constant — namely, c² — and so, if you define mass to be “relativistic mass“, then different observers disagree about an object’s mass m, though all agree that E=mc².

But rest mass, or, as I would call it, “mass“, does not depend on the observer, which is why it is also called invariant mass.  All observers agree on an object’s mass m, with this definition.  And all observers agree that if you were stationary with respect to the object, you would measure its energy to be mc², and otherwise you would measure its energy to be larger.[3]


Newton’s equations still differed from Maxwell’s equations in that they implied instantaneous action, that is, infinite velocities. Special relativity had decisively shown that the fastest velocity was that of light, thus limited the speed at which even gravity could influence matter.


E equals m cee squared

One of the consequences of Einstein’s theory is that mass and energy, rather than subject to separate and independent conservation laws, are conserved together and are therefore at some fundamental level equivalent. This famous equivalence of mass and energy is expressed in the equation known across the world: E=mc2. The speed of light links small amounts of mass to enormous amounts of potential energy. Originally thought to be only of academic interest, this conversion was later carried out through the mechanism of the nuclear fission chain reaction. The energy released by the two atomic bombs dropped by the United States at the end of World War II, which each incinerated a city, was the equivalent of less than one gram of mass.


 

References

  1. http://archive.ncsa.illinois.edu/Cyberia/NumRel/GenRelativity.html
  2. https://www.forbes.com/sites/startswithabang/2017/08/04/americas-previous-coast-to-coast-eclipse-almost-proved-einstein-right/#214629e737c3
  3. https://profmattstrassler.com/articles-and-posts/particle-physics-basics/mass-energy-matter-etc/more-on-mass/the-two-definitions-of-mass-and-why-i-use-only-one/
  4. http://ircamera.as.arizona.edu/Astr2016/lectures/physicallaws.htm
  5. https://www.sciencenews.org/article/einsteins-genius-changed-sciences-perception-gravity
  6. https://www.wsws.org/en/articles/2015/12/07/ein1-d07.html
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