[McQueen (OP)]

       Newton’s achievement in postulating the manner in which gravity works is today often underrated because of the importance given to Einstein and his General Theory of Relativity.  Yet, the simplicity and lucidity of Newton’s explanation of how gravity works, still remains.  In fact Newton’s concept of Gravity, or rather of how gravity works, is so compelling, that one is tempted to wonder what is so special about General Relativity.

   For more than a decade after coming up with the theory of Special Relativity, Einstein struggled trying to evolve an alternate theory for Gravity, in the end he succeeded. The question is did he really succeed in overthrowing Newton’s version of gravity OR did he merely assign different functions and characters to Newton’s gravitational equations? By following this strategy it was possible for Einstein to reach the same results that Newton’s equations yielded albeit in a hidden and obscure manner.  If looked at in an unbiased manner, this is plain plagiarism at the highest level.

   How true could this assumption be? In order to discover the truth it is necessary to examine Einstein’s  field equation relating the curvature of spacetime to energy sources, which serves as the bedrock principle of general relativity:



where is the Ricci curvature tensor, R is the scalar curvature, is the metric tensor,  G is Newton's gravitational constant, c is the speed of light in vacuum, and is the stress–energy tensor. What it means is that :

(gravity) = 8 G × (energy and momentum).

The amount of gravity is proportional to the amount of energy and momentum, with the constant of proportionality is given by , where G is a numerical constant. This is interesting  because Einstein takes Newton’s theory one step further when he uses the principle of mass energy equivalence to state that gravity is due to energy and momentum.

   This is truly a wonderful approach and deserves appreciation. The question is how did Einstein achieve such a close and uncanny approach to Newton’s results? Einstein’s equations achieve such uncannily similar results to Newton’s that it is absolutely mind-boggling, his results vary by those of Newton only by one in several decimal places. How is this possible?

   One of the problems is that although Newton’s equation for gravity remains one of the most influential in the history of science, it, unfortunately, leaves out one of the main objects of the theory, namely an explanation of why gravity works in the way it does.  Instead, Newton’s theory of gravity seems to depend on action at a distance — two objects exert a gravitational force on each other from far away, without any intervening substance. Newton himself considered this to be an unacceptable state of affairs, although he didn’t really have a good answer as to why this was so. He could have easily postulated that gravity was carried by an invisible field called the Aether but he was adamant that he would not speculate:  Hypothesis non fingo! (I make no hypothesis.)

Einstein’s solution to this conundrum was to postulate a Universal gravitational field the effect of which was to shift the focus from the force of gravity, F, to the gravitational potential field, (Greek letter “phi”), from which the force can be derived. The field \phi fills all of space, taking some specific value at every point. In the vicinity of a single body of mass M, the gravitational potential field is given by the equation:



The introduction of a field (or Aether) can be considered to be a mere technicality when taken in the context of Newton’s equation, it is something that is presumed to be present.  Notice how closely this equation of Einstein’s resembles Newton’s original equation :



with the added advantage in that it depends inversely on the distance, rather than the distance squared, because it’s not the gravitational force directly; the force is given by the derivative (slope) of the field, which turns into .

         It is possible to see the similarity in structure to Einstein’s equation: the left hand side is the force of gravity between two objects, and on the right we find the masses m_1 and m_2 of the objects in question, as well as the constant of proportionality G. (For Newton, mass was the source of gravity; Whereas, Einstein reasoned that mass is just one form of energy, and upgraded the source of gravity to all forms of energy and momentum.) Both equations, Einstein’s and Newton’s, divide by the square of the distance r between the two objects.

   The nub of the problem is that what has been done by Einstein, is to merely name the filed (Aether) that Newton refused to hypothesise about, as a gravitational field, with a value for every point in space, and to substitute the term force with the term gravitational potential.  Can we say with any surety, using Einstein’s equations that so much mass gives rise to so much gravity? Of course, it is possible because what we have here is more or less a clone of Newton’s ideas, dressed up a bit to include energy and momentum it is true but equally true is the fact that without the underlying basis of Newton’s ideas and interchanged with new terminology.  Nothing in Einstein’s General Theory of Relativity would make sense without this venture into Newton’s ideas.  I wonder what Newton himself would have had to say about it?

   

[Bored chemist]

If looked at in an unbiased manner, this is plain plagiarism at the highest level.

No.
Plagiarism implies dishonestly passing someone else's work off as your own.
Building on  the universally acknowledged work of others is different.

Newton’s achievement in postulating the manner in which gravity works is today often underrated

By whom?

(gravity) = 8  G × (energy and momentum).

Energy and momentum have different units.
You can't add them.

[McQueen (OP)]

Normally it shouldn't but with time dilation and length contraction it happens..... according to Einstein: Quote from Wikipedia:

"The Einstein field equations (EFE; also known as Einstein's equations) comprise the set of 10 equations in Albert Einstein's general theory of relativity that describe the fundamental interaction of gravitation as a result of space time being curved by mass and energy. First published by Einstein in 1915 as a tensor equation, the EFE relate local spacetime curvature (expressed by the Einstein tensor) with the local energy and momentum within that spacetime (expressed by the stress–energy tensor). "

[Bored chemist]

Normally it shouldn't but with time dilation and length contraction it happens..... according to Einstein: Quote from Wikipedia:
The Einstein field equations (EFE; also known as Einstein's equations) comprise the set of 10 equations in Albert Einstein's general theory of relativity that describe the fundamental interaction of gravitation as a result of space time being curved by mass and energy. First published by Einstein in 1915 as a tensor equation, the EFE relate local spacetime curvature (expressed by the Einstein tensor) with the local energy and momentum within that spacetime (expressed by the stress–energy tensor).

OK, so the issue there may have been your failure to use the correct notation to indicate that you were referring to a tensor.

What about the other problems?