What Does General Relativity Have To Do With Mercury’s Orbit?

This post may not be for everybody!  When Einstein developed his theory of general relativity, the relevance of his theory depended on someone photographically observing the planet Mercury during an eclipse.  Photons of light (little packets of light energy) are not technically affected by large gravitational fields, because they do not have mass, however they do have momentum.  A change in momentum will yield a force, so this property allows light to be able to physically interact with matter.  This effect was conclusively observed during the solar eclipse of 1919, when the Sun was silhouetted against the Hyades star cluster, for which the positions were well known.  Sir Arthur Eddington stationed himself on an island off the western coast of Africa and another group of British scientists was sent 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 an instant celebrity overnight, when the results were announced.

Relativity begins with a modest question of, ‘How does your physics relate to my physics if we are moving relative to each other?’  Galileo thought that we find exactly the same laws of mechanics if our relative speed is constant.  Newton said the same thing, but more elaborately by referring to all motion, and relating this to an absolute frame of reference in space and time.  Einstein once said about his 1905 theory of special relativity, “The term relativity refers to time and space.  According to Galileo and Newton, time and space were absolute entities, and the moving systems of the universe were dependent on this absolute time and space.  On this conception was built the science of mechanics.  The resulting formulas sufficed for all motions of a slow nature; it was found, however, that they would not conform to the rapid motions apparent in electrodynamics.  This led the Dutch professor, Lorentz, and myself to develop the theory of special relativity.  Briefly, it discards absolute time and space and makes them in every instance relative to moving systems.  By this theory all phenomena in electrodynamics, as well as mechanics, hitherto irreducible by the old formulae, and there are multitudes, were satisfactorily explained.  Till now it was believed that time and space existed by themselves, even if there was nothing else, no Sun, no Earth, no stars, while now we know that time and space are not the vessel for the universe, but could not exist at all if there were no contents, namely, no Sun, Earth and other celestial bodies.  This special relativity, forming the first part of my theory, relates to all systems moving with uniform motion; that is, moving in a straight line with equal velocity.”

In 1912, Einstein began to devote a major portion of his time and energy to an attempt to construct a relativistic theory of gravitation.  General relativity is derived from Isaac Newton’s “Principia” that he wrote in 1687, where gravity is a force exerted by objects with mass and the greater the mass, the greater the gravitational force.  The larger the distance between objects, the lesser the force (it decreases with the square of the distance).  The gravity of the Sun pulls on Earth and holds it, along with the other planets, asteroids, comets, etc., in orbit.  In 1916, Albert Einstein disagreed and said this was not the way that gravity worked.  He came up with a completely new, and quite radical, alternative explanation.  Einstein’s crazy idea is that the presence of mass warps the fabric of space around it.  Then, that warped space controls the motion of other masses nearby.  Newton’s idea of a gravitational force is thus replaced with four-dimensional space-time geometry.  Planets orbiting around stars, and stars traveling through galaxies, these are space-time distortions moving within other space-time distortions.  General relativity is a description of mass telling space how to warp, while warped space tells mass how to move.

On the face of it, Isaac and Albert are just describing the same phenomenon from two different points of view, where Newton sees a force, while Einstein sees geometric distortions.  Since the algebraic equations of the gravitational force are so much simpler than the tensor calculus needed to explain General Relativity, is it really worth all the trouble trying to understand Einstein?  The answer is yes, because Newton’s gravity is wrong when extremely large masses are involved.  The most famous of these is the precession of the perihelion of Mercury.  The orbit of Mercury is not fixed in space.  Each time Mercury orbits the Sun, its orbit rotates by a minuscule amount.  The position when Mercury is closest to the Sun, called perihelion, is used to measure this orbit rotation, called precession.  While Newton’s gravity predicts a precession of the perihelion of Mercury, the measured value is significantly higher.  This mismatch between prediction and observation is resolved by Einstein’s general relativity in that the warping of space at such a close distance to the Sun produces a slightly stronger precession than gravitational force.

Written for Linda G Hill’s October 25, 2017 One-Liner Wednesday – Mercury?

6 thoughts on “What Does General Relativity Have To Do With Mercury’s Orbit?

  1. I’m often puzzled why light, which is without mass, should bend around a massive object although I accept that it does appear to do that since there is observational evidence. It also doesn’t make sense to me that light should have momentum. If momentum (p) is the product of mass (m) times velocity (v), then p = m * v. But if m = 0, because light has no mass, then why isn’t momentum also 0 for light? I guess I could look this up on the internet, but I haven’t been puzzled that much by it.

    It might have to do with space-time curvature around massive objects, but then I suspect one could say that light has no momentum. It is simply moving through the shortest path which happens to be curved.

    I also wonder why should I consider Einstein’s gravitational theory correct if it needs dark matter (and dark energy in some circumstances) which haven’t been found? Doesn’t the faster than expected rotation of galaxies and clusters of galaxies empirically falsify Einstein’s theory?

    Just some thoughts.

    Liked by 1 person

    1. Thanks for taking the time to read my post and you do have some interesting thoughts. I understand that General Relativity can be confusing and I did not write this post to explain everything about it. A photon is considered to have relativistic mass that is proportional to its momentum, which is inversely proportional to their wavelength and Einstein specifically proved that relativistic mass is an extension or generalization of Newtonian mass, so conceptually we can treat the two the same. Light moves in a straight line through curved space and I am not sure how dark matter and dark energy fit into this, but I don’t think that anyone else knows that either. Man keeps learning and getting smarter because we are curious, and wondering why and how things in the universe work is what drives science.

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      1. The relativistic mass comes in with E = mc^2. Replace E with the energy of a photon to get its relativistic mass. I don’t know much more than that, but thinking about it makes me realize there is a lot I don’t understand. The missing dark matter makes me wonder how correct any of this is. Of course, I have to accept whatever technology works that is based on this theory, even if the theory is ultimately wrong. Technology is the best experimental evidence a theory has.

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    1. Galilean relativity is simple enough to understand, saying that it is impossible to tell whether or not you are moving unless you have a frame of reference, but Einstein’s Special and General Relativities are more complicated. I am not familiar with Fandango Relativity, but it could hold the key to all the knowledge in the universe.

      Liked by 1 person

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