November 25th Centenary Date for Einstein’s General Theory of Relativity

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Rμν – ½ Rgμν +Λgμν = 1/c4(8 π G Tμν)

Over the centuries, many have tried to explain gravity but none have done more or come closer to a full explanation or understanding of it than the great physicist, thinker, philosopher and Nobel Laureate, Albert Einstein. Isaac Newton published his Principia Mathematica in 1687. It contained all of his work, including but not limited to his derivation of Differential Calculus, his famous three laws of motion and the law of Universal Gravitation. In a word, it is the compendium of a life’s work in a single volume.

Today we celebrate the Centenary of Einstein’s theory on gravity, his General Theory of Relativity (GTR). On four consecutive Thursdays in November of 1915, he presented his General Theory of Relativity to the Prussian Academy of Sciences. In his final lecture, delivered on November 25th, 1915, exactly one hundred years ago today, he presented the following equation to those gathered:

Rμν – ½ Rgμν = 8 π G Tμν

This first iteration of an expression, which came to be known as the Einstein Field Equation, is written in compact Tensor form. Tensors allow for physical systems to be described in a coordinate independent manner, that is without regard to a certain physical geometry (planar, spherical, cylindrical, etc). This expression describes the gravitational-inertial field, the interplay between the curvature of space-time and distances along the curve formed on the space-time fabric by any object (with mass), expressed on the left side of the equation and the nature of the object itself, the source of the curvature, on the right side. Two years later in 1917, after publishing a paper in which he applied GTR to the universe as a whole, concluding that the universe would have long ago collapsed in on itself, Einstein added an additional term that “opposes gravity”, accounting for what astronomers in 1917 thought the universe was, static and fixed.  Since the universe, obviously had not imploded in on itself, this term was deemed necessary. Known as the Cosmological Constant, it applies a small, negative “push” to space to account for what was observed.  When it emerged that the universe is expanding, Einstein, in what he would later describe as his “greatest blunder”, dismissed this idea entirely and removed the term from his equations. It turns out, however, that including that term was another stroke of genius not realized at the time. It would come to describe what is today referred to as “Dark Energy” or exactly what he described it to be back in 1917, the increased expansion rate of the universe at cosmologically significant distances. Today, the Einstein Field Equation includes the Cosmological Constant, Λgμν and is written

Rμν – ½ Rgμν +Λgμν =  1/c4(8 π G Tμν)

R and g are tensors that describe the structure of space-time, T pertains to the matter and energy affecting that structure (the physical aspects of the object that include its matter and energy); G and c, the Universal Gravitational constant and the speed of light, respectively are conversion factors that arise from using traditional units of measurement. When the Cosmological Constant is zero, the Field Equations revert to those as originally published in GTR. When T is zero, the Field Equations describe vacuum space or a space devoid of any matter.

Theories remain theories until repeatable, dependable and predictable results are obtained by many independent investigations. Newton’s “Law of Gravity” remained a theory until numerous experiments produced predictable, calculable, reliable results, repeatedly, over the course of centuries; only then was it deemed worthy to be regarded as a “law”. It perfectly describes most of the macro behavior of objects under the influence of gravity; with it we can deduce orbits, trajectories, periods, mass based on period and everything else related; so well do we understand gravity that the unseen presence of Neptune was deduced from the orbital perturbations of Uranus. Newton’s Universal law of Gravity explains the “how” of gravity, the behavior of objects under its influence, that it is a mutually attractive force whose magnitude is proportional to the product of all the masses and inversely related to the square of the distances separating them. The “why” of gravity, by his own admission, Newton was perfectly content to relegate to the “Invisible hand of God”, the “God of the Gaps” and thus, Newton made no hypothesis in that direction. As well, there were some observations that defied explanation using standard Newtonian dynamics; one famous example, known to Newton and defying explanation until GTR, was the precession of Mercury’s perihelion (the point in Mercury’s orbit about the sun that is closest to the sun) at a rate of 43 arc-seconds per century.

To test a prediction of GTR, that an apparent shift of a star in the vicinity of a massive object would occur, Sir Arthur Eddington measured the positional changes of a star in the Hyades cluster during the famous total solar eclipse of 29 May, 1919, observing the event from the West African island of  Príncipe.

Total solar eclipse of 11 July 1991 as imaged by the author in Cabo San Lucas, Mexico with his 15 cm Newtonian astrograph
CURVATURA
The path of a beam of starlight, moving along space-time as it passes the limb of the sun, illustrating a prediction of GTR. Point A represents the true position of the star, point B the apparent position.

According to GTR, everything must follow the curvature of space-time, including a beam of light. In this famous experiment, the position of a star in the Hyades star cluster, located proximally to the sun’s limb during the eclipse, was compared to its position as determined by Eddington during January and February of that year. A second contingent was sent to Brazil to observe the eclipse just in case bad weather would preclude observations from either location. Clear skies prevailed in both locations and the rest is history! GTR predicted a change in position of 1.75 arc-seconds and that is precisely what Eddington and his team observed!

Well, many of the inconsistencies and seeming contradictions in much of what had been published or what was being  published at the time didn’t sit well with the the imaginative young Einstein. While working in the Bern, Switzerland patent office a few years after the turn of the 19th century, he would look out the window at the trains coming and going.  This work in the Swiss patent office led him to develop and publish his “Special Theory of Relativity” (STR) in 1905, special in that the theory considered only inertial (non-accelerated) frames of reference. Another ten years would go by for him to complete GTR, where inertial and non-inertial frames of reference would be considered. That he was employed at the patent office at that time, with the nature of his job duties and the demanding personalities of his employer would come to serve him well and, by extension, the next hundred years of scientific discovery. On one particular occasion, while observing the trains and reviewing patents for clock synchronization technology by radio, he began to wonder about the timing of events, about their “simultaneity”. This singular thought experiment, occurring to him whilst he imagined what would happen if one were to ride on a light beam, would become one of the key aspects of a theory that would revolutionize science and the world for the next hundred years. He considered two lightening strikes on a set of railroad tracks with an observer standing on the station platform exactly midway between the lightning strikes; a passenger onboard a train passing through the station, observing the lightning as they pass the stationary observer on the platform would observe the strike in the direction of motion as having occurred first whilst the individual standing on the platform would observe the lightning “simultaneously”. Einstein realized that both cannot be correct, that there is no reason to assume that the station platform is at rest and that the train is moving and deduced, in an act of absolute creative genius, that there are no absolute reference frames and that time, itself, is relative. What is “simultaneous” is relative, depending on your state of motion. That time was “relative” had far-reaching implications. The greater the relative motion between one object and another, the more “relative” time becomes between the two. In other words, time slows down for an observer onboard the moving train whilst time remains as it was for the individual standing on the platform. The greater the velocity of the train, the more time slows down relative to the individual on the platform. This relative nature of time sets the universal speed limit at the speed of light; nothing but light can travel at light speed. At light speed, time would have stopped for the individual on the train. Additional consequences of Special Relativity include shortening of length and increase of mass in the same proportion as “time dilation”. The magnitude of these relativistic effects, represented by the Greek letter Gamma, is described as RelGamma (invert)

. A first-year mathematics student will quickly note that as v approaches c in the denominator of this expression, the whole expression becomes undefined (approaches infinity). These aspects of nature: time dilation, length contraction, mass increase and light speed as the universal speed limit came out of STR, while the grand question, the heretofore inexplicable nature of gravity, its “why”, came out of GTR. A postulate of STR  worth noting is that all physical constants are location invariant (they are the same everywhere: in all inertial reference frames); how would the universe look if, for example, the speed of light were different in the Virgo Cluster of Galaxies? GTR is Einstein’s general theory of gravity just as the Universal Law of Gravitation was Newton’s. Instead of thinking of gravity as a mutually attractive force, Einstein thought of gravity as the behavior of objects moving in accordance with the curvature of space in the vicinity of a massive object or, more precisely, the curvature of space-time, since space and time are inexorably linked. Einstein’s Field Equation is the mathematical description of this and is the answer to the “why” of gravity. One of the principal assumptions of GTR is Einstein’s principle of Equivalence. The behavior of objects in an accelerated reference frame (a spacecraft accelerating at one “g” in deep space) is the same as the behavior of an object under the influence of  gravity (an individual standing on the surface of the earth), that one is indistinguishable from the other.

Over the intervening century, there have been many challenges to both STR and GTR, experiments conducted in attempts to affirm Einstein’s revolutionary ideas and some to disprove them. Of all these challenges, all have  affirmed the veracity of both STR and GTR, elegant experiments such as the 1919 total solar eclipse with none even remotely calling into question any aspect of these theories.  Of particular note is the famous Muon half-life experiment, an experiment that compared the half-life of a Muon traveling at relativistic speeds and the half-life of a Muon at rest. In this case, the half-life of the Muon traveling at relativistic speeds had increased according to the predictions of STR.

Another brilliant success story concerning a direct challenge to STR concerned recent experiments at CERN. During high-energy particle collisions, where the fundamental building blocks of protons and neutrons are ejected in a maelstrom, tiny sub-atomic particles, known as “neutrinos” (Enrico Fermi’s “little neutral ones”), are released. That the energies involved are so great and that the neutrino has such a tiny mass means that they will be ejected at very high, relativistic speeds, speeds approaching 99% the speed of light. Due to timing errors in the detectors located on Gran Sasso in the Italian Apennines, the speed of the neutrinos produced in multiple iterations of the same experiment by independent research teams indicated that the neutrinos were traveling above light speed, 60 nanoseconds ahead of schedule! Had this been true, it would have been a huge problem not just for physics but for all of science. It would have meant, literally, a rewrite of all physics textbooks for the last one hundred years. Where was the problem with STR? Why are some aspects of the theory demonstrably correct while this one, a cornerstone principle of the famous theory, now called into doubt? These were some of the questions the entire scientific world was wrestling with.  The problem was traced to a GPS fiber-optic cable that carried timing signals from the surface of Gran Sasso, down the 8.3 kilometers to the detector. With each of these challenges overcome, a new triumph is won and Einstein’s brilliance shines once again!

We take for granted much in our technical age, not the least of which is GTR. We use it more than we think; the accuracy and success of GPS technology, that it works at all, relies heavily on the veracity of GTR.

Black_Holes_-_Monsters_in_Space
Artist’s rendition of an accretion disk surrounding a black hole exhibiting polar, vortex-like synchrotron radiation
BlackHole_Lensing
Artist’s rendition of a foreground black hole bending (lensing) the light from the Galactic center

GTR has had fundamental implications on our understanding of the large-scale universe. The concept of a Black Hole, an entity whose gravity is so intense that not even light can escape its clutches, was first introduced in GTR. A massive star, usually in excess of 10x the mass of the sun, ends its life in a catastrophic explosion known as a Type II supernova. The “remnant” can form a rapidly rotating neutron star, known as a pulsar or, if the progenitor star was massive enough, a Black Hole. The first modern solution to general relativity that would characterize a black hole was found by Karl Schwarzschild in 1916.

In this special case of gravitational lensing, captured with the HST, an “Einstein Ring” is produced consisting of the distorted images of background galaxies from the bending of light around the massive foreground elliptical galaxies

The warping effects a black hole or any massive object has on the local space leads to gravitational lensing; the space is so distorted that any object in the background will appear to be “lensed” or distorted to the point where its real shape will be undetermined.

It should be pointed out that Einstein did not receive the Nobel Prize in Physics for Relativity; he received it for his work with the Photoelectric effect, that an electric current will be produced when light of a high-enough frequency (bluer color) is incident upon a metal substrate. This experiment demonstrated that photons of light (massless particles-the particle aspect of light’s wave-particle duality) are quantized packets of energy, affirming another watershed idea, that atoms have discrete, quantified and non-random energy states. Only light of a high enough frequency will produce the electric current; even very intense light of a lower frequency (redder color) will not work; the light has to be a minimum frequency in order to produce the electric current. This experiment has led to modern, beneficial applications such as the development of Solar Photovoltaic panels to produce clean, carbon-free electricity. Einstein’s papers on the Photoelectric Effect (Titled: On A Heuristic Point of View Concerning The Production and Transformation of Light) and Special Relativity (Titled: On the Electrodynamics of Moving Particles) were two of four papers published during his Annus Mirabilis (miracle year) of 1905.

There never will be another Einstein; yes, we have brilliant physicists but none with the imagination he had. No one in the previous 100 years has introduced fundamental, paradigm-changing ideas that have revolutionized science and our understanding of the universe as Einstein did and I don’t believe there will be another, ever. We will continue to apply Einstein’s theories in ever more creative ways in an effort to more fully understand the universe but the root-basic foundation, the essence of all of our science will forever retain his mark, his signature, his gift to all future generations as its pinnacle. This has been set in stone by him and I don’t believe it will change.

Imagination is more important than knowledge585px-Albert_Einstein_signature_1934(invert)

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