**The most beautiful physical theory ever invented**

**Einstein’s World Part III**

In this third and last part of my series on Einstein I want to talk about *General Relativity*, which, according to some scholars, is the most beautiful physical theory ever invented.

Let us think of cosmological speeds for a while. As passengers on our planet earth, we travel along the earth’s revolution about its axis at the speed of over one thousand miles per hour, if we are in the tropics. That is about twice the speed of a Boeing 747. If we are in New York, our speed is more like 800 miles per hour, because our orbits become smaller as we move away from the equator. Those are good speeds but nothing close to our orbital speed. On our orbit around the sun we travel at 67 thousand miles per hour. That’s a better speed but pales in comparison with the speed of light. Our sun orbits around the centre of our galaxy at 43 thousand miles per hour, dragging all of us along at that phenomenal speed. At 107 thousand miles per hour on its orbit around the sun, Mercury is the fastest planet. So, it turns out that Mercury is the fastest object in our solar system. Quite appropriate for a planet named after the God of speed! But even Mercury’s speed is only a tiny fraction of the speed of light, so tiny in fact, that its Lorentz factor is 1.00000002 which means that any relativistic corrections to planetary speeds are meaningless and Newtonian mechanics apply!

According to some scholars, Einstein’s General Relativity Theory is the most beautiful physical theory ever invented. The mathematical formalism is rather difficult as it uses tensor mathematics, curved spacetimes and non-Euclidean geometries. This is advanced mathematical symbolism and we will avoid it as much as possible. We are not Einsteins but we should be able to translate the symbolism into our natural language in order to grasp the physical concepts.

Einstein had restricted his Special Relativity Theory to *inertial frames*, which means frames with bodies that are either at rest or are moving at constant speed. No forces were acting upon bodies and therefore no acceleration was allowed. Gravity could not be accounted for, because gravitational fields create forces and accelerating bodies. Einstein embarked on a major effort in 1908 to include the effects of gravity in a more generalized theory and published the theory in 1916 in a treatise titled *Foundations of the General Theory of Relativity*. A few months later he published a small book titled *On the Special and the General Theory of Relativity Generally Comprehensible*. As its title suggests, the book was intended for a wider audience and was written with the minimum amount of mathematical language. We can plainly say that there is no better place than this book for a non-mathematician to understand relativity. It is a must read for anyone wishing a good insight on the meaning of relativity and, thankfully, the book is in the public domain and downloadable at no cost from web sites such as the Gutenberg Project web site. Bertrand Russell’s excellent little book titled *The ABC of Relativity* is another great source that explains the theory in non-mathematical language and provides an excellent discussion of the philosophical aspects of relativity.

With all the recognition Einstein received for his Special Relativity, especially after Max Planck’s endorsement and support, the new theory did not achieve immediate appreciation in the scientific community. That changed after Arthur Eddington’s expedition to southern Africa and the successful empirical confirmation of the theory. The confirmation of the theory made worldwide headlines and Einstein became an instant celebrity, the best known person in world science.

**Matter and Gravity**

The General Theory of Relativity is a theory of matter and gravity and its mathematical formalism is complicated. That, of course, will not prevent us from trying to understand its physical meaning. Everything in General Relativity is interesting but we will have to limit our review to a few outstandingly significant points.

The first important idea is that light is deflected by gravity. This is not so difficult to understand and we saw that it was confirmed in the Eddington expedition. But still, the idea is not intuitive. Why is light, which consists of photons without mass, deflected by gravity? What happened to Newton’s law that gravity is a force of attraction between masses?

A possible explanation might be that, due to mass-energy equivalence *E=mc2*, packets of energy behave like mass and display mass-like characteristics in a gravitational field. But questions remain. Could something else other than gravity be happening in the vicinity of the solar surface that might be attracting light and be equally consistent with Eddington’s result?

Remember, the solar surface is not a fun place to be, certainly not recommended for a winter vacation in the sun (pun intended). It is a boiling environment in constant motion, full of helium and hydrogen atoms, free electrons colliding with everything on their aimless paths, naked atomic nuclei, loose protons and neutrons, magnetic fields, flares and solar winds. Is it reasonable to expect that light photons passing through would leave unscathed, even in the absence of gravity?

**Why is light deflected by gravity?**

So, the basic question is: why are massless light photons attracted by gravity? If we really want to answer this question effectively in relativity’s favor, we can do it in a couple of different ways. First, photons may have zero mass but they have energy which in relativity is equivalent to mass. The photon therefore has inertial mass which, by one of the postulates of relativity, is equivalent to gravitational mass. Second, relativistic gravity does not arise from the force of the gravitational field but from a *geometrical distortion of spacetime* that occurs near large masses. These two answers may prove adequate if we just go through the math but then another question arises: is this a pure theoretical construct or does it also have a physical meaning?

The second important idea of General Relativity is exactly the geometrical distortion of spacetime suggested in the above paragraph. Spacetime gets distorted and acquires curvature characteristics near large masses. This idea presents conceptual difficulties which arise, most likely, from our lack of empirical knowledge of spacetime as a single frame. Our lack of direct experience of high velocities and curved non-Euclidean geometries does not help either. The need for non-Euclidean geometries arises from the curvature of space. Straight lines and perfect circles are Euclidean idealizations and do not really exist in nature.

Think for a moment of the meridian that goes from the equator through New York and ends at the North Pole. Then think of the meridian that goes through Athens, Greece. These two meridians together with the equator segment between them form a huge triangle which has two right angles at its base, each being exactly 90 degrees. The triangle is completed with a 100 degree angle at the top. The sum of the three angles is 280 degrees, far exceeding the 180 degrees required in Euclidean geometry that we all had to learn at school. This is the result of curved space.

A straight line drawn between two cities on a flat map is not the shortest distance between the two cities and our commercial airlines know this quite well. The flight from Frankfurt to Seattle does not head directly to the west from Frankfurt. It travels northwest toward Greenland and passes over the southern part of Greenland before heading southwest toward Seattle. The shortest distance between two cities is a curved path and similarly the planets in the solar system follow the shortest paths, those that require the least amount of energy. The planetary motions we observe are the result of this economy. In their motion around the sun, the planets take a curved path because the huge solar mass bends spacetime around it and Euclidean geometry is not the most accurate mathematical tool in dealing with problems such as this.

Einstein’s theory does not prove in any way that large masses cause a distortion of spacetime. It just describes gravitational effects as distortions of spacetime rather than as outcomes of physical gravitational forces. In General Relativity, gravity is not a force as Isaac Newton had proposed. Gravity is a consequence of the curvature of spacetime near large masses. The reader should be assured that this is a difficult concept and even physicists find it difficult to visualize what a distorted curved spacetime looks like. If we cannot visualize spacetime, it is rather hard to visualize a distortion of curved spacetime.

Just think about this for a moment. Can space be transformed into time and vice versa? In other words, are space and time equivalent in the same sense that mass and energy are equivalent? Probably a good question and an avenue for exciting new research.

Common concerns regarding relativity are not necessarily a criticism or refutation of the theory. They arise from a disconnect between intuitiveness and plausibility. Certain aspects of relativity are far from being intuitive but are not necessarily implausible. The difficulty arises from the fact that we have learned to be intuitive only about ideas that are believable. Our intuition has been formed by cause-and-effect relationships that our empirical past has shown to be possible.

**The CERN experiment**

An extraordinary experiment took place in 2011 in the CERN nuclear research facility in Geneva. The experiment found neutrinos that were moving faster than the speed of light. The results were published and many scientists were shocked, while others hailed the result as a refutation of relativity. The idea that the speed of light is the maximum speed in the universe is one of the cornerstones of relativity and modern physics. The difference in speed between the neutrinos and light was greater than that allowed by the statistical error of the experiment. Other labs around the world were unable to reproduce the same results. CERN replicated the experiment in 2012 and found that the neutrinos did not exceed the speed of light and that the first result was due to various measurement errors. What a sigh of relief for concerned pro-relativity scientists!

The fact is that, one hundred years from Einstein’s publications, the vast bulk of his ideas are standing up to the test of time. At the same time, hundrends of scientists around the world are still trying to find new experimental methods of verifying or refuting his theories.

Regardless of the failure or success of these tests, Einstein is the undisputed greatest scientific mind since Newton. Einstein’s unique mind and vision has turned our attention to a very different and totally unexplored view of nature. He gave us radically original visions and concepts of natural phenomena and opened up scientific exploration in may new areas. The scientific research based on Einstein’s ideas is as vigorous and enthusiastic today as it has ever been.

**Quest for the Holy Grail**

Quantum theory and relativity marked the dawn of a new age in man’s understanding of the natural world. In our discussion of Einstein we briefly mentioned his efforts to develop a general theory that would unify the forces of the universe and the laws of physics into one framework. Einstein felt very strongly that all of nature must be described by a single theory. He spent the latter part of his life at Princeton on this effort and was not successful in achieving a general theory. He was successful, however, in motivating thousands of other scientists into this *Road Not Taken* of scientific exploration.

A proposal was made by German mathematician Theodor Kaluza to expand Einstein’s four dimensional spacetime into a five dimensional space that would include spacetime together with Maxwell’s equations, uniting gravity and electromagnetism. Einstein was enthusiastic with the proposal and wrote to Kaluza that *“the idea of achieving unification by means of a five-dimensional cylinder world would never have dawned on me. At first glance I like your idea enormously.”* Kaluza’s idea was later abandoned but Einstein never gave up his quest for a unified theory.

Einstein never quite accepted quantum theory and his failure to develop a unified theory may be due to this fact. Near the end of his life he found himself somewhat isolated from the scientific community and became absorbed in mathematical formalism, detached from the physical intuition that inspired his early discoveries. Sixty years after Einstein’s death, unified theory is still the holy grail of modern physics.