Einstein, Your GPS (and Me)

Just 100 years ago, Einstein announced his General Theory of Relativity.  Four decades later, I used it to calculate the rate of a clock orbiting the Earth.  It has turned out to be of importance for the GPS system, which depends on accurate clocks in navigation satellites.

Einstein and the General Theory of Relativity (GR)

In a Wall Street Journal op-ed (“Without Albert Einstein, We’d All Be Lost”), Robbert Dijkgraaf (director of Princeton’s Institute for Advanced Study) reminds us that on Nov. 4, 1915, Albert Einstein, working alone in wartime [World War-I, 1914-18] Berlin, submitted the first of four scientific papers that would change the course of physics and our view of the Cosmos: “His general theory of relativity (GR) is perhaps the greatest achievement of a single human mind.” Although it made Einstein the most famous scientist in history, he did not live to see the full impact of his ideas.  He did not foresee earth satellites, lunar landings, or the application of GR to GPS, the Global Positioning System of navigation satellites.

As Dijkgraaf writes:

“Only now, a century later, are we gathering apples from the tree he planted: black holes that tear stars apart … ; cosmic gravitational lenses that distort images of faraway galaxies, as if seen through a funhouse mirror. And perhaps the biggest wonder of all: a comprehensive and detailed understanding of the evolution of the universe. Amazingly, in just 100 years, humankind has uncovered 13.8 billion years of cosmic history.

“Only after Einstein’s death in 1955 did his theory become an active and respected scientific field.  Fifty years ago the first physical evidence of the “big bang" was observed.  The past decade has brought a new cascade of discoveries. The most important is that we now know precisely what we don’t know. Einstein’s theory allows us to measure the weight of the universe and thereby its energy content. This has been a shocker.

“All known forms of matter and energy—that is, all the particles and radiation that make up us, the Earth, the sun, all planets, stars and intergalactic clouds—comprise just 4% of the grand total. The remaining 96% is made of unknown forms of “dark matter” and an even more mysterious “dark energy,” which permeates all of space and drives the universe to expand faster and faster. These days there is a lot of talk about the 1% of society, but from a cosmic point of view, we are all part of just 4% of the Cosmos.”

Dijkgraaf continues:

“Many of the effects Einstein predicted were too small or too distant to observe in his lifetime. We had to wait for new technologies to magnify these minuscule effects. For example, without the theory of relativity the GPS devices that we all use every day to find our way would not function. The effects of time delays in the rapid communication with satellites of a few billionths of a second, as predicted by Einstein’s theory, translate into a drift of GPS positions of 7 miles a day. Without relativity we would all be lost.”

MIT science historian David Kaiser tells us in the New York Times how

“right-wing political opportunists in war-ravaged Germany began to organize raucous anti-Einstein rallies. Only an effete Jew, they argued, could remove ‘force’ from modern physics; those of true Aryan spirit, they went on, shared an intuitive sense of ‘force’ from generations of working the land. Soon after the Nazis seized power in 1933, they banned the teaching of Einstein’s work within the Reich. Einstein settled in Princeton for the last 22 years of his life; the German relativity community was decimated.”

The US certainly gained from the influx of European refugee scientists, like Einstein, Bethe, Fermi, or Teller. Just think what might have happened if Germany had developed nuclear weapons during World-War-II.

GR and Me     

About sixty years ago, I was a physics professor at the University of Maryland and got into a friendly argument with my colleague James L. Anderson, who was then teaching general relativity and has written a widely praised textbook since.  The question was: What will be the rate of a clock orbiting the earth? Would it slow down, or would it speed up?  We finally settled the argument with a bet.  I would write up my conclusion and send it to the prestigious Physical Review; if they published it, I would win my bet.  If they turned it down, I would concede defeat. 

To pass my PhD exams, I had of course studied relativity as a graduate student but had never used it.  I actually met the great Einstein just once; but we never talked about relativity.  I remember him as very kind and patient; he asked me to describe my PhD thesis research.

My thesis advisor, Professor John Archibald Wheeler, was an expert in GR; but my thesis topic dealt with cosmic-ray particle- “showers” produced in the upper atmosphere by extremely high-energy cosmic-ray primaries from outer space.  Of course, I made great use of the “Special” Theory of Relativity published by Einstein in 1905 -- especially the well-known formula E=mc­2

To solve the clock problem, I used a rather standard approach called Schwarzschild equation, which is based on Einstein’s GR theory.  All I really added to the problem was a method of overcoming the inadequacy of atomic clocks at the time.  I suggested that by counting “ticks” and by using a number of clocks in orbit instead of just one, one might achieve the necessary accuracy.  I have to confess that at the time I did not regard my paper as a big deal; its preparation was mainly in response to a bet.  In retrospect, however, I am glad I wrote up my calculations.

My published result was actually quite interesting.  I found that the clock rate would depend on the altitude of the orbiting satellite.  If the orbit altitude was one-half earth radius (about 3200km), the clock rate will be the same as on the earth’s surface.  At a lower altitude, a clock would run slower; at a higher altitude, it would run faster than on the surface.  In a separate publication, in Nature, I addressed the famous “twin paradox” that claims that the space-traveler twin would age less quickly than his earth-bound brother.

There is still much unexplored territory for research in relativity.  I became interested in a topic that Einstein called frame dragging (FD).  Does the Earth’s rotation affect the clock rate -- and to what extent?  A prize awaits the enterprising researcher; but the experimental requirements, I have concluded, are too demanding.  What a pity.

The most ambitious attempt to-date to measure the FD effect was Project Gravity-B, a satellite experiment by Stanford physicists. The multi-billion dollar effort was a marvel of technology but the hoped-for effect was too small to surmount inherent noisiness of the measurement. In recent weeks, the European Space Agency announced a plan to use atomic clocks in their Galileo satellites for detecting FD. However, I have great doubt about the success of their project.

GPS and Me

In 1987, some 30 years later, I found myself in the Department of Transportation and learned that the global positioning system (GPS) made use of exactly the results that I had published in the Physical Review.  But by then the whole matter had been re-discovered by the designers of GPS.  Still, it was a very satisfactory conclusion of a small chapter in my research experience.

My main task as DOT’s chief scientist was to look after the FAA’s revision of the Air Traffic Control system.  An additional responsibility was to keep track of and promote civilian applications of the GPS -- then a new military system.  Making the Federal Aviation Administration aware of the potential of GPS took a lot of effort; in fact, conservative FAAers  still harbor deep suspicions about using satellites.  But civilian GPS applications have grown explosively since then; every day brings new applications for this remarkable technology.

I still remember a meeting of our senior DOT staff with the Secretary.  I held up an early rather bulky GPS receiver and announced:  “Just turn on this gadget when you wake up some morning, and you don’t know where you are or where you are going.”  They all thought I was kidding.           

S. Fred Singer is professor emeritus at the University of Virginia and a founding director of the Science & Environmental Policy Project; in 2014, after 25 years, he stepped down as president of SEPP.  His specialty is atmospheric and space physics.  An expert in remote sensing and satellites, he served as the founding director of the US Weather Satellite Service and, more recently, as vice chair of the US National Advisory Committee on Oceans & Atmosphere.  He is an elected Fellow of several scientific societies and a Senior Fellow of the Heartland Institute and the Independent Institute.  He co-authored the NY Times best-seller Unstoppable Global Warming: Every 1500 years.  In 2007, he founded and has chaired the NIPCC (Nongovernmental International Panel on Climate Change), which has released several scientific reports [See NIPCCreport.org].  For recent writings see http://www.americanthinker.com/s_fred_singer/ and also Google Scholar.