**V - RELATIVELY RECENT CONNECTIONS**

You know the drill. You’re not sure about how to get to your destination and you turn on the GPS, having full confidence it will get you there, even if it has to “recalculate” a few times. The next time you depend on this little electronic wonder and you wind up exactly at the right place, give a quiet thanks to Mr. Albert Einstein, actually Dr. Albert Einstein – he does have a PhD. Without his Theories of Special Relativity and General Relativity, who knows where you may have ended up. Yes, there’s a lecture coming up, so sit back and take it in. Hopefully it will demonstrate that Relativity isn’t just for those professionals studying the Cosmos.

The Global Positioning System (GPS) consists of up to 30 satellites (of which 24 are operational at any given time), ground stations, and receivers (GPS units, cell phones, cameras, etc.). The altitude of the satellites is about 12,500 miles (22,000 km), called Medium Earth Orbit (MEO), high enough to be clearly “seen” by the ground stations. No, they are not in geosynchronous (which geostationary refers to) orbit (matching the Earth’s rotation); they each orbit the Earth twice per day. The 24 operational satellites each cover one zone, and the zones are configured such that 4 satellites will be in communication with you if you are in a receptive area. So, 4 satellites are giving their position to your receiver via the ground stations at any given time. And speaking of time, it is calculating the distances to the satellites based on time differentials for their signals. So, it’s very much a time-based system. A discrepancy in time means a positioning discrepancy, and you don’t arrive at your destination.

You’re catching on, I can tell. Relativity; time is relative. All of the above. First, the clocks on the satellites are less affected by the Earth’s gravity than the receiver is, therefore the satellite clocks are a bit faster, 45 microseconds per day faster. This is from Einstein’s Theory of General Relativity, as we’ll see later on. His Theory of Special Relativity, however, states that the satellite clocks are ticking more slowly (7 microseconds per day worth) due to “Time Dilation” effects.

The bottom line is that the satellite clocks are 38 microseconds per day faster than the receiver’s clocks on Earth. It doesn’t sound like much, but it’s really a serious error, as the system requires nanosecond accuracy; that’s an error factor of about 1,000. Actually, the clocks must be synchronized to 50 nanoseconds (50 millionths of a second) to attain a positioning accuracy of 13 ft. If the GPS system was not properly calibrated to account for Relativity, the system would start to go off the track in a couple of minutes; the cumulative errors would be 6 miles per day, which isn’t exactly practical. When you hear of Generals and other officers working in tactical operations (anything involving accurate positioning) taking courses in Relativity, you really get this is superpractical stuff. And there’s much, much more. Let’s have a look.

**FROM NEWTON TO MAXWELL TO EINSTEIN**

Sir Isaac Newton was truly the Father of Physics. Just think of the era of his major achievements, 1660-1700, and what he managed to accomplish in those times. His three Laws of Motion (F = ma, inertia, action-reaction) and related equations laid the foundation of Classical (Newtonian) Mechanics. His mathematical formulation for the Universal Law of Gravity (with the inverse square of the distance) is still very much in play. Developing the calculus (as a tool for his own use), inventing the reflecting (Newtonian) telescope, advancing the science of optics and color, and being the 2ndscientist to be Knighted (after Sir Francis Bacon). He gave us the Laws to explain the world in which we live, and for the most part, they still do.

We jump ahead almost a couple hundred years to discuss the work of James Clerk Maxwell. His major accomplishment is simple (not easy, just elegant), basic, and profound; Maxwell was the first scientist to unify the fundamental forces of magnetism and electricity as one force, “electromagnetism”; his equations brilliantly derived the relationship. Further, these equations showed that electromagnetic radiation always travels at the speed of light, thereby proving that light was an electromagnetic wave. Light was now linked with electricity and magnetism. In his Classic paper (

*A Dynamical Theory of the Electro-Magnetic Field),*presented to the

*Royal Society*in 1864 (and published in 1865), Maxwell said,

*“We have strong reason to conclude that light itself - including radiant heat and other radiation, if any - is an electromagnetic disturbance in the form of waves propagated through the electro-magnetic field according to electro-magnetic laws.”*

*1*

Maxwell's Theory of the Electromagnetic Field is fundamental to the understanding of modern theoretical physics and really laid the background for Einstein, when he developed his Special Theory of Relativity. Note that Maxwell’s equations, yielding the speed of light as the velocity of electromagnetic wave propagation, make no mention of an observer. Newton’s Laws did, meaning that the speed of light varied, based on the point of reference. Einstein felt that Maxwell’s equations proved that the speed of light was a constant, no matter who was observing, where they were, or if they were in motion. At the same time, the equations also showed that some of the other physical phenomena (including length and time) varied from observer to observer, especially if one was in motion and the other was not. This was also critical for Einstein, especially after physicist Hendrik Lorentz (winner of the

*Nobel Prize*, 1902) did the first proofs for him, using what is mathematically known as Lorentz Transformations; basically, this demonstrated the importance of “frame of reference” to the Theory of Special Relativity.

**It is not generally known that the Theory of General Relativity was originally called by some (including Max Planck) the Lorentz-Einstein Theory.**This point is not widely referenced, and Lorentz himself feels that Einstein alone received the proper credit. By the way, it was Max Planck, the Father of Quantum Theory (who we’ll discuss shortly), who first used the term “Relative Theory.”

Tosum up, Maxwell’s Theory of Electromagnetism, including his equations, was the greatest advance in science since Newton’s grand achievements. While Einstein certainly respected both great men, when asked if he stood on the shoulders of Newton, he is said to have replied,

*“No, on the shoulders of Maxwell”.*

As a footnote, Albert Einstein was born in the same year that James Clerk Maxwell died, in 1879. Maxwell was only 48 when he succumbed to stomach cancer. He received no honors when he died and was buried quietly in a small churchyard in Scotland.

Most people with an interest in science have a general idea of Einstein’s early years - considered a genius as a child, mastering integral and differential calculus at 14, cutting school (bored with the curriculum and rote learning), sensitive to the arts, and fascinated with forces he couldn’t see, especially magnetism. Here is a quote from the young cynic named Einstein:

“

*Common sense is the collection of prejudices acquired by the age of 18”.*

*2*

It is true that Einstein did not think advanced mathematics was as important as physics, and he cut many important math classes by renowned Professors. This would cost him a considerable amount of time between his Special and General Theories of Relativity. Fortunately, Einstein had a number of colleagues who supported and helped him, despite his stubborn ways. In 1896, he attended the

*Swiss Federal*

*Polytechnic School*in Zurich for training as a physics and mathematics teacher. Due to his habit of not attending classes, he couldn’t get a recommendation for a teaching job after graduation in 1900 – not surprising. The following year, he got his Swiss citizenship, which then allowed him to apply for and receive the famous job as a Clerk in the

*Swiss Patent*

*Office*.

The Patent Clerk position afforded Einstein time as well as compensation. The time was obviously well spent. The more he read Newton’s and Maxwell’s Laws, the more Einstein realized that there was a fundamental conflict regarding the speed of light. According to Newton, the speed of light varied by observer. To an observer on a train, the light probing the darkness in front of the train was certainly travelling at the speed of light. But to an observer on the ground the light was travelling at the speed of light plus the velocity of the train. As Maxwell’s equations did not account for an observer, Einsteininterpreted this to mean that the speed of light was invariant. He had to choose one or the other, and it was not an easy decision; Newton’s mechanics were solidly entrenched in physics for well over 250 years (with a great deal of proof), while Maxwell was a relative newcomer without universal acceptance (or, back then, substantial proof). Einstein followed his hunch and sided with Maxwell. This was obviously a major decision, and it’s not often referenced in this manner.

**What is truly ironic is that the Theory of Special Relativity begins with an Absolute – The Speed of Light.**

Once the speed of light was considered absolute, in order to make any calculation work for a given observer, Einstein had no choice but to consider time and distance as relative, which is also in complete disagreement with Newton, who considered them as absolutes, regardless of the observer.

Let’s do a proof of Einstein’s logic, with a couple Einsteinian thought experiments. Remember, speed is distance over time, including the speed of light – 300,000 km/sec (or 186,000 miles/ sec). First, I’m going to ride my bicycle to a building while driving carefully at 10 miles per hour. I get there in half an hour and calculate that the building was 5 miles away.

Too easy, I know. Now, let’s look at the same event from the viewpoint of an observer (Jo Jo) on the Moon, equipped with a Cosmic-rated spyglass. To Jo Jo, I have travelled much further (as the Earth has rotated during my short ride), so the distance has changed. The duration of the ride is pretty much the same (we’ll ignore time dilation effects for this experiment) and the calculation shows a much higher velocity, which is allowed since I was certainly not travelling at the speed of light. We’re still okay so far.

Now, instead of me riding that bike, I’ll aim my high intensity laser beam at a mirror outside said building (warning: don’t do this; high intensity laser beams are dangerous). I have the instrumentation necessary to calculate the distance the laser beam travelled and the time it took to get there. The velocity is fixed, remember. It’s also fixed for Jo Jo, but the distance the beam travelled will be longer once again (adding in the distance the Earth rotated) so the time it took for the beam of light to reach the building must be shorter than by my calculations. Not by much in this case, but you see the point.

Let’s take things one step further using the 2ndthought experiment. If the speed of light is fixed, if you increase the distance, then you shorten the time as was done from Jo Jo’s perspective. This means that distance (space) and time are fundamentally linked at relativistic velocities (near or at the speed of light), but it was the mathematics of Einstein’s former Professor, Hermann Minkowski, that was essentially the foundation for Einstein’s concept of spacetime. More on this soon.

You see where this is going. And it went pretty much the same way for Einstein, although he didn’t use laser beams in his thought experiments. By the way, there’s another little point here that is seldom discussed. We’ve all read about Einstein’s thought experiments, with lightning bolts hitting two areas of the train, and words to the effect of, “Imagine an observer at x and another one at Y.” It is appropriate to point out that the Patent Office was not a laboratory, and thus thought experiments were Einstein’s only way of showing exactly how his theory worked. Another observation about his Patent Office work was that several of his assignments involved questions about the transmission of electric signals and electro-mechanical time synchronization. His work was not just a distraction and a way of earning money.

If you remember our earlier discussion of Newton’s Miracle Year (

*Annus Mirabilis*) of 1666, where he accomplished so much while “waiting out the plague” for a year at his mother’s house, it is said that Einstein had his Miracle Year in 1905. That was the year he received his PhD, an academic achievement not many are aware of. Not that it’s much of a surprise. Then he went on to publish four significant papers in one of the leading physics journals of the era, the

*Annelen Der Physik*. Two of the papers were on the

*Theory of Special Relativity*and the equivalence of matter and energy (E=mc2) both of which we will discuss shortly. Another paper was on the Photoelectric Effect, which relates to the release of “

**photo**

**electrons” (or Light Quanta as he called them) as a form of energy when light shines on a material.**Here, Einstein states that a beam of light is a collection of particles, now called photons, while the flow of photons is a wave

**.**

**This is the first time that the dual nature of light had been formally proposed as well as the statement that light itself was a form of energy.**Einstein was actually supporting Max Planck’s discovery (in 1900) of the quantization of energy (or a quantum of action) called “Planck’s Constant”, - the beginning of the Theory of Quantum Mechanics.The difference is that Planck stated that it was the energy of the radiating atoms that was quantized, while Einstein proposed that it was the electromagnetic radiation that was quantized - in the form of what we now call photons. Also of note here that Einstein received a

*Nobel Prize*in 1921 for this paper on the Photoelectric Effect. He never received a

*Nobel Prize*for his work on Relativity, as there was evidently a bias against pure theoretical physics; in addition, there were members of the Committee that awards the prize that did not accept the Theories of Relativity based on lack of proof.

The last of the Miracle year papers was on Brownian Motion, which was an elaboration of his PhD dissertation. It’s the first time I’ve seen atomic theory applied to botany. Robert Brown, a botanist, observed (in 1827) what he thought was, and still often described as, random motion of pollen grains in a fluid. I won’t go into the details, but Einstein explained the observation using the Atomic Theory of Matter, stating that the pollen grains were bumping into many atoms and molecules of fluid. Atoms change direction billions of times a second due to collisions with each other; molecules have these collisions as well. While this had been suspected for some time, Einstein actually placed food coloring in the fluid and observed the rate and dynamics of its dispersion. His work actually settled a dispute that was going on for nearly a hundred years; it was also one of those unification moments – physics, chemistry, and thermodynamics.

**1905 – It was a very good year, one of the best for Albert Einstein**.