At the end of the TSI 2009 (the Summer Institute at TRIUMF, dedicated to particle physics every 3 years) we had an interesting open discussion. The theme was “Is fundamental research more useful than applied research to society?”. Studies are on-going from an economical stem-point. It has been shown that gain factors are slightly higher for fundamental research than for applied science. Nevertheless, this is the perennial question asked by non-science oriented friends, young students, and mainly the agencies supporting our research. A good example of applications is the development of the semiconductor technology (for instance chip for computers) which is based on quantum phenomena. In the medical field, MRI and particle accelerators used for cancer treatment are now every day techniques made possible by fundamental research in the past 30 years.
What about Einstein’s theory of special relativity ? One of the two central assumptions in special relativity is the Galileo’s principle: the laws of physics are the same in any system moving at constant speed. If you are in a standing ship and drop an object, it will fall downwards. If the ship moves at constant speed, the object falls at exactly the same position on the ship. If people on the ship observe the falling object, they cannot tell if they are really at rest or if they are moving with the ship. They cannot distinguish their state of rest from the ship’s state by observing motion that takes place within the “reference frame” of the ship. Galileo proved that absolute space does not exist.
However he maintained the assumption of absolute time. Special relativity instead relies on the breakdown of absolute time. This concept is more difficult to grasp. The fundamental notion here is that the speed of light is constant in any system (you should read about the extremely elegant experiment carried out by Michelson and Morley!). This seems in contradiction with our every day experience. If you are standing and throw a ball towards a friend at a given velocity, the friend of yours will perceive the ball standing on his/her side if he/she is running at the same velocity and in the same direction. This does not hold for the light. If the light is shining out of a flashlight, regardless of how fast the person runs, he/she will always see the light moving at 299,792,458 m/s. The genius of Einstein lies in accepting a preposition which, at that time, seemed unreasonable and build a theory on that. This theory will prove to be correct and crucial to any further discovery and advancement in science.
What’s the main implication of assuming the speed of light constant ? Think again of a train, and let’s assume it is standing in the station for the moment. We place inside two mirrors and shines light from one side so it gets reflected back and forth. If the distance between the two mirrors is 1 m, then the light travels 2 m. Since the speed of light is 299,792,458 m/s, the light shines on the second mirror after 6.67 nano sec (tiny amount of time! 0.00000000667 sec). What happens if the train starts moving at some speed v ? We can apply the Pythagoras’s theorem and calculate the distance traveled by the light between the fist and the second mirror and find out that the distance is larger than before. But the light travels at the same speed. What does this imply ? That the clock on the train must take longer to tick. Time ticks at different rates depending on the speed at which we move compared to an observer, namely it is stretched on the train. The absolute time does not exist.
If you travel on a train moving at 300 km/h for 100 years, the station clock will be faster than the train clock by one-tenth of a 0.001 sec. It is not a large difference, but a real effect nonetheless!
Are there applications of this principle ? The answer is yes, and one of the most common is the GPS system (Global Positioning System). Originally developed for military used, the system is based on an array of satellites orbiting the Earth, each carrying a precise atomic clock. Using a GPS receiver detecting the radio emissions form any satellite, we can determine latitude, longitude and altitude with good accuracy and local time. The satellite clocks are moving at 10,000 km/h and Einstein’s theory of special relativity says that rapidly moving clocks tick more slowly, by about seven microseconds (millionths of a second) per day. Also, the orbiting clocks are 20,000 km above the Earth, and experience gravity that is four times weaker than that on the ground. Einstein’s general relativity theory says that gravity curves space and time, which makes orbiting clocks to tick faster by about 45 microseconds per day. The final result is that time on a GPS satellite clock ticks faster than a clock on the ground by about 38 microseconds per day. Without correcting for the special and general relativity effects, the GPS would fail in its navigational functions within about 2 minutes!
