The Apple, the Cat and the Barometer

What is heavier, a kilogram of nails or a kilogram of feathers? If you said, “Neither, they have the same weight”, you are normal. If you said, “It depends, on what you mean by a kilogram, and what you mean by heavier, because it is possible for the feathers to be heavier”, then you must be a physicist.

In the world of science, physics is king. Physics is the explanation, the logic behind the existence of things physical. The earth and the heavens and everything in between are the realm of physics. While mathematics form the basis of scientific thought, reasoning, analysis and quantification, physics brings the abstraction of mathematics closer to reality. Or so it used to be.

The Beginnings

The Greeks, during 550BC-100AD were the first to think carefully about the world we live in and to observe methodically the phenomenon that surrounds us. Pythagoras laid the foundations of number theory. Euclid took mathematics to new heights. Aristotle decided the there were four earthly elements: Earth, Air, Water and Fire. He expounded that the universe is spatially finite but temporally eternal. He prescribed the appropriate age of marriage, 37 for men and 18 for women. (When he was 37, Aristotle married Pythias who may have been 18). Plato added the fifth element to Aristotle’s list: Ether. Anaximander, Parmenides, Heraclitus, Anaxagoras, Leucippus, Heracleides were amongst the luminaries of the time. Amongst this cast of characters, there appeared Archimedes, the experimentalist. He discovered how pulleys and levers work and the relationships between surfaces and volumes (supposedly while in a bathtub). Later, Hippocrates laid the foundations of modern medicine.

Quaint as it may sound today, the philosophy, the mathematics and the physics espoused by the Greeks were cutting edge. The dominance of Greek terminology and symbols in modern science is a fitting tribute to the early thinkers. The people of that period were free to think, observe and deduce. They were not bound by prior knowledge; they probably did not even know what scientific discovery meant. They laid the foundations of logical stepwise refinement.

After the Greeks, the study of science was largely abandoned in the Western world. In the so-called dark ages (about 500AD-1000AD), the scholarly work consisted of copying and studying religious documents. Science flourished in India, China and Egypt. Discoveries include the water wheel, paper, algebra, basic optics and some astronomy. Sadly, the details are sketchy and we think many important discoveries may have been lost due to obscurity.

Newton’s Apple

The Middle Ages saw the slow return of learning and culture. This culminated in the boisterous period called the Renaissance, or rebirth. Largely a phenomenon in the Western world, the Renaissance was the rebirth of materialism and interest in everything tangible. Leonardo da Vinci, an artist by profession, emerged as one of the best scientists and artist and philosopher the world had ever seen (and may yet to see). Amazingly, de Vinci discovered the parachute, capillary action, and predicted the possibility of mechanized flight. He developed theories of mechanics, aerodynamics and hydraulics. All this and much more have been attributed to the person who also brought us the most intriguing smile ever, painted on a canvas titled Mona Lisa.

The parade of legendary scientists and thinkers abound during the renaissance. Galileo observed the heavens with his invention, the telescope. Kepler charted planetary motion and invented the concept of energy. Descartes rationalized rationalism and Bacon developed the scientific method. Copernicus re-discovered that the earth was not the center of the universe and Boyle discovered many properties of air.

Then the apple fell off a tree and gravity was discovered. Until Sir Isaac Newton, the father of modern science, connected the apple with gravity, people had no idea why the toast always falls the butter side down. Newton’s work on mechanics, optics and gravity is seminal and till today form the basis of classical physics.

Schrodinger’s cat

Classical physics in its various forms have been alive and well since the Renaissance till the twentieth century when Albert Einstein messed it all up, with the general theory of relativity. All that was well known was turned on its head. The speed of light became the invincible frontier of modern physics. Now, everyone wants to own a car that travels faster than light. Imagine, you can wake up at 10am, and be at work by 8am. Doppler shift makes the red lights look green. The cyclists never see you coming. The cigarette butts you flick, will not land in the back seat, they would land in last week.

Beyond relativity is particle physics and quantum mechanics. Particle physics is the science of chasing imaginary particles that should exist but do not seem to. Quarks and leptons float around us all, bound by Mesons and Glouns. If you are lucky, you may find the elusive Tachyon. The Tachyon travels faster than the speed of light, and as it loses energy, it accelerates (the slower it travels, the more energy it has). If it was not concocted by eminent physicists and published in the top research journals, we could have written it off as intoxicated babble.

Quantum mechanics is the merging of probability with reality. A vacuum traditionally is devoid of matter. According to quantum mechanics, that’s not quite true. The vacuum is full of matter; the matter just disappears when you try to observe it. Heisenberg is quite certain, that you cannot measure both the speed and location of an object. Heisenburg was also certain that Schrodinger’s ideas about wave mechanics were “disgusting”. Schrodinger returned the favor by saying he was “discouraged and repelled” by Heisenberg’s ignorance of particles.

Schrodinger explained the philosophy of quantum phenomenon with a cat. Suppose a cat is in a box along with a Geiger counter and some radioactive material. The Geiger counter is rigged such that if it detects a radioactive particle, it will electrocute the cat, and kill it. The radioactive material is chosen such that there is a 50% probability that it will decay and set off the Geiger counter, in one hour.

After an hour, we look at still closed box and wonder, “Is the cat dead or alive?”

To most of us normal people the answer is simple. The cat is either dead or alive, and if we open the box we will know. According to quantum physicists, the solution is much more complex. The cat is both dead as well as alive. It exists in both states. When the box is opened, one of these states disappear and you observer he other. If you do not find an amazing sense of enlightenment in the story of Schrodinger’s cat, you are well advised not to pursue a career in Physics.

The Professor’s Barometer

Physicists take pride in thinking in non-obvious ways. If we always deduced the obvious from our observations, then relativity, particle physics and quantum mechanics would never had been discovered. Thinking “outside the box” is exemplified by the barometer parable.

A physics professor, in a final exam, asked the question: “How would you measure the height of a tall building with a barometer”. An otherwise bright student wrote, “I would drop the barometer from the top of the building and count out the seconds till it hit the ground and thus calculate the height”.

The professor was quite upset and asked the student to see him. The professor wanted an explanation and demanded the correct answer.

“You taught us to think, and not just follow the obvious”, the student retorted. “The obvious answer it to measure the air pressure using the barometer at ground level and then on top and calculate the height. But that is too simple, too boring, too classical and quite inaccurate. I thought of many other solutions, most of them better in accuracy and innovativeness, and wrote one of them”.

“What are the others?” asked the professor.

“I could use a string and dangle the barometer, like a pendulum and measure the time it takes to swing at ground level and then at the top of the building. Then the difference can be used to figure the difference in gravity and hence find the height”, he replied, “but that method is quite inaccurate too”.

“To be more accurate, I would use a long string to lower the barometer from the top of the building till it reached the ground. Then pull it up, and measure the length of the string. Or, I could climb up the stairs, and as I climb I mark off the length of the barometer along the wall. The number of marks will give me the height of the building in barometer units. On a sunny day, I could measure the length of the shadow of the building and then the length of the shadow of the barometer, and then calculate the height of the building knowing the height of the barometer.”

“However”, he smiled, “the best solution I have is as follows. I take the go to the office of the building superintendent, and use the barometer to bang on his door. When he opens the door, I tell him, ‘Here is a fine, shiny, expensive, scientific barometer for you, sir. You can have it, if you tell me the height of the building’”.

Partha Dasgupta is on the faculty of the Computer Science and Engineering Department at Arizona State University in Tempe. His specializations are in the areas of Operating Systems, Cryptography and Networking. His homepage is at http://cactus.eas.asu.edu/partha