Saturday, November 28, 2009

Theory of Relativity and the Quran

In the Quran, God tells us that during doomsday each day will be 1000 years of our earthly days. “32:5 He governs all that exists, from the celestial space to the earth; and in the end all shall ascend unto Him [for judgment] on a Day the length whereof will be [like] a thousand years of your reckoning.” -- As-Sajdah (The Prostration).
Also, “70:4 All the angels and all the inspiration [ever granted to man] ascend unto Him [daily,] in a day the length whereof is [like] fifty thousand years…” Al-Ma'arig (The Ways of Ascent).

And finally, “22:47 And [so, O Muhammad,] they challenge thee to hasten the coming upon them of [God’s] chastisement: but God never fails to fulfill His promise - and, behold, in thy Sustainer’s sight a day is like a thousand years of your reckoning.” -- Al-Hajj (The Pilgrimage).

In both cases the Arabic word used for ascend is “Yaruhu.” I am here attempting to understand how a day can be 1000 years or even 50,000 years.

Before Einstein, scientists assumed that time is constant. The journey of the change in that concept began with the Danish astronomer Ole Christensen Roemer. He did so by observing the Jupiter moons. Jupiter is the largest planet in the solar system. He observed that the times it took the moons behind Jupiter were not evenly spaced if the moons went around Jupiter at a constant rate. As the earth and Jupiter went around the sun, their distance varied, therefore the distance of the moons to the earth also varied. He argued that that this was because the light from the moons took longer to reach us when they were farther away. He calculated the speed of light to be 140,000 miles per second, an error of 25% compared to the currently measured speed of light at 186,000 miles per second.

The second major progress was the development of Maxwell’s theorem. Maxwell’s work predicted that electromagnetic currents and waves must be traveling at a constant speed. The way he discovered that was by attempting to mathematically explain Farday’s experiments that showed that when an electric current passes in a wire, it deflects the compass. Conversely, the movement of magnets generates an electric current in wires. This means that changes in electric fields generate changes in magnetic fields and vice versa. In a rare event in history of science in which a mathematical equation predicts physics first, Maxwell’s mathematical expression predicted in the absence of magnets and wires the disturbances in electric fields generate disturbances in magnetic fields and they interact together to travel at a constant speed. That constant speed was estimated to be exactly the speed of light to be exactly 299,792,458 meters per second. Maxwell literally stumbled on the speed of light.

The problem here is, as we all know, speed must be relative to something else. The problem with Maxwell’s equation is that it doesn’t have any frame of reference. That speed was not relative to anything else. Scientists of that time did not bother too much about that. They assumed that waves must have been occurring due to the oscillation of something. This something they called the ether. The ether was conceived to permeate everything. The sun and the earth must be moving in the ether. Scientists conceived that this motion must be generating ether winds. That means that in the earth’s journey around the sun, at one point it is moving with the ether waves and at others moving against the ether waves. That means that because the speed of light is relative to the ether, the speed of light relative to earth must be changing depending on the position of earth relative to the sun. Michelson and Morley tried to measure any variation in the speed of light at different seasons. They couldn’t detect any and by 1881 they published their results indicating that the only feasible assumption is that ether does not exist. This means that that speed of light must be a constant independent of the speed of the observer. No matter how fast you are moving, the speed of light is a constant. This was bizarre. Commonly, if we jog fast enough we should be able to catch up with light. Not any more. No matter how fast you jog, the speed of light relative to you will be constant at 299,792,458 meter per second.

Einstein came in and made two axioms:
1- That laws of physics including Maxwell’s are applicable no matter what the speed of the observer or source is. This called the principle of invariance, meaning laws of physics do not change from one place to the other. Seems simple but has profound impact.
2- There is no experiment that is capable of identifying absolute motion. This assertion dates back to Galileo. It means that if I am sitting on a train and the train is moving, I cannot really tell if the train is moving or the earth around me is. There is no experiment I can make to assert which way it is, while sitting on the train.

To understand the consequences of the above, Einstein started to make thought experiments. This was his favorite way of thinking. Einstein argued to develop a light clock. The clock consists of two mirrors, between which a beam of light bounces back and forth. If the two mirrors are 1 meter apart, then the light takes 6.67 nanoseconds to complete a round trip. If the mirrors are put on a fast moving train. For an observer on the train, the light takes 6.67 nanoseconds to bounce back and forth. For an observer on earth however the light is traveling a longer distance since by the time the lights lands on the mirror is has already moved at the speed of the train and by the time it bounces back to the source mirror, it too has moved. Therefore, for the observer on earth, light is traveling longer. The only way for this to happen is that light must travel faster relative to the observer on earth. However, the speed of light c is the same no matter what as Einstein postulated. Therefore, the only way to resolve this is if the clock ticks at different rates. In order for the light to traverse the longer distance, time must be slower on the moving train compared to time for the platform observer. This is what is called the theory of special relativity. A person on the platform is therefore aging faster than a person sitting on the train. Let us try to understand that. For a passenger on a train the clock takes 6.67 nanoseconds and each of her heartbeats takes 150 million ticks of the light clock. However, for a person on the platform the clock on the train takes longer than his own clock. It takes slightly more than 150 million ticks of the train clock to make one heartbeat. Time moves slowly for the train passenger. This means that life itself can change because of speed. An experiment at Brookhaven national lab confirmed that. The scientists at Brookhaven in the late 1990s built a machine that produced beams of muons (the muon is identical to an electron except it is heavier. Scientists to date do not understand the reason of muon’s existence) circulating around a 14-meter diameter ring at a speed of 99.94 percent the speed of light. At normal speeds, the lifetime of those muons is only 2.2 microseconds. These muons survived for 60 microseconds, which is exactly the number predicted by the Einstein’s special relativity. This concept is referred to as time dilation.

Basic trigonometric equation can be developed to show that g = square root ( 1 – square(v/c)). It is actually a surprisingly simple derivation. A nice video of the light clock thought experiment can be found at:
http://galileoandeinstein.physics.virginia.edu/more_stuff/flashlets/lightclock.swf
The proof itself can be be found at: http://en.wikipedia.org/wiki/Time_dilation

According to relativity, a clock traveling at speed actually slows down compared to a clock standing still. g is the slow down ration and it is in our case will be 1000*365 = 365000. According to Einstein, g = square root ( 1 – square(v/c)), where v/c is the ratio between our speed during doomsday and the speed of light. Therefore, during doomsday, we must be moving at a speed = 0.999999999996247 of the speed of light. This is very close to the speed of light.

Now, for the angles ascending to the sky in a day worth 50,000 years, it is even closer to the speed of light. They will be running at a speed of 0.999999999999998 of the speed of light.

Next time, let us try to understand the implication of those figures and what it means to ascend at that speed and why God said ascending in reference to the angles, all inspirations, and then in doomsday to all creatures.

No comments: