In the late 19th Century and early 20th Century, scientific discoveries were on full throttle, with discoveries being made left right and center such as radiation, nature of the atom, thermodynamics and astronomy. Major among them were the Maxwell’s laws, and the speed of light, which was found to be constant in a vacuum, which clashed against what was then then common knowledge. With scientists looking for an explanation, a young German scientist working as a patent clerk would revolutionize the field of gravitational physics, and science as a whole.
In 1905, Albert Einstein, then a 26-year-old working as a Patent Clerk in Bern, Switzerland, published four papers that would propel him into the world of science. One of them was “On The Electrodynamics of Moving Bodies”, a paper detailing what happens when events are observed from stationary points or moving points, especially when the speed is a significant fraction of the speed of light. It is called special relativity in that it accounts only for frames, or scenarios that are inertial, in that, there is no acceleration between the points of the event and the observer.
There are two basic postulates of special relativity:
1. The laws of physics are the same in all references and do not change
2. The speed of light in a vacuum is constant
This brings about some interesting phenomena, and paradoxes, as I will illustrate.
Albert Einstein, Photo credits: Google images
Albert Einstein incorporated the use of Lorentz transformations into his work. These transformations are used to compare motion and phenomena between different reference frames. They bring up the factor, gamma which is shown below.
Diagram: Gamma, where v is the velocity of the object and c is the speed of light.
Time dilation occurs when a reference frame is moving relative to you, hence time in that reference frame slows down in relation to you according to the formula:
Since the speed of light is very large (c=300000000 m/s), time dilation is not observed in normal circumstances. However, for particles that move at very high speed (cosmic radiation, neutrinos and muons) time dilation is observed. Muons are unstable sub atomic particles that are formed when cosmic rays hit the upper atmosphere (story for another day). They have a very short half-life of 1.5 microseconds, hence in classical sense, only 0.3 out of a million should be able to reach the ground. However, due to special relativity, and the fact that they are travelling at 0.98C ( 0.98 times the speed of light) its half-life (time taken for a particle to decay to half its mass. Think of it as time taken to eat half a pizza, then taking the same time to eat a quarter, then the same time to eat an eight and so on and so forth) is extended by a factor of dilated, to an extent that 49000 out of a million particles are detected on earth’s surface, hence an increasing its half-life by a factor of 5. In short, the faster you move, the slower time moves for you.
Diagram: (a) muons travelling without taking relativity into effect and (b) taking relativity into effect. Photo credits: Physics for Scientists and Engineers, 6th edition, Serwey and Jennet
Time dilation also brings about the twin paradox. There are a set of twins, James and John. James leaves for space in a shuttle at half the speed of light, and travels for twenty years, leaving John behind. When James comes back, he will be younger than john by a significant age gap, due to the fact that time was dilated for him as he travelled at a high velocity, hence time was dilated, and physical, chemical and biological processes for him were slower while for John, who was rather stationary, time moved at the normal rate.
Length contraction is another effect of relativity. The length of an object measured by two observers, one who is at rest and another who is in motion are very different. The observer who measures the length while in motion will always get a smaller value than the one who is in motion. This is as a consequence of time dilation, and the measured length will be:
Where Lp is the length of the object measured by the stationary observer (for v and c refer to the above image).
Another circumstance of relativity is that it brings question to simultaneity, in that, events that may be simultaneous to one observer who is stationary may not be simultaneous to another who is moving. A famous thought experiment goes as follows. An observer is on a train platform, observing a train, and the train is travelling at a fraction of the speed of light towards the right of the observer. Inside the train, is another observer, facing the platform. Just as the train reaches the middle of the platform, lightning strikes both ends of the train at the same time. What does each observer see? Well, the one on the platform will see lightning strike both ends at the same time, while the observer in the train will see the lightning strike the front end of the train, then the back end. Hence, simultaneity is destroyed, and events that may seem to be simultaneous to the observer who is stationary, are not simultaneous to the moving observer. Crash course physics does a great job showing this concept.
Perhaps the most famous product of special relativity is the concept of relativistic energy and mass, with the rest energy of a mass of an object being equal to:
E = ER = MC2
Where E is the total energy of the system and ER when it is at rest, M being mass of the object, and C being the speed of light. Now, enough with the E = milk *cofee2 memes and jokes.
While the theory of Special relativity was groundbreaking, it left a lot of questions, especially about objects that seemed to be accelerating relative to each other. This led Einstein to work on General relativity, whose works he published in the year 1916.
For further reading, I would refer you to the first volume of the Feynman Lectures chapters 15 through to 17 to get a deeper feel of Relativity.
That’s all for today folks, and once again, feedback is highly appreciated. Remember, it’s all relative.
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