From the archives #2: To E = mc² and beyond!
Theory of Relativity — Simplified
This article was written by Pooja Balasubramani in 2015, for the original Pragyan Blog hosted on WordPress. The present editors have taken the liberty to make minor changes, without changing the meaning of what the author intended to convey.
Before delving into the daunting task of understanding physics at its core, let us start with ‘The theory of relativity’. Mind you, it might sound arcane to most of us, but understanding this has led to the development of technology to an indescribable extent.
Sir Isaac Newton in 1687 coined that Gravity affects everything in the Universe. But he never puzzled out the source of gravity. More than 2 centuries later, the prodigal Sir Albert Einstein accomplished the task. He proposed two theories which have revolutionized the way the world perceives space, time, mass, energy and gravity.
Here, we’ll split it into 3 parts and try to apprehend.
Part 1: Classical relativity
In school, we’ve all crammed Sir Newton’s three laws of motion. Hence, it is safe to say that most of us, (if not all of us) know this:
There is no such thing as absolute motion or absolute rest. Every object on earth moves relative to each other.
The Earth itself is constantly in motion. It moves relative to other planets. Similarly, stars move relative to other stars, and so on. This right here, is “classical relativity”, and not much else needs to be said about this.
Part 2: Special theory of relativity
Here, we introduce the famous “3 x 10⁸ m/s”. This number is no stranger to most of us (for the uninitiated, this happens to be the speed of light). One more widely known fact is that nothing can travel faster than the speed of light and it’s speed is the same in any system.
What seems fairly obvious now, took more than 150 separate experiments involving more than 100 scientists just to accurately determine. Since the year Galileo conducted his famous hilltop experiment, it took about 350 years to conclude the exact value. Prior to Sir Einstein, scientists had thought the speed of light to be relative. But he changed the course of thinking.
Here’s how he did it.
Imagine a beam of light reflecting between two mirrors (let us call it case A). Now, consider another similar setup where the mirrors themselves are moving at a speed, comparable to that of light (let us call this one, case B).
In case B, light will have to travel a greater distance than case A. Now consider two people X and Y sitting inside the two sets of mirrors. According to Sir Einstein, the speed of light must be the same for both X and Y, and must hit the two mirrors at the same time. How is that possible? Time Dilation!
In this example, time moves slower for the people in the moving mirrors, when compared to the set of people in Case A. This has led scientists to hypothesize that ‘time’ can very well be the 4th dimension.
But what if they travel at the speed of light? Their time stops altogether. And if they travel at a speed more than the speed of light, they literally travel backwards in time, into the past. So… Is time travel possible?
Sadly, it isn’t. No object with any finite rest mass can move at the speed of light. That is why all the particles that move at the speed of light (e.g. photons) have zero rest mass. If a particle with mass approaches the speed of light, it causes an increase in mass, and to achieve the speed of light you need infinite mass. Infinite mass equals infinite energy (E=mc²) and we know that any phrase with ‘infinite’ in it, does not happen in reality.
Previously, we saw how time compensates for the increase in distance traveled when we approach speeds nearing that of light. However, there is another factor that comes into the picture at these insane speeds. Length Contraction!
When objects move close to the speed of light, not only does time slow down, the object itself contracts to compensate for the distance. Hence the speed of light is the same for everyone, and in everything.
Part 3: General theory of relativity
Special Theory of Relativity is for when objects move at a constant pace. What about the accelerating cars which we see everyday? What about the apple which fell on Sir Newton’s head? And the most critical question of all, what exactly is ‘gravitational pull’?
Sir Einstein interlinked space and time to theorize the space-time concept. He thought of it as a single entity and proposed that objects (really massive ones) warped space-time around them, causing it (the space-time) to become curved. This warp is known as the ‘gravity well’. As a result, objects experienced gravitational pull towards each other. This theory perfectly explained why objects move in space the way they do.
For example, according to General Theory of Relativity, orbiting objects follow the shortest path which requires least amount of energy. Hence planets move in ellipses around the gravity well of Sun, as it is the most energy-efficient path. This is General Theory of Relativity in layman terms.
Finally, how do we know any of this is true?
Countless experiments have been carried out around the world for decades, to prove its veracity and Sir Einstein’s equation proves to hold true. We will not getting into the details, but know the GPS whose utility we are exploiting every day? Yeah, that is mainly because of Sir Einstein and his theories of relativity.
There is no better end to this article than this beautiful quote by John Wheeler, who sums up this entire article in two lines:
Mass tells Space how to curve,
and Space tells Mass how to move.
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