Why do things fall?
Why do rocks from a mountain fall to the ground? Why does anything fall? Well, we have been told that the elusive force of gravity is to blame. So there we have it, things fall because they are attracted to the center of the earth.
Well, not really. See what I did there? The seeming solution was nothing but a mere transposition of the previous problem. Why would anything be attracted towards the center of the earth in the first place? Except, they are not.
Welcome to Einstein’s principle of General Relativity. Things fall not because they are attracted to something, but because they are not.
This bizarre thought, only possible by the wildest stretches of the imagination, that perplexes great minds till date, was visualized vividly by Einstein, a visualization that we struggle to create even today.
In this article, I will try to push our understandings further, towards perhaps what Einstein had dreamt of. As he once said, “Any fool can know. The point is to understand”.
Space and Time
In discussing physics, or any science, a clear and working conception of the two most fundamental ingredients of the universe is required. Einstein’s theory of Special Relativity, which was published approximately 10 years before General Relativity, was extremely simple, and yet revolutionary. Why? Because it completely overturned the concepts of space and time.
Pardon the context, which might seem boring, but be assured that it is crucial in gaining an understanding of what gravity is.
Space and time, before Einstein’s relativity, was thought to be absolute. Implying that two moving clocks, that were started at the same time, would measure same lengths and time. In other words, there would be complete agreement on what distance was traveled, and how much time had passed.
Einstein proved this concept wrong. Space and time are not absolute, they are relative. He incorporated Minkowski’s theory of 4-dimensional space-time into his theory of special relativity. Space and time were hence, no longer separate. It was space-time that existed. Any changes in an object's movement in space directly interfered with its experience of time.
I won’t go on explaining Special Relativity here. It deserves an article of its own. But the takeaway from here is critical in grasping gravity. So, to recap, space and time exist as one space-time continuum, and it is not absolute, it is relative to the observer and the motion observed.
Lines, curved and straight
Understanding straight lines hold the key to gravity. What is a straight line? What is the distinctive feature of a straight line that separates it from non-straight lines? The question might seem silly and obvious at first, but let me warn you, it is not.
Imagine two straight, parallel lines that never meet. Now imagine a curved line. We certainly know that the straight line is completely different than the curved one, but not always.
Look closely at something spherical, something curved, a globe for example. Take a minute and look at the picture. Which lines look straight? The latitudes or the longitudes? Even though the latitudinal lines may seem straight, they are not. Why? Because they turn, and straight lines, by their very definition, do not turn.
So then, straight lines on a plane are not exactly the same on a sphere or curved surface.
It is important to create this mental distinction of straight lines on surfaces of differing geometry.
With the previous observation in mind, let's try to imagine a straight line on a curved surface. For simplicity, let’s use a cone as our curved surface. Keep in mind that the line should never turn. Got a picture in your head? Most probably you did not. Rather get a piece of paper with a straight line drawn on it and fold the paper into a cone. It should roughly look like the one in the picture below.
See it now? What does our straight line look like now? We had a straight line on the coordinate plane, but on the cone, there is no straight line. Well, the straight line obviously is on the cone since all we did was just fold the paper, but once folded into a cone, it no longer resembles a straight line.
Let me introduce you to Geodesics. A straight line on a curved surface is a geodesic. This means that any straight line when plotted on a curved surface, remains straight but does not look straight.
Space-time geodesics
Now that we understand the concept of space-time and geodesics, understanding gravity is within our reach. We start by visualizing some graphs. Imagine a graph of space vs time, much like the graph on the picture above. Now think about what the straight line on the space-time graph represents. It represents an object’s motion over time. The line represents the sum of all individual events in space and in time.
In this graph, let the y coordinate depict changes through space and the x coordinate represent changes in time. This graph then serves as a space-time diagram for a stationary object.
Now, what would happen if you were to take this graph and fold it into a cone?
The result, as expected, would be extremely similar to our previous cone observation.
So, what does this imply?
If we look at the line on the cone, we see that the space-time events have been altered. We see the line gradually dropping down. A static object in flat space-time retains its spatial position through time, as seen on the unfolded graph. But as seen on the graph folded into a cone, a static object in curved space-time falls down through space, over time. See the point? The object and the scenario is one and the same in both the cases, all that has changed is the geometry of space-time, its shape, its curvature. The latter observation is a symptom of what we call gravity.
Hence, there is a possibility that gravity is no mysterious force, but just curved space-time continuum. This would explain how and why things fall, without assuming the existence of any force, a push, or a pull.
An object, static or moving, is seemingly attracted to some other object not because there is a force called gravity, but because those objects simply follow their space-time geodesic. Straight lines in curved space-time.
Conclusion
All that I discussed in the article so far was but a mere thought experiment for Einstein. This made him realize that the apple fell on Newton, not because it was being pulled by the earth, but because it was always following its space-time geodesic.
This raises another question though. How and why is space curved? Einstein came up with the theory that mass bends space-time. Described in probably the most elegant equation, known as the Field Equation.
This is how General Relativity was born and it has passed every single test till date. Einstein correctly redefined gravity, which, throughout all of human history had puzzled scientists.
Realize, that in flat space-time, things would not fall, there would be no time. But due to the sun and the earth, and everything else in the universe, space-time is curved, giving rise to what we see as gravity and experience as time.
Gravity is not a force, it is space-time.
