I distinctively remember my General Relativity classes.
Every one of them was a joyful experience, and yet I often came home frustrated because I hadn’t understood a particular equation, mathematical reasoning or structure that day. Even so, the feeling of anticipation was nearly overwhelming. A great and beautiful mystery was increasingly within my grasp, if only I could reach out beyond what felt like a mental fog clouding my understanding.
This was not just any mystery. General Relativity is a theory of space-time. It describes the very “stuff” which surrounds us, the reality we are probably a part of.
According to this theory, mass and energy curve the very fabric of reality1. Straight lines are bent, and are renamed as geodesics. In the absence of any external force, objects simply follow these geodesics2. Physicist John Wheeler put it well when he said, “Matter tells space how to curve, and space tells matter how to move.” So, for instance, the trajectory Earth follows around the sun is actually a geodesic—an otherwise straight line, curved under the Sun’s influence.
This makes General Relativity (GR) a theory of gravity too.
All those documentaries I watched as a kid come to mind. They were full of these wonderful pictures of a warped mesh, like an elastic sheet distorted under the weight of a heavy ball. Space-time, the documentaries announced, behaved just like that when interacting with planets and stars.
That’s when I would get the look—the “is he all right?” look.
But how could these short equations I was learning in class encompass all of this complexity? I didn’t know, and I couldn’t yet know, as Calculus–the math I needed to unlock and understand the equations–still presented its own mystery.
But I dreamt of finding out.
Actually, I couldn’t keep my excitement to myself. I could be seen repeatedly and enthusiastically explaining—complete with wide and wild gestures and sparkling eyes—this beautiful elastic, dynamic picture of the Universe to anyone who’d listen. And sure enough, most of my listeners would become somewhat infected by my enthusiasm, only to hit a stout and ominous wall when I began to show them the equations. That’s when I would get the look—the “is he all right?” look.
They just couldn’t grasp the meaning. But the thing was, neither could I!
But I did grasp its significance!
Then, one day, it came. Sort of.
After numerous days of deduction, employing mathematical and physical reasoning, we got somewhere: Einstein’s Field Equations of GR! I didn’t grasp all that they were saying. No one can. But, I tell you, that piece of math right there was a thing of beauty and elegance. Yes, the math is complex, and there are still parts of it that are beyond me, even today.
But the picture they paint is simple, elegant, and beautiful.
It’s a picture—even if just an approximation–of reality itself!
This process of learning, discovering, and being challenged changed me. Now, when I look at anything, really, my mental picture includes these beautiful connections—visual representations of things that are not obvious in “regular” space. As three dimensional beings, we cannot really even visualize these concepts, but we can think them with math!
This fills me with such a profound and unutterable sense of awe for the Creator. All of this beauty and elegance beckons me to search further and deeper, and to ask still more questions.
Piece by piece, I am wanting to build an increasingly accurate picture of the Universe, even, with God’s help, unifying the spiritual and physical realms!
In this process of study and discovery, as amazing as this sounds to many, we are coming to know a bit more of the mind and the ways of God!
Am I completely satisfied with the answers I’ve received and grasped so far? Not at all. I am trying to prove myself wrong all the time. In this way, I find inconsistencies and push boundaries and, hopefully, find out even more. There is still so much to understand! It’s such a big, intricate, beautiful, and astonishing Universe!
Aren’t you curious? I know I am! Sure, some things will remain hidden, but the search is pure joy!
Imagine what the God who made it must be like! Powerful. Brilliant. Artistic. Precise. Beautiful.
Eternity itself won’t be long enough to answer fully all the questions. And that is a very, very good thing, because boredom is then impossible!
“Call to Me, and I will answer you, and show you great and mighty things, which you do not know” (Jeremiah 33:3).
Great and mighty things! So many mysteries come to mind when I read these words! The Portuguese translation literally reads, “marvelous and hidden things that you do not know” (emphasis mine). How wonderful is that? Can you now, with me, begin to imagine the wonders that God’s Universe has in store for us?
“For now we see through a glass, darkly; but then face to face; now I know in part; but then I shall know even as I am known” (1Corinthians 13:12).
Aren’t you curious? I know I am! Sure, some things will remain hidden, but the search is pure joy!
So, when was the last time you pursued a hidden mystery? Have you considered asking God to explain it to you?
Do it! You’ll be in for a real treat!
- Space and time were unified in one single entity with Special Relativity.
- It’s a bit like ships at sea. They can’t really follow straight lines because the Earth is round. Let’s say that you wanted to go from Rio de Janeiro, Brazil to Lisbon, Portugal. If you just pointed to Lisbon and followed what you perceived as a straight course, you’d actually just spiral up to the North Pole! This because the earth is round. The Portuguese mathematician, Pedro Nunes, solved this problem in the sixteenth century, when he discovered a way of calculating the correct bearing to avoid this. And, in a way, GR includes a generalization of his conclusions.
Paulo Torres
Paulo Torres is a physicist, working mainly in the field of cosmology. He has been studying dark energy and dark matter, the mysterious ingredients of the Universe that are massively more abundant than all the visible stars and galaxies. Curious by nature, his interests extend to several other fields of physics and beyond, be it exotic languages, neurology or music.
