## A bottom-up explanation of general relativity

## Please correct me if I’m wrong.

Let’s first forget ideas like “space” and “time”. There is only one type of quantity. Let’s call it “*spacetime*” — we’ll see later how “space” and “time” are related to it — and the universe has 4 dimensions of it. Just like how the surface of a sphere isn’t euclidean and doesn’t satisfy the “usual” laws of trigonometry, these 4 dimensions are not euclidean, but of a particular kind called Minkowski Space. This space is parametrized by a constant. Let’s call it “*c*”.

Next thing is that in this 4-d space, we don’t have “masses” whose “positions” vary with “time”. All those concepts are our inventions so let’s ditch them. We simply have points in this 4-d spacetime with coordinates *(x,y,z,t)*. We can call each point an “*event*”. This is really the key bit to understand. Study of motion in 3-d is nothing but study of geometry in 4-d. For example, let’s take the sun-earth model in 2-d. You can think of it either as motion (earth rotating around the sun) or geometry — a helix (earth with time) and a line at the center of it (the sun with time). May be this diagram will help:

Now what kind of properties does our universe have? Well, first is that there is some sort of ordering of events. Cause always comes “before” the effect. A bulb cannot turn on before the switch is pressed. This is the law of causality.

What’s more, these pair of points in our 4-d world of events are always within a limited distance. Google.com cannot receive my data packet from India within 1 nanosecond. This is a different kind of limitation. Effect cannot be too “far” from the cause.

This means that there’s a limit at which information can travel. This “travelling information” is what we call a signal and the maximum limit of it is actually “*c*” which we call the speed of an electro-magnetic field where no mass is present (the speed of light in vacuum). What is “mass”, you ask? Mass is a name that we have given to certain curved regions of spacetime.That’s all. “Matter” is simply a construct of our mind that simplifies calculations and helps us make useful predictions.

Another property of our universe is that there are certain symmetries in these relations between events — which, according to Noether’s theorem, means that some quantities like momentum, energy are always conserved.

That’s all. Only two special things about our space. Rest is just details like the geometry of the space (which explains gravitation) and the list of quantities that are conserved.

At low speeds, the space is euclidean enough (just like on the surface of a sphere) that we can consider think of 3 of the dimensions as “space” and the fourth one as “time”. That leads us to concepts like “position”, “velocity”, “mass” and theories like Newton’s laws of motion etc. The spacetime is curved in some places and we call those places as “particles” that have a “mass”. But those theories are only our models that work at that scale. The above model of 4-d events works at both low and high speeds.

So that’s the bottom-up model. The trouble is that it’s too abstract for most people to understand easily. We can’t visualize a 4-d universe. The helix diagram above explains the sun-earth model in 2-d, not 3-d. The ideas of “space” and “time” are too firmly entrenched in our minds. So people resort to simpler models like “time slows down at high speeds”.

Now the above picture isn’t complete. Few years after Einstein, it turned out that this model too breaks down at quantum scale. We have a different model that works there but it is an open problem of physics to unify the two models. That’s called the “Theory of Everything” and that’s the ultimate goal for physicists. I suspect that it’s going to take more math than “physics” to achieve it.

If you’re a professional physicist, please point out my mistakes and help me improve this explanation.

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