The Newsletter is back this week – get ready to continue getting closer to our goal: what happens when two black holes collide?
A couple of weeks ago we discovered the theory of special relativity, and learnt that space and time are actually part of the same thing, spacetime. We saw some instances that show that relation (for example, how things that move fast appear thinner to those who look, and how time moves slower for those who move fast), and we actually thought a little bit about how even something that appears obvious in daily life, saying whether two events were simultaneous, is actually more complicated than that.
Today we will get another step closer to our black holes colliding, by learning the very basics of General Relativity and the concept of “curved spacetime”. With this, our next Newsletter will finally cover the concept of black holes… so rest assured, it will be worth it!
As we were saying a couple of weeks ago, space and time are both part of this “spacetime” thing, and one can influence the other. Special relativity, however, does not include gravity in the framework, and as you can imagine, when one talks about planets, stars and all these things, gravity is kind of important! In fact, it is so important that this is probably the single most important insight that Einstein discovered (and this is a rather strong thing to say, Einstein discovered several things of immense value!).
If you stop and think about it, “space is straight”: if you do not exert any forces on a moving object, the object moves in a straight line. This applies in all three directions of space (although we cannot really see this on Earth for the vertical direction unless we prepare a specially designed experiment due to Earth’s gravity), and so if you roll a ball on a flat surface and let it do its own thing, it will indeed move on a straight line. This is the concept of “straight space”.
Now, if I ask you about gravity and you know a bit of physics, you will talk to me about the Newtonian gravitational attraction, the force of gravity that binds together the solar system, and so on. Einstein, however, thought a completely different thing. He realized that if you are on a free fall towards the ground, or somewhere in space moving under the effects of a replica of the force of Earth’s gravity, you have no way of distinguishing one situation from the other. So much so, that if there weren’t air to tell you that you are accelerating, you wouldn’t even notice that you are accelerating and everything would feel, to you, exactly the same as if you were standing still!
You might be wondering now: sure, thanks, but how does this relate to spacetime and gravity? And the answer is: Einstein realized that there is no such thing as “the force of gravity”. Gravity is not a force that links you to the Earth (or to anything with mass, such as the couch when you don’t want to go to the gym). The astonishing breakthrough Einstein made was to assert that space (well, spacetime!) is not actually straight, but curved. And the trick to how this works is this:
Matter tells spacetime how to curve. And spacetime tells matter how to move.
This means that the Earth curves space and time very lightly, like this:
And so, when we were talking before about things moving in straight lines, what happens actually is that matter simply follows the “straightest possible path” that it can follow under the surrounding curved spacetime (each of the white lines defines a “straight path”, so you can clearly see how curvature would alter the definition of “straight”). This is why you can roll a ball on a table perfectly straight (spacetime is almost perfectly straight in these two directions), but as soon as it leaves the table, “the straightest possible path” (despite whatever our eyes are telling us – our eyes cannot see this curvature!) becomes going towards the ground. And we feel gravity as a force precisely because we cannot follow this straight path (the ground prevents us from doing so, and if we try to go in the opposite direction you are actually climbing uphill (in spacetime), so the natural thing is that as soon as your impulse ends, you fall back downhill to the ground). This is confusing, so let’s use the ball example once more to look at the solar system:
(The speed at which you are moving with respect to the massive object is thus crucial: if you’re moving fast enough you’ll be able to escape the curvature and, like the comet, be able to simply have a slightly curved trajectory instead of the straight one and avoid becoming trapped like the Earth and Mars are!)
So, let us quickly summarize:
On the one hand, time and space are part of a whole called “spacetime”. And thus they are interconnected and do not exist as separate entities.
On the other, it turns out that gravity is not a true force but actually the consequence of the fact that matter interacts with spacetime and curves it. Since things try to move through space in straight lines (as it happens when you roll a ball over a table), when space is curved they will simply follow the straightest possible path they can follow (as it happens when the ball rolls off the table and curves downwards toward the ground!). This also affects time, essentially by slowing down the clocks of anyone in the vicinity of a big mass (and the Earth is not a “big mass”).
And the final summary – if you are to remember anything from today, let it be the aforementioned sentence: Matter tells spacetime how to curve. And spacetime tells matter how to move.
This is a little bit like the fact that we all are influenced by our circumstances, but certainly we also have an influence over our circumstances. And this is very true for the larger universe: spacetime might be the canvas where all the events around us take place, but it is a rather special canvas, as everything that happens in it also alters the canvas itself!
Before finishing, we will change one thing from the above. It is not actually “matter” that curves spacetime, but energy in general. The thing is that mass is basically the most concentrated form of energy there is, and thus when thinking about this “ball in the elastic” picture above, matter is essentially the only thing capable of such “hardcore” curvatures. But this point is important for another reason: light also follows these ideas, and thus light also follows spacetime just like everyone else*. Let that last point sink in, because together with the previous summary these are the key ideas to understanding what a black hole is.
I know this just got tougher this week, but bear with me: the toughest is already over, and now that we have these two ideas in our minds, we can concentrate on understanding what a black hole is (and all the interesting things that can be said about them) –and what happens when two of these collide.
Bonus to relax the mind: a picture of the Andromeda galaxy.
The Andromeda galaxy is the closest neighbor to our home, the Milky Way. Probably the biggest galaxy in our “local group” of around 30 galaxies. It has a supermassive black hole right in the middle, just like our own galaxy (and like most galaxies). If we had better visual acuity (or a decent pair of binoculars), we would see this galaxy on a clear night as 7 times bigger than our moon… despite being so far away that you would need 19 zeroes to describe the distance in kilometers (for comparison, the moon would require “only” 5 zeroes, as it is “only” 348,000 km away, and the Earth is just ~6400 km wide).
It definitely is a humbling experience to think about black holes as big as our entire solar system, stars so dense that a teaspoon of their core would have a mass of around 10 billion tons –more mass than all plastic humanity has ever produced, or something 1 million Eiffel towers right there–, or about scales of distance to which we represent the 22st decimal place. It’s just baffling. So get ready for the trip we begin on our next newsletter – it will be worth it!
* (Only for extra-nerds) Photons are super weird. However, if you feel invincible today, feel free to hit me with an email and I’ll send your way a couple of ideas about photons and spacetime that will surely break your brain if this didn’t (no shame – they break mine every time I think about it, too!).
Kike Miralles 
