Newsletter: Black holes, collide! (Pt. 1/4)

WARNING: nerd alert – don’t attempt reading this newsletter unless you are, at heart, a true nerd who thinks that black holes and galaxies are (somehow) a cool thing! If you are, however, I promise the read will be worth it!

Today we are going to talk about gravitational waves. Or, well, to be honest with you, we’ll talk about it in about four or five weeks. This is the first of a series of three newsletters in which we will try to go from the very beginning of the theory of special relativity up until the minimum we need to know about the general theory of relativity to understand the concept that won this year’s Physics Nobel prize: gravitational waves. So now you’re thinking: “I’ve got better things to do! Why would I read this huge, complex thing?”

[Black holes merging]

And the answer is: wouldn’t you want to know what happens when two black holes collide?

If you do, then bear with me and keep reading 🙂

The first thing we need to do is to take a step back and talk about space and about time. You see, up until ~1900, space and time were believed to be two different things (I know you just thought “wait, they aren’t????”, so bear with me while we walk through the last (mostly unknown to the general public) 100 years of (a part of) physics). After all, while we can go back and forth in space without much hassle –how would life be if you could not go back home after you left?–, we all know that we can’t go back in time –and for this case we do have thousands of books and movies trying to imagine what that would look like!–. In short: there is a fundamental difference between space and time that makes them appear to be two unrelated things.

But physicists weren’t happy about this. Symmetry is a powerful concept in physics (the more symmetries there are in a problem, the easier to solve it is), and the fact that the equations of classical physics treat space and time differently always bugged some. There was a key problem relating to this issue, in fact: the equations governing electromagnetism (think about light or radio waves, for example) didn’t quite follow the Galilean rules that should allow one to move “points of view” (that is, there is a set of rules that establishes how a problem looks like depending on your perspective -or, more precisely, how to move from one point of view to another-; for example, how throwing a ball looks like from the perspective of the ball and of the thrower). Several theoretical physicists set out to find the rules that would give the correct answer when talking both about the ball and thrower, and about light. (A physicist called Hendrik Lorentz found them.)

This, however, merely solved the mathematical problem: the set of rules had been found. But they presented a new, fundamental issue, which was to be solved by Einstein. Up until now, it was thought that there was something static called the “ether”, which permeated the entire space and provided an absolute point of view for events in the entire universe (so that all other points of view would be the result of moving from the absolute to the particular, and thus we could agree in theory when and where anything happened). This set of rules, however, did not need such an absolute point of view: these rules actually resulted in space and time being relative magnitudes, always dependent upon who is looking! Moreover, this results in an additional, even more profound insight: if space and time can be relative magnitudes (and we’ll delve deeper in a sec into what this means), and moving points of view actually has an effect on both that make one dependent upon the other, it must be because we do not live into “tridimensional space” and “time” as separate entities, but rather into “tetradimensional spacetime”. And so, despite this fundamental difference that prevents us from going back in time, it turned out that space and time were actually part of the same entity, “spacetime”.

That was a lot to absorb: not only space and time are actually part of the same thing (“spacetime”), but there is no absolute point of view in the universe! Let us finish for today by thinking a bit longer about the implications…

If there is no absolute point of view in the universe, then how can we say whether two events are “simultaneous” or not? How can we say whether something happened before or after another thing? It depends, but somewhat of an order can be established (i.e., the math does allow you to assert that the client request came before the crunch) because this wiggle room between space and time is not arbitrary and the rules have bounds! Let’s look at an example. Imagine that you are traveling by train at constant speed (a very special, motorless train with no seats, no people but you, and just two walls so that we can see you from the outside), and the wagon has a light bulb in the middle, right under its ceiling:

[The train – 1]

If we turn on the light, what happens? Does the light reach one of the walls first, or both at the same time? Well, the answer is that it depends! From your point of view, standing in the middle of the train, the light reaches both at the same time, since the room looks completely still to you and both sides are at the same distance of the lightbulb. But from our point of view outside of the train, the light reaches first the back wall, since the train is moving forward and thus the back wall is moving towards the light that was just emitted from the lightbulb, and the front of the train is moving away from the light that was emitted!

[The train – 2]

So, who is right? Well, both. As incredibly unintuitive as it might seem, the fact that you are on the train, moving with respect to us that are standing outside, means that we will see different things! (In ordinary life you cannot notice these things because the differences are incredibly tiny – you would need to move really, really fast (as in at least ~20-30% of the speed of light) to start noticing anything…) And it also proves that indeed space and time are much more intertwined than we can imagine by looking at things in everyday life.

Special relativity, in fact, has even more bizarre implications: the faster you move, the”thinner” everyone else would see you! (Unfortunately, you would still see yourself perfectly normal, opening once again the entire “who is right?” question!)

[A relativistic cartoon rocket]

[c is a constant that represents the speed of light, so that for example the second row means 86.6% of the speed of light]

And another one: the faster you move, the slower clocks move for you (effectively, time “dilates” for you). This one results in the so-called paradox of the twins, and here I recommend watching this 5-minute video about relativity and explaining this very interesting paradox! [https://www.youtube.com/watch?v=ERgwVm9qWKA]

With all this (I know your brain hurts right now – feel free to hit me with an email if you have questions!), we now have a firm grasp on the fact that space and time are part of the same thing, “spacetime”. It is this spacetime concept that will provide the framework for our next Newsletter: we will be moving from the basic idea behind “special relativity” (what we covered today) to the basic idea behind “general relativity” (the full-fledged theory that also includes gravity!).

I hope you enjoyed it and persist with this tougher set of newsletters to discover a completely different way in which the universe is “talking” to us… that we couldn’t even hear three years ago!

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