Love einstein

It’s the year 2100. You wake up alone in a small, windowless room. The only other thing in the room is a small ball. Maybe the room is located in your city, but maybe it’s inside that new spaceship everyone’s talking about. How can you tell?You pick up the ball and drop it. It falls vertically to your feet. You time the fall and calculate that the ball accelerates at 9.8 metres per second per second, exactly the acceleration of gravity at the surface of the Earth.But a spaceship in the middle of deep space can also accelerate by that much, producing the exact same results. So where are you?In 1911, Einstein formally proposed that gravitational mass (that which produces a gravitational field) and inertial mass (that which resists acceleration) were one in the same, and this became known as the “equivalence principle”. According to this principle, you can’t tell whether you’re in a gravitational field (such as on the surface of the Earth) or experiencing constant acceleration (a spaceship speeding up, pushing you to the floor, like the g-force of a roller-coaster).Another example is the infamous “Vomit Comet”, officially the Weightless Wonder (see video below), used by NASA for training, and occasionally by Hollywood for filming. Just as with our example with the ball, there’s no way to tell the difference between free fall, and being in the absence of a gravitational field, say in deep space.This principle led Einstein to consider incorporating gravity into the framework of his special theory of relativity, culminating in his General Theory of Relativity.At face value, that doesn’t appear such a difficult thing to do. Until this point, the properties of objects in isolation could be described by equations with great accuracy. But what to do about gravity? How does one calculate the properties of a system in which acceleration can be due to either gravity or changes in velocity? It seems to depend on how you are looking at it.That led to the idea of a “reference frame” – the stage on which the objects you are looking at play out their roles. There may of course be other frames in which the objects appear to behave differently, so we need a description of all the frames, and the way to relate them.The trick was to consider space and time as a four-dimensional object in itself – not a fixed stage on which the objects are defined, but something that itself can change. Let’s say you and I are going to meet for coffee. How do you describe this “event”? One option is to look at a map – “I’ll meet you at the cafe on level two of the building that’s at G5 on the map”. We have described three coordinates: G, 5, and level two. This is another way of saying a set of x, y, and z coordinates. So that we both actually meet for coffee, we’ll also need to add a fourth coordinate: time – say 2:00pm. These four points are what we call a space-time event.

General Relativity says the map can be distorted; and our coordinates will depend on how that happens. If I were to bend the map a little, the distance between two locations changes.

If you measure and add the angles of a triangle on the flat map you would get 180 degrees. If you do this on the curved map, you get a little more or a little less (depending on which way it’s curved). In the same way, the universe itself can have areas of different curvature.

Now for the mind