A Quick Introduction to the Concept of Spacetime

Jillian's Guide to Gravitational Waves : Quick Intro to the Concept of Spacetime

Spacetime is a peculiar thing, and I have the sneaking suspicion that it's commonly used incorrectly. It's a very tricky concept, even more so because it seems so simple. I mean, there's just all this space around us, and we see it change with time. How is that difficult? Where do all those funny-looking grid diagrams come into play?

Okay, start with the basics. The idea of spacetime is that it is something that represents all spatial directions plus time in one simple graph. The problem arises that we have only three spatial dimensions in which to represent this. We can't draw four dimensional diagrams just like no one can draw a two dimensional sphere without cutting some corners and using some artistic tricks to make it seem like a sphere. It is for this reason that when folks give examples of spacetime, they like to describe a universe with only two spatial directions (thus freeing up a dimension for representation of time). Such a universe would be just like living on a piece of paper or on the surface of a lake.

Having a representation of all of spacetime of a two-dimensional plus time universe isn't that useful---it would probably resemble a large tank filled with bubbles of liquid with different densities. What is useful to do with it is to slice it up. Hmm, now what does that mean? An analogy: a stack of paper. Imagine this stack of paper is a chunk of spacetime. Now, the spatial directions are usually chosen as being on/in the sheets of paper. Each sheet represents the condition of spacetime at a certain instant of time. That's what slicing means---taking a snapshot of spacetime at an instant.

When you take that sheet of spacetime-at-a-certain-instant, it might have some bumps and ripples in it. See, whenever our spacetime paper bends, it manifests as gravity. What makes the spacetime bend? The presence of matter or energy. A star would make a smooth dip or a bump called a gravity well. A neutron star would make a really deep and somewhat pointy dip. A black hole would make a very deep well that ends in a sharp point...sort of. The ripples are gravitational waves.

Things would be nice if I left them here, for this is all very confusing, but there is one more thing I should mention. It has been determined that spacetime is expanding. What a curious statement! I mean, the distance between me and the door is not getting any larger, nor is the distance of our sun from the center of the milky way increasing. The best way to explain this is the balloon-and-pennies analogy, since I haven't found a better one and am suffering from a creativity block in thinking up one for myself (heh!).

Okay, take this balloon. Here. There are pennies glued all over it. Those pennies represent big lumps of matter like nebulae and galaxies. The balloon rubber represents spacetime. Now, if you blow up the balloon a little, the rubber expands and the pennies are suddenly further away from each other---but the pennies themselves haven't changed size! Get it? That's how spacetime can be expanding and distances increasing and galaxies all rushing away from our own without the galaxies themselves expanding along with it.

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