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What Is the Space-Time Continuum?

Everyday Einstein explores the 4 dimensions of the space-time continuum

By
Lee Falin, PhD
December 22, 2013
Episode #081

Page 2 of 2

The 4th Dimension

Instead of just moving in the three dimensions of space, we are also moving along through time. As you read this article, you've already moved along several seconds along the time dimension. Unfortunately, 4-dimensional shapes are harder to think about visually, which is why we spent all of that time talking about coordinates. Math makes it easy to discuss higher dimensional space.

If we assign 0 to be the time in seconds when you started standing at the centre of your living room, then your coordinates in 4-dimensional space are: x = 0, y = 0, z = 0, and t = 0, which we could write as (0, 0, 0, 0). Notice that 4 dimensions means we have 4 values in our set of coordinates.

5 seconds later, our coordinates in space time would be (0, 0, 0, 5). If during that 5 seconds we happened to have taken a step backwards (going backwards along the z axis), then our coordinates would be (0, 0, -1, 5). Now it's important to remember that our time dimension being measured in seconds is again, completely arbitrary. We could have used minutes, hours, milliseconds, years, or anything else.

With all of these arbitrary choices of direction and measurement, it's important to think about a frame of reference, or something to compare our coordinates to. So if we wanted to give someone our absolute position in space-time, using the last set of coordinates we mentioned, we would need to tell them:

"I'm at coordinates (0,0,-1,5) relative to the centre of the living room at the start of my experiment."

We'd also need to tell them the directions of the x, y, and z, as well as our units of measurement for each of the dimensions:

"If x is the distance in meters north of the centre of my living room, y is the distance in meters above the centre of my living room, z is the distance in meters east of the centre of my living room, and t is the amount of time in seconds since I started standing in the centre of my living room, my coordinates (x,y,z,t) are:  (0, 0, -1, 5)"

Fortunately you'd only need to tell them all of that once, and then any coordinates you told them afterwards would use the same information.

Now that you know what space-time is, let's talk about the space-time continuum. A continuum just means something that continues. So if you think about moving up and down from the centre of your living room, you could continue to move up forever, and you could continue to move down forever. (assuming you could fly and tunnel through the centre of the earth, respectively). When you move along in space-time, you are moving through the space-time continuum.

Conclusion

So now you know all about the space-time continuum. An important thing to remember about the space-time continuum is that It goes on forever in each direction of each dimension. We can move in both directions in each of the 3 dimensions of space, but (currently) only one direction in the dimension of time that is, until Math Dude and his colleagues at Caltech build that time machine.

Thanks for listenting or reading. I'd love to hear from you, so please connect with me on FacebookTwitter, and Google+.

Space-time image courtesy of Shutterstock.

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