What Is the Space-Time Continuum?
Ask Science explores the 4 dimensions of the space-time continuum
Lee Falin, PhD
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What Is the Space-Time Continuum?
A few weeks ago, a listener wrote in with this question:
“Can you please give me a brief description of the space-time continuum?”
That’s a big question, but I’ll do my best. As you probably know, we live in space, which is a 3-dimensional thing. The fact that space is 3-dimensional means that you can move in three different ways. You could think of those as side-to-side, up and down, or forwards and backwards.
Scientists usually assign letters to those directions: x, y, and z. So if you move 4 steps to the right, you would move 4 steps along the x direction or the x “axis” as scientists call it. If you move 4 steps to the left, you would move 4 steps along the negative (or opposite) x axis..
Of course you can also move diagonally, but this is really just a combination of two or more of those three ways of moving. So if you took one step forward and to the right, you would be moving along the x axis and z axis at the same time.
Stand in the Place Where you Live
Let’s imagine that the middle of your living room is the centre of the universe. So we assign that spot the coordinates of x = 0, y = 0, and z = 0. This location is called the origin.
We’ll also say that if you move north or south from that spot, you’re moving along the x axis, if you move up or down, you’re moving along the y axis, and if you move east or west you’re moving along the z axis.
We could write the coordinates (or location) of your current position like this: (0, 0, 0).
If you move one meter to the right, we could say that your new position is x=1, y=0, z=0, or (1, 0, 0). Then if you jump into the air, we could say that your new position (while in the air) is x=1, y=1, z=0, or (1, 1, 0).
Now it’s important to note that we arbitrarily said that x=1 means 1 meter of distance from the centre of the living room (or origin). We could have said that x=1 means 1 foot, or 1 inch, or even 1 mile. It doesn’t matter as long as we’re consistent with our measurements. The direction we assigned to x, y, and z also don’t matter, as long as we keep them the same during our discussion. We could have just as easily said that z means left and right instead of x.
Space-time adds a 4th dimension to this idea.
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.
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Space-time image courtesy of Shutterstock.
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