Relativity I : Newtonian Spacetime

This is the first post in a series which will cover one aspect or another of Einstein's Special Theory of Relativity. I probably won't put these posts all in a row...that would be too simple :-)In this post I will focus on the concept of spacetime.

If you're reading this you probably have heard at some point in the past that one of the consequences of Relativity is that space and time have to be merged together into a new, exotic-sounding beast known as "spacetime". Perhaps you have gained the impression that space and time have somehow been shown to be equivalent, or to be different aspects of the same thing, in spite of the apparently enormous differences between them in everyday life.

I will argue here for a considerably more prosaic interpretation, one which I hope will demystify spacetime to some extent. Relativity is a theory of motion and it is motion, i.e. changing position with time, which leads to mixing up position and time and necessitates the concept of spacetime. Motion is nothing new and indeed the concept of spacetime is just as relevant to old-fashioned Newtonian physics as it is in Einstein's theories. It has always been part of our commonsense understanding of movement, but it didn't receive a name until the more bizarre predictions of Einstein's Relativity drew renewed attention to it.


To understand the actual content of the spacetime concept, in either classical or modern physics, we ask a very simple question: are you sitting still right now? Before answering, consider that you are sitting on the Earth, which revolves around the sun, which revolves around the galaxy center, which moves within its supercluster, etc., etc. By what criterion can we distinguish any of these as being "sitting still" while the others are "moving"? It is hard to think of any, and indeed nobody has managed to think of any so far.

So we have no absolute criterion to determine whether an object is moving or not. But this means that we also have no absolute way to specify its spatial location! For if we could define locations absolutely, then we could also define motion simply by saying that something is moving if and only if its location changes with time.

To put this a different way, when you move you take your concept of "here" along with you. If you eat dinner and then watch a movie on an airplane, you feel that these two things happen in the same place - seat 27D, or wherever you are sitting. Of course in this case you might think that it's more "correct" to say that you ate dinner over Colorado and watched a movie over Kansas, but this just means defining the Earth itself as "sitting still", which we have just seen to be equally unjustified; and if we extend the example from airplane to interstellar spaceship moving through space at some random location in the universe, it becomes pretty clear that anyone's concept of "here" is as good as anyone else's.

And more than just "here", observers in different states of motion have different, equally valid perceptions of the locations of all objects and events in the universe. If someone asks, for example, how far you had to walk to get to the restroom at the front of the airplane, you would probably say about 100 feet, even though the distance you covered over the Earth during that walk was probably closer to a mile. In your "reference frame" aboard the plane, you walked 100 feet, while in the reference frame of the Earth below, you covered a mile; and there's nothing to prefer either reference frame over the other.

We can describe this situation by saying that motion causes space to get "mixed with" time. I see myself as sitting still, but if someone else sees me as moving, then they see my position as changing with time, i.e., "mixed with" time. Mathematically, I see my position as a constant x = x₀, while the other person sees my position as x = x₀ + vt, where v is the speed he sees for me. Space gets mixed with time by using a factor of speed. Note that we are certainly not suggesting that space and time have some equivalence or even similarity; the "mixing" doesn't need to go any deeper than what was just described.

Now, in Newtonian physics there is an asymmetry, because spatial reckoning varies depending on motion, but time measurements do not vary at all. Time, in Newtonian physics, is absolute, and every observer measures the same time for a given event, regardless of motion. This is the big difference between Newtonian Relativity and Einsteinian Relativity, for in the latter theory the assignment of times to events does vary among observers. The addition of time, however, doesn't add greatly to the rationale for "spacetime", it just makes things more complicated. The main point remains the same - moving observers see things differently, and the different viewpoints are equally valid.

So we see that the spacetime concept arises from very trivial observations. We simply note that different states of motion give rise to different conceptions of the locations of things. The different viewpoints are related to one another in a simple way, so we can easily convert between them, but we can't refer just to "the position" of a thing, without specifying which viewpoint we are using.

Since all of this is just common sense, we see that "spacetime" is just a fancy word for our ordinary understanding of space and time. We use spacetime concepts every day when we discuss our experiences aboard jetliners or any other form of conveyance. It doesn't mean that space is somehow "equivalent" to time, and it has nothing to do with the bizarre time-slowing and ruler-shrinking effects for which Einsteinian Relativity is famous.

All of this is not to say that space isn't merged to time in some way. It may be; nobody knows at this point. But if it proves to be the case, it won't be because of Special Relativity. General Relativity - Einstein's theory of gravity - is a stronger candidate, but here too the "merging" of space and time is less deep than it appears. If it were otherwise, we would call it Einstein's theory of spacetime rather than Einstein's theory of gravity, and theorists around the world would not be racing each other to figure out the actual underlying structure of space and time.