Matt Strassler [12 Jan 2012]
I’ve given you some examples suggesting how extra dimensions — dimensions of space of which we are unaware — might be present in nature. But I haven’t explained to you yet how scientists could figure out that they are there.
There are several basic strategies that one can employ, and over time I’ll describe a few of them. But for the moment I’ll just focus my attention on one basic consequence of extra dimensions that is very general, and leads to a particle physics strategy that is relevant in many contexts, including research at the Large Hadron Collider.
I’m going to explain it in two steps. In the first step, using some rather simple physics, I’ll give you intuition that is rather simple, but imperfect (because it leaves out a basic feature of quantum mechanics), and gives an answer which is partly wrong. In the second step, I’ll fix the wrong part, which will require one more step in sophistication, and then you’ll see the full answer.
But before I explain it, let me tell you the answer first, so you know what it is that I have to explain to you. Here it is, in a few different versions to help you get the point.
Any type of particle that moves in extra dimensions, as well as in the dimensions we know about, will appear, to naive observers such as ourselves who are unaware of the extra dimensions, as multiple types of particles that move only in the known dimensions and which differ little from each other except in their masses.
Said another way: if a type of particle can move in all the dimensions, it will appear to the uninformed observer as though nature has not only this particle (moving only in the known dimensions) but a set of partner particles, called “KK partners,” also moving only in the known directions, that differ very little from the original one, except that they are heavier. “KK” stands for Kaluza and Klein, for reasons to be explained later.
To be more concrete: suppose that we live in four spatial dimensions, where three of the dimensions are large (the ones we know about) but the fourth is rather short in extent (as in the short dimension across a strip, the case I used extensively in previous examples.) [Short may be very short indeed, much smaller across than a proton.] Let’s call the distance across that dimension L.
Now suppose there is a type of particle that is very tiny, much smaller than L, and can move around freely within all four spatial dimensions. And suppose that there are clever observers who know this: they will say, “here is a type of particle that can move around in four dimensions, and it has a mass m”. Now consider naive observers such as ourselves, who are unaware of the small spatial dimension and think we live in a three-dimensional world. What we will say, after doing some experiments, is shown in Figure 1: “here is one type of particle that can move around in three dimensions, and it has a mass m; and lo, here is another type of particle that also can move around in three dimensions, and it is something like the first except that it has a mass M, much larger than m; and wow, here is yet another type of particle that moves in three dimensions, is something like the first, but it has a mass M’ larger than M; and now another type, of mass M”; and now another, and another …”
What sets the masses M, M’, M” and so forth is a combination of the fundamental mass m and the geometry of the extra spatial dimensions — in particular, M, M’, M” and so on are all inversely proportional to L. The smaller is L, the larger are M, M’, etc., and the more difficult it is to discover the heavy KK partners. Moreover, the pattern of masses exhibited by the KK partners gives direct insight into the number and size and shape of the extra dimensions. [For those musically inclined, this fact is related to the observation that the precise harmonics that a musical instrument emits can give insight into its internal shape and size.]
Explicitly: if photons (particles of light) could move in one or more extra dimensions, like the small boat on a ship canal, then an observer who knows about the extra dimensions would describe them as massless particles (m=0) moving in all the dimensions. But what human scientists (who at present only know about a massless photon that travels in the three known dimensions) will discover, eventually, is a set of heavy photon-like particles. The smaller the size of the extra dimension, the larger the masses of the KK photons, and the harder they would be to discover — more precisely, the heavier they are, the more energetic a particle accelerator would have to be in order to have a chance of producing them.
Now it may very well be that several types of particles can move in the extra dimension(s), and in this case human scientists will discover heavy KK partners for each of these types of particles (see Figure 2). The discovery of a small number of heavy particles that resemble some known lightweight particles, and which exhibit a similar pattern of masses, as in Figure 2, would strongly suggest these new particles are KK partners, and the presence of one or more extra dimensions.
So — that’s the basic answer: a type of particle that travels in extra dimensions as well as the known ones would reveal itself to us through the discovery of its heavy KK partners. Later I’ll talk more explicitly about how one might try experimentally to produce and discover the KK partners. But first, why is this answer correct?