Multiple Universes vs. Higher Dimensions

I recently got an email out of the blue from a woman who was my childhood baby sitter.  She has been reading popular physics books and was hoping that I could help with a lingering question:  what
exactly is the difference between multiple universes and higher dimensions? This is a great question!  As my answer grew longer and longer I realized maybe I should just turn it into a blog posting!  Many of my students have asked me the same thing (see related earlier blog posts here and here), and it takes some work to explain.


In science fiction and in our casual vocabulary, "dimension" and "universe" may seem like similar or equivalent ideas.  But, in current physical theory, they are really different.  "Dimension" is a technical term with a very specific meaning that deals with the geometric properties of space.  In contrast,
interestingly, "universe" has no single technical definition in physics, so it is often used by physicists to mean lots of different things.  This vocabulary sloppiness creates a lot of confusion.

About Higher Dimensions

Most people are probably familiar with the idea that a piece of paper can be thought of as a "two dimensional"object or space.  What does this mean?  It means that if you want to specify the location of a dot on the piece of paper, you will need exactly two numbers to do so.  These could be, for example, the distance of the dot from the left edge of the paper, and the distance of the dot from the bottom edge, in inches or centimeters or whatever. Any point on the paper can be described using a pair of these coordinates, which you might express as (x,y). Equivalently, there are two perpendicular
directions in which motion can take place within the space of the paper. An ant confined to the paper can move left and right and from the top to the bottom of the page, but can't move "in" or "out" of the paper.

"Dimension" to physicists always has the meaning expressed in these examples:  it is an "axis" to the space you are talking about, or, equivalently, a direction that is available for the motion of objects in
the space.  All positions in a one-dimensional space can be specified using just a single number (x), all positions in a two-dimensional space can be specified using two numbers (x,y), and all positions in our
familiar everyday three-dimensional space can be specified with three (x,y,z).

Since Einstein's work in the early 20th century, physicists have described our universe as a "four-dimensional" space (or "spacetime") in which time acts as a fourth dimension (or axis, or coordinate).  This is just saying that to properly specify "positions" in our universe, you need to specify (x,y,z, t). We
can also write down equations that talk about spaces with even higher dimensions, which would require more coordinate axes to describe.  Higher dimensional mathematics is something that math and science majors commonly encounter early in their undergraduate careers if not in high school, so it's not really even that exotic.  What's new is the idea that higher dimensions might actually exist in physical space.

Relatively recently, the popular string theory (also called M-theory) has postulated that space in our universe might contain extra dimensions beyond our ordinary four.  This is a very hard concept to get
your head around, because all of our mental mechanics for visualization are confined to ordinary three-dimensional space (even getting your head around four-dimensional space-time is tricky). Usually people try to explain this by an analogy, so I will do the same.

If you were the ant on a piece of paper, without the ability to look or move out of the paper, then visualizing or fully experiencing the third dimension would be impossible for you.  If a person poked a finger through the piece of paper from above, your experience within your space would be of a barrier suddenly appearing at a particular location, but you would have no idea that the barrier you encountered was a two-dimensional "slice" of a larger three-dimensional object (the
finger).  However, you might be able to infer the existence of higher dimensions by observing weird things happening in your space like the sudden appearance or disappearance of something that could be explained by, say, a three-dimensional finger poking its way through your space.

We too, like the ant, have no way of seeing "out" into higher dimensions if they exist.  We can't directly perceive higher dimensions.  But it is more than just that we lack some kind of "sense" for those
higher dimensions, the way that we lack the ability to hear a dog whistle or see infrared light. It's important to remember that our senses themselves derive from various forms of physical "detector" systems (our eyes, for example, are light detectors).  All of those sensory detector systems play by the same physical rules that govern everything that is made out of atoms and molecules.   So, for us to "sense" higher dimensions, it would have to be the case that  systems made of ordinary atoms and molecules could move in those extra "directions." Apparently, they don't, or at least not in any obvious ways.

In fact, if the extra dimensions postulated by string theory or M-theory are there, they will be very hard for us to detect in any way even with the fanciest  equipment out there.  These extra dimensions really are supposed to be extra "directions" in the space around us, everywhere through the universe.  But all of the physics of ordinary particles, atoms, and molecules is still operating in three spatial dimensions (plus time).  So, finding any subtle clues of those extra dimensions is going to be really hard.

About Multiple Universes

Multiple universes pop up as speculative possibilities in a lot of different physical theories.  And, what's meant in each case is different. There's a semantics point here that is important:  if in the word "universe" you include every phenomenon that is observable by scientists, then by definition science can only ever really know about "one universe." If you subscribe to that definition, then all "multiple universe" ideas are purely speculative.  But, physical theories leave room for a lot of possibilities.

A few "multiple universe" ideas (not an exhaustive list):

• there exist wholly separate areas of three-dimensional space operating by the same basic physical laws as ours, but yet somehow not connected to ours.
• there exist many simultaneous versions of the universe in the same physical space but inaccessible to one another (this pops up mainly in many-worlds theories of quantum mechanics)
• there exist wholly separate physical entities in which the laws of physics may be completely different from the laws of physics in our observable universe.

All of these ideas are possible within the realm of current physical theory.  We may never know whether any of them are true, unless somehow these other universes affect ours in an observable way (in which case, you run into the semantics problem - does that now count as part of our universe?).  Physicists like to throw around multiple universe ideas because they're exotic playgrounds for speculative physics, and they get people's attention.  But annoyingly, it is really hard to tell what version of "multiple universes" a particular person means.

One particular point of confusion is that the string theories that postulate higher dimensions also can provide explanations of the Big Bang and the origin of our universe in the context of many universes.  Moreover, if you postulate extra dimensions, then you could imagine a "superspace" in which our three-dimensional "universe" is one of many.  This is a hot topic of discussion right now.  But, to wrap up the original question, the concept of a "dimension" and the concept of a "universe" are, even in this case, distinct and potentially independent.  We could have the extra dimensions of space in our universe without there being other universes.  Or, there could be other universes without any universe needing more than the ordinary three space dimensions and one time dimension.  Dimensions are really just "directions" in space, while "universes" usually refer to some kind of totally separate space from the one accessible to the atoms, light, and particles we know.

These are pretty difficult concepts to express concisely, so I encourage followup questions!