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Q & A: How many dimensions?

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Most recent answer: 10/22/2007
Q:
The physical space we move through consists of three dimensions, and yet we tend to percieve physical space as one unified thing. If I understand correctly, time is considered to be the fourth dimension. Are we really sure that the phenomenon we experience as "time" is actually only one dimension? If so, why are we so sure? Has anyone considered the possibility that time, like physical space, is an interaction between two or more directions, but that we percieve the interactions and relationships between these dimensions as a single phenomenon? As a follow up question, I’m wondering if there is a field of study devoted primarily to the question of time and what it is, how it works, etc. What would such a field be called? Are there any accessible books for the non-scientist that discuss history or current thinking about what time is? Thanks!
- Charles (age 25)
Yamagata Prefectural Government, Japan
A:
Hi Charles,

You can check out our answer to the question "What is a dimension" for some more information about space, time, and dimensionality. You ask some good additional questions, though.

I'm not sure that "perceiving space as one unified thing" is really all that strange even though there are three spatial dimensions we are familiar with. There are different ways to go (up, to the right, and forwards), even though empty space is really the same in all directions (we say it's "isotropic"). Spacetime gets bent around due to the presence of matter and energy, but that's another story.

Our explanations of the physical phenomena we observe make sense only if we use Einstein's theories of special and general relativity. Using these theories, we treat the time coordinate as another number we need to specify an event -- we need three space coordinates and a time in order to say when and where something happened. If we express the coordinates of some event as viewed by someone else, we use Einstein's prescriptions, and these usually involve formulas which include the spatial coordinates and the time coordinate in one observer's frame of reference combined together to calculate the space coordinates and time coordinates of the same event viewed in another observer's frame of reference. It was Einstein's work that showed us just how much like a space coordinate time really was (and just how unlike it is! See the dimensionality answer for an explanation of how time comes in with an opposite sign in the "distance" formula).

As for your question: "how are we sure that's all the dimensions there are?" the answer is "We're not sure at all". There could be more dimensions lurking out there. Some may be very small -- you may only be able to go a tiny fraction of a proton's radius in one of the proposed extra dimensions before winding up back where you started. We sometimes call these extra dimensions in these models "rolled up" or "compactified". One reason why these models seem kinda kooky is that we also have to come up with some explanation for why we may have not noticed these extra dimensions yet in experiments. Maybe we just haven't done the right experiment yet, and the smaller the rolled-up extra dimensions are, the harder it is to test them with today's equipment. But the predicted effects are testable -- one predicted effect is that gravity gets stronger than the usual 1/r^2 dependence if you get within a radius similar to the size of the curled-up extra dimensions of something.

Also the distinction between space dimensions and time dimensions really comes down to how many dimensions have the opposite sign contribution to the distance formula (physics jargon: the "metric"). Time also has some interesting special properties. One is that thermodynamics gives rise to the "arrow of time" entropy inceases with time; stuff spontaneously breaks much more often than it spontaneously fixes itself. The different gases in the atmosphere spontaneously mix (by random diffusion even if no stirring is going on), but do not spontaneously unmix. We remember the past and not the future. Space dimensions seem to be equally good going either way, but time has this "arrow" pointing from the past to the future, and past events can effect future events but not the other way around (we have found no reason to believe that this rule, called "causality" is violated).

Most explanations of time's arrow are historical -- for some reason the universe started in a very special 'unscrambled' state, and the odds are overwhelming that it will fall into more 'scrambled' states, because they are much more numerous. We don't understand the reason for the special starting state.
Evidence for a different arrow of time comes from particle physics experiments. Exchanging particles for antiparticles, changing the signs of all the spatial coordinates, and making time run backwards is a combined symmetry operation which is supposed to leave all the laws of physics unchanged (this is called the "CPT theorem"). Some experiments have shown that by swapping particles for antiparticles and changing the signs of the space coordinates produces measurable differences in some reactions ("CP violation"). The inference here is that the time symmetry by itself is not a good symmetry of nature. The laws of physics would be different if time ran forwards instead of backwards. Direct violation of +-time symmetry was found in the neutral kaon system in the mid 1990's.

One last thought on your question whether there can be more dimensions. Occam's razor is a principle expounded centuries ago that our explanations should be no more complicated than necessary. In fact, the original formulation is that "entities should not be multiplied beyond necessity" (a very rough paraphrase of the original Latin). In short, if we do not need to invoke the idea of any extra dimensions to explain what we observe in nature, then we shouldn't do it -- it just makes our models more cumbersome without improving their ability to explain nature. And furthermore, it opens the number of ways the models can be wrong to possibilities limited only by our imagination.

That's not to say Occam's razor prevents thought and even speculation -- it merely pares down the possible final explanations we are willing to accept as "the best we can do". Science proceeds by formulating hypotheses and checking them with experiment. I am delighted when people come up with ideas that add things (like extra dimensions, or extra particles) to what we think we already know, but I am even happier if these ideas can predict something we can test in the laboratory so we can tell the difference between these models and simpler ones not including the extra dimensions or particles.

Tom (w. a little editing by Mike)

(published on 10/22/2007)

Follow-up on this answer.