“The idea we’re exploring is that the universe has an imperceptibly small dimension (about one billionth of a nanometer) in addition to the four that we know currently,” Kavic said. “This extra dimension would be curled up, in a state similar to that of the entire universe at the time of the Big Bang.”
Now, here’s the part that’s throwing me: How could a dimension be small? It’s one thing to say that an object is (for example), one meter in length, but you can’t exactly talk about how long length itself is. I’d think a dimension would always be infinite in relation to itself, and even trying to measure something in it in relation to some other dimension just wouldn’t mean anything. If you imagine a four-mile-long one-dimensional object, its breadth, depth, and duration would still be zero; saying it has zero breadth means absolutely nothing about how long it would be, etc.
I’m left with two, non-exclusive hypotheses: (a) the physicists are using “small” as some kind of shorthand term for something more complex that they knew better than to try to work into a news release, or (b) it has something to do with using the speed of light as a kind of comparison metric. Since I’ve never really been able to wrap my brain around the conceptual underpinnings of relativity, I always suspect (b) as the answer to physics stuff that baffles me.
This may not be terribly helpful, but the April '08 issue of Astronomy Magazine had a feature called “Is This The Shape of our Universe?” where it mentions the concept of very small dimensions. I read the article and it went way over my head, but you may want to track it down and read it in case it’s helpful to you.
The simplest example I can give you is a hose. The surface of the hose is two-dimensional. One dimension, along the length of the hose, can be arbitrarily long. The other dimension, around the circumference of the hose, is small even though it is unbounded (that is you can move in the same direction indefinitely; you just return to your starting point and repeat.)
Talking about extra dimensions being “curled up” is pop science talk for compactification. In essence, the space defined by those dimensions is bounded and closed off to a normal Euclidian metric, thus removing those dimensions from normal mechanics, but allowing their existence to permit higher order symmetries between elementary particles (both observed and hypothesized). This is done by (some) string theorists and cosmologists in order to allow for a unifying set of equations between particle interactions while ignoring the fact that these dimensions play no direct role in the observable world. If this sounds a bit like assuming the horse is round to make the math easier, then you’re absolutely right, and has created a lot of contention between people who insist that its the only way to make peace between quantum mechanics, the Standard Model, of particle physics, and General Relativity, and people who believe that the people who believe that will also believe any other bit of gibberish spouted off by wandering madmen, flat tax advocates, and Joe Isuzu.
Occasionally some science fiction author writes a story about unfolding compactified dimensions and using them to travel between stars in the blink of an eye without directly upsetting the ghost of Albert Einstein and other people who are insistent on local causality. It is an appealing thought, but it is little more than the kind of technobabble that allows Captain Picard to escape from the entire Zorlonix battle fleet by using the zoonwindle flux to amplify the transtenegral energy and blingjoople forty megaflonks to safety. In reality, we can’t observe or measure these alleged dimensions, or indeed, give any physical substantiation to them, and have no idea how you’d unroll or access them even if we had the literally cosmological energies likely needed to influence them. The illustrations in the above link are for metaphorical conception only; we don’t have any idea what a compactified dimension actually “looks” like, and aside from fans of the space opera genre the concept is really only of use to theorists who spend twenty hours sessions filling sheet after sheet with obscure mathematical symbols but regularly forgetting where they parked their cars. Nice work if you can get it.
This is just a layman’s explanation, I’m sure a scientist could pick it apart, but I think I’m close enough for internet work…
The extra dimensions are usually said to be smaller than the Planck Length, which is basically a point billions and billions of times smaller than a proton at which normal physics breaks down and the only thing that works is quantum physics. They don’t have any effects on anything, but the math often works. They came about when scientists realized that some problems could only be solved by calculating them as if there were extra dimensions. The people in the article are trying to see if they really exist or not.
it wouldn’t surprise me if they did. Physicists are always doing things like that, calculating equations that would lead to some weird things, then the weird things are discovered later!
>really only of use to theorists
>Aha! You’re an experimental physicist!
OK, so there’s a theoretical physicist and an experimental physicist. The experimentalist comes running into the theoretician’s office, all excited, and says, “Guess what!! I just measured and found out that A is greater than B!! This will be a Nobel, for sure!!”
The theoritician says “Humph” and gets up and goes to his blackboard and starts scribbling, and after a while, says, “That’s no big deal. Look, it isn’t that hard to prove that A would have to be greater than B.”
The experimentalist looks puzzled, and then brightens and says, “Wait, wait, I’m sorry, in all the excitement I misspoke. What I measured was actually that B is greater than A.”
The theoretician grabs his chalk again and says, “Hah! Well, that’s even easier to prove!”
Theoretical physicist: Have you heard the one about the experimental physicist?
Experimental physicist: I’ll have you know I happen to be an experimental physicist.
Theoretical physicist: That’s OK, I’ll tell it very slowly.
The real trick is to prove that A<==>B by a T-duality transformation, then it all becomes clear and trivial, and man can go on to demonstrate that water isn’t really wet and subsequently drown in a highly embarassing attempt to cross the Bering Strait in a tutu and a pair of bunny slippers.
Byzz, the compactified dimensions don’t have to be smaller than a Planck length, and in fact can be arbitrarily large, but sufficiently ‘distant’ from the standard plenum that we observer, or turned upon themselves, that they’re too small to be involved in classical mechanics. It’s also possible that the four dimensional universe we live in is just a bounded twist (or a brane) in a higher dimensional universe where the other dimensions are of normal size (whatever that means) but closed off to us entirely, so that we’re like an ant walking around the inside of a closed balloon. Or its possible and perhaps equally likely that our entire universe is just some speck of dust on the brow of some transdimensional being named Rudolph. All we really know about higher dimensions and branes for sure is that they’re convenient mathematical constructs that allow for higher order symmetries to (hopefullly) tie together the fundamental forces into a single set of operating instructions for how the Universe actually works.
So are you saying that compactified dimensions could be so large as to be unobservable as well as so small as to be unobservable (like the balloon the ant is in or Rudy’s eyebrow)?
If so are these two possibilities equal within the equations? Can they go so far as to co-exist without killing anyone’s cat?
Speaking of “size” as if extra dimensions or branes are physical objects that we can measure is really a misnomer. Consider this; let’s say that you are watching Lawrence of Arabia on your High Definition LCD TV, and you’ve gotten to the scene where T.E. Lawrence goes back into the Nefud Desert under the height of the noon sun to rescue Gasim. Next all you see is a vast expanse of desert with the sun burning overhead, and you watch for what seems an eternity until one pixel changes color; then the blob takes up a few pixels, and then more, until it resolves into an image of two men riding a camel. Peter O’Toole didn’t grow in size, of course; he merely rides closer and closer to the camera, and the objective size of the image is dependent upon what kind and size of screen you project it onto; if you’re watching it on a 70mm projection screen at the Arclight, he’s massively larger than a normal person. His size in real life is irrelevant except in relation to other objects on screen.
Similarly (or at least as close of an analogy as I can make) these compactified dimensions may be of any arbitrary size, but their influence on a Euclidian metric is small enough that they can be assumed to be very, very small, to the point that they are practically infinitesimal and thus disappear from the equation.
As another example, consider a swinging pendulum. A real pendulum will have angular motion in two directions or degrees of freedom (say, angles θ and φ) resulting in the pendulum mass inscribing some kind of periodic epicycloid like a Spirograph that hasn’t lost too many teeth. (In the trivial case that the period of each angular motion is the same, and in opposing phase, the mass inscribes an ellipse, if that makes any sense.) However, if we can assume that motion in the φ direction is much, much smaller than in the θ direction, I can “compactify” or dimensionally reduce motion the world of my theoretical pendulum to one plane thus simply my motion to one degree of freedom in the θ direction. This is conceptually similar to what physicists do when they take a high order dimensional model and compactify all of the extra dimensions (though the actual math is substantially more involved than the simple pendulum example).
“Truth decays into beauty, while beauty soon becomes merely charm. Charm ends up as strangeness, and even that doesn’t last, but up and down are forever.” - The Laws of Physics
A theoretical physicist had been told that only a miracle could cure his arrogance, so he decided to try for one.
“Dear God,” he prayed, “please make me less arrogant. By the way, God, let me remind you that the word ‘arrogant’ should be defined as follows…”
An experimental physicist and a theoretical physicist went hiking together and were soon lost. After several hours, the theorist grabbed the map and studied it intently.
“Boy, are you stupid,” he finally told his friend. “You see that mountain peak over there? *That’s * where we are.”
Actually, Stranger, it can be perfectly meaningful to discuss the size of these extra dimensions, using familiar length units like nanometers. You can (in principle, at least) measure them by timing how long it takes a graviton to travel once around the circumference. Now, such an experiment would be be prohibitively difficult to perform with any technology we’re likely to have in the next million years, but it is in principle possible, and therefore within the purview of science. And there may well be other, doable experiments that would yield the same measurement.
It should also be noted that, first of all, a billionth of a nanometer isn’t a small extra dimension; it’s a somewhat large one, compared with the Planck length. String theory doesn’t imply any particular size for the extra dimensions (or at least, if it does, nobody’s yet figured it out), but they’re often assumed to be about the Planck length for lack of any better size to assume for them, and because in many models, if they were too big, we’d already see evidence of them (but we don’t).
Second, I don’t know which particular models are motivating the search the OP linked to, but in the most prevalent models which call for large (compared to Planck) extra dimensions, if there’s one dimension of that size, there should probably be many.
Thank you Stranger and Chronos, I think I understand the relative irrelavance of the size of extra dimentions however I’m still confused about whether the math would work with an astronomically sized dimention. One so large as to be unobservable either directly or by affect. Without actually knowing the math and without digging out my copy of The Elegant Universe and rooting through the appendex, my instincts say 1. Yes the math would be compatable and 2. By reversing the equation relative to what is theoretically observable on a quantum level one could define “So Large As To Be Unobservable” independant of observation thereby replacing infinity with a theoretical maximum.
But then again, my instincts have been off before.
