More Research on (Small) Multiple Dimensions

travisbecker writes "As a follow-up to this ./ article, take a look at this U. of Washington study (article courtesy of SpaceDaily.com) that shows that *if* other dimensions exist, as postulated in string theory, these dimensions would have to occupy a space smaller than 0.2 millimeter. Research is continuing in the 0.1 millimeter regime. The findings will be published in the Feb. 19 issue of Physical Review Letters."

Comments

Huh?

[waldoj]

I'm not totally dumb about the basic concepts of multi-dimensional theory, but I've got to admit: I have absolutely no idea of what this means. Could somebody explain this in layman's terms?

-Waldo

Re:Huh?

[slcdb]

I'm no physicist, but my take on it is like this:

a) They measured the gravity due to these small (0.02mm) objects to be just as weak as Newtonian physics says it will be.

b) The multi-dimensional theories think that gravity is so weak because after it "travels" a small distance some of it "leaks" off into these other dimesions.

c) If they can later measure gravity to be much STRONGER than normal using objects that are, say, 0.002mm in size, then they know that these other dimensions are either between 0.002mm and 0.02mm in size, or between 0.002mm and 0.02mm away from our dimension (depending on which theory you're specifically using). This is because the objects (in their entirety) would be close enough to each other that none of the gravity has yet "leaked" away.

(Theoretical physics from this programmer's perspective.)

Re:Huh?

[krlynch]

I'll try...

Strictly speaking, what this U. Wash. group has done is to confirm that the Newtonian formula for gravity (or the Einsteinian weak field limit, if you prefer), is correct for objects separated by more than a certain distance. In other words, in the weak field limit, gravitational force falls off exactly as 1/r^2. Although this may not be the way the experiment is done and analyzed, you can think of it this way: suppose gravity "really' acted like (1-exp(-r/a))/r^2. Then, if r >> a, you would find that gravity at larger distances fits the 1/r^2 model. In essence then, this experiment has put a limit on how big "a" can be, since if it was any larger, they would have seen the deviation.

Now, why is this interesting? One reason is that it is yet another confirmation of the weak field limit of General Relativity (this is not that interesting a confirmation, really). Another is that it tells us that there aren't additional dimensions that are "curled up" which are bigger around than a few millimeters. If there were, they would lead to specific types of deviations in gravity at small distances (curled up, or compactified dimensions are kind of difficult to get your head around, but here is a model to think about: get out a garden hose, and stretch it out straight. Then, go a few hundred feet away. That there garden hose would appear to be a one-dimensional object (a line segment). But if you go closer, you would see that it had extent in a second "curled up" direction. Just like this experiment does with the more topologically complicated world we live in).

Frankly, if this experiment had been done a few years ago (say five or six), it would not have been very interesting. "Hold on!", you might say, "Doesn't string theory expect extra dimensions?" And the answer would be "Yes, But", since the dimensions in string theory are expected to be so small that they would never be seen in this type of experiment. What is interesting about this result is that there are new (last five years or so) types of models which remove (in a sense) a certain "aesthetically unpleasant" aspect of the Standard Model of Particle Physics by adding relatively large extra dimensions (meaning fractions of millimeters, not fractions of fractions of Angstroms). So, what is interesting in this new result is that it directly accesses the most relevant size scales for these new models, placing (potentially) strong constraints on some of the most interesting (and easy to understand) versions.

[This unpleasant aspect is that the current version of the Standard Model receives corrections that are proportional to the next highest energy scale above the Standard Model's highest scale, and those corrections are quadratic in the higher energy scale...and the next energy scale is the scale of gravity, some 20ish orders of magnitude above the Standard Model scale. Corrections of this size would be in conflict with the predictions of the Standard Model. In order to eliminate them, you have to assume that certain parameters have ratios which are finely tuned to within 1 part in 10^30 (for example). This is the classic "hierarchy" problem. But, if you put in extra dimensions in a certian way, you lower the fundamental scale of gravity to the point where the corrections to the Standard Model are not large, and hence there is no "hierarchy" to become problematic. Personally, I don't think these models will survive the next few years, but I've been wrong before!]

Re:Time?

[caffeinated_bunsen]

Time is not required to be all that different from a spatial dimension. Some theories describe perception of time merely as a consequence of increasing entropy, which is itself a consequence of an expanding universe. If I understand the explanation I read correctly, time is simply a name for a direction in which a certain characteristic of the universe changes predictably. Specifically, a 4-dimensional (3 space, 1 time) universe is described as the surface of a 5-dimensional sphere. Most theories today use plenty more than 4 dimensions, but this case is easy to explain.

Along the 'time' dimension, the entropy of the universe varies roughly with size. That is, as the universe increases size, entropy increases. As the universe decreases size, entropy decreases. Our perception of time is proposed to be simply a function of increasing entropy, so we must always observe increasing entropy and an expanding universe.

So time is not fundamentally different from other dimensions, but simply happens to be the property of the universe on which our consciousness depends. It is consciousness, not time, that introduces all the wierdness in relating the different dimensions. Or so goes that particular theory. Such theories are quite popular for speculation, but have no real evidence in their favor thus far. As I previously mentioned, this is where philosophy begins to take over from science. If you want to do anything useful, you still have to treat time and space as being fundamentally different.

Time?

[QuantumG]

So someone in the know: is time a dimension or not? When string theory talks of 10 dimensions it is talking about 10 physical dimensions. So the question is, if time is a dimension, is it a physical dimension and we just experience it differently to the other physical dimensions, or is it inheriently different?

Re:Time?

[Christopher Thomas]

Time is not required to be all that different from a spatial dimension. Some theories describe perception of time merely as a consequence of increasing entropy, which is itself a consequence of an expanding universe.

While entropy does indeed determine the direction in which time appears (to us) to "flow", timelike dimensions _are_ physically distinct from spacelike dimensions. There's a - sign instead of a + sign in front of them in one of the SR equations, which has important consequences.

A more detailed explanation is left to someone with a better background than I have.

Re:Time?

[ruck]

Actually, time is fundamentally different from the spatial dimensions. This can be easily seen by looking at a Lorentz transformation equation from relativity. These describe how things "rotate" (in a way analogous to rotation in 3 dimensions) through the 4 dimensions of spacetime, and basically, in such a equation there's a minus sign in front of the time term which one doesn't see in front of the others (x, y, and z, in cartesian coordinates). This minus sign indicates a certain asymmetry which is very important. In a way, the geometry of spacetime is hyperbolic rather than spherical. This ensures handy things like the preservation of causality, which is really a separate issue from the entropy arguments you bring up.

The hypersphere (4-D sphere) you mention, by the way, is more of an image that cosmologists like to use for picturing a closed universe. Time would generally behave the same way whether the universe is closed or not, however. Also note that it's only a 4-D rather than 5-dimensional sphere (the definition of a sphere is just the surface of a "ball," not everything inside). You're probably picturing the hypersphere residing in a 5-d space the same way a 2-D beachball sits in our 3-D world. It's important to remember that spacetime is all there is, though, so there really is no place for it to sit and in this case it's important that we're only refering to the surface.

Also, to respond to two other comments in this thread:

1. Brane theory (or M-theory as it's more often called) really is the same thing as string theory these days. No one really focuses only on strings (or 1-D "branes") anymore, and the name you call the theory is really a matter of taste (and publicity). Also, it's important to keep in mind that there are severaly formulations of string theory (though most have been shown to be equivelant).

2. Unless I'm mistaken, the 10 or 12 or more dimensions you hear advertised always either include time or are quoted as being in addition to time. In short, time is still treated as another (albeit special) dimension.

I don't claim to be an expert, by the way, and welcome corrections.

Re:Time?

[caffeinated_bunsen]

>Time does not exist. It is an illusion.

And lunchtime doubly so, right?

Seriously, though, what theory are you using that completely does away with time? Every one I've heard of incorporates time in the same way as spatial dimensions, or at least a very similar way. Perception of time is another matter entirely, and statements like "Time does not exist" are still strictly the domain of philosophy and metaphysics. Take some of your own advice.

Also, this is not an article about string theory. The subject of the article is a test of a particular brane theory. This is somewhat similar to string theory, but is definitely not the same thing. At the very least, read the article to which this is a follow-up.

If you're just trolling (which is a definite possibility, seeing as how you appear to know nothing of what you speak), I think "All your string are belong to us!" or something similar would have been more effective.