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Dark Energy May Lurk In Hidden Dimensions
Magdalene writes in to let us know about a sketch of an idea, that might one day become a theory, to explain the dark energy that is making the universe flee faster and faster apart. It posits that dark energy may be the result of a new kind of neutrino wandering in tiny extra dimensions above our familiar three. She adds, "There is no word yet on whether Sphere or Square are available for comment." From the article: "The mysterious cosmic presence called dark energy, which is accelerating the expansion of the universe, might be lurking in hidden dimensions of space. This idea would explain how the dimensions of space remain stable — one of the biggest problems for the unified scheme of physics called 'string theory'... To get the same amount of acceleration seen by astronomers, Greene and Levin calculate that the extra dimensions should have a scale of about 0.01 millimeter."
First of all, it seems to me that...wait, is that a NewScientist link?
Sorry, nevermind.
According to the calculations, however, these vibrations should either possess a ridiculously high energy density - 122 orders of magnitude larger than are observed - or cancel out to exactly zero.
What's 122 orders of magnitude between friends?
In case you haven't read it, Flatland (The first non-wiki link in google) is the tale of a square named (conveniently) A. Square living in his comfortable home in a two dimensional world, who is eventually visited by a sphere from a *third* dimension and is both vexed and eventually exhilarated (and then vexed again) by what he learns in terms of geometric and social implications.
It's a wonderful bit of British satire and more written by Edwin A. Abbott around 1884. Check it out - it's a wonderful short story, and a very nice example of the treasures that lie within the public domain.
Ryan Fenton
It's not dead, it's just in another dimension.
Task Mangler
Please join me in tagging this article "LSD".
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...Midi-chlorians.
Next article, please!
(WIAK's Law: The longer a Star Wars discussion goes on, especially on Slashdot, the greater the likelyhood that someone mentions either Han shooting first or George Lucas raping their childhood.)
"Accept that some days you are the pigeon, and some days you are the statue." - David Brent, Wernham Hogg
I'm sorry, you seem to have the wrong thread. Mindless flames are over here
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Can you please enlighten me how exactly this is anything like "a scientist who fixes the observation to meet their theory". Two things are wrong with your reasoning:
1. They are trying to fix the theory. Note that this does not automatically implie their results/ideas are right nor that I am defending them. I always found the whole "large extra dimesions that are just small enough so we haven't observed them but will at the LHC,..." thing total nonsense.
2. As clearly explained in TFA these should be observable in the near future. On the other hand, a theory of everything (if it does exist) is bound to at least have some features that are unobservable. Reproducing the big-bang, or some equivalent singular event near the origin of the universe is probably impossible.
(I am a former string theorist, which does not imply I am a believer)
#1) Respect the privacy of others. #2) Think before you type.
Unfortunately there is often just enough truth in some crackpot ideas to keep people pursuing them. We do have biological cycles which are influenced by the Moon (astrology), there probably are some numerological bits of weirdness in the Bible -it would be amazing if there weren't given the range of authors and their interests - and Freud had some genuine insights. It's this that can help to draw in intelligent and curious people.
Pining for the fjords
Hi, I'm a first year graduate student in Physics, so I probably understand string theory at just about the right level to explain the basics. If I knew any more about it, I would be smart enough to not try to explain it. If I knew any less, I couldn't explain it at all. This will all make a lot more sense if you've ever studied complex numbers. If you haven't, here's your chance to start!
First, you need to understand the geometry of regular spacetime in Einstein's Special Relativity, which isn't the Euclidean geometry with several real coordinates that you learned about in high school school. The time coordinate is a regular real variable, just like in Euclidean geometry. But the space coordinates are three different imaginary units whose square is 1, call them i, j and k. A point in spacetime is characterized by 4 coordinates, like (1t, ix, jy, kz). This system is called the hyperbolic quaternions, or Minkowski space. Why hyperbolic? Read on!
Next, how do you calculate distance in spaces with imaginary coordinates? Recall from high school geometry that in a plane with 2 real coordinates, the distance between the origin (0,0) and a point P=(1x,1y) is d^2 = x^2 + y^2 = P dot P. In imaginary coordinates you do it a little differently, you take the dot product of P with P*, P* being the complex conjugate of P, and the dot product being multiplication of only the corresponding coordinates. Complex conjugation leaves the real coordinate unchanged but flips the sign on the imaginary coordinates, so 1 goes to 1, i to -i, j to -j, k to -k. Now the distance between the origin (0,0,0,0) and a point P=(1t, ix, 0, 0) is d^2 = (1t,ix,0,0) dot (1t,-ix,-0,-0) = 1^2 t^2 + (-i)(i)x^2 = t^2 - i^2 x^2, but i^2 = 1, so we have just d^2 = t^2 - x^2. In general we have d^2 = t^2 - x^2 - y^2 - z^2. Note that different points can be distance zero from each other. These points lie on each other's "light cones" because photons travel along these zero distance trajectories. Points with positive distance from each other are called timelike with each other and can have a cause and effect relationship. Points with negative distance are called spacelike with each other and are totally disconnected.
Now we're ready to see why this geometry is called hyperbolic! What are the points which are distance 1 from the origin? Let's use the distance equation with 1 for the distance, ignoring y and z to keep the math simpler . Then 1 = t^2 - x^2, that's just a hyperbola with two branches, one in the past and one in the future! These hyperbolae go on forever and therefore so does this kind of space. This hyperbolic spacetime stuff is why objects become distorted at high relative velocities. The two spherical gold nuclei that they smash together at the relativistic heavy ion collider see each other as flat hyperboloidal pancakes.
Ok, now we're finally ready to look at these small circular dimensions. Now we use a real coordinate for time and imaginary coordinates for space, just like before. However, this time we use the normal imaginary unit whose square is -1, not 1. It's usually called i, but I've already used i, so let's just call it u. Now the distance from the origin (0,0) to a point P (1t,ux) is P dot P* = 1^2 t^2 + (u)(-u) x^2 = t^2 - u^2 x^2, but u^2 = -1, so d^2 = t^2 + x^2. The minus has become a plus! What are the points which are distance 1 from the origin? 1 = t^2 + x^2, the equation of a circle! The circumference of this unit circle gives a characteristic length to this space, usually taken to be something like the Planck Length of 1.6 x 10^-35 meters.
In string theory, spacetime becomes the product of our familiar and beloved big, hyperbolic spacetime with a bunch of these small, circular spacetimes. Particles with electric charge go around in a circle, particles with weak nuclear charge fly around on a sphere, and particles with color like quarks and gluons move around on a hypersphere. Mass is related to the size of the particle in these circular spaces, with bigger particles being lighter. When he tal
We don't actually need 2-dimensional euclidean space to describe the topological structure of the circle.
There are several different concepts of dimension in mathematics. The one you are probably thinking of is the dimension of a vector space. What we seem to need here is the dimension of a manifold. Intuitively, a n-dimensional manifold is something that locally "looks like" our familiar n-dimensional euclidean space (R^n). You already got that right with the ant example.
Manifolds can be described in different ways. One way is as a certain kind of subset of some higher-dimensional vector space R^m, this is the way you are probably imagining. But it is also possible to describe a manifold without any reference to a surrounding space.
For this we need the concept of a topological space. Informally, a topological space is a set in which we can talk about connectedness, continuity and which sets of points are "a neighborhood" of a given point.
As a topological space, the circle can be seen as the usual interval [0,1] (of real numbers), but with the points 0 and 1 identified (that is, they are considered to be the same point) (usually one would use the analogy "0 and 1 glued together", but this would evoke the intuition of a surrounding space again, which we are trying to avoid
Likewise, topologically a sphere is equivalent to a square (or a disk) with the whole boundary[1] considered to be a single point. A torus is a square with every point on the left edge identified with the corresponding point on the right edge, and every point on the top edge identified with the corresponding point on the bottom edge.
Generally, a n-dimensional topological manifold is defined as a topological space with the following property (+ some technical conditions):
For every point on the manifold, you can find a small region U around the point (a "neighborhood"), such that U is topologically the same ("homeomorphic") as a disk/ball or a box[2] in n-dimensional euclidean space. A homeomorphism is essentially a map f which puts the points of one space into one-to-one-correspondence with the points of another space, and respects convergence in the sense that some sequence[3] x_n converges to x if and only if f(x_n) converges to f(x). It can't tear regions apart which are connected, or vice versa.
For example, if we have some point of the sphere, we can take a small neighborhood U of it and map U to a disk in the obvious way. This mapping respects convergence. Thus, the sphere is a 2-dimensional topological manifold.
Now I only described the topological structure; topology is "qualitative" and doesn't talk about concrete distances, angles etc.. If you want to have these, you need a structure called a Riemannian manifold. But I haven't taken a course on differential geometry yet, so I won't talk about that
I hope I didn't tell you things you already know and that I didn't sound condescending. You are asking good questions and I think you would like topology courses
Whether the surrounding spaces are "real" is a matter of philosophy, but as you can see they are not absolutely necessary...
[1]: For the topologists: I'm using "boundary" in the informal sense here; of course the boundary (in the formal sense) of the whole space is always empty.
[2]: Actually it doesn't matter whether you require it to be homeomorphic to a ball in R^n or to the whole R^n.
[3]: In general it's a net, not a sequence
I tried topology once, but I couldn't wrap my head around it.
When our name is on the back of your car, we're behind you all the way!
Blasting physicists (or any scientist) for speculating on unsolved, scientific mysteries is just an astounding step backwards intellectually and I'm afraid that as a society we've taken that huge leap backwards.
If the mob stopped spouting their own specious dogma, showing their own Newtonian-based cognitive dissonance and actually RTFA:
That folks, is science in action. Don't make me go through the checks and balances between experiment and theory.
It stops being science when critical thinking and the scientific process are overruled by non-scientific reasons.
The corollary is that it stops being scientific criticism when the basis of the contrary views also fall prey to non-scientific reasonings. Reasonings such as "I don't see any _______" - fill in the blank with "atoms", "neutrinos", "monkeys giving birth to human babies" - all of which were used as arguments against theories about things we did not yet know and were considered unprovable at the time.
Well, I for one DO NOT welcome the creationist tagging overlords.
Besides, there's nothing wrong with inventing something new to preserve some theory. The neutrino was "invented" to preserve conservation of energy. Antimatter was "invented" to keep quantum theory consistent with relativity.
Despite common memes about the history of science, the vast majority of new ideas don't require tossing out the old ideas. IE: dark matter, dark energy, string theory, etc. I think that's why we've seen theories like MOND become more popular. MOND is not by any means more popular than dark matter; indeed, the observational evidence implies that even if MOND were true, you would still need additional dark matter to fully explain the observations, with which MOND alone is inconsistent.
You're being hypocritical to boot. MOND is also an invention of something new to try to save a theory. Dark matter introduces new kinds of matter to try to save our theory of gravity. MOND introduces a whole new theory of gravity to try to save the existing particles we know about. Arguably, the former is a more conservative choice than the latter! Of course, both modifications may be necessary, but right now it looks like you can do it all with dark matter, and there are already reasons coming from particle physics, independent of any astrophysical evidence, for why those kinds of dark matter particles should exist.
There is also nothing wrong with inventing a theory of quantum gravity, such as string theory, in order to save existing theories of relativity and quantum mechanics, since both of them have enormous amounts of evidence in their favor.
Continuing on string theory, the theory has not "failed", nor do people "add more strings" to fix it; indeed, the string content of the theory is determined by the overarching M-theory and cannot be adjusted at will. My point is we need to stop pushing stories that aggrandize theories until some serious research has been done on the issue. Serious research has been done on the issue. This story is merely reporting one of the latest proposals. This proposal is not necessarily more plausible than any of the others currently floating around, but that's why the story said it was "a sketch of an idea, that might one day become a theory". It is nevertheless interesting, and is consistent with some things we know about dark energy.