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.
Exactly! Sorry to be redundant, but apparently at least some Slashdotters don't realize this-- New Scientist is not a credible reference for articles. It is filled with crackpot speculation, because it looks sexy and it sells. Don't trust them as a source of credible information.
They also don't give a good picture at all of what is important and interesting in physics. If you want to know that you're much better off directly reading the blogs of respected physicists. I rec http://cosmicvariance.com/ [cosmicvariance.com] in particular.
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.
You misread the article, it clearly states "- 122 orders of magnitude larger". So while the magnitude of the energy density is "ridiculously high" it is the sign that is truly interesting. Negative energy has some bizarre properties.
by Anonymous Coward
on Sunday July 15 2007, @01:10AM (#19864931)
OK, this story was "edited" by kdawson, but I don't see the standard anti-Microsoft crap, and it wasn't submitted by Roland. kdawson must be getting tired.
In case you haven't read it, Flatland [alcyone.com] (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.
...dark energy has fallen into an interdimensional rift in the fabric of space/time, can we shove the astrophysicists who insist on inventing the unobservable to fix their theories in with them, and get on with fixing whatever the error in the models really is? Please?
There is nothing worse than a scientist who fixes the observation to meet their theory, to paraphrase the illustrious but equally fictional Sherlock Holmes.
Hm... That's a really very tough one. First of all, take dark matter... I can count 7 (much-publicized) theories off the top of my head. Which one are you going to fix?
Second. Well, there has been a few theories about dark energy but none of them have been greatly publicized. The truth is they are more whackier than dark matter theories. Now, you are suggesting that we go and fix the errors in them?! Huh? We dont even know which one is the one that matches reality most closely.
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)
What part of such an LHC-observation scenario do you find as "total nonsense"? Afterall, physics (especially the LHC) needs two things: 1) a multitude of theories to debunk and 2) money. There are theorists which will "die" if the LHC does not observe large extra dimensions. So most such theorists say: "if this theory is correct, then large extra dimensions must be small enough so that we havent observed them before but are large enough to be observed at the LHC." I can see nothing that can be called total nonsense here -- as long as the clause "if this theory is correct" is included.
And I am an experimentalist. With very little taste for things that theorists believe to be true. So there you go... I spend my days hoping to reproduce a mini-singularity one day...;)
If Adelberger's pendulum does start to see gravity grow below 0.01 millimetre, it could be a sign that Greene and Levin are right, and the force that's tearing our universe apart really is an invader from another dimension.
I've seen Bush called a lot of things, but this takes the cake
If Adelberger's pendulum does start to see gravity grow below 0.01 millimetre, it could be a sign that Greene and Levin are right, and the force that's tearing our universe apart really is an invader from another dimension.
I've seen Bush called a lot of things, but this takes the cake
I'm sorry, you seem to have the wrong thread. Mindless flames are over here [slashdot.org]
(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.)
(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.)
Godwin's curse: As an online discussion of nerds grows longer, the probability of lame jokes created by making fun of Godwin's law approaches one.
"A THEORY in technical use is a more or less verified or established explanation accounting for known facts or phenomena: the theory of relativity. A HYPOTHESIS is a conjecture put forth as a possible explanation of phenomena or relations, which serves as a basis of argument or experimentation to reach the truth: This idea is only a hypothesis."
You were saying? Those successes you mention were deemed successes because they were bolstered by emperical evidence, not more math.
So.. let me get that straight. We solve the problem of energy we can't detect and dimensions we can't prove exist? Simple! We tuck the one into the other and thus explain everything in a single shot. Brilliant!
Now allow me walk away for today as I am laughing my guts out.
Currently tagged as "crackpot", which is odd as this sounds like String theory - which may be incorrect, or may not be science, but is surely NOT crackpot. You don't get people with enormous pulsating brains like Ed Witten devoting his career to crackpottery.
Some of the most intelligent people in history have devoted their entire careers to things like numerological analysis of the Bible, astrology and hermetic and unverifiable systems like Freudian psychoanalysis. Intelligence is not proof against being totally and utterly wrong about things which are not readily demonstrable. String Theory unfortunately has all the hallmarks of a belief system which, because we do not currently have the ability to falsify its predictions, lends itself to being entirely wrong.
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.
there probably are some numerological bits of weirdness in the Bible
There are numerological bits of weirdness everywhere if you want to find them. Remember these words of wisdom:
If you want the number 216 you can find it everywhere. 216 steps from your street corner to your front door, 216 seconds you spend in the elevator. When your mind becomes obsessed you filter everything else out and find that thing everywhere. Whatever. You've chosen 216 and you'll find it everywhere in nature. But, Max, as soon as yo
Currently tagged as "crackpot", which is odd as this sounds like String theory - which may be incorrect, or may not be science, but is surely NOT crackpot. You don't get people with enormous pulsating brains like Ed Witten devoting his career to crackpottery.
As a case in counterpoint, Newton devoted at least as much of his research to alchemy as he did to the "non-crackpot" sciences.
You don't get people with enormous pulsating brains like Ed Witten devoting his career to crackpottery.
Isaac Newton was into numerology and astrology. I'm not saying String Theory is crackpottery, just that genius doesn't immunize one against crackpottery.
Wow! It sounds like the Dark Matter guys and String Theory guys should get together. Soon we will have theories for everything and with no experimental validation required. I am going to try this excuse on my Quantum Physics Professor, "The reason I didn't turn in my last lab report is that it wandered into an alternate dimension." LOL! See my previous posts for what really happens in the future.
It's finally happened, the war against science has extended itself onto Slashdot. The Slashdot commentary on this is the width of one rolled up dimension away from calling for the end of physics research funding, gathering the pitchforks and torches and taking over Universities' physics departments to install only approved, generally accepted science. "There's no room in science for idle, fanciful speculation" is what they'll yell as they institute teaching only what Newton told us or better yet, what the bible tells us is true.
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.
...and now the mob chants in spooky unison: "But it's not provable, it never will be provable"
If the mob stopped spouting their own specious dogma, showing their own Newtonian-based cognitive dissonance and actually RTFA:
"Eric Adelberger and his team at the University of Washington in Seattle, US, have run a series of experiments using a twisting pendulum to measure the short-range strength of gravity, and they have already ruled out extra dimensions larger than a 0.1 millimetre. They are planning a new experiment to probe shorter distances still."
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.
That's actually a very interesting result, as it's on a similar scale to some other theories of large hidden dimensions. Doesn't mean it's right, but it's at least interesting when multiple theories arrive at similar results coming from different angles.
This analogy has always bothered me. How can extra spatial dimensions exist at different scales? Dimensions are a result of the shape of space. For instance we have our 4D space (x, y, z, time) but that describes the dimensions at all scale levels. How can you have dimensions that are only apparent to objects of some fixed scale or size? How can the shape of space have little curls that only affect particles, but nothing else?
This analogy has always bothered me. How can extra spatial dimensions exist at different scales?
The parent poster explained it. Some dimensions are infinite, and have no scale. Others are finite, and have a scale, because you can measure them. A telephone wire is essentially an infinite cylinder. One dimension has no scale. The cross-sectional dimension is circular, and has a scale: the circumference of the circle. In a universe with such a geometry, you can literally wrap a tape measure around the closed dimension and see how big it is. For the very small dimensions being discussed here, you can't construct a literal "tape measure", but you can do things like send particles around the circle and measure how they come back.
How can you have dimensions that are only apparent to objects of some fixed scale or size?
The poster gave you an example. If the dimensions are so small you can't even see them, they're not going to be apparent to you. They might be apparent to an ant, though.
How can the shape of space have little curls that only affect particles, but nothing else?
It affects everything, but it doesn't affect big things very much. Big things will be smeared out across the extent of the small dimensions, while small things will be more localized, and therefore the particular geometry influences their behavior more.
Length would only make sense in the other dimension by comparison to lengths we know already, so scale cannot be an issue. Try thinking of it this way: the new dimension is not given by a line like your x- and y-axes, but by a circle. Each time you travel a certain distance in the z-direction, you come back to where you started. Disclaimer: IANAST (I am not a string theorist) but IAAT (I am a topologist).
I suppose part of my problem is that I think of dimensionality in a cartesian sense. If I have a dimension curve back on itself (form a circle) I am conceptualizing that I have to go through another dimension to do it. So, if I have a line in one dimension I need to go through a second dimension to curve the line into a circle. Circles are two dimensional...and yet they are being used to describe a single dimension. I must somehow convince myself to think differently about what a dimension is I suppose.
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:)). For example, the sequence (1/n) converges to 1 (=0), and the path
f(t):= t if 0 <= t < 1, f(t):= t-1 if 1 <= t < 2
is actually continuous in this space (it isn't continuous in the usual topology of [0,1], because f(t) "jumps" from being close to 1 to being zero again, as t approaches 1).
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;) But these manifolds can also be constructed without referring to a surrounding space.
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 just don't get how a dimension has a size/scale. If I go from 2 dimensions to 3 the added dimension is orthogonal to the first two. The axes of the new dimension (as with the first 2) go to infinities in either direction creating a volume that is unbounded.
The key word here is unbounded.
The extra dimensions are "compactified". That mean they are bounded.
Example of spaces with bounded dimension are the circle or sphera. They both have maximum diameter - that mean the distance between the points of t
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
Except for the math, the concepts are simple. For this we have computers.
But being a freshman your not stuck into one theory or another yet, lets examine this statement of theirs for your thoughts:
The mysterious cosmic presence called dark energy, which is accelerating the expansion of the universe....
I have never understood this expanding universe theory at all. The universe expanding in all directions would also make us the center of it. Not likely, as that makes as much s
I just wanted to mention that it seems utterly ridiculous that every time something doesn't fit into the model of physics someone's trying to push, they try to "invent" something completely new to save their theory.
Dark energy itself is a new theory, not an old theory being "saved". Actually, it's not even really a theory. It's just a catch-all term for "something that makes the universe's expansion accelerate". That could be the quantum zero point energy, a new kind of particle, extra dimensions, modifications to the laws of gravity, and so on. All of these ideas are being pursued; why are you so down on this particular one?
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.
New Scientist (Score:5, Insightful)
Sorry, nevermind.
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Re:New Scientist (Score:5, Informative)
Parent
Well... (Score:5, Funny)
What's 122 orders of magnitude between friends?
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That'd certainly get you to Kevin Bacon a few times.
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Huh? (Score:3, Funny)
Land of the Giants (Score:2)
So this explains Land of the Giants [imdb.com]
"Sphere or Square" reference... (Score:5, Informative)
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
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I haven't read that one but I loved The Planiverse [amazon.com]
Now that... (Score:3, Interesting)
There is nothing worse than a scientist who fixes the observation to meet their theory, to paraphrase the illustrious but equally fictional Sherlock Holmes.
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Hm... That's a really very tough one. First of all, take dark matter... I can count 7 (much-publicized) theories off the top of my head. Which one are you going to fix?
Second. Well, there has been a few theories about dark energy but none of them have been greatly publicized. The truth is they are more whackier than dark matter theories. Now, you are suggesting that we go and fix the errors in them?! Huh? We dont even know which one is the one that matches reality most closely.
Third. Yes, astrophysici
Re:Now that... (Score:4, Insightful)
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)
Parent
Re:Now that... (Score:4, Interesting)
What part of such an LHC-observation scenario do you find as "total nonsense"? Afterall, physics (especially the LHC) needs two things: 1) a multitude of theories to debunk and 2) money. There are theorists which will "die" if the LHC does not observe large extra dimensions. So most such theorists say: "if this theory is correct, then large extra dimensions must be small enough so that we havent observed them before but are large enough to be observed at the LHC." I can see nothing that can be called total nonsense here -- as long as the clause "if this theory is correct" is included.
And I am an experimentalist. With very little taste for things that theorists believe to be true. So there you go... I spend my days hoping to reproduce a mini-singularity one day... ;)
Parent
evil invader (Score:2, Funny)
I've seen Bush called a lot of things, but this takes the cake
Re:evil invader (Score:4, Funny)
I'm sorry, you seem to have the wrong thread. Mindless flames are over here [slashdot.org]
Parent
Acid (Score:5, Funny)
Oh yea.. (Score:2, Funny)
I wonder what inspired all of this thinking? (Score:2)
http://www.theonion.com/content/node/29433 [theonion.com]
We all know where Dark Energy comes from... (Score:5, Funny)
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.)
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erp...
I'm telling you... (Score:4, Informative)
Seriously: without some experimental evidence to back up these theories, they aren't worth the paper they are written on.
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"A THEORY in technical use is a more or less verified or established explanation accounting for known facts or phenomena: the theory of relativity. A HYPOTHESIS is a conjecture put forth as a possible explanation of phenomena or relations, which serves as a basis of argument or experimentation to reach the truth: This idea is only a hypothesis."
You were saying? Those successes you mention were deemed successes because they were bolstered by emperical evidence, not more math.
Funniest title ever (Score:4, Interesting)
So.. let me get that straight. We solve the problem of energy we can't detect and dimensions we can't prove exist? Simple! We tuck the one into the other and thus explain everything in a single shot. Brilliant!
Now allow me walk away for today as I am laughing my guts out.
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Crackpot?? (Score:3, Insightful)
Actually untrue, unfortunately (Score:5, Insightful)
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.
Parent
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There are numerological bits of weirdness everywhere if you want to find them. Remember these words of wisdom:
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As a case in counterpoint, Newton devoted at least as much of his research to alchemy as he did to the "non-crackpot" sciences.
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Isaac Newton was into numerology and astrology.
I'm not saying String Theory is crackpottery, just that genius doesn't immunize one against crackpottery.
Hidden Dimensions.... Riiiigghhht (Score:2)
The Bush administration's war against science... (Score:4, Insightful)
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.
Re:Nothing for you to see here. Please move along. (Score:5, Funny)
Parent
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That's actually a very interesting result, as it's on a similar scale to some other theories of large hidden dimensions. Doesn't mean it's right, but it's at least interesting when multiple theories arrive at similar results coming from different angles.
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A telephone wire looks one dimentional from a distance, but up close there are ants walking on it's 2D surface.
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Re:How does a dimension have a scale? (Score:4, Informative)
Parent
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dimensions, manifolds etc. (Score:5, Informative)
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
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I tried topology once... (Score:5, Funny)
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4th Dimension (Score:2)
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A second is roughly 299792.8 kilometres long.
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The key word here is unbounded.
The extra dimensions are "compactified". That mean they are bounded.
Example of spaces with bounded dimension are the circle or sphera. They both have maximum diameter - that mean the distance between the points of t
Re:How does a dimension have a scale? (Score:5, Informative)
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
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Really simple, right?...
Except for the math, the concepts are simple. For this we have computers.
But being a freshman your not stuck into one theory or another yet, lets examine this statement of theirs for your thoughts:
The mysterious cosmic presence called dark energy, which is accelerating the expansion of the universe. ...
I have never understood this expanding universe theory at all. The universe expanding in all directions would also make us the center of it. Not likely, as that makes as much s
Re:Being a non-Scientist (Score:5, Insightful)
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.
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.
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