I see I’m going to have to eat my words a bit here… The extra dimensions proposed by string theory are not necessarily the same as the extra dimensions that the Universe (might) curve into… As a matter of fact, they can’t be the same, since the stringy dimensions have an upper size limit of about a millimeter, and the Universe is a lot bigger than that. The stringy dimensions may be testable in the very immediate future, if they’re large enough, and even if they’re only Planck-sized, they’re testable in principle, even if the technology to do so is completely inconceivable (just dump all the power output of the Sun into a linear accelerator twice the length of the Galaxy, and you’ve got it). The reason that the millimeter-length dimensions, if they exist, haven’t shown up yet is that only gravity propagates along those dimensions, and it’s very difficult (but not impossible) to measure gravity at those scales.
As for Einstein’s hot table analogy,
Combine the two points, there: The difference in “temperature” of the table is a function of the proximity of mass, so the rods change length near stars and thereby distort the path of light. The Universe is a bit more complicated, but there are functions that you can use such that every point appears to be the center, and yet from any given point, all others appear to be different. As for embedding in higher dimensions being the simpler theory, that depends on the type of curvature you’re trying to explain. Any n-space with a (n-1) space embedded in it, if the (n-1) space is homogeneous, isotropic, and negatively curved (hyperbolic), then the n-space must also be negatively curved, so now we’ve got to explain that one, too. It works fine for positive (spherical) curvatures, but I’m not sure we can consider it the simplest theory if it doesn’t accomodate all the possibilities.
In response to Tretiak, most physical theories break down completely and utterly anythime before 10[sup]-43[/sup] seconds after The Beginning. There’s a few folks (such as Hawking) who are trying to address the issue of what there was before the Big Bang, but their theories are even less testable than String Theory, and it’s debateable whether "before the Big Bang is even meaningful. I’ll go check out that thread, thanks for mentioning it.
I would agree. However, from what I have read, researchers in the field believe that the mathematical richness and completeness, the ‘elegance’, of string theory, is a compelling argument for its validity. If you’re not a platonist I guess this doesn’t carry much weight, but the thinking seems to be that string theory must represent a higher reality.
barbitu8: IIRC, the SA article Chronos cited says currently planned experiments will be completed by 2010.
Yes, I’m eagerly awaiting the results of those experiments, but I’m not too optimistic about them. There’s basically three possible outcomes: First, they detect an anomolous (by Newtonian standards) effect consistent with the predictions of String Theory. If this happens, we have experimental confirmation of String Theory, and a whole slew of further experiments that we can perform leading (hopefully) to a Theory of Everything. Everyone’s happy. The second possible outcome, is that they detect an anomolous effect inconsistent with String Theory. In some ways, this is even better, because it gives us something new to explore. Again, we’d have new data, and the opportunity for even more data, and everyone except those who have a huge investment in String Theory is happy. The final possibility, which I personally consider most likely, is that the experiments don’t turn up anything anomolous, and are totally consistent with Newtonian gravity. In this case, all that we’ll have learned is that if the extra stringy dimensions exist, they’re smaller than a millimeter. Important to know, yes, but not nearly as exciting as either of the other results.
[tangent/hijack]
[B/]Chronos** gives a good hypothetical example about how scientists are not “close minded” to new discoveries. New data are incorporated, rather than rejected because they contradict current explanations. Also, proof of String Theory would not invalidate Newton or Einstein, but instead would be an additional Theory that would expound upon existing theories or would explain a particular aspect of nature.
sorry for the tangent/hijack, but there are plenty of other threads where science is accused of being tautological or closed to new ideas.
Sorry, I just had to jump into this Mongolian Cluster F**k.
I feel that it WAS appropriate for Darkcool to start another thread. As he explained, no one was addressing his basic question. And still hasn’t, really!
No disrespect at all intended, but I will match my knowlege of physics with Chronos’ any day. But if I understand the question correctly, it is a matter of spatial geometry not physics. To the point: Can you constuct a 3 diminsional model of our percieved universe?
If you can, you don’t need 4 diminsions for anything. Chronos waxes on about never-ending 2D models but on the subject of a 3D model he says only this, “…if you really wanted to you could build a three-dimensional model of it with wires and beads, and it’d show the same behavior”.
Oh really! Cites? Links to even one site that this has/can be done - even a CG model? In his original post Dc grants you the wires and I still don’t believe it can be done. I have tried this thought-experiment myself and the beads will ‘stack up’ on themselves when pushed into 3D corners.
I realize that this board is a terrible place to try explain this. But let’s get down to brass tacks.
Forget raisin-bread, forget pink unicorns and belief systems. This is relitively simple geometry, folks. Can the model be built or not?
To answer your question, Darkcool - No. Not even “if you really wanted to”. Yes there are 4 real spatial dimensions.
No disrespect intended Warmgun but you’ll need to do a little bit better than that post as well. You claim to be able to match knowledge with Chronos regarding physics and that may well be true (heck…for all I know you blow him away in this field). Still, Chronos is a known quantity to the SDMB.
While I’m not a post count prig you have dropped the glove on someone who’s opinion is respected here. That’s fine, I even applaud it. It makes this whole board that much more interesting. Still, you have done so without providing cites or examples of your own. Indeed, you take Chronos to task for this yet don’t follow your own advice.
As you mentioned this isn’t an ideal place for a discussion on physics. We’re simply not equipped for intense mathematical proofs that only a dozen people in the world could understand. Even so you claim this is relatively simple geometry. We’re probably capable of following at least that much math.
Frankly, if you’ve read my posts on this subject, I’m with you Warmgun and believe that there must be higher (spatial) dimensions beyond three. I will, however, readily admit that my opinion is based on not much more than a strong preference for that model…it appeals to me. Hardly scientific I know but I do try to base my preference on as much info as I can absorb (within reason…I’m not about to spend 3-4 years learning field equations).
So, convince me (us). I really do want to know! In fact, if you pan out, I’m looking forward to the showdown at the Ok Hyper-Corral!
Someone understood the question/problem.
Now hopefully things will get interesting.
However, I’m afraid both Chronos and (apparently) Warmgun are a little ahead of me in the math curve so like you, Jeff, I’ll be behind the water trough when the shoot-out begins.
Promises to be excitin’ though.
A tip Warmgun - Stand with the sun at your back.
Winner gets fresh-killed marmots and my recipe for ‘Marmots and Collard Greens’. Yummmmmm!!!
Sorry, I don’t seem to have anything to contribute to the original question, at the moment, but Chronos wrote something that I wanted to address:
I’m just an armchair physicists, so I don’t claim that this is necessarily right, however I don’t think there’s anything specifically (or rather mathematically) that requires that the extra dimensions of string theory be tiny. That’s just been the intuitive assumption of why we might not see them. I think an alternative assumption is that they might just be non obvious. What if three of the extra dimensions actually overlayed on the three spacial dimensions that we perceive today? How would we discern and distinguish these dimensions? Actually, we have to take a step back and ask, how do we discern the 3 spacial dimensions that we know and love? Answer: we look at the way objects move or remain stationary within these dimensions. We don’t actually see dimensions - we see the flotsum and jetsum of the universe distributed throughout these dimensions. So that brings us back to the question of is it possible that there are other gargantuan dimensions that we’re merely overlooking? I think that’s possible and I think it’s possible that gravity and the curvature of space is a manifestation of these dimensions, or rather the interaction between the 3 conventional dimensions and three others.
To describe what I’m thinking, I revert to a 2D model, but it’s extensible to 3 dimensions. Imagine that the ‘fabric’ of space (in 2d) is like a sheet of invisible foil. Now imagine that there’s another sheet of invisible foil that forms basically a sandwich. Now suppose the two sheets of foil are made of two different materials with very different coefficients of expansion. Let’s also imagine that the two sheets of foil are bonded in some way so that they effectively share common points along their surface (in 2D space). Now we’ll introduce a point of intense heat at some place in the foil sandwich. Since the materials have different coefficients of expansion, the 2D sheet will form a bubble. Here’s where the analogy starts to break down, but it doesn’t have to if you remember one thing. While our model was originally a 2D structure and the warp has turned it into a 3D structure, when we extend the model into 3 dimensions, the warpage does not necessarily require additional apparent spacial dimensions. The dimensions can still overlap, sort of like intersecting soap bubbles. I’m not sure I did a good job of describing this - it’s all pretty clear in my head… Anyway, to return this back to the subject of gravity, it’s possible that the fabric of space is similar to our sheets of foil except that it’s not heat that warps the fabric, it’s mass.
I don’t have any cites for this theory because it’s entirely original (although I don’t claim it’s unique - someone else may have thought of it independently). Actually, I hesitate to call it a theory - it’s more of a gedanken experiment to suggest how it might be possible that there are large ‘other’ dimensions that are not apparent to our senses. This particular gedanken experiment just happens to demonstrate an explanation for gravity, as well…
There are other thought experiments that I’ve seen to describe how there might be large ‘other’ dimensions that are not visible to us. One of them relies on an observation from string theory that a universe of radius R is functionally equivalent to a universe of radius 1/R. It suggests that in our known universe where R is huge, there could be a very tiny equivalent universe that looks like 1/R to us. However, if you were a native of that universe, you would see a huge expanse of dimensions and our universe would be very tiny (1/R) in comparison. These universes (universii?) might even share some dimensions. To understand how this is possible, consider that our universe is somewhat like a large room. The side walls represent one dimension, the front and back walls represent another dimension, and the floor and ceiling represent the third dimension. All we can see is captured within these dimensions, however that does not preclude other dimensions that share our walls or shares our floor and ceiling. Where this analogy breaks down is that you can eventually walk to one of the walls and knock… then wait to see if anyone knocks back. In our 3 dimensional universe, the walls are not readily accessible.
As to the original question, I don’t think that a 4th spacial dimension is required, however multiple other dimensions can be useful tools to explore the world around us, but they might not, in fact exist. Perhaps our concept of 3 spacial dimensions and 1 time dimension is equally flawed - perhaps these are merey useful models that don’t have any real physical relevance.
JoeyBlades, I’m afraid that I don’t know enough about String Theory to respond intelligently to that. All I know is, the folks who do know about String Theory are always talking about the extra dimensions being small, not large, so I’ll take their word for it. As a WAG, also, I’d venture to say that the extra dimensions have to interact gravitationally with our own, and if they were large, we’d see very noticeable effects from that.
Nen, when you’re doing ASCII graphics, there’s two things that you need to do. The first is to enclose it in [[sup][/sup]code] tags, so it’ll be in a fixed-width font. The second is that you need to replace all spaces with either the HTML code &[sup][/sup]nbsp; or with ASCII character number 160 ( ), which looks like a space but isn’t, or the Web browser will compress all the spaces. If you use the HTML method, you have to make sure to preview it exactly once, so I prefer the char160 method. For instance:
Since Warmgun hasn’t re-appeared I’ll throw more fuel on the fire…
I thought that while the upper dimensions, shoud they exist, are very tiny I also thought they manage to impinge on our 3-D universe at every point. Let’s say we build a linear accelerator twice the length of our galaxy and grab a nearby star to power the thing. Is it being suggested that we cast about our whole universe for the millimeter (or worse…Planck-Length) BB that are the higher dimensions to stick at the end of our accelerator? I was under the impression you could probe for higher dimensions in your cat’s litter box if that’s where you wanted to start looking.
To get an idea of how a thing the size of a BB (or smaller) impinges at all points of our universe go back to a 2-D flatland world. Say we are all 2-D creatures living on the surface of the earth. Everything looks flat to us but really our flat plain is wrapped around an earth sized BB. If we want to travel to Sydney, Australia, for the Olympics we have a long walk ahead of us but if we could manage to tunnel through a theoretical 3[sup]rd[/sup] dimension in a ‘true’ straight line our trip would be considerably shorter.
You might be thinking that my example would still indicate an enormous 4[sup]th[/sup] dimension but I don’t know that it has to equate that way. Perhaps the fourth dimension can wrap up really small and still touch everywhere.
This example, I believe, only works if we live on a hypersphere (4-D sphere–positively curved space). If space is flat or negatively curved (like a horse saddle) this may all fall apart. I also think that the most recent evidence suggests we in fact live in negatively curved space.
Still, it’s fun to talk about.
P.S. Someone was talking about possibly ‘seeing’ these higher dimensions. I’m not sure if that’s what they really meant but FTR you will never ‘see’ a higher dimension…even if it’s right in front of you…heck, even if you’re in it. Our mere mortal minds will never see anything more than 3 dimensions. Mathematically these dimensions can be represented easily but even putting a hypercube together in our imagination is quite beyond us.
Ok, in light of warmgun’s and darkcool’s recent posts, I guess my response would be that I don’t know of any valid cosmological models that need only 3 dimensions (we need to model 3 space + 1 time) or of any valid models with 4 space dimensions. I too have trouble picturing the curvature of 3D space (is the 4th time-like dimension used to model the curvature?), but AFAIK, a 4th dimension of space has not been invoked by cosmologists. If someone could provide scientific references that say otherwise, I’d be interested to see them. I don’t think a replacement for Big Bang Theory is going to be developed in this thread, but it will be interesting to see if this thread goes any further.
I have two different thoughts on that. First, in my gedanken experiment, I indicated exactly your point. In fact, I suggested a model that EXPLAINS gravity via concurrent dimensions. Second, I’m not sure why you would assume that extra dimensions would have gravitational effects in our four… and I’m not sure you would be able to recognize these gravitational effects, if they did exist. Sorry, that stikes me as a “If I can’t see it, it must not exist” sort of attitude. Of course, some string advocates have an equally invalid view point - “If I can imagine it, it must exist”.
Jeff:
In the Scientific American article that Chronos mentioned they proposed a sort of folded universe that looked something like this:
Hopefully that came out right. Here the extra dimension is possibly 1mm, but it’s not obvious that there are folds and curves in our normal 3-space that might put points separated by possibly millions of light years, only a milimeter away from each other (across the 4th dimension).
Before I start, a few points.
I respect Chronos’ knowege and enjoy reading his posts. I certainly did not mean to throw down any glove, I was just frustrated that people were rehashing what is now standard fare and seemed afraid to tackle to the OP.
And Jeff_42, thanks for your support, but I notice you defer to Chronos alot while admitting you don’t fully understand his physics.
As for my low posting numbers, that doesn’t mean I haven’t been here a while. You guys generaly do a great job without my two-cents. And I’ve noticed that it is not at all uncommon for poster 2 to ask poster 1 to back up his statements with cites as I did.
Further, you ask me to prove that it can’t be done. This would be trying to prove a negative. I feel the ball is still in Chronos’ court. I notice his next reply didn’t deal with proof at all. Or the OP.
Quantum physics therorys is a quirky subject. But what a lot of people don’t know is, so are the people who propose them. Science annals or overflowing with great sounding theories that did not pan out. Einstein himself said his greatest mistake was inserting a ‘constant’ to bolster a pet theory of his. These are just people after all.
Which brings us to ‘string theory’ and how we ended up with it.
Subatomic particals can be divided into two classes: Those whose spin is fractional and those whose spin is an integer.FS partiacles are called ‘fermions’. IS particlesare ‘bosons’.Fermions constitute matter while bosons carry force.Physisists were able to link ferms with ferms and bosons with bosons but no theory could cross them (so to speak). Enter ’ supersymmetry’ theory (in the late 70’s I believe). Though it’s ‘supergravitiy theories ultimately failed, they paved the way for ‘superstring’ theory. (I wont explain it (as I understand it) here,there are any # of books that would do a much better job than I. (besides I’m at work - no reference)
Anyway,it explains how the universe got from ten dimensions to four. Six of the orig dimensions collapsed by way of phase transition. Basically, our one temporal and 3 spatial dimensions THAT WE ‘LIVE’ IN continued expanding while the remaining 6 remain small. Curled up, if you will. But they are apparently there.
There’s a catch of course, the theory isn’t finished yet.
Ten-dimentional mathmatics is dizzing mental gymnastics at best. And it demands a thorough command of ‘topography’.
So basically strings are shards of space.
The exciting thing is it could hold the key to ‘dark matter’ and that points to’ inflation’, a bigger universe and flattening of local space. I don’t see how Chronos could deduce that we would see the effects of other dimensions based on this. The accumulated dark matter is supposedly (according to mathmatics) greater than the observable universe!
Now the easy way:
Picture a bowling ball on a trampoline (yes, I know, back to 2D models). If you roll a tennis ball by it, it will ‘fall’ towards the bowling ball because the BB has warped its 2D space 3 dimensionally (unbeknown to the ‘hypothically’ 2d tennis ball). Now toss the TB above the surface of the BB. No such attraction occurs. Why?
Think about it.
Now picture a massive object in space. It also attracts less massive objects by ‘warping’ space.But no matter where the object comes from or how it approches, it will always fall into the more massive object.
Question: Where is the mass warping space into?
Again I say this is a difficult place to explain these concepts, but instead of reading Einstein or Hawking for answers, find a quite place (like…oh, a patent office) and let your mind think for you.
Start with 3D curved space…
Oh, and WAG: The reason GUTs isn’t working - the 4D creates gravity (via 3D warping) and magnatism is something entirely different.But thats a really WAG. No reflection on the views above.
Oh, and Phobos, there is no reason to change the Big Bang Theory just because there are other spatial dimensions.
I’m hoping to spur you guys on to do a little free-form thinking. Who knows, someone here might stumble upon a piece to the puzzle.
Jeff and DarkCool, come on out - there’s no need for ‘gunplay’ . This is the Fighting Ignoance corral.
The problem is as I see it is there are no ‘proofs’ for 3 dimensions and it’s impossible to build a 3D model of our present universe. One has got to be right.Let’s tackle DarkCool’s question in his second (follow-up) post. I gave $.02’s worth. Anyone else?
Well, if we’re going to be getting too deeply into string theory, I’m afraid that I’m going to have to bow out of this discussion. I don’t know String Theory, myself… Anything I say about the subject is just what I’ve gleaned from sources more knowledgeable than myself. warmgum may well have better sources than I; he may even be a better source, himself, for all I know. I’ve heard it said that large extra dimensions ought to produce visible effects; I have not seen any proofs of that. Meanwhile, warmgum, of which three-dimensional model did you want to see more details?
