The Validity of an 11- or 26-Dimensional Universe

[chefurbo]

I have heard multiple theories about the universe having more spacial dimensions than humans can perceive or conceptualize (more than 3), but I'm still unclear as to the validity of these proposals. I'm assuming the ideas materialized as a result of physicists and astronomers dealing with multi-dimensional mathematical equations in real-life applications? Someone told me that "it's been proven that the universe must have more than 3 spacial dimensions." Is this true or is it just hogwash? And if it is true, what do the other dimensions actually represent? What is their purpose?



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In addition, please excuse me for my deluge of initial posts. These are questions I have accumulated over the past year that I haven't been able to find any decent answers to. Thanks in advance for everyone's input. :)

[Enola Straight]

It is valid insomuch as to generate formulas which describe that which is observed.

Einstein's General Theory of Relativity is based on a four dimensional field. When this field is distorted by mass (or perhaps a massive dollop of energy ;) ) the result is a gravitational field. The validity is uphelddue to the theory being able to describe thing the previous gravitational theory (Newtonian) could not, such as the precession of equinoxes of Mercury's orbit, or the distortion of starlight in the immediate vicinity of the coronal disc during a solar eclipse.

Furthermore, when you take the mathematical rules which govern General Relativity and apply them to a 5 dimensional field, you get gravity AND electromagnetism a set of physical phenomena of known observables.

Add enough dimensions and you get all the forces which govern the universe.

Of course, different competing theorys consist of 10, 11, or even 26 dimensions.

I'll leave it to a real physisist to explain that one. ;)

[squeegee]

I'll wait for a real physicist to happen by, but here's some more tidbits. The "extra dimensions" idea is a theory, not proven. The idea is that the universe had all these dimensions (11/2, whatever) at the time of the big bang, and the extra dimensions "curled up" so small as to be indetectable. Think of standing on a rope -- you can move in one long direction, but you can also move around the perimeter of the rope in a smaller dimension. Now shrink the rope's diameter to smaller than an atom, and the "extra" dimension is now invisible, but still there.

[chefurbo]

I kind of understand what you are saying... but my original questions still remain. Hopefully someone out there can give some more insight? What do the other dimensions actually represent? What is their purpose?

[Apos]

I admit right off the bat to not knowing anything about string theory, and I can't conceptualize extra dimensions. But can someone explain how time can really be the same SORT of dimension as length, width, and depth? I mean, I understand that a dimension in some sense is just a mathematical description of a variable on a plot... but then why do string theorists talk about how the extra dimensions have to be "rolled up" and that's why we don't "see" them? I mean, we don't "see" time either (although we might experience it, but that's not the same thing). If the fifth dimension could just be electromagnetism, then why couldn't the sixth be Democrat/Republicanism and so on? Why would the other dimensions have to be "rolled up" if they could just be things that we know of and can measure just fine already?

And what's all this about their coming a point when those dimension UNROLL and basically wipe out everything we know? Man, that would SUCK.

[Nobody]

I admit right off the bat to not knowing anything about string theory, and I can't conceptualize extra dimensions. But can someone explain how time can really be the same SORT of dimension as length, width, and depth? I mean, I understand that a dimension in some sense is just a mathematical description of a variable on a plot... but then why do string theorists talk about how the extra dimensions have to be "rolled up" and that's why we don't "see" them? I mean, we don't "see" time either (although we might experience it, but that's not the same thing). If the fifth dimension could just be electromagnetism, then why couldn't the sixth be Democrat/Republicanism and so on? Why would the other dimensions have to be "rolled up" if they could just be things that we know of and can measure just fine already?

And what's all this about their coming a point when those dimension UNROLL and basically wipe out everything we know? Man, that would SUCK.
Each spatial dimension is perpendicular to the other one. Length is perpendicular to height which is perpendicular to width. The fourth dimension is perpendicular to all of those. The directions you can travel in the fourth dimension are usually called ana and kata. I don't know why.
However, as for the other dimensions being "rolled up" or tiny, I don't know how that's supposed to work.

[Apos]

Well, I get the perpendicular thing, but I can't see how time would be "perpendicular" to any of the other three since it's not spatial in any way I understand.

[Nobody]

Well, I get the perpendicular thing, but I can't see how time would be "perpendicular" to any of the other three since it's not spatial in any way I understand.
It's not spatial. It's included as a dimension because dimension isn't limited to physical things. Just about any type of measurement could be concidered a dimension. Time is included as another dimension to length, width and height because you can measure in time where something is, as well as where it is physically located. If we used a grid, I could be located at (3, 15, 42), and so could you. But how could be at the same exact location? Well, I could be there at 8:30AM and you could be there at 5:00PM
And I hope that helps, instead of sounding like I'm babbling (which I am :cool: )

[Apos]

But then how does electromagnetism fit in as a 6th dimension? And if any measured thing can be a dimension, what need to limit it to 11 or 20 or even 100? And why would they need to be rolled up? I'm back where I started. They should call it "all tangled the fuck up" theory.

[Cabbage]

I admit right off the bat to not knowing anything about string theory, and I can't conceptualize extra dimensions. But can someone explain how time can really be the same SORT of dimension as length, width, and depth? I mean, I understand that a dimension in some sense is just a mathematical description of a variable on a plot... but then why do string theorists talk about how the extra dimensions have to be "rolled up" and that's why we don't "see" them? I mean, we don't "see" time either (although we might experience it, but that's not the same thing). If the fifth dimension could just be electromagnetism, then why couldn't the sixth be Democrat/Republicanism and so on? Why would the other dimensions have to be "rolled up" if they could just be things that we know of and can measure just fine already?
I am not a physicist either, and I know even less string theory, but I think I have a general idea. (I will also admit that I'm posting this partly in the hope that someone more knowledgable will come along and correct my errors and misunderstandings).

As far as I know the idea behind string theory is this: Every elementary particle is made up of a string. If that string vibrates one particular way, it is realized as one particular elementary particle; if it vibrates another way, it is realized as another.

Now imagine a loop of string in a two dimensional plane. Sure, it can vibrate, but the freedom of its vibrations is somewhat limited (it can't vibrate outside of the plane). On the other hand, if that same loop of string lives in three dimensions, it's vibrations can be considerably more complex.

Now, I know absolutely none of the details or history behind this, but as string theory progressed it became evident that three dimensions are not sufficient to provide for the freedom of movement needed by the strings to realize the assortment of elementary particles we have. Eleven dimensions are necessary, apparently.

We only perceive three of these eleven (spatial) dimensions because eight of them are "rolled up", or "compacitified". For example, say you are a two dimensional being, but the two dimensional universe in which you live is actually the surface of a very thin wire. It might be the case that you only perceive one of the dimensions--the length of that wire. The fact that the surface is two dimensions (rather than one) may not be perceived by you, because that second dimension is very small, being curled up around the (tiny) diameter of the wire.

I welcome any corrections here, because again, I'm not a physicist, and am curious to know if this is the basic idea of string theory.

[Nobody]

But then how does electromagnetism fit in as a 6th dimension? And if any measured thing can be a dimension, what need to limit it to 11 or 20 or even 100? And why would they need to be rolled up? I'm back where I started. They should call it "all tangled the fuck up" theory.
This will be my last post on this for a while, and then I'll those who know what they're talking about give it a shot.
1) Electromagnetism is't the 6th dimension (or the 5th, which is what I've usually seen mentioned when talking about electromagnetism). There is a link between electricity and magnatism. I've read that we can't actually observe the link in 3 dimensional space, we need more. If we could take a peek into 5 dimensional space, we could then see how they are related. Or so I've read.
2) Although most or all measurements can be described as dimensions, in this context, the only ones that count are spatial dimensions and time.
3) Why would they need to be rolled up? I have no clue.

[Apos]

We only perceive three of these eleven (spatial) dimensions because eight of them are "rolled up", or "compacitified".

You know, I just realized that "rolled up" and "compactified" have about as little meaning to me as if you'd said that they were "Dolemitized baby!"

But the idea that the strings would need more degrees of freedom does sort of sound on the right track to me understanding it, unless I am completely wrongly associating it with my much more extensive knowledge of statistics.

[Cabbage]

You know, I just realized that "rolled up" and "compactified" have about as little meaning to me as if you'd said that they were "Dolemitized baby!"
That's understandable, it's not necessarily an easy subject (in fact, I'm currently writing my (math) dissertation on certain compactifications).

In some cases, however, it's fairly intuitive, like the example I gave regarding the two dimensional surface of a thin wire. This is a very basic "compactification":

First, imagine the basic two dimensional (infinite) plane. Now compare that with the two dimensional surface of a thin wire. What's the difference? A fundamental difference is that in the latter, one of the dimensions has been "rolled up" (compactified) into a circle (namely, the circumference of the wire). In the former, on the other hand, that same dimension extends infinitely in either direction--it is not "compact", or not "rolled up".

It's much harder (if not impossible) to visualize this when you're talking about higher dimensions (such as eleven), which is why I chose this particular (low dimension) example to illustrate it.

There are also compactifications which are much more complicated than simply "rolling up" a single dimension into a circle, though I don't know whether or not they would have any applications in string theory.

[SentientMeat]

I'm not so sure anyone will turn up here who is of the calibre to facilitate an "Ask the String Theorist"-type thread, and so we might largely have to make do with the understanding gleaned by those of us who've dabbled here and there.

Admittedly, I am limited only to popular books, articles and maybe the odd paper on the subject, but it seems to me that there is a blatantly obvious question which needs answering:

Why do we only have three spatial dimensions?

Three is a rather arbitrary number in physics (one lecturer told me that if the answer isn't zero, infinity or one, and can;t be normalised to one, you've probably gone wrong somewhere).Why not two, or four? Granted, a two dimensional universe wouldn't have strong enough gravity to allow for "interesting" structure like galaxies, stars and ultimately us, and a 4-D universe's gravity would be too strong: Three dimensions appears to be the little bear's bed and porridge which the Goldilocks of intelligent life finds just right. But that is taking the anthropic principle a bit far, surely?

No, say some. Indeed, they ask, would it not make non-arbitrary sense if we merely lived in a three dimensional region of the universe? Might evidence of the 2-D or 4-D region be apparent at high enough energies in the Large Hadron Collider in Geneva next year, or its successor, or its great-great-grandchild in centuries or millennia?

Perhaps, perhaps not. String theory was, itself, far too arbitrary to be the Theory of Everything: it gave five different types of string with no reason to favour one over another except by inelegantly forcing our universe's variables into it with a veritable tyre iron. Its successor, M theory (http://en.wikipedia.org/wiki/M_theory), attempts to remove its arbitrariness by explaining the 3-Dness of the universe we inhabit. (As this excellent article (http://www.guardian.co.uk/life/feature/story/0,,1393722,00.html) implies, maybe those 'extra' dimensions are unnecessary, or so Witten suspects). However, it is not yet strictly a theory, but a model. Models only become theories if they predict things, and we are at too early a stage for that. (Sadly, it might never if the required engineering slips out of reach of the physics - what if it needed a collider bigger than Earth?)

As for the dimension called 'time', this is just a measure of the change in a spatial configuration of the universe: if the universe does not change in any way (eg. expanding or contracting), no time can be said to have "passed": Time is just an axis on which configurational 'events' exist. The Big Bang, Big Crunch (or whatever) and 26th January 2005 are all different places in the 3-D region of the universe. There is no such thing as 'now'.

[KidCharlemagne]

Time is included as another dimension to length, width and height because you can measure in time where something is, as well as where it is physically located. If)

My understanding is that time isn't a dimension but simply the way that dimension is revealed to us. It is the way we experience a 4th dimension. Someone correct me if I'm wrong.

[SentientMeat]

It is the way we experience a 4th dimension.As I understand it, there are important differences between the dimension we call time and the ones we call length, breadth and depth: it is clearly does not have exactly the same relationship with breadth as breadth has with, say, depth (two need a ruler, one needs a stopwatch!). However, the idea that time as an axis on which different configurations are placed (just as those configurations are placed along axes of length, breadth and depth) is a common one.

[MMI]

IIRC all of the "extra" dimensions are space-like, rather than time-like.

[KidCharlemagne]

As I understand it, there are important differences between the dimension we call time and the ones we call length, breadth and depth: it is clearly does not have exactly the same relationship with breadth as breadth has with, say, depth (two need a ruler, one needs a stopwatch!). However, the idea that time as an axis on which different configurations are placed (just as those configurations are placed along axes of length, breadth and depth) is a common one.

The difference in how we measure space and time is a function of our limitations as 3-dimensional beings; the fourth would probably appear like a spatial dimension to a 4th dimensional creature. The 4th dimension is considered physical, not temporal. If you're using time as a 4th coordinate, whose "time" are you using? I would probably liken measuring the 4th dimension with a clock to measuring mass with a scale. As long as your at 1g (keeping the extra variagble constant) your ok, but change that variable and a scale is no longer useful. For instance, the twin who takes the trip on the spaceship may appear to have been "lost in time" because it was traveling along the 4th dimension. Maybe as velocity increases, more of the movement occurs along the 4th axis relative to the other three. Just speculating.

Another thing: If Gravity warps the space around it, perhaps the attraction is a collapsing/expanding of the 4th dimension.

[SentientMeat]

If you're using time as a 4th coordinate, whose "time" are you using?The universe is static from this perspective: configurations differ over shorter scales within it according to Special Relativity, and the position of a clock hand is a configuration of the universe.
For instance, the twin who takes the trip on the spaceship may appear to have been "lost in time" because it was traveling along the 4th dimension.In a static, time-as-an-axis universe, one does not "travel" in time, one simply exists as different configurations. The twin configuration merely differs on a shorter or longer scale.

[FriendRob]

Someday when I have time I'll start the "Ask the (Former) String Theorist" thread, but for now...

The answer to the OP is: NO, extra dimensions have NOT been proven. They show up in many theories, but there is as yet not a single shred of experimental evidence for them. All of these theories are extremely speculative, and most physicists who write about them say that (tho maybe not clearly enough).

Check out Brian Greene's books (The Elegant Universe, The Fabric of the Cosmos) for a good introduction to these ideas.

Cabbage did a good job of explaining why there needs to be extra dimensions, and the reason they need to be rolled up is that we only see three spatial dimensions. In fact, they DON'T need to be rolled up if you treat them as "internal", non-spatial dimensions (like the Republican/Democrat dimension someone mentioned). I believe this type of theory is equivalent to a rolled-up theory if you pick the correct rolled-up space.

[KidCharlemagne]

The universe is static from this perspective: configurations differ over shorter scales within it according to Special Relativity, and the position of a clock hand is a configuration of the universe.
In a static, time-as-an-axis universe, one does not "travel" in time, one simply exists as different configurations. The twin configuration merely differs on a shorter or longer scale.

I don't quite get what you mean by "configurations" and "scales." Is any one configuration one of an infinite number of parallel universes?

[KidCharlemagne]

You know, I just realized that "rolled up" and "compactified" have about as little meaning to me as if you'd said that they were "Dolemitized baby!"

But the idea that the strings would need more degrees of freedom does sort of sound on the right track to me understanding it, unless I am completely wrongly associating it with my much more extensive knowledge of statistics.

I got dolemitized just last week. Completely embiggened my spirit.

[Lumpy]

I thought the unification of General Relativity with electromagnatism in five (or whatever) dimensions was purely formal; that is, it simply translated the known laws of electromagnetism into dimensional terms without predicting anything new or useful. Is this the case?

To muddy the waters further information theory, along with the predicted properties of black holes seems to say that the amount of information that a space can contain is related to the surface area, rather than the volume, of that space. Some people speculate about a "holographic universe", in which our universe make more sense if you consider it as a hologram within a two-dimensional space!!!

[JasonFin]

As to the dimensionality of time:

It aids understanding to observe that Special and General Relativity both treat space and time in a completely symmetric fashion. Both are capable of considering a universe with one "space" dimension and three "time" dimensions, and it would be in every respect indistinguishable from ours.

From this perspective, the true physical fact is that we have three dimensions of one type and one of the opposite type. Travel through space is different from travel through time simply because our universe has more space dimensions than time dimensions. The linearity of time follows from the fact that, in one dimension, objects don't have any room in which they can turn around.

[Apos]

Why should the rolled up dimensions all be spatial then? Could we figure out how to unfurl an extra rolled up time dimension and take a spin back in time?

[Loopydude]

The idea is that strings and branes need to vibrate to have the properties of the particles we observe. With only three dimensions, there aren't enough degrees of freedom for the strings to vibrate in which would allow them to resemble anything we actually see. So, what happens if you posit the existence of some greater number of dimensions? Seems with M theory, the numbers work out best if you have 11 dimensions; or rather, in 11 dimensions, the 5 most promising 10- or 10+26-dimensional string theories, plus a particle theory called "11 dimensional supergravity", can be shown to be related, and hence equivalent in a certain sense. If the dimensions are incredibly small, we'd never even notice they're there; and hence, we can't deny they might exist.

I am utterly unqualified to comment on the merits of M Theory, but that never stopped me. Some aspects of the theory, if I comprehend what is being reported at all, make me a bit uncomfortable. For one thing, it takes absurd amounts of energy to probe string scale physics. I keep hearing figures quoted like "It will take an accellerator anywhere from the diameter of the Milky way, to the size of the universe" to pack enough energy into a particle such that you could "see" strings/branes. Sooooo, how is anybody supposed to test this? Thing is, they theory's apparent versatility makes it potentially impossible to disprove, unless you can push things all the way up to those energy scales. Some folks have wondered "What if the extra dimensions were big...even a mm across?" Well, that we could test, and it turns out, no, they must be smaller than that. That's OK, because the theory can work all the way down to the Plank scale, it seems. So where does it end? M Theory is highly flexible and fecund, so I hear. It can accomodate perhaps an infinite number of kinds of universes (or vacua in a giant multiverse, in which we inhabit...well, an inhabitable corner). So, with an essentially endless number of possible permutations (or even "only" 10100 permutations they posit in the "Landscape"), how can we ever say M Theory is wrong? String theory gave rise to Supersymmetry. If they find evidence of SUSY, it bolsters the case for String/M Theory. But if they don't, it won't discount M Theory, because it seemingly can be formulated without SUSY. Again, where does it end? Is this a refutable theory? I honestly don't know. If it isn't, well, what can you do with that?

[Apos]

I actually read an article on a collected volume of the best science writing discussing how the real problem was that there were litterally an inumerable, if not almost infinate "correct" solutions to the string theory equations given the data we have now, and almost no way whatsoever to nail down any further which particular one is THE one.

[SentientMeat]

I don't quite get what you mean by "configurations" and "scales." Is any one configuration one of an infinite number of parallel universes?A configuration is just the how-it-is of the universe compared to a different arrangement (and whether possible arrangements have any 'reality' is a question perhaps best left elsewhere). Consider two triangles, both different arrangements of three entities. First, think of them just sitting there. If they don't change, I am saying no time has passed, since time without change is identical to timelessness. Now think of one triangle becoming a right angled triangle, while the other simply gets bigger: the two configurations change. Time "has passed". Now think of the first becoming a right angled triangle quicker than the other one gets bigger: the configurational change occurs over different scales - one could change so quickly with respect to the other that the other became timeless because its rate of change tended to zero.

The universe is the set of triangles. Special relativity governs the configurational change scales of the triangles. If none of the triangles change, the universe is timeless. For example, the universe cannot have a configuration that is smaller than zero, and therefore time cannot continue 'before' the Big Bang.

Is this a refutable theory? I honestly don't know. If it isn't, well, what can you do with that?I think the entire theoretical physics world shares your reservations, Loopy. Personally, I find the whole uncertainty of it quite exciting: How dull to live at a place in the universe (ie. 21st Century Earth) when it hasn't simply all been 'worked out'! (Worse still, how depressing to live in a time when we know that the physics will forever be outwith the reach of what our engineering can physically observe.)

As I said to Lib here (http://boards.straightdope.com/sdmb/showthread.php?t=296492), even the simple Standard Model has us absolutely straining at our engineering leash to confirm its most important features by observation: bookies offer only 6/1 of the Higgs boson and 500/1 of gravity waves being detected by 2010 even after billions of dollars have been spent thereon. What if the most important aspects of the explanation for how our universe has 3 dimensions of space and one of time, after decades or centuries of humanity’s most fiendishly cunning attempts to rig up the necessary apparatus, are simply unconfirmed by observation? “Ha ha! Look!” would cry the critics, especially those of a theistic persuasion, “They’re as credulous a cult as Xenu-believing Scientologists!” Even some evidence supporting that explanation would probably be like showing a single archaeopteryx tail bone to a Young Earth Creationist: “What? You’re basing a supposedly scientific theory just on that? That could mean anything!”

At this point, yes, all we would have would be our opinions. We would have to look around us and plump for either that explanation or another one, based solely on which neuropsychological configuration induced by each one made us happiest. The one I considered closest to, most consistent with, those strictly scientific theories, would be my choice.

If a solely physical universe existed over all time, there is no law that an explanation for its configuration must be confirmable by observation (nor even understanable) by 3 dimensional, temporal configurations of matter having senses and memory existing somewhere within it. Indeed, it is a constant source of wonder and joy to me that we’ve got as far as we have.

It’s like passionately watching a footy match knowing that you might lose!

[SentientMeat]

How dull to live when it has all been worked out, I beg your pardon.

[Loopydude]

even the simple Standard Model has us absolutely straining at our engineering leash to confirm its most important features by observation: bookies offer only 6/1 of the Higgs boson and 500/1 of gravity waves being detected by 2010 even after billions of dollars have been spent thereon. What if the most important aspects of the explanation for how our universe has 3 dimensions of space and one of time, after decades or centuries of humanity’s most fiendishly cunning attempts to rig up the necessary apparatus, are simply unconfirmed by observation? “Ha ha! Look!” would cry the critics, especially those of a theistic persuasion, “They’re as credulous a cult as Xenu-believing Scientologists!” Even some evidence supporting that explanation would probably be like showing a single archaeopteryx tail bone to a Young Earth Creationist: “What? You’re basing a supposedly scientific theory just on that? That could mean anything!”


I think the unconfirmed aspects of the Standard Model are a bit more constrained than you are making them out to be. For instance, if the proposed Higgs mechanism of spontaneous symmetry breaking at the electroweak unification scale is anywhere near what we think it is, the LHC has at least a 95% chance of finding the Higgs boson. That means if they don't find the Higgs, we pretty much have to seriously consider tossing the SM. It won't be anyone's mere oppinion at that point. The observations will dictate the future direction of particle physics.

Since M Theory could be "safe" from observation consraint for any forseable future, I don't think M Theory and the Standard Model are really on par in this regard.

[SentientMeat]

That's fair enough, Loopy, but my point was that it is hardly M Theory's fault that it might be so damnably expensive and difficult to wring out the observable consequences necessary to turn the model into a scientific theory proper (although I undrstand that black holes might provide some pretty specific indirect measurements by which to gauge its predictions). And of course I agree that the Standard Model is a veritable medical autopsy of direct physical measurement compared to the nebulous ghost-hunting at the forefront of contemporary theoretical physics.

[Loopydude]

I guess, in my mind, fault, smarts, merit, whatever, really have nothing to do with my reservations. It pretty much boils down to testability and falsifiability. The latter depends completely on the former. What testable predictions has M Theory made that would, should reliable contrary data be gathered, allow M Theory to be disproven? And what incorrect predictions has M Theory made that could prove the theory wrong? I certainly don't know all the answers to these questions, and I await them with eager interest. Critics of M Theory claim such falsifiability is lacking in the theory, in principle, because it's impossible to do the kinds of experiments necessary to rule out extra dimensions. As far as I can tell, the core principles of M Theory are that branes of d dimension exist, their vibrations determine their properties, and that extra dimensions are needed to provide the needed degrees of freedom such that these vibrations yield real-world physics.

There are competing theories. None of them, so far as I know, unify all the forces of nature the way M Theory has the potential to do. But they also don't rely on extra dimensions that we may not be able to observe even in principle. If both yielded equivalent testable predictions, and those predictions were verfied, which theoretical frameword would be choose? Personally, I have no idea. Some folks appear to want to use Occam's Razor in such an eventuality. Others appear to prefer the elegance of unification that extra dimensions can accomodate. I cannot think of any way to determine, in such conditions, who is wrong and who is right. It's a philosophical issue, at that point. In my bone-headed oppinion, if you need to resort to philosphy to tell you what to do, you've stopped doing science. I guess, then, one would need other standards of "validity" besides experimental evidence to assess a theory's merits. As a career experimentalist myself, I cannot get my head around that problem. Maybe it is just a matter of oppinion, I simply don't know.

[FriendRob]

Why should the rolled up dimensions all be spatial then? Could we figure out how to unfurl an extra rolled up time dimension and take a spin back in time?
Well, that's exactly the problem. According to SR, any object must be moving forward in time. If there were extra time dimensions, something could veer off into one of them, leaving it "parked" in our time. What would that look like to us? (I think) it would look like energy disappearing from our spacetime. We don't see energy disappearing, so we conclude the extra dimensions are spatial.

At least that 's the way I think it works....

[SentientMeat]

I guess, then, one would need other standards of "validity" besides experimental evidence to assess a theory's merits.Well the mathematical consistency seems to be largely there already, and it is at least slightly falsifiable insofar as it must be consistent with every possible observation and result our 3-D universe provides, even if those observations cannot distinguish the falsity of it versus a competing model. Models of abiogenesis have shown how eminently possible it is that life could have arisen from molecules: even though it is not yet fully backed to the hilt by actual observation, I'm sure we would all agree that it is not sheer pseudoscience on a Freudian scale.

But yes, I agree. "Validity" depends on observation if we are to say that a model describes reality. Without observation, all we are left with is "happiness". Like I said, perhaps it is only to be expected that a question as fundamental as "Why do we see three dimensions?" might simply leave us scrabbling in the evidence-less dark, since we cannot by definition look at or examine those three dimensions from "outside".

[chefurbo]

It has long been a mystery to me as to what physical medium electromagnetic and gravity waves acted on. Gravitational forces obviously act with the presence of air (Me sitting on this chair on Earth), but they also act with the absence of air (The Earth orbiting around the Sun). Light obviously travels just fine with or without air, just as magnetic waves can attract/repel other magnetic waves in a vacuum.

So I once inquired of a physics professor..."How can gravity and electromagnetism act in the absence of a physical medium?" I suggested that these waves might act on a medium of 4+ dimension(s). He seemed to disagree and simply said that "electromagnetic and gravitational waves don't need a physical medium to travel on". I was unsatisfied... and so the mystery still remains. :(

[Loopydude]

Like I said, perhaps it is only to be expected that a question as fundamental as "Why do we see three dimensions?" might simply leave us scrabbling in the evidence-less dark, since we cannot by definition look at or examine those three dimensions from "outside".

I'm not sure why looking "from outside" is at all relevent, except to construct models. In effect, physists create models and examine them from a "God's-eye-perspective" all the time, but they know this sort of arrangement is artificial and illustrative only. Some have gone so far as to wonder if this artificiality is part of the problem of solving the puzzle, like Lee Smolin, who has rightly pointed out that, from a physics perspective, there's nothing "outside" of the universe, because anything that can be explained by physics is by definition part of the universe. Talking about being "outside" is perhaps complete nonsense.

As it is, I can explore some of the consequences of three extended spatial dimensions by waving my hands around. It's that easy. Other spatial dimensions could, in fact, be probed in no less a concrete way if we can pack enough energy into a small enough space to probe very tiny length scales. No "outside" comes into play here. And indeed, there's really nothing that says these extra dimensions couldn't be a LOT bigger thant he Plank scale, in terms of order-of-magnitude. A micron may as well be a mile given the vast gulf between that and 10-33 meters. If I understand correctly, we don't have equipment sensitive enough to tell if there are extra spatial dimensions of, say, a micron in extension. What about a nano- or a femptometer? There's nothing really saying they couldn't be that big. There's nothing saying they couldn't be smaller. At any rate, you don't need to look from "outside" to figure it out, I don't think. You do need, however, some pretty sophisticated equipment. What if your equipment needs to be so powerful the universe couldn't contain it? Well, maybe then you need to get "outside", but good luck arguing what, if anything, that's supposed to mean.

[SentientMeat]

Talking about being "outside" is perhaps complete nonsense.I meant it in the sense that the 2-D region with our 3rd dimension rolled up, or the region with the 4th, or 5th through 11th (or 26th or whatever) dimensions not rolled up, is 'outside' our 3-D region. Can we explore the 2-D region in which our 3rd dimension is rolled up? I'm not sure we could, since we're in the place it isn't. I suspect we both fundamentally agree on the whole business, and you dislike some of the words I'm using. Apologies for my laymanship here if that's the case!

[Loopydude]

Hey, I'm a total layman here too, and readily admit I may know fuck-all of what I speak. I'm at the mercy of the popularizations, and those may well give a picture too dumbed-down for me to properly appreciate certain strengths and weaknesses. I guess I try to take what I'm told and apply common-sense logic to it, where that approach appears to have some hope of not being totally pointless and self-defeating. Actually, on the subject of self-defeating, I'm thinking about ordering Penrose's new book, which I suspect could apply the kind of intellectual smack-down to my poor brain required to put me into fits of lamenting my own inadequacy. But I can't help it: This stuff interests the hell out of me.

Anyhoo, I never thought "curled up" meant somehow "outside". If there are 10, 11, 26, whatever dimensions, we are very much "inside" all of them. They just don't give us very far to go. We spend all our time moving in these tiny spaces, actually, vibrating like mad, but the vibrations are so tiny, we don't notice. It's conceivable that you could "blow up" one of these dimensions, and voila!, now you can move perceptibly in a direction that happens to be orthogonal to up-down, left-right, backward-forward. Getting this new elbow room would allow you to do things like grab the contents out of a safe without opening it, or perform brain surgery on a patient without cutting through his skull. Wild, yes, but there's no "outside vs. inside" the dimension thing going on here. You're always in it. But do you notice?

[QuarkChild]

I work with string theorists, so I know a little of what goes on in string theory research, although I only understand the introductory stuff at this point. I'm sure other people here know more than I do about some of the technicalities, but one thing I can offer to this discussion is that it is not necessary to build an accelerator the size of the galaxy (or something) to hope to falsify string theory. My advisor does work on the string landscape, and tries to relate physical parameters like the cosmological constant to the solutions of string theory. His goal (and others') is to use a statistical model of string theory solutions to determine whether the reality we observe is "likely" or not.

For example, a large cosmological constant (one too large to allow galaxy formation, say) would falsify string theory if it was found that 99.999% percent of string theory solutions required a cosmological constant at least that large. (This is an extreme case--I don't expect anything quite that definite to come out of the statistics.) If something like that was discovered (and confirmed by further research), I think many (all?) string theorists would give up on the theory altogether. (I'm sure my advisor would. And I would.)


Anyway, many string theorists are working hard on trying to get predictions / falsifiability out of this model.

The paper my advisor just wrote on this topic is here (I'm one of the co-authors) http://arxiv.org/abs/hep-th/0501214

[Loopydude]

Thanks for the link. Most of it reads like Swahili to me, unfortunately, but I'll do my best to wrap what little brain I can around it.

Just a quick question: Why do probabilities matter in anthropic theories? I mean, with 10100 potential vacua, and the ability to try every possible configuration that vast number can accomodate, what does it matter if ten, or a thousand, or a billion, or whatever number, have small cosmological constants? All we can know of is our own, so if the other 10100 are unihabitable for whatever reason, yet ours is, how do the odds improve understanding, or present us with a useful criterion for the winnowing of theories??

[chefurbo]

It has long been a mystery to me as to what physical medium electromagnetic and gravity waves acted on. Gravitational forces obviously act with the presence of air (Me sitting on this chair on Earth), but they also act with the absence of air (The Earth orbiting around the Sun). Light obviously travels just fine with or without air, just as magnetic waves can attract/repel other magnetic waves in a vacuum.

So I once inquired of a physics professor..."How can gravity and electromagnetism act in the absence of a physical medium?" I suggested that these waves might act on a medium of 4+ dimension(s). He seemed to disagree and simply said that "electromagnetic and gravitational waves don't need a physical medium to travel on". I was unsatisfied... and so the mystery still remains. :(

any ideas?

[FriendRob]

For example, a large cosmological constant (one too large to allow galaxy formation, say) would falsify string theory if it was found that 99.999% percent of string theory solutions required a cosmological constant at least that large.
(Bolding mine)

That if is the rub, of course. Right now, no one (that I know of) can say that 99.999% of string theory solutions have any one particular testable property in common. I know there are many people working on this, but many people have been working on it for twenty years, and there's still no good experimental test available.

Good luck to you, QC, but I wish some of you bright young things would focus on areas where there's real physics to be done, like solving QCD....

[FriendRob]

chefurbo, if you imagine a physical medium that supports (say) EM waves, then you should be able to detect our motion with respect to the medium. Especially, the speed of light would no longer be constant for all observers, since the light would be moving at a particular speed with respect to the medium. This was the importance of the Michealson-Morley experiment.

You can fix up the problem by posulating some bizarre consequences of being in motion with respect to the medium (length contraction and so forth) - but why bother? Why introduce a medium and a bunch of arbitrary postulates about it, just to end up with the same predictions you have with the mediumless theory? It's a matter of Occam's razor: don't introduce additional postulates unless you need to.