I don’t quite get what you mean by “configurations” and “scales.” Is any one configuration one of an infinite number of parallel universes?
I got dolemitized just last week. Completely embiggened my spirit.
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!!!
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.
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?
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” 10[sup]100[/sup] 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?
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.
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.
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, 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!
How dull to live when it has all been worked out, I beg your pardon.
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.
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.
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.
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…
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”.
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. 
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[sup]-33[/sup] 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.
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!
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?
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
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 10[sup]100[/sup] 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 10[sup]100[/sup] 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??