Q re: the nature of dimensions

Factual Questions
21

Define “move”. Better yet, define “move” without some prior reference to time. We can discuss “motion in the x direction” as dx/dt, or “motion in the y direction” as dy/dt. But if we try to talk about time moving this way, we get dt/dt, which of course is equal to 1. Which is of course never negative, but that’s not very useful.

Enola, time being imaginary is one way to look at it. In other words, instead of the time coordinate being t, it’s it. But this way of looking at it doesn’t really buy you anything. You might as well just say that the t term has a minus sign.

22

I am nowhere near qualified to critique String/M Theory on its mathematical foundations, but I do have to wonder where it all is supposed to end. Every once in a while I read about a new “discovery” in the field, but it turns out what has been “discovered” is essentially a new bit of math. That’s great, but does it have any relevance at all to the physical world? I know String/M Theory will prove to be useful, even if it’s totally wrong, because mathematical physicists are pushing the envelope of mathematics itself. Doubtless people even today are finding interesting and powerful new insights that grew out of M maths that give them better tools to pack spaces or tie knots or what have you.

But when does physics turn into pure mathematics? I understand that M-Theory is tightly constrained in some respects by nature. You can’t have arbitrary numbers of dimensions and have it resemble our universe. The dimensions can’t have too many holes; the strings/branes can’t be too tightly or loosely wound; and so on. But it seems that even with these constraints, the possibilities that are left over are virtually endless. There could be an infinite number of ways to formulate consistent M Theories, and if one doesn’t turn out to fit what we observe, maybe another one will. I have to wonder if M Theory could ever be disproven, since it appears to be so adjustable. Dimensions can be curled up; or not. We could live in a “brane-world”. Or not. The curled-up dimensions might be big enough to measure with the LHC. Or not. Things can get bigger or smaller, wound up or unwound, string-like, brane-like, perforated, etc., etc., and it’s all allowed, it would seem, so long as it isn’t strictly forbidden by our current level of understanding (which everyone claims is poor).

Meanwhile, we’ve got massive neutrinos, dark matter, dark energy/cosmological constant, an estimation of the cosmological constant that is 120 orders of magnitude too big, the Higgs mechanism, and so on, and as far as I know, M-theory hasn’t given us a single testable insight into any of it that sets it apart from other candidates. We’ve got tons of new observations that may take us way beyond the Supersymmetric Standard Model, and yet did M Theory anticipate any of it? I would guess, since it’s got so many free parameters, one could probably argue yes, it did, but obscure postdictions tend not to be very convincing to skeptics. When are the M Theorists going to nail something down? Can they be effectively refuted by any observation, or will a new version of M-Theory inevitably be formulated to fit the new constraints?

That’s my biggest question about extra dimensions.

23

Heh - Earlier, I was attempting to distinguish between temporal and spacial dimensions using perception since almost all of us are used to it. Another difference lies in the fact that I was explainly extended spatial dimensions and not curled up spatial dimensions. Sure, perception fails later on, but I was going for simplistic. I couldn’t really think of anyway to distinguis between the three directions that we can move in and the temporal dimension without using perception. Oh well!

24

We (AFAIK) don’t have observations beyond the Standard Model.

Actually, one of the biggest motivations for string theories and M theory is that the Standard Model has so many free parameters. In theory, the “proper” theory will have a very small number (one or zero, say) of free parameters. The move to M theory, mind you, hasn’t been made because string theory was refuted and they needed to patch it up. In fact, the realm where M theory and string theory diverge noticeably from the Standard Model is still well beyond our experimentally accessible energies.

25

These are things that seem to be getting bandied about in the media. Perhaps some of it is journalistic hyperbole, I don’t know.

The original Standard Model does not accomodate neutrino mass (for no particularly deep reason), though that has been added as another free parameter.

If dark matter turns out to be something other than the lightest supersymmetric partner, then even the SUSY-SM does not accomodate it at all.

Nothing in the SM deals with dark energy.

There is no mechanism within the SM to explain cosmic inflation.

In the SM, matter and antimatter are symmetric. Some efforts have been made to work CP violation into the SM, but the predictions are off by a factor of 10 billion. Kaon and B meson violations of CP symmetry have so far not made obvious the new physics needed to explain the preponderance of matter in the universe.

GUT extensions of the SM predict proton decay, but observations have elimnated most or all of the candidate GUTs that use spontaneous symmetry breaking to incorporate the SU(3)xSU(2)xU(1) framework of the SM.

What does String/M theory bring to the table to help with the above that makes it a uniquely worthy candidate? How, if at all, does String/M Theory help experimentalists attack these problems so that they can test theoretical predictions against observation? If observations were made that were incompatible with predictions made by String/M Theory, would that mean Strings were dead, or would the theory simply be adjusted to accomodate the new observations? Could this process of adjustment continue in an endless regression such that String theory cannot be refuted, even in principle?

26

A little searching (related to Roger Penrose’s rather vocal critiques of String/M Theory) brought up this amusing blog. I lack the intelligence to say the author is right or wrong, but what I can gather is he things Strings are “pseudoscience”.

http://www.math.columbia.edu/~woit/blog/

27

Found it: Here is a quote by Penrose:

FASHION, FAITH AND FANTASY IN THEORETICAL PHYSICS

String theory has had a kind of tulip-mania fad or craze and now seems
to be in decline. But it is also a kind of religious faith for some of
those who have invested a lot of effort in understanding it.

So there are some diehard believers who will give you elaborate
specious arguments why it is impossible that any of the newer
approaches to quantizing gravity can work.

And it lives in a kind of fantasy realm, making no testable
predictions and ungoverned by experimental evidence, so the
researchers indulge in untrammelled mathematical inventiveness.

Finally such an embarrassing richness of possibilities has emerged
that the distinct variations of the theory have been estimated by its
insiders (Susskind, Douglas) at ten-to-the-100 different base states
and things like the Anthropic Principle, a latterday Hand of God, are
being invoked in a desperate effort to find the right one.
So it has gotten bogged down in its own fecundity.

28

A quote from the blog that I just read, apropos to my questions (it’s an assertion I don’t necessarily make, since I’m not qualified to make it, but it does get at some of the questions I have):

Are Fermion Masses Like Planetary Orbits?

An exerpt:

“What string theorists have now is not a single, consistent theory, but a set of several inconsistent fragmentary theories that they hope can be turned into a consistent whole. This circle of ideas is significantly more complicated than the standard model that it is trying to explain.”

Again, one of the biggest complaints about the Standard Model is its big list of free parameters. The author suggests that String (and the putative M) Theory has many, many more free parameters, and hence doesn’t look much like an improvement over what we already have. Where is the promised simplicity and beauty? Where is the guide for experiment? According to critics of higher dimensions, String Theorists are able to deflect these questions by invoking a multiverse of perhaps infinite vacua, one of which we reside in (an Anthropic approach), or by pushing the proofs into an physically unattainable realm whenever the physically attainable one seems to be at odds with the theory. Either way, the assertions are untestable. Is this science?

29

Part of this is a mismatch in our interpretations of the phrase. Even so

The Standard Model doesn’t explicitly reject a neutrino mass either. It’s just another free parameter like the score of others floating about. Massive neutrinos don’t really change the character of the model.

But we don’t really have any “observations” of dark matter or dark energy. We have hypothesized dark matter as an explanation of the mismatch between theory and experiment. This is the semantic misunderstanding: I meant we have no direct observations, while you meant something different.

This I regard properly as cosmology. The stabs we have at an explanation (slow symmetry breaking of a Higgs field, for instance) don’t really leave the Standard Model, as far as I can tell.

Even if the CP violation were made explicit (and I seem to remember there being one in there) the CPT is still a theorem. We seem to see more matter than antimatter, but on a cosmological level we don’t know that the antimatter isn’t beyond the horizon.

Keyword: “most”.

If observations were made that were fundamentally incompatible with a given string theory, that theory would be dead. I can’t at all explain the fact that you asked this question than that you really don’t see the difference (or don’t trust the difference) between science and pseudoscience. You assume that string theorists would behave, if the theory were tested and found lacking, like carnival snake-oil salesmen. What string and M theory bring is some formal properties that make certain very general observations come out nicely. There have been no tests and there isn’t really any solid evidence for or against it. I believe any string theorist would agree on this point.

30

Oh, of course. I forgot that because some researchers in a field behave like idiots means that the whole field is wrong.

Look, this is just as specious an argument as any other. Some people on one side overstate their case, some people on the other side use sloppy rhetorical tools. In the end, the truth will be decided when the relevant experimental field comes within our grasp and we run some experiments. Everything else is beside the point. Simply put: we can’t answer right now the question of whether string theory is right or wrong.

31

Actually, I don’t assume anything. I’m just curious. However, some physicists have suggested exactly the above. They claim that String Theory, to use a tired metaphor, is coming unravelled, and the String Theorists won’t admit or accept it. These aren’t small minds in the field; they include the likes of Penrose and Glashow, to name but a few. Again, perhaps its all journalistic hyperbole. I simply find the opposing arguments interesting. I work in a field where if I don’t have exeprimental evidence for something, or can’t even hope to get it, it’s not worth even thinking about. That may bias my perspective. Of course, my field is not nearly as demanding as theoretical physics, and I’m quite happy to admit those folks are a lot smarter than myself. I’m humble in my assessment of my own intellectual abilities. However, the fact that other incredibly bright people think extra dimensions, beyond being unobservable and unassailable by anything resembling the scientific method, aren’t even at all necessary to quantize gravity, makes me wonder a lot.

32

I guess one of the accusations being made is that the question is unanswerable because of the nature of the theory (a point related directly, I gather, to the hypothesis of compactified extra dimensions and the brane-world-derived Anthropic theories). I’m curious about that. How sound are these criticisms?

33

Again, another critique along these lines, provided by the Woit, the author of the blog:

Is String Theory Even Wrong?

A quote:

“Although I am skeptical of science writer John Horgan’s pessimistic notion that physics is reaching an end, the past 15 years of research in particle theory make depressingly clear one form such an end could take: a perpetual, well-promoted but never-successful investigation of a theory that has no connection with the physical world. If only physicists have the will to abandon a failed project and start looking for some new ideas, this sad fate can be avoided.”

Again, I know not sor sure if this critique is with or without merit. Sometimes I have to wonder if it is. Extra dimensions, and their “reality” are directly related to questions of this sort. Is their “nature” unscientific? Is there justification for the open accusations that the nature of extra dimensions, as currently investigated, is not science?

34

People have been saying this since it was first introduced all the way to the first string revolution (Feynman said “there are more than one ways to skin a cat”) till the present. Luckily, a lot of opposition has died down in the recent years. No other theories even come close to incorporating as much as physics as superstring theory does. For one, even though it was known before hand thus making it a postdiction, string theory in a way predicts gravity. It is also the only theory which unites quantum mechanics and general relativity, both of which have been proven seperatly yet shown to be imcompatible when thought of together, without string theory of course. What is also nice about string theory is it also predicts why their are families of particles, something else no other theory comes close to. All of this stemming from a simple and eleoquent idea makes it quite hard to not believe it is true. The experiments involved (and the math, for that matter) are still far in future. In fact, if we were to build an accelerator with modern techinological understanding, it would be the size of the galaxy or universe in order to reach the energy needed to smash to the size of a string. So, as mathochist put it more eleoquently than I ever could, we just don’t know.

35

I’m aware of all of those qualities that String Theory purports to have. I do not know myself if all of the criticism are fair. However, the big, very serious question, I think, isn’t “can String Theory be proven in principle”, but “can it be disproven, in principle?” If the answer to the latter is “no”, then it’s safe to say String/M Theory is not what one would conventionally call science. Whatever it is, it’s pursuit is quite separate from the exploration of the physical world. The most damning criticism I’m coming across so far is that String Theorists themselves have abandoned science, and misuse terms like “proof” and “discovery”. Again, I’m not qualified to say this is fair or not. However, some folks who do appear to be emminently qualified have not only levelled this criticism at the field, they’re doing it now more loudly than before. They claim, quite literally, that String Theory predicts nothing; or worse, it’s one shot at so far at predicting something measureable, the cosmological constant, is off by 55 orders of magnitude, at least. (I’m not sure if these critics are choosing to selectively ignore the “explanation” String Theory has provided for black hole entropy, or if they consider extremal black holes to be not worth considering).

There is another school of thought still: Folks from this school ask “Why must we unify all the forces to formulate a workable theory of quantum gravity? Why is unification important? If we can get a theory of quantum gravity that works in 3+1 dimensions, instead of 10+1, or 11+1, or 26+1 diminsions, isn’t that a better way to go than positing the existence of at least six other dimensions that we cannot, and perhaps will not ever, observe?” The folks in String Theory seem to claim you need these extra dimensions to make General Relativity and Quatum Mechanics agree, that no other approach is as fruitful. Maybe. Maybe not. All I know thus far is that some of the maybe nots are making strides without asking anyone to believe that the universe contains many more spatial dimensions than we can see. In other words, they’re trying to quantize gravity in the world we know. Does that count for something, over other approaches?

I honestly don’t know. But it seems hard to get around the fact that these extra dimensions are perhaps one of the biggest points of (sometimes heated) contention in theoretical physics right now. I wish I understood it better myself. Hell, I wish I had the intellectual capacity to understand it, so I could contribute something more useful than a bunch of questions.

36

Those are all very fair arguements IMHO. Another thing that seems to bother some scientests is that now we are theorizing before having an experiment. As in, in the olden days we would come up with some weird result in an experiment and then theorize to support why it occured. Either we are getting ahead of ourselves or we are making major technilogical contributions for the future, distant or not. It also seems like physicists of today are trying to come up with such exact answers even though we have no technilogical use for them. The physicists of today are also just trying to have one complete theory - although we have an understanding that predicts the every day world, they need to know why it predicts the everyday world.

(This post in particular is now getting out of GQ territory even if I am supporting the crtics of string theory. I feel that if string theory is right, critics will point out the flaws which will make it strong and if string theory is wrong, critics can have a cookie.)

37

Loopydude (what an appropriate name, for this discussion), your criticisms of string theory are pretty much valid. The fact is, it’s very difficult to get any hard numbers out of string theory. There are particular varieties of string theory which do make testable predictions, but as you say, when those tests are made, all they really do is rule out those particular varieties of string theory. There is some hope of eventually setting up some sort of exhaustive classification of all string theories, such that one might hope to rule out whole categories of theories by experiments, or even to conceivably rule out all of string theory in a finite number of experiments. However, no such exhaustive classification yet exists, so this is not yet possible.

That said, we don’t have anything better, either. There’s an awful lot we don’t know yet about quantum gravity, and string theory is at least as good a place to look as any.

38

What does it take to get some critical reading skills around here? I said there’s no way to test it right now. I never said (and don’t agree) that it was untestable in theory.

39

Of course it can, and anyone who’s not acting like a zealot would agree with that. It cannot be proven or disproven right now, since the places where the theories differ is so far beyond our experimentally accessible energies.

This is pure rhetorical bullshit. String theorists use the terms in a sense much closer to their (IMHO, proper) mathematical meanings. A physicist, acting as a physicist, has never proved a thing to begin with. Yes, the argument can be made that string theorists are currently behaving more like mathematicians than physicists, but that’s just because the theory is currently working beyond what experiements are possible. The GR predictions of frame dragging were made decades ago, but are only now being tested. Is this a point against GR?

So there are competing theories. So what? Since when does the fact that someone disagrees with you make them objectively wrong (in science, I mean. Obviously in general the answer is “the Republican party”)?

The way things are done in science is to devise possible models, construct experiments which will say one thing if the model is an accurate description of the physical world and another if it isn’t, and then to run those experiments. There are many outlines of experiments, but all are held back by the need for such huge energies. So we have to wait until we can run those experiments or to find other experiments which don’t require that amount of energy at our control.

To flip this around, if someone really wanted to derail string theory, they should get to designing experiments to test string theory. If someone can find a series of experiments that rules out all branches of string theory, they’d win instant fame and as many Nobel prizes as can be justified. Alternatively they should devise an alternate theory that works as well or better than the predictions made by string theory and which can be tested currently. Same results.

If they do neither of these things, but instead spend their time attacking string theory, they’re doing nothing at all to advance any field. It’s a lot of nonproductive bitching and moaning. Ultimately, all the accusations levelled at string theory boil down to a complaint that string theory is being unfairly championed. “Waaah, they get all the press and we don’t.”

40

I’m no physicist and can’t keep up with the posts in this thread; can’t understand them, so please be gentle as you disassemble my question.

Isn’t the assignment of three physical dimensions arbitrary, based on one-point observation and the need to measure location?

Yes, with three dimensions we can describe the location of an object relative to a given point, and that’s all we need, since we transit the time dimension together. But does that mean that’s all the dimensions there are? or just that’s all we need to measure something?

If I stand 90 deg. in relation to you, then my “forward-back” is your “left-right” - no problem, I guess. But if I stand at 45 deg. to you then my “forward-back” becomes your diagonal, or requires two of your dimensions to measure.

It seems that physical 'dimensions" turn out to be not real, but just a convenient device for measuring the relationship between two objects in space. A construct.

So then, are three dimensions just artificial? A simplified description of our perception?