On the arbitrary idea of some String Theorists that some dimensions are small .

[cdux]

On the arbitrary idea of some String Theorists that some dimensions are "small".

[Disclaimer: I'm not an expert; a genuine question on basic notion of the theory follows, pardon the excitement:]

I don't get the arbitrary idea of some String Theorists that beyond the 3rd/4th dimensions the others are "small". They often use videos to show that if you zoom in you may see an "ant" on an object. But that's quite nonsensical and arbitrary. I mean, I could have good eyesight and see that. Or I could have good eyesight and see some of that. Where does the "small dimension" ends and when does "zooming" start? I think it's pretty much nonsense.

Now, what if the extra dimensions basically make objects and space simply "bigger"?

Look at what string theorists do in their basic tutorials:

"We have 1 dimensions, if we stretch them we get a "bigger", 2 dimensional object".

"If we stretch that, e.g. a rectangle, we get a "bigger", a cube, in the 3rd dimension".

Now, why do they stop there and say the next dimensions (apart from time) don't apply?
Why don't they apply the same principle and say an extra dimension would simply make something bigger?

Or at least, it might make something have multiple instances of itself. But, I don't think that's necessary. Going from 2 dimension to 3, we never got something so bizarre, we just got something more .."spacious" and practically "big".

What if, Doctor Who's Tardis?

 

[Nabeshin]

Well, it's not really arbitrary so much as an observational necessity. String Theory predicts (indeed, REQUIRES) all of these extra dimensions, none of which have ever been observed. So naively, you would assume string theory is not correct. But since there are hints of ST doing some nice things, people didn't abandon it that easily. One fairly obvious way to have the other dimensions not affect current physical experiments is to make them small and curled up.

In my opinion, it would be quite a triumph of string theory if it could be made a generic prediction that all but 3 spatial dimensions became compactified, but the theory is not quite there yet.

 

[cdux]

Wait a second, I didn't say it's not correct. I said, assuming it's correct, why do they arbitrarily - some of them - teach to people that the extra dimensions 'might' be 'small dimensions'? They see the mathematics are correct, but the picture, the 'imagination' about it seems very far fetched to me. This "ants" and "zooming" idea seems preposterous.

 

[rorix_bw]

My non-scientific understanding of ST is that either the extra dimensions are very small, or that we are trapped in a subset of the available dimensions, or some combination of both. Nova's TV shows say M-theory has 6 small dimensions we cannot perceive, plus 3+1 of time we can perceive and 1 higher 'bulk' dimension that contains many 10d "universes".

It may or may not be correct.

But do not base "correctness" on how "preposterous" things sound. Many "preposterious" things have been verified by experiment. For example, whether or not two events (that are separated in distance) occur at the same time is not absolute but depends on the observer (Relativity of Simultaneity). Some folk will see the 2 events occurring simultaneously, and some will not. Time is not absolute but depends on observer. That's pretty weird.

 

[mitchell porter]

cdux, are you familiar with the idea of a closed universe in general relativity? I'm not talking about extra dimensions yet, just the idea that space can be joined up to itself so that if you traveled in any direction for long enough, you would eventually find yourself heading back to the point from which you started, but from the opposite direction to the one in which you left.

Once you have the possibility of a direction in space being finite rather than infinite, you can then ask how big it is. If the universe was an 10-dimensional hyperellipsoid, some directions might be "large" and others "small". The reason that people decided there were only 3 large directions is that we don't see matter go drifting off into extra directions - everything seems to be stuck in 3 dimensions. So it's postulated that the other N dimensions are smaller than the wavelength of an elementary particle, and so there's no opportunity for lateral motion in those directions.

However, in string theory we now have "branes" as well, to which strings are attached, and so we now know that it is after all possible to have our world as a 3-brane, or as a 3-dimensional intersection between branes of more than 3 dimensions, embedded in a space in which more than 3 of the dimensions are large. In this case, we only see 3 large directions because the strings are stuck to the brane.

Also bear in mind that these hypotheses are not arrived at by someone just saying, "What if reality consists of blobs in hyperspace with strings attached? Let's work out a theory like that." People introduce these ideas to explain something, and then the reception of the idea depends on detailed calculations. Kaluza introduced a fifth dimension in order to unify electromagnetism and gravity, Klein made it small to explain charge quantization. Randall and Sundrum are the ones who got string theorists talking about large extra dimensions, but that wasn't their intention at all, they were solving some other problem with their model.

 

[ohwilleke]

One of the constraints that drives the need for so many dimensions in string theory is that you have to find some way to deal with the fact that gravity sufficiently weak and subtly complex. The SUSY subpart of String Theory that handles the Standard Model forces and particles with some extra garbage along for the ride can manage just fine in 4 dimensions. But, to explain gravity as simply another aspect of the same force that is behind the other three forces in a form that reduces to the ten differential equations of GR, you need to have many more dimensions to dilute gravitational effect and give them more degrees of freedom.

I'm also inclined to think that the extra dimensions of String theory in its mathematical expression are not rightly taken too literally. Mathematicaly, a dimension is just a continuous quantity that can be assigned a value at a given point that is orthogonal to all other dimensions, and a lot of the entries in the stress-energy tensor that give rise to the many differential equations of GR which make gravity (and as a result, any unified theory that will include it) so complicated are decompositions of mass-energy fields taking place simultaneously in the same four dimensional space-time (pressure, linear kinetic energy, angular momentum, electromagnetic flux, Lorentz boosts, rest mass).

I suspect that part of the issue is that in the course of decomposing these elements out of four dimensions and then trying to squeeze them back in again that something (like the choice of coordinate system) that isn't actually independent for each of those tensor values is being treated mathematically as if it was. For example, when Kaluza-Klein did his unification work, one way to think about what he was doing is to imagine the fifth dimension not being a physical and fundamental space-like dimension, but a "gravitational potential" dimension that is a function of the other four. Now, I'm sure that I've done Kaluza-Klein a great disservice by summing up their theories in a grossly non-rigorous single sentence, but the point is that a mathematical dimension is a much more flexible notion than what educated lay people think that they are talking about when they say that space-time has four dimensions.

In the same way, Euler's statement that 1+2+3+4+5+. . . = -1/12 isn't using a definition of the value of the sum of a diverging infinite series that makes any sense when a layman's definition of the sum of a infinite series is applied. Weird stuff in math often involves the use of definitions at odds with the lay meaning of a defined term.

 

[Nabeshin]

Wait a second, I didn't say it's not correct. I said, assuming it's correct, why do they arbitrarily - some of them - teach to people that the extra dimensions 'might' be 'small dimensions'? They see the mathematics are correct, but the picture, the 'imagination' about it seems very far fetched to me. This "ants" and "zooming" idea seems preposterous.

Oh sorry, I see. I had some trouble with your original post, but is your question actually about how string theorists (and/or journalists) communicate with the public with all this business about ants and whatnot? If that's the case, I can't really comment, beyond saying that all scientists have their favorite analogies to explain complicated subjects. Apparently some string theorists find ants and zooming to be instructive.

 

[cdux]

Klein made it small to explain charge quantization.

OK that's a good point.

By the way, when I said it's unintuitive, I didn't mean it's unintuitive in our 3D world, I meant the opposite: It's the "easy way out" to say "I can't see them, therefore they are small, therefore ants on a stick analogy and zooming on them". And hence I went "wait a second, that doesn't make much sense; when does that zooming end and when does it start? I may have good eyesight; it certainly isn't explaining it well, and it appears to be a cheap way to explain it". It's like the Feynman argument on "why". He claimed it's a cheap (and wrong) way to explain electromagnetism with imaginary rubber bands because it goes full circle explaining a phenomenon with a phenomenon [which is closely related and] he didn't explain yet.

One of course could claim "your intuition, even if it claims to be more quantum mechanical than others may still be incorrect" and I'd agree but just making it clear, I didn't mean it seemed unintuitive to see small dimensions in our 3D world, rather it seemed "too intuitive" to the point of becoming cheap and not explaining anything.