Extra Dimensions

Extra Dimensions

We can clearly observe 4 dimensions.

  • 3 spacial dimensions (objects, including us, have length, width, and depth)
  • 1 time dimension (objects exist over a period of time)

All things in the universe, from ordinary matter to exotic dark matter and dark energy, and even electromagnetic radiation, which travels through the universe at the time-bending speed of light, are subject to these four dimensions even if some may engage with them in different ways.

One of the most mind-bending implications of string theory is that it requires between ten and eleven dimensions to exist in the universe. There are a few different versions of string theory, some of which differ in the number of dimensions they predict. I’m going to focus on the latest theory that has superseded the others, called M-theory. It requires eleven dimensions to exist in the universe.

Some things only become possible if you change your assumptions about the playing field.

For instance, it is impossible to draw a triangle with three right angles on a piece of paper.

But it becomes possible if you draw it on a ball. The difference is that you’ve added another dimension – depth, and this makes the previously impossible shape possible.

Why does M-theory need eleven dimensions?

Any other number of dimensions makes the mathematics of string theory produces intelligible results. Just like how considering time as a fourth dimension allows general relativity to explain gravity, considering eleven dimensions allows string theory to explain all the forces at once. With eleven dimensions, the maths suddenly makes sense.

What it does not tell us is how these dimensions fit into the universe that we see around us. There are two leading explanations, called compact dimensions (i.e. “they’re tiny”) and hyperspace (i.e. “they’re enormous”).

It’s like we’ve learned that a triangle with three right angles is possible, and the only explanation is that the universe has eleven dimensions.


Compact dimensions

One explanation is that there are tiny six-dimensional shapes called Calabi-Yau manifolds everywhere. They are about the size of the Planck length, and repeat again and again at every point in our regular four dimensional universe. Strings sit on the surface of these shapes, where they vibrate and interact with each other across all of these dimensions. The fact that these strings are on such a crazy six-dimensional shape allows them to pull off weird and wonderful moves between dimensions that let them create the fundamental particles of the Standard Model.

The further you zoom out from this very tiny world and into our own macroscopic world, the more these extra dimensions appear ‘compactified’. This means that they just get too small for us to see, like how a garden hose viewed at a far distance does not appear to have any depth. In this way the extra dimensions appear to be rolled into the four dimensions that we observe.

An artist’s representation of a Calabi-Yau manifold, a six-dimensional shape.
An artist’s representation of a Calabi-Yau manifold, a six-dimensional shape.

Branes in hyperspace

The other explanation is the more interesting of the two. It explains that the four dimensions that we perceive as our universe are just the surface of an object called a D3-brane. This ‘brane’ is one of many that exist simultaneously, next to each other like slide magazines in an old slide projector.

The universe that we see may be just one slide of a ‘hyperspace’ that contains many others. Pictured: The Kodak Carousel slide projector. The space that contains all of these branes is called ‘hyperspace’ or the ‘bulk’.

Certain kinds of strings are attached only to the four dimensions of our local brane, and they become the fundamental particles described in the Standard Model. But there is another kind of string that is not attached to our brane; it floats free in hyperspace and interacts with our brane only as it moves through it, making it’s influence much weaker than the others. It is this kind of string that forms the graviton, the particle responsible for gravity.

This explanation is interesting, as it predicts the presense of other branes. These we can imagine as parallel universes, and they may be infinite in number.

Working notes

  • Dimensions by RobotRollCall
    • *RobotRollCall** 1335 points 7 years ago
    • Okay. So. Dimensions. What is a "dimension?" If you go by bad science-fiction B-movies, a "dimension" is a sort of parallel plane of existence, one that intersects but is distinct from our own.
    • This is absolute, unfettered nonsense, so go ahead and put it out of your mind for now.
    • What a "dimension" actually is is a way of describing the extent of a space. Given a space with n dimensions, you can uniquely identify any point in that space using no fewer than n numbers. These numbers are called coordinates. To identify a spot on a piece of paper, you need just two numbers; a piece of paper represents a two-dimensional surface. To identify a spot on the surface of the Earth, you also only need two numbers: latitude and longitude. So the surface of the Earth can be thought of as two-dimensional. But to uniquely identify a spot near the surface of the Earth, you need three numbers: latitude, longitude and altitude. So that space is three-dimensional.
    • The universe in which we exist is four-dimensional, because you need a minimum of four numbers to uniquely locate a point: three numbers for space, and one number for time.
    • Think of it as the difference between asking somebody to meet you at 313 West 63rd Street on the 9th floor, and asking somebody to meet you at 313 West 63rd Street on the 9th floor at ten past noon.
    • So that's what "dimension" means. The dimensionality of a space is the minimum number of coordinates needed to locate a point in that space.
    • We're going to change gears for a second now to talk about compact versus non-compact dimensions. I want you to imagine a cylinder, infinite in length but with a finite radius. Okay? Like a pencil, say, only infinitely long. The surfaceof that cylinder is two-dimensional: you only need two numbers to uniquely locate a point on that surface. But the two dimensions of the surface are not exactly the same. One of them is infinite — the dimension that runs along the axis of the cylinder. The other of them, though, is finite. If you go far enough in the circumferential dimension, you'll come back to where you started from.
    • The axial dimension of the surface of an infinite cylinder is non-compact; it just keeps going and going. The circumferential dimension is compact: eventually it wraps back around onto itself.
    • There are some speculative theories in physics that imagine that our universe has, in addition to the three dimensions of space and one of time that we all know and love, extra compact dimensions. These dimensions are imagined to be incredibly small in spatial extent; in fact, we know they must be, because everything we've ever observed in the universe (so far!) can be adequately explained if we assume these extra dimensions do not exist. If they were very large, the laws of physics we use to understand the universe would break down because we weren't taking everything into account. Because the laws of physics we currently use don't break down, we know that these extra dimensions, if they exist, must be extremely, extremely small. Much smaller than the diameter of a proton.
    • It's possible that, someday, we might observe a phenomenon that cannot be explained by the laws of physics currently at our disposal. It's possible that this phenomenon might only be explained by postulating that one or more extra compact spatial dimensions exist, and then finding ways to test that postulate.
    • But we're not there yet. Right now, physics works just fine if we assume that no extra compact spatial dimensions exist.
  • https://www.reddit.com/r/AskScienceDiscussion/comments/ayqvvh/how_does_dimensions_works/
    • forte2718
    • 2 points·4 days ago·edited 4 days ago
    • How does dimensions works?
    • In physics/mathematics, a dimension is just a coordinate that you use to specify the unique location of an object in a physical or mathematical space. The number of dimensions of that space is the minimum number of independentcoordinates that you need to uniquely identify every point/location. For example, if I tell you that an object is located at (x=4, y=20), that doesn't specify a unique point in space because there are an infinite number of points with those same two coordinates. To distinguish a unique point from all others, you'd need a third coordinate at a minimum, so our physical space is 3-dimensional. If you include time, then our physical spacetime is 4-dimensional.
    • Importantly, from a mathematics perspective you can consider different spaces that are not physical spaces, but which plot different aspects of systems and treat some of their properties as independent variables. For example you can consider the "momentum space" of systems, which plots their momenta rather than their physical location (this tells you how objects are moving, but not where they are located). Other examples of mathematical spaces commonly used to model and analyze the behavior of systems include configuration space, phase space, and other abstract mathematical spaces. But usually "space" just refers to the space of physical locations, also known as "position space."
    • A dimension (coordinate) is also known as a "degree of freedom" because it can vary independently from the other variables/coordinates of space.
    • I have heard and read that there may be up to 9 dimensions, but how is this supposed to be understood?
    • There are some (purely hypothetical) theories of physics which use models of space(time) that have more than 3 physical dimensions. In experiments, we don't seem to need more than 3 dimensions to specify unique locations, so these hypothetical models need to explain why the extra dimensions are undetectable. One common way of doing this is to consider the extra dimensions to be "compactified," meaning they are rolled up like a circle and loop back around to the starting point after you travel a very small distance -- so small that experiments can't distinguish between differences in the extra coordinates.
    • In (super)string theory for example, space is modelled as having 9 physical dimensions (10 if you include time), where 3 of those dimensions are "large" and do not wrap around while the other 6 are compactified so that when you travel a very short distance in them you end up back at the same point.
    • I understand up to 3 dimensions, but at the 4th dimension, as stupid as I am, i have a hard time understanding and imagining how it works. Can anyone explain to me the fourth dimension? And the rest if possible?
    • You can imagine an extra compactified dimension as if you had a very tiny circle that was attached to every point in space. You could travel around this circle if you were small enough in size, but because the circle is so tiny, you'd quickly loop around back to the starting point. To imagine 6 extra compactified dimensions, you might imagine there are 6 independent tiny circles at every point, and you could travel around each circle independently of the others.
    • And in fact this is closely related to how we think of "gauge symmetries" in quantum field theory, which describe how some of the known fundamental forces work. For example, electromagnetism has something called a U(1) gauge symmetry that is like having an extra 1-dimensional circle, while the weak force has a two-dimensional SU(2) gauge symmetry (like having not just a circle but a whole 2-dimensional sphere to move around on, like the surface of the Earth) and the strong force has an SU(3) symmetry (like having a 3-dimensional "ball," which is a filled sphere, like the interior of the Earth).
    • One of the main hypotheses/goals of string theory is to identify a connection between how the 6 extra dimensions are compactified such as to reproduce the degrees of freedom in these extra gauge symmetries. It is not known if or how this can be successfully done ... but is an active area of research. It is known that at least electromagnetism can potentially be explained this way, though the jury is still out on the other two fundamental forces. If it can be done successfully, it might potentially explain the presence of all the other fundamental forces as simply being extra compactified dimensions of space that have a certain unique geometry. Then instead of having 3 dimensions of space with 3 fundamental forces dictating how objects move dynamically, you just have 9 dimensions of space and no forces; objects move inertially according to the geometry of these dimensions, and that gives the illusion of there being only 3 dimensions with extra forces.
    • Also in movies when you see these portals where they jump from one so called dimension to another, are we then talking about dimensions with other meaning? Or what does it exactly mean they jump “dimension”?
    • That is a different, non-scientific definition of "dimension" which comes from science fiction. This definition is loosely equivalent to "parallel universe" or "alternate universe" and is more or less a completely separate concept. There is no convincing scientific evidence to support the existence of alternate universes. The scientific concept of extra dimensions that I explain above is intended to apply only to our universe and does not implicate any alternate universes.
    • Hope that helps!