Multiple dimensions in one universe?

Question

Can there be multiple dimensions in one universe? So the first dimension is uni 1, second uni 2, third uni 3? Or are they all packed into one?

Answer 1

Are you in Pointland, Linearland, or Flatland?

Here in Cartesianland universe, we have 3 orthogonal space dimensions and one time dimension. So that is a multiplicity of 4 dimensions in this universe. And they serve us pretty well, really.

Of course you can IMAGINE that there are a lot more, and for some mathematical and physical problems you need to consider arbitrary n-dimensional spaces.  

Answer 2

It is possible that there are more than 3 "physical" dimensions in our universe.  We are not equipped to perceive them, though.  

Imagine an ant crawling along a straw, moving up it lenghtwise.  Then, suddenly, it "discovers" it can also move AROUND the circumference of the straw.  

I think it's entirely possible there are more physical dimensions...  but what way would they go?  How would we detect them?  

Also, it might even be possible that we are existing on a piece of the universe that only has three physical dimensions, but it's "folded" in a way that the only portion visible to us exists only in three physical dimensions.

I'm not saying either way whether it's likely or not, just that the "maybe" has not been significantly proven as a "definitely not."

Answer 3

In terms of direct observation, we believe that our universe has four dimensions. Three of the dimensions are those of spatial directions such as (say) x, y, and z. Furthermore, within Einstein's Theory of General Relativity, time is the fourth dimension - so that space and time become space-time. This fourth dimension is then incorporated into calculations of the 'metric' or measure of a small element 'ds' of (here flat or Minkowski) space, in an equation of the type: -

ds² = dx² + dy² + dz² - c²dt²

Thus, in relativistic calculations time becomes a fourth dimension!

However, many modern theories of space and time such as string theory require space and time to have more dimensions. Wikipedia comments,'...An intriguing feature of string theory is that it involves the prediction of extra dimensions. The number of dimensions is not fixed by any consistency criterion, but flat spacetime solutions do exist in the so-called "critical dimension." Cosmological solutions exist in a wider variety of dimensionalities, and these different dimensions—more precisely different values of the "effective central charge," a count of degrees of freedom which reduces to dimensionality in weakly curved regimes—are related by dynamical transitions.

Nothing in Maxwell's theory of electromagnetism or Einstein's theory of relativity makes this kind of prediction; these theories require physicists to insert the number of dimensions "by hand," and this number is fixed and independent of potential energy. String theory allows one to relate the number of dimensions to scalar potential energy. Technically, this happens because a gauge anomaly exists for every separate number of predicted dimensions, and the gauge anomaly can be counteracted by including nontrivial potential energy into equations to solve motion. Furthermore, the absence of potential energy in the "critical dimension" explains why flat spacetime solutions are possible.

This can be better understood by noting that a photon included in a consistent theory (technically, a particle carrying a force related to an unbroken gauge symmetry) must be massless. The mass of the photon which is predicted by string theory depends on the energy of the string mode which represents the photon. This energy includes a contribution from the Casimir effect, namely from quantum fluctuations in the string. The size of this contribution depends on the number of dimensions since for a larger number of dimensions, there are more possible fluctuations in the string position. Therefore, the photon in flat spacetime will be massless—and the theory consistent—only for a particular number of dimensions.

When the calculation is done, the critical dimensionality is not four as one may expect (three axes of space and one of time). Flat space string theories are 26-dimensional in the bosonic case, while superstring and M-theories turn out to involve 10 or 11 dimensions for flat solutions. In bosonic string theories, the 26 dimensions come from the Polyakov equation. Starting from any dimension greater than four, it is necessary to consider how these are reduced to four dimensional space-time.

Two different ways have been proposed to resolve this apparent contradiction. The first is to compactify the extra dimensions; i.e., the 6 or 7 extra dimensions are so small as to be undetectable by present day experiments.

To retain a high degree of supersymmetry, these compactification spaces must be very special, as reflected in their holonomy. A 6-dimensional manifold must have SU(3) structure, a particular case (torsionless) of this being SU(3) holonomy, making it a Calabi-Yau space, and a 7-dimensional manifold must have G2 structure, with G2 holonomy again being a specific, simple, case. Such spaces have been studied in attempts to relate string theory to the 4-dimensional Standard Model, in part due to the computational simplicity afforded by the assumption of supersymmetry. More recently, progress has been made constructing more realistic compactifications without the degree of symmetry of Calabi-Yau or G2 manifolds.

A standard analogy for this is to consider multidimensional space as a garden hose. If the hose is viewed from a sufficient distance, it appears to have only one dimension, its length. Indeed, think of a ball just small enough to enter the hose. Throwing such a ball inside the hose, the ball would move more or less in one dimension; in any experiment we make by throwing such balls in the hose, the only important movement will be one-dimensional, that is, along the hose. However, as one approaches the hose, one discovers that it contains a second dimension, its circumference. Thus, an ant crawling inside it would move in two dimensions (and a fly flying in it would move in three dimensions). This "extra dimension" is only visible within a relatively close range to the hose, or if one "throws in" small enough objects. Similarly, the extra compact dimensions are only "visible" at extremely small distances, or by experimenting with particles with extremely small wavelengths (of the order of the compact dimension's radius), which in quantum mechanics means very high energies.'