WHAT IS 4TH DIMENSION?

A dimension is a measurement or system of measurement. When we talk about 'the three dimensions' we
tend to be referring to the three spatial dimensions; vertical, horizontal, and depth. We further tend to
think of these dimensions as existing at right angles to one another but that is not a necessary property; we
could have them at any angles to one another except multiples of a full rotation and still be able to
uniquely define any point in space given some origin to relate it to. Neither is this the only way to
describe points in space; we could uniquely identify a point in a plane by the angle it makes to some
origin-vector and its distance from the origin (though these dimensions are measured differently to one
another and hence we lose the property of interchangeability).

Time is considered by many to be the fourth dimension because it is a fourth perceivable dimension to our
reality; that is to say, things occur at a specific point in space (identifiable by 3 spatial dimensions) AND
at a specific instant in time. A mathematician or scientist however would consider the next dimension to
be a 4th spatial one (a natural extension to the first three that we perceive).

To imagine the 4th spatial dimension follow this simple analogy to the first few dimensions:
In 0 dimensions you can have a single point; everything exists at just one point, the origin.
In 1 dimension you can have a line or series of line segments; these lines, if sliced at every place along
this one dimension will produce 0 dimensional objects (points) that in the 1st dimension exist at different
distances from the origin.
In 2 dimensions you can have flat areas. Consider in particular a square; if sliced at every place along this
second dimension it would produce 1 dimensional objects (lines), each the same length as either side of
the square.
In 3 dimensions you can have solids. Consider in particular a cube; if sliced at every place along this third
dimension it would produce 2 dimensional objects (squares), each the same size as any face of the cube.
In 4 dimensions you can hyper-solids. Consider in particular a hypercube; if sliced at every place along
this fourth dimension it would produce 3 dimensional objects (cubes), each the same size as any facet of
the hypercube.
(Etc.)

To give you a proper idea of what hypercube could look like let us map the dimension of time on to the
fourth dimension; now a hypercube looks like a normal cube that appears instantaneously, exists for a
moment, then disappears instantaneously. The duration of its existence corresponds to the length of its
fourth dimensional edges. The slices of the fourth dimension now correspond to slices of time and its
transparently clear that at every slice of time, along this side of the hypercube, a normal, three
dimensional, cube is produced.

To convince yourself this is a legitimate analogy (and further, to convince yourself that time and the
fourth dimension are not one in the same), consider the mapping of the dimension of time on to the third
dimension; now a cube looks like a square that appears instantaneously, exists for a moment, then
disappears instantaneously...

Some mathematicians interpolate that just as a line may cast a point shadow, a square a line shadow, and
a cube a square shadow that a hypercube would similarly be able to cast a cube shadow. Naturally we can
perceive from the analogy above how this would be the case (albeit we have to generalize our
understanding of a shadow)! Turn a square and it will cast the shadow of a parallelogram. Turn a cube
and it will cast the shadow of two parallelograms joined at corresponding corners. Mathematician's will
tell you that the general shadow of a hypercube looks like the image below (though personally I find this
"explanation" of the fourth dimension a little less accessible!):

Note: A mathematician's "hypercube" like this one has 8 facets. Each a cube (with its perpendicular
edges) and each the exact same size. Try imagining that based on the 'shadow' line drawing above! ;)

Hints of the 4th dimension have been detected by physicists

Even if there are other dimensions somewhere out there in our universe or in others, should we travel to a
place which includes them, scientists aren’t so sure we could even experience them. Our brains may be
incapable. Mathematically, we can describe the 4th dimension but we may never experience it in the
physical realm.

Even so, that hasn’t stopped us from looking for evidence of higher dimensions. One model which helps us
conceive of it easier and understand it better is a tesseract or hypercube. This is a cube within a cube.
Though a helpful metaphor, it doesn’t actually exist in the real world. So how might scientists actually
detect the 4th dimension? Two separate research teams, one in the US and one in Europe have completed
dual experiments, to do just that.

Both of these were 2D experiments which hinted at a 4D world, utilizing a phenomenon known as the
quantum Hall effect. The Hall Effect is when you have an electrically conducive material, say a sheet of
metal or a wire, which you pass current through. The electrons move in one direction. Place a magnetic
field perpendicular to the material and instead of electrons get diverted to the left or right, by what’s called
the Lorentz force.

The result of the Hall effect is that electrons get stuck within a 2D system. They can then only move in two
directions. The quantum Hall effect occurs at the quantum level, either when the material is at very low
temperatures, or is subject to a very strong magnetic field. Here, an additional thing happens. The voltage
doesn’t increase normally but instead, jumps up in steps. By restricting electrons with the quantum Hall
effect, you can also measure them.

Follow the math and you’ll realize that the quantum Hall effect is also detectable within a 4D system.
Professor Mikael Rechtsman of Penn State University was part of the American team. He told Gizmodo,
"Physically, we don't have a 4D spatial system, but we can access 4D quantum Hall physics using this
lower-dimensional system because the higher-dimensional system is coded in the complexity of the
structure."

We ourselves as 3D objects cast a 2D shadow. A 4D object should then cast a 3D shadow. We can learn
something about a 3D object by studying its shadow. So it stands to reason that we could also gain
knowledge about a 4D object from its 3D shadow. Both teams in these experiments did something of that
kind. They used lasers to catch a glimpse of the 4th dimension. The results of each experiment were
published in two reports, both in the journal Nature.

In the European experiment, scientists took the element rubidium and cooled it down to absolute zero. Then,
they trapped atoms there within a lattice of lasers, creating what researchers describe as, "an egg-carton-
like crystal of light." Next, they introduced more lasers to excite the atoms, creating what’s known as a
quantum “charge pump.” Though atoms themselves don’t have a charge, here they simulated the transport
of electrical charges. Subtle variations in the atoms’ movements coincided with how the quantum Hall
effect would play out in the 4th dimension.

In the US experiment, glass was used to control the flow of laser light into the system. This was basically
a rectangular glass prism with a series of channels within it, which looked like a number of fiber optic
cables stuck inside, running the length of the box and terminating at both ends. Researchers were able to
manipulate the light using these channels as wave guides, in order to make it act like an electric field. When
light jumped from opposite edges into the corners, researchers knew they had observed the quantum Hall
effect, as it would occur in a 4D system.

Scientists at ETH Zürich, a university in Switzerland, conducted the European experiment. Researcher
Oded Zilberberg was among them. He said that before these experiments, observing actions occurring in
the 4th dimension seemed more like science fiction.

“Right now, those experiments are still far from any useful application,” he said. Yet, physics in the
4th dimension could be influencing our 3D world. As for applications Rechtsman said, “Maybe we can come
up with new physics in the higher dimension and then design devices that take advantage the higher-
dimensional physics in lower dimensions.”

In these experiments, the photons and electrons didn’t interact. In the next, scientists believe it might be
interesting to see what happens when they do. Rechtsman claims we could gain a better understanding of
the phases of matter by investigating the 4th dimension. Say we get a healthy grasp of it, is that the end?
Certainly not. Theoretical physicists believe there may as many as 11 dimensions.