How can we perceive higher dimensions

A question of perspective

Why things that seem complicated to us could be very simple in a universe with extra dimensions

An article by Virginia Dippel

In theories like string theory, our world inevitably has more than the three spatial dimensions that we know from everyday life. On the one hand, this is a disadvantage, because physicists have to think about how it happens that we perceive only three of the ten spatial dimensions of the string theories in everyday life (for this question, the in-depth topics are extra dimensions - and how to hide them and the embedded world dedicated). The additional dimensions also have advantages, and to put it bluntly, things that seem very different in a room with fewer dimensions can be one and the same in a higher-dimensional room - two sides of the same coin!

Objects in the plane

To illustrate this, let's go into a flat two-dimensional space, into a plane, and look at the following two objects:

I now claim that triangle and square are in reality (i.e. in our three-dimensional space) the same (i.e. one thing), while they look different for a two-dimensional surface being that lives in the plane. How do I come to this claim? Let us consider a three-dimensional object in which at least one side is triangular and (at least) one other is square. A pyramid with a square base is probably the best-known example. In the two-dimensional world we can never see the whole pyramid but only one of its sides or a cross-section - depending on where the pyramid is in relation to the plane.

A unified description

In the case that the base surface of the pyramid is parallel to the plane considered here, the inhabitants of the two-dimensional world see a square:

But if you turn the pyramid in space in such a way that one of its side surfaces now lies in the plane, the surface residents see a triangle:

One cannot blame the surface dwellers if they come to the conclusion that triangles and squares are two different objects. Those who perceive higher-dimensional (in this case: three-dimensional), on the other hand, see that only one object is involved - the pyramid.

The example shows: What seems different in fewer spatial dimensions can be one and the same in higher spatial dimensions. There we saw that in three dimensions the apparent square is not a square and the triangle is not a triangle, and that a “theory” which restricts itself to two dimensions and describes triangles and squares in them does not even grasp half the truth. It is similar with the theories that postulate that our space has more than three dimensions. The various elementary particles that we observe in three-dimensional space can turn out to be different manifestations of one and the same higher-dimensional particle from a higher-dimensional perspective. This is a tempting tool for the theoretical physicists who have traditionally sought to describe the world in as uniform and simple a way as possible. In fact, there is, for example, the hope that, with string theory, the whole variety of elementary particles will ultimately be traced back to a single type of extended thread, a string - with a variety of manifestations, some of which result from the higher spatial dimensions in which the string vibrates can and which we ignore in everyday life.

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was a PhD student in the Quantum Gravity and Unified Theories department at the Albert Einstein Institute in Potsdam from 2004 to 2005. For Einstein Online she wrote the advanced topic A question of perspective.

Citation

To be quoted as:
Virginia Dippel, “A Question of Perspective” in: Einstein OnlineVolume 04 (2010), 01-1129