Are Higher Dimensions really possible?

Parallel Universes - Part 1

Dec 25, 2022

We all live day to day completely oblivious to the fact that we’re a part of a much larger and stranger reality than we can possibly imagine.

― Blake Crouch, Dark Matter

Greetings, Fellow Bohron

It is a widespread belief that perhaps gods and ghosts live in a higher dimensional plane. We usually ascribe the superpowers of invisibility and walking through objects to gods and spirits. If higher dimensions really exist, these properties are possible.

Artist’s description of parallel universes. *Source*

Parallel Universes! Most likely, you would have heard this term in the past. Maybe in a web series or in movies or perhaps because you are a researcher in this field. It is a very active topic open for discussion in theoretical physics. While talking about alternate realities, three types of possibilities are considered:

Hyperspace
Multiverse
Quantum parallel universes.

Greek and Curved Geometry

Three spatial dimensions form the fundamental basis of Greek geometry. In AD 150, Ptolemy offered the first proof that higher dimensions were impossible. In his book On Distance, he reasoned: we know how to draw three mutually perpendicular lines, but if we do, there’s no room for the fourth. Hence a fourth dimension must be impossible.

On June 10, 1854, German mathematician Georg Riemann delivered a celebrated lecture “On the Hypotheses Which Lie at the Foundations of Geometry” which proved to be a blow to Greek geometry. Reimann’s work established the basic mathematics of the higher, curved dimensions and is now considered one of the most important works in geometry.

Riemannian geometry is the study of curved spaces. *Source*

Higher Dimensions in Popular Culture

After Riemann's discovery, the concept of higher dimensions was popularized in Europe among artists, musicians, writers, philosophers, and painters. Picasso's Cubism attempted to visualize the fourth dimension. Salvador Dali's painting Crucifixion depicts Christ crucified on a four-dimensional cube known as a tesseract.

In Oscar Wilde’s short story, "The Canterville Ghost," the ghost haunting the Canterville mansion lives in the fourth dimension. The same theme is also explored in H. G. Wells's works like The Invisible Man, The Planner Story, and The Wonderful Visit.

The Weeping Woman is a cubist painting by Picasso, a depiction of 4th dimension in art. *Source*

Hyperspace

Hyperspace explores the possible existence of higher dimensions. Our common sense regards our 3-D world as the complete truth. With the help of three coordinates, the position of everything in the universe can be described.

As soon as we think of a fourth spatial dimension, our brains start to blank out. We never see objects suddenly disappearing and appearing out of nothing. This might be because perhaps higher dimensions are very small to be observed with the naked eye, even smaller than an atom.

This is a tesseract, a four-dimensional version of a cube. *Source*

Kaluza-Klein Theory

In 1919, mathematician Theodor Kaluza wrote a groundbreaking paper describing the maths of higher dimensions. Playing with the Einstein field equations of general relativity (GR) and Maxwell equations for the propagation of electromagnetic waves, he developed a unified field theory of gravitation and electromagnetism. Swedish physicist Oskar Klein contributed by joining Kaluza’s model with principles of quantum mechanics. The result was a 5-D model (4-D space and 1-D time) that came to be known as Kaluza-Klein Theory.

His paper proposed that light is a consequence of ripples travelling in the fifth dimension. Kaluza also gave an answer as to where the fifth dimension was. Imagine seeing a line head-on. From the front, a 1D line looks like a dimensionless point. Similarly, since we see no evidence of a fifth dimension, it must have "curled up" so small that it cannot be observed.

These attempts would eventually kickstart the journey of string theory, an emerging field of theoretical physics.

String Theory

Everything is made of atoms. Inside atoms, we find the nucleus composed of protons and neutrons. That’s what we knew until we asked the question: What’s inside protons and neutrons? And then…

Boom-Bam-Bap. Bada-Bap-Bop-Pow. *Source*

…we smashed and smashed and smashed atoms inside powerful particle accelerators. And we got more than we had bargained for.

A number of sub-sub-atomic particles were found. So many that the physicists started scratching their heads in order to arrange them. Finally, they classified them to present us with the Standard Model. The model describes three of the four known fundamental forces of nature: electromagnetic, weak and strong nuclear force. However, it makes no mention of gravity.

The Standard Model of physics describes the known particles and forces that operate at the tiny quantum scale. Source

Quantum Theory and the Theory of General Relativity are two greatest scientific frameworks ever developed. Any attempt to join these two theories had always led to infinite and nonsensical answers.

Enter: String Theory. The basic proposition of this “Theory of Everything” candidate is that all the subatomic particles are not point-like entities but 1-D strings vibrating with their own characteristic frequencies. In this way, string theory explains the hundreds of subatomic particles that have been discovered so far in our particle accelerators.

String theory suggests that everything in the universe is made of 1-D vibrating strings. This is an artist’s depiction. *Source*

The reason why many critics of the theory term it a crazy idea is that these strings can only vibrate in ten dimensions. For any other number of dimensions, the theory breaks down mathematically. Now, we consider our universe as 4-D (with three dimensions of space and one of time). Where are the other six dimensions? If they exist, looks like they must have collapsed like Kaluza's fifth dimension.

How to find these higher dimensions? One way is to look for deviations from Newton's law of gravity. It states that the earth's gravitational pull diminishes as the square of the distance. But this is only because we live in a three-dimensional world. For an n-dimensional universe, gravity should diminish as the (n - l)th power. The bad news is, no proof of higher dimensions has been found until now.

The gravitational force of the Sun keeps the planets in their respective orbits. *Source*

In addition to higher dimensions, there is another parallel universe predicted by string theory, known as the Multiverse. We will discuss this idea next time.