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The Man Who First Saw the Fifth Dimension

Rahul Bhattacharya
18th December 2014

Fifth dimension may be where ghosts and Gods live. But there was one human being, a German mathematician, who, almost a hundred years ago, first saw it hidden deep within the fabric of our universe.

In the movie Interstellar, did Cooper (Matthew McConaughey) actually become a ghost when he entered the fifth dimension towards the end of the movie? The answer may be both yes and no, depending on how much you understand physics and how you interpret its theories. Cooper's ten year old daughter, Murphy, seems be talking to or seeing ghosts in her bedroom but as the story unfolds, towards the end it becomes evident that what she thought of as a ghost was actually her own father who had time travelled from the future and entered the realm of the fifth dimension.

There is a long sequence of dialogue between the robot, TARS - who is left behind on the black hole, Gargantua - and Cooper about the fifth dimension and how "they" - meaning, some advanced versions of human beings in some very advanced civilization - were cognizant of the fifth dimension and indeed living in a five dimensional space-time.

So, what or where is this fifth dimension?

We cannot see the fifth dimension because the way we, human beings, have evolved, the way our biology has conditioned us we can only see and perceive a four dimensional universe, three dimensions of space, i.e. length, breadth and height, all measured as distances and one dimension of time. Anything beyond these four dimensions is out of our sight and consciousness. But that does not mean physics stops at the fourth dimension. Indeed, physics goes all the way up to eleven dimensions (but that's another story).

After all, you may say that physics is all about reality and if the fifth dimension isn't real - and certainly it is not real, otherwise we could have seen or perceived it - then how can physics incorporate this mysterious, invisible dimension.

The origin of this notion of fifth dimension in physics has an interesting history (even though, all through the latter half of nineteenth century mathematicians have talked about and worked with higher dimensional space, most physicists were either blissfully oblivious of a higher dimensional space or thought it was something that didn't make sense and hence it didn't warrant any attention).

From 1905 until 1915, Albert Einstein developed two of the greatest theories of twentieth century, the special and the general theory of relativity, by combining three dimensional space with one dimensional time. This four dimensional "space-time" - something, with which both the common man and the physicist can reconcile in their own ways - became the bedrock for all theories in physics. This was the reality (remember this was before the birth of quantum mechanics, the other great theory of physics developed in the early twentieth century, that completely changed our perception of reality). Any talk of a higher dimension beyond the fourth would be an absurdity.

Yet, in 1919, barely four years after Einstein had come up with his general theory of relativity - and you heard a lot of that in the movie Interstellar - an obscure German mathematician named, Theodr Kaluza, at the University of Konisberg in a mere five page article, proposed a solution to Einstein's field equations of general relativity and sent it to Einstein.

It was as if, the great man, Einstein, was struck by thunder, for in those brief five pages Kaluza was saying something that was so bizarre, so absurd and yet so feasible and correct that he was literally making physics stand on its head. Using very elegant mathematics - the same language of tensor analysis that Einstein had used to understand the geometry of space-time - Kaluza was proposing the existence of a fifth dimension hidden deep within Einstein's theory of relativity that even Einstein had been unable to discover. The brilliance of Kaluza's proposition was that this fifth dimension in one single stroke unified Einstein's theory of gravity - the general theory of relativity - with the other great theory of nineteenth century, Maxwell's theory of electromagnetism.

Remember that except for the effects of gravity that we feel while walking, sitting down and then getting up and through our weights, rest of all of physics that we, the ordinary human beings on this planet, encounter in our lives is the product of electromagnetic theory. Our television sets, radio, satellites, telephones, mobile phones, the internet, the electricity in our homes, the working of all these are governed by the electromagnetic theory, which was developed more a century ago by the great Scottish physicist, James Clerk Maxwell.

What Kaluza said in his paper was that there is indeed a fifth dimension that combines two of the greatest theories of physics known to mankind in the early twentieth century, namely, Einstein's general theory of relativity and Maxwell's theory of electromagnetism. In essence he was saying that there is a deep and firm connection between light and all electromagnetic radiations and gravity but to understand or perceive that linkage one has to climb up one dimension higher than the fourth.

This was indeed the first step towards the unification of physics, an idea that would become Einstein's obsession for the rest of his life. This was a mathematical revolution of epic proportion. Yet, it begged the question: where is this fifth dimension?

Reference:

  1. Barrow, John D. and Tipler, Frank J., The Anthropic Cosmological Principle, Oxford University Press, 1986.

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