By Alice Blake

Have you ever thought about whether the universe is united by fundamental laws of physics? Whether anything unites how atoms interact and how planets and solar systems interact? Most things we see and observe, such as throwing a ball or driving a car can be described by Newtonian physics, which is sometimes referred to as classical mechanics. On a large scale, such as describing gravity on a planetary scale, the universe is governed by general relativity. General relativity, discovered by Albert Einstein, describes the gravitational effect that is warped spacetime. It is often described with the example of a trampoline. Imagine the fabric of spacetime is the surface of a trampoline. When you put a bowling ball on the trampoline, the fabric bends and subsequent items are drawn towards it. On a small scale, the world is adequately described by quantum mechanics, which deals with how small particles interact with each other. Quantum mechanics is a probabilistic theory which explains, with decent precision how particles interact. It includes the idea of wave-particle duality, which is that some things, especially light, can behave as both a wave and a particle.

String theory is an attempt at a unified theory between quantum mechanics and general relativity. It was a paradigm shift in physics that gained traction in the 1980s and the 1990s. Physicists who specialize in string theory continue to develop the theory, which claims that there are more dimensions than those evident to the human eye. We see four dimensions: the three spatial dimensions and time.

Prior to “Spacetime in String Theory: A Conceptual Clarification” by Keizo Matsubara and Lars-Goran Johansson, string theorists have claimed that there are 11 dimensions, 10 dimensions of space and 1 dimension of time. Six spatial dimensions form manifolds, which is a small, compact space that serves to hide dimensions. Because we, as humans, are so large in comparison to these manifolds, we see the world in only 3 spatial dimensions. Below is a picture of a manifold:

(Lunch 2007)

According to the math behind string theory, there are actually 26 dimensions, but 16 of those dimensions are commonly interpreted as degrees of freedom, rather than dimensions (Matsubara et al). Degrees of freedom can be thought of as a direction you can move in, which bears similarities to dimensions. The remaining 6 hidden dimensions are hidden, and we perceive 3 spatial dimensions and time. However, according to this paper, there is not enough evidence that string theory demands a specific number of extra dimensions. Based on what we know about the universe, there are extra dimensions, yet it is not yet possible to determine exactly how many extra dimensions there are. Currently, there are multiple mathematical representations of spacetime.

Since the important concept of this paper is that there are indeterminate hidden dimensions, an important aspect to understand is how dimensions are hidden. The aforementioned methods are manifolds and d-branes (Matsubara et al). A manifold is a small space that was initially invented as a way to represent dimensions. A d-brane is something that holds down the end of an open string, since the strings in string theory can either be an open loop or a closed loop.

This paper set out to clarify the concepts of how spacetime is defined by string theory. Since this is a realm of theoretical physics, there was no experiment done to determine a result. Instead, theoretical physics develops theories through math. One of the important messages from the paper was the conceptual flaws of how physicists have thought about manifolds. Historically, manifolds have been interpreted as a representation of an extra dimension. However, since the scale that manifolds exist on is so small, the classical way of thinking about manifolds does not work.

Finally, string theory has been an important paradigm shift in physics since it has been a breakthrough in explaining how quantum mechanics and general relativity work. It definitively states that there are more than the 4 dimensions that are eminently visible to people. The dimensions that are not apparent are hidden in manifolds.

Works Cited

Lunch. (2007). Calabi-Yau [picture] Wikipedia. __https://en.wikipedia.org/wiki/File:Calabi-Yau.png__

Matsubara, Keizo and Johansson, Lars-Goran. (2018 July 25). Spactime in String Theory: A Conceptual Clarification. *Journal for General Philosophy of Science*, 49:333-353. https://doi.org/10.1007/s10838-018-9423-2(0123456789().,-volV)(0123456789().,-volV)

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