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Wednesday, December 26, 2018



FOURTH DIMENSION, WHEREFOURTH ART THOU?

In a previous post, I referenced the possible existence of a fourth spatial dimension,[1] possibly a small fraction of a millimeter above (outside?) the three with which we are familiar. In truth, string theory,[2] superstring theory, and M-theory demand ten or more dimensions to satisfy theoretical equations. It’s difficult to imagine just a four-spatial-dimensional reality. In fact, even professional physicists of all stripes cannot fully comprehend that fourth dimension, much less ten dimensions.
By the way, it’s also not easy to recognize or visualize less than the three dimensions to which we are accustomed. To appreciate the difficulty, try to imagine an object in only two dimensions. Most people will cite a sheet of printer paper, an artist’s canvas, a tissue or some other seemingly flat, two-dimensional object. However, they don’t qualify as a two-dimensional object – not in physics. The sheet may be 11” along the X axis and 8½” along the Y axis, but it also has dimension along the Z axis.
A sheet of printer paper extends upward along the Z axis, i.e., perpendicular to the X and Y axes. The thickness of a sheet of printer paper is nominally 0.1mm (0.004” – 4 mils), therefore it is three-dimensional, not two-dimensional. Even a drawing of a triangle on a sheet of paper is two-dimensional because the graphite, crayon, or ink has a Z component rising vertically from the sheet of paper. These distinctions may seem like hairsplitting; however, the field of physics is exacting, or as exacting as is humanly possible given today’s technology. 


So, what is an example of a true two-dimensional object? Imagine an object that only extends along the X and Y axes but that extends along the Z axis only the thickness of the smallest possible particle. The smallest known particle so far is the quark, one of two particles in a proton, itself one of the two types of particles in the nucleus of an atom. A quark is on the order of 10-15 mm. That’s 0.000000000000001 mm, folks.
We do not encounter such a two-dimensional object in everyday life, so visualizing such an object is difficult to imagine although not as difficult as visualizing or even imagining a fourth dimension. We are left with a question: Can or should a 2D plane with a Z axis extending to the diameter of the smallest particle known to us be considered a valid 2D object? Should it be smaller? This is not only a physics question; it is also a philosophical question, begging for a definition of “two-dimensional.”

My view, right or wrong, is that, if the thickness (diameter?) of the smallest known particle disqualifies any object as two-dimensional, then there can be no X or Y axes either since they could only be represented by the same smallest particle. Therefore, without some thickness on the Z axis, there can be no other axis. We end up with a theoretical, imaginary plane along only the X and Y axes. No measurement can be taken, no observation can be made, the object will be massless because, logically, it does not exist except as a theoretical, imaginary plane. It is arguable that, in our reality, a true two-dimensional object, much less a one-dimensional object, is impossible, or undefined at best.
Likewise, the logic remains the same for one-dimensional objects.

String theory and its various permutations are outgrowths of quantum mechanics. String theory proposes that the smallest particle is not a particle at all, but a “string” of energy. Much like the notes from a stringed instrument, the loose characterization being that strings of energy of varying lengths and shapes vibrate at different frequencies and determine the function of each string. If valid, this characterization presents some interesting implications.

For example, it may render our previous discussion about the definition of a 2D object and allowed limits for the Z value moot. After all, what are the dimensions of energy?
Let’s allow for a moment that there is a fourth spatial dimension just outside our senses. Sight and tactile senses allow us to recognize the three dimensions with which we are familiar. I wonder what, if there are objects or beings inhabiting all four – or less – dimensions, what they might see or feel.



[1] Kaku, Michio. Parallel Worlds: A Journey Through Creation, Higher Dimensions, and the Future of the Cosmos, Doubleday, New York, New York, 2005, pp. 219-220,330.
[2] Often referred to as a theory, it is a misnomer. In truth, superstring hypothesis is more appropriate and accurate since a theory attempts to understand observed phenomena whereas a hypothesis is a “possible” reason for that phenomena which is then, itself, tested. In this context, a proven hypothesis is an underpinning – and therefore support for – a theory. In short, a theory is a more wide-ranging possible explanation for a set of observed phenomena than a hypothesis.

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