Are there Secret Dimensions in Our Universe? Part 3: The Graviton Tower
Welcome to the third installment of our exploration into the intriguing concept of large extra dimensions. If you haven’t already, be sure to check out Parts 1 and 2 for foundational insights on this captivating topic.
To begin, let’s engage in a thought experiment. Picture yourself taking a sheet of paper and tightly rolling it into a cylinder. If you have paper handy, feel free to try this out in the real world; either way, the analogy will work just fine.
The elongated tube represents one of the dimensions we commonly experience in our universe—the space where all cosmic events take place. Meanwhile, the tightly rolled-up side symbolizes an additional large dimension, perhaps as extensive as a millimeter, which is enormous when you consider the scale of subatomic particles.
Now, let’s visualize a particle, such as a photon (which is massless), traveling along the length of this cylindrical paper. In a one-dimensional scenario, the photon would zip down the tube at light speed, as is characteristic of photons. However, if this photon could also access the extra curled-up dimension, its trajectory wouldn’t be merely linear. That would be rather mundane! Instead, it would spiral around the circumference of the rolled-up dimension while simultaneously moving down the length of the tube. Consequently, although it would continue to travel at the speed of light, part of its movement would be concealed in dimensions that remain unseen to us.
From our limited perspective, this would result in the photon appearing to move slower than light, because some of its motion is effectively ‘hidden’ within these extra dimensions. In fact, any particle that travels at a speed slower than light must possess mass. Therefore, if photons could traverse these extra dimensions, they would masquerade as typical massive particles. Yet, since we observe photons as massless, we can deduce that they do not have access to these hidden dimensions.
This leads us to consider gravity. While we currently lack a comprehensive quantum theory of gravity, it’s widely believed that the force of gravity might be carried by a hypothetical massless particle known as the graviton. If this graviton were able to explore extra dimensions, it would no longer appear massless. Due to the unique geometry of these dimensions, it would seem as though it possessed mass from our viewpoint.
Moreover, we must incorporate quantum mechanics into our discussion, as it’s essential for understanding these concepts. Quantum mechanics posits that every particle is associated with a wave. In the long dimension of our analogy—corresponding to the familiar dimensions of reality—this graviton can adopt any wavelength without restrictions. However, in the compact, rolled-up dimension, the wavelengths must conform to specific constraints. It could accommodate one wavelength, two, three, and so forth.
When we roll up one of the universe's dimensions, it creates a fascinating quantum effect for any particle that can access it. This effect essentially causes a single massless particle, which yearns to freely navigate through the extra dimensions, to appear as multiple distinct massive particles—one for each allowable wavelength that can fit around the rolled-up dimension, akin to musical notes on a guitar string.
To clarify, I’m using the guitar analogy purely for illustration; this is not to be confused with string theory!
Not only does this lead to a few additional particles, but it actually results in an INFINITE number of them, each possessing unique wavelengths and differing masses. It’s important to remember that there is still just one massless particle, but because our perspective is so restricted (we can’t track the particle's path through the extra dimensions), it appears to us as an infinite collection of massive particles instead.
This phenomenon is referred to as the graviton tower, the Kaluza-Klein tower, or simply 'the tower' for short.
What does this discovery imply? We now have a means to probe into the universe's extra dimensions—not directly, unfortunately, as we are still like tiny ants scurrying on the ground in search of crumbs. Nevertheless, these additional gravitons can now be considered real entities. They possess mass, energy, and momentum, as well as lifetimes and properties in the observable universe.
Critically, these gravitons have the ability to slip away into the extra dimensions, much like a villain escaping in a low-budget sci-fi film. Just as we are about to apprehend the nefarious mastermind… there he goes, vanishing into another dimension!
As a side note, there’s some specialized terminology that might be helpful here. For various technical reasons stemming from string theory, our conventional universe is often referred to as "the brane" (not to be confused with a brain!) while the extra dimensions are termed "the bulk". I tend to steer clear of this jargon, as it often leads to confusion and complicates our understanding of these concepts, so I won’t delve further into it.
Although we cannot follow the gravitons into the extra dimensions, careful measurement allows us to identify potential omissions in our observations. When we conduct high-energy particle collider experiments (which we absolutely love doing), certain reactions can yield this tower of gravitons (a name reminiscent of epic tales but I digress). These gravitons exhibit mass, energy, and momentum before slipping away into the hidden dimensions.
During our experiments, we can account for a specific amount of mass, energy, and momentum at the outset—thanks to the meticulous design of our tests. At the conclusion, if we notice discrepancies in the mass, energy, and momentum, it may indicate that the graviton tower has siphoned off some of that momentum into the elusive extra dimensions.
Stay tuned for more insights in the next installment!
