What is “Extra” about Extra Dimensions: Are You In or Out?

|Difficulty level: Medium|

For ages, the mighty ‘night sky’ has been a prime center of many theoretical developments in Cosmology, Astro-Particle Physics, and Astronomy. ‘Black Holes’, ‘Gravitational waves’, ‘Supernovae’, ‘Cosmic rays’ are just tiny characters of this huge stage. It not only provides information about the ‘astronomical’ objects but also motivates to question the very existence of us. One such question is, “What is reality?  Do we really live in a 3-spatial dimension universe?” If yes, then why and if not, then what are those ‘Extra Dimensions’? The understanding of extra dimensions can help us to look deeper into nature and demystify it in a better way.

“But I still haven’t found what I’m looking for”  — Song by U2

There is an ant, named Bob. Say, he lives on the wall of an abandoned house. He is a fancy one! He wears shoes that are sticky so that he never falls from the wall. No matter what happens – irrespective of storms, rain, or anything else – he stays on the wall. Bob is also smart, he is a physicist! For his whole life, he has been believing that the world is two-dimensional (the wall). But does he really live in such a world? How will he know that the world he lives in is not actually what he believes?  

Famous theoretical physicist Lisa Randall writes in her book “Warped Passages”, “Physics has entered a remarkable era. Ideas that were once the realm of science fiction are now entering our theoretical – and maybe even experimental – grasp. The brand new ideas and theoretical discoveries about extra dimensions have irreversibly changed our viewpoint to understand the theories of particle physics, astrophysics, cosmology, etc.”  

Ideas such as Black Hole, Wormhole, Extra Dimensions, Dark Matter, Dark Energy, etc. easily attract young minds. Popular Hollywood movies like “Interstellar” and “Gravity” presented such ideas in a dramatic manner. People may think of these ideas as fiction only. The truth is, these ideas are based on consistent theoretical and mathematical frameworks. The sheer number and pace of discoveries tell us that we’ve most likely scratched only the surface of the wondrous possibilities that lie in store. Having these new ideas is actually the start of a new journey; this journey will explore the deep mysteries about the universe and about us.  

Particle physicists want to know why are there some particular forces in nature and not others?  Are there any more? What are the ‘fundamental’ building blocks of the universe? What is the origin of the masses and properties of familiar particles? Why is there a dominance of matter over antimatter in our ‘observable’ universe?  

Dimensions – What Are They Anyway?

As the title goes as “Extra” dimensions, the first question one could ask is, “What does the ‘number’ of dimensions really mean?” In a loose way, we can say that the number of dimensions is the number of independent quantities that one needs to locate a point in space. Well, this is not the ‘correct’ and ‘complete’ definition of dimension. If one is aware of the recent developments in physics, he or she might ask about the meaning of 10 or 11 dimensions appearing in theories like ‘String Theory’. Obviously, they are the extra dimensions and one should not think of those as I have presented in the loose definition of ‘dimension’.  

Such duality suggests that our notion of dimension isn’t quite as firm as it looks. Dual descriptions of a single theory tell us that no single formulation is necessarily the best one. The definition of such terminology depends on the theory or the context in which we are using it. As no single theory is always the best description, the question of the number of dimensions doesn’t need to have a simple answer. This ambiguity in the meaning of dimensions and the apparent emergence of an additional dimension in different interacting theories are among the most important theoretical physics observations of the last one or two decades.

Bob discovers something interesting!

Using the loose definition of dimension, we can say that Bob needs only ‘two’ coordinates to locate his position in the wall. Therefore, his world is 2-dimensional. We need at most 3 space coordinates to locate our positions. Considering ‘time’ as an evolving coordinate, we are ‘living’ in a 3+1 or 4-dimensional world. For us, surely Bob is not living in the world with 2-spatial dimensions but rather in a world with 3-spatial dimensions. But, how will he know? One way he can have a sense of the existing ‘extra’ one dimension is by observing the sunlight. As the sun is located at a very far distance, the spherical wave-front coming from it behaves like a plane wave. This may leave some imprints in the world where Bob lives. So he will wonder, from where these have come from?  

Say, Bob holds a stick at the surface of the wall and observes a shadow of it in the presence of the sunlight. He makes a mathematical hypothesis and imagines an object such as a large ‘sphere’. He formulates that the moment the surface of these objects ‘hit’ the stick, it makes the imprint of the shadow by not allowing it to pass. Observing for a sufficient time he concludes that in order to prove his hypothesis, those hypothetical ‘spheres’ must have entered from higher dimensions as they need to have an ‘extra’ spatial dimension to explain the geometry of it. His discovery surprised him! He finds that the world he is living in is actually 2+1 or 3-dimensional and he is like ‘floating’ in 2-dimension.  

What if like Bob we are also ‘floating’ in a 3-dimensional world and some ‘Extra’ dimensions are out there?

One fun experiment we must have done while we were high school kids, which is to comb out dry hair and pick up small pieces of paper. It is the ‘static electric charge’ that plays a crucial role while lifting those pieces. The forces between these charges are known as the electrostatic force or, in general, the electromagnetic force, one of the four fundamental forces of nature. Later, we came to know about the gravitational force between large and small bodies. Because of this force our solar system, our galaxy, and all the celestial bodies are held together.  

It is quite surprising that the force of gravity is being defied by just a comb! This leads to a puzzle, known as the ‘hierarchy problem’ in physics – why the force of gravity is so weak compared to the force of electromagnetism and others.

How the idea of ‘Extra Dimensions’ begins? 

In the late 60s and 70s, physicists tried to unify the fundamental forces of nature and successfully did so to some extent. Weinberg-Salam gave their famous electroweak theory where electromagnetic force and the weak force, which is responsible for reactions of subatomic particles, is unified. Later, the strong force, responsible for binding neutrons and protons together inside the atomic nucleus, along with the other two forces gave the most well-tested and well-verified theory in physics, the ‘Standard Model’ (SM). But a problem still remains, the force of gravity is left out in this unification.  

The idea of extra dimensions started from the attempts to solve the hierarchy problem. Though the Standard Model of particle physics has passed every direct experimental test with flying colors, yet it is unable to answer many phenomena of nature. String theory and other related theories such as ‘Supergravity’ theories predict that we are living in a brane-world. For example, in some theories, the brane that we are living in is called the IR brane. For Bob, it is the 2-dimensional wall. Another brane is known as the UV brane or the Planck brane. In between, there is a compact geometry which is known as the ‘extra-dimension’. In principle, these extra dimensions are so tiny that it is not trivial to verify it experimentally.

Particles can travel in the bulk of these two branes. The influence of these particles or the physics that is going on inside this bulk may lead us to understand and solve many unsolvable problems within the standard model. For example, in 1999, Lisa Randall and Raman Sundrum proposed an extra-dimensional theory known as the ‘Warped Extra Dimension’. It successfully provides a deeper insight into nature and solves the hierarchy problem, at least theoretically.  

Are we the same as Bob?

Like Bob, we have also successfully formulated our version of the theory, which claims the existence of extra dimensions. But do they really exist? Well, the answer is not that simple as it looked in the case of Bob. Bob got to know that he is living in a 3-dimensional world by observing the sun rays and its imprints. He hypothesized an abstract (for him!) geometrical objects to verify the reality.  

In our case also, to verify the mathematical reality provided by the Extra-Dimensional theories, we have to look for the ‘imprints’ that those extra dimensions can produce in our world. But imprints from what? Clearly, it was the ‘sun-ray’ in Bob’s world. In our world, we will be looking at the ‘imprints’ made by the hypothetical particles, known as the ‘Kaluza-Klein’ particles, that are moving between the two branes. They can ‘hit’ (interact) with the familiar particles of our universe and may leave a trace of it. If we find those traces, like Bob, we can also claim that we are living in an extra-dimensional universe. For that, we have to wait for the next HE/HL-LHC run, the treasury of golden experiments of our world, where the mysteries of the universe are being demystified.    

“Look deep into nature, and then you will understand everything better” -Albert Einstein

Notes:

1. The idea of the name “Bob” is inspired by the famous “Alice and Bob” experiment.
2. According to Wikipedia, a brane is a physical object that generalizes the notion of a point particle to higher dimensions. While propagating through space-time, it follows the rules of quantum mechanics. IR means ‘infrared’ and UV means ‘ultra-violet’.
3. HE/HL-LHC – High Energy/High Luminosity Large Hadron Collider.

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