Warped fabric of spacetime (Source)
Start with the Massive
It has been more than 100 years since Albert Einstein finalized his famous Theory of General Relativity, describing his idea of 4 dimensional spacetime and redefining how mankind views its universe. In short, he was able to mathematically demonstrate that time is not linear as we once thought, but rather warped by gravity and relative speeds of objects to each other. For example, time moves ever so slightly faster at high altitudes on Earth than it does at low ones. The effects are almost negligible to humans, although GPS Satellites must be periodically adjusted to account for the fact the time moves faster for them than it does for slow-moving humans closer to the center of the Earth. If you had a twin that left at nearly the speed of light and returned, you will have aged and likely died while they would have only perceived a few minutes passing by (Read about the Twin Paradox). It seems like science fiction, but it is true. And it has been experimentally demonstrated through use of extremely accurate atomic clocks on fast moving planes and rockets (Example here). Einstein’s revolutionary theory describes well the universe on a massive scale (galactic, etc.) – but not at all on a minutely small one (subatomic).
Image source
Now the tiny
Fortunately, the physics of the very small did not go unexplored in the 20th century. The development of the mathematically and conceptually complex nature of what is called quantum mechanics has told us a lot about how the four fundamental forces act on a subatomic scale. It has led to the discovery of the building blocks of protons and neutrons (quarks), the understanding that light can also function like particles and matter like waves, and the discovery of antimatter, amongst other things. It helped us finally answer how gravity holds on to mass and observes that it can do so from an infinite distance (with gravitons). Much of the work of contemporary particle physicists has centered around observing and proving the existence of the many particles that govern the fundamental forces. In this endeavor, they have had a great deal of success in recent years. The search for particles to prove quantum theories is the main purpose of the famous CERN Large Hadron Collider in Geneva Switzerland. Much of quantum theory is very new and absent from many high school and college textbooks.
Elementary particles of quantum mechanics (source)
How do these two generally accepted theories come together?
Short answer: they really don’t- and that is the question that has kept physicists busy for the past century. The mathematics used by both are incompatible and inconsistent. Both theories have observational evidence validating them yet they do not follow the same rules of physics. The goal of modern theoretical physics is to develop what they call a Grand Unified Theory, thus bridging the gap between general relativity and quantum mechanics and unifying the forces. None of the most influential people in physics have been able to this. In fact, many believe that classical physics is not capable of such a theory.
So did they all give up?
Not at all. Though many have accepted the possibility that deriving a grand unified theory will require abandoning the constraints of the four dimensional reality that we can perceive. It is thought, for example, that perhaps gravity seems so weak compared to the other forces because most of its energy is manifesting in other spatial dimensions. One of the leading schools of thought on this are is Superstring Theory. It takes us much closer to a grand theory but its mathematics require the existence of at least 10 dimensions. Some theories require as many as 26. Opening our minds to this possibly might be the key to underusing the universe.
What would a 5th or higher dimension even look like?
Short Answer: We do not and probably cannot know. Our perception is limited to the 3 spatial dimensions (X,Y,Z) and the fourth, time (t). While we can continue to mathematically probe higher dimensions and gather more and more evidence of their existence, we will never be able to perceive and experience them. A helpful way to think about it is imagining a 2 dimensional being. If such a being existed (imagine a shape on a piece of paper), it would have no concept of what the third dimension could possible look or be like (Read about Flatland). Yet as third dimensional beings us humans can easily observe and manipulate something 2 dimensional. If a 3 dimensional object were to visit a 2 dimensional plane, its true form would not be perceived correctly (only as a 2D cross section). The same holds true with us and higher dimensions. If they do exist, we are just as oblivious to its reality as a 2 dimensional shape would be to ours. If there are 5th dimensional beings, we are only perceiving their 3 dimensional cross sections and are completely oblivious to their true form (pretty mind-blowing).
The takeaway here is that this is not science fiction. Math and logic point to the existence of higher, imperceivable dimensions that we might very well need to understand if we are ever to explain the true nature of the universe. But of course, as we learned in class, human intuition is extremely limited and it is always possible that we have been going about this all wrong!
Sources:
http://www.livescience.com/33816-quantum-mechanics-explanation.html
http://phys.org/news/2014-03-elusive-graviton.html
https://www.theguardian.com/science/2016/mar/18/excitement-grows-over-large-hadron-colliders-possible-new-particle-lhc
https://press.cern/backgrounders/extra-dimensions
http://theory.caltech.edu/people/jhs/strings/str115.html