Theoretical and quantum physicists are on the hunt to discover the mathematical formula that expresses a truth that most indigenous peoples of the world already know: There exists a shared "field" that connects everyone and everything together, from the stars in the night sky to the worm tunneling its way beneath the ground.
The Sioux say "Mitakuye oyasin," which means "all is related," or "we are all related," depending on the translation. From the Aborigines in Australia to the Dogon tribes of Africa to the Maori tribes of New Zealand, these indigenous people all believe everything we can and cannot see shares a connection. Scientists are on their way to proving this in the Theory of Everything.
TL;DR (Too Long; Didn't Read)
Physicists are on the hunt for a grand unified field theory that describes the framework of the universe from which the four forces arise: gravity, electromagnetism, and the strong and weak nuclear forces. They hope to uncover a single equation that outlines how the universe works by linking everything together in a single Theory of Everything.
Einstein's Relativity Theories and the Unified Field Theory
Einstein died before he finished work on his final concept – the Unified Field Theory – that would provide an answer and a connection between everything in the universe. He wrote more than 40 papers on the topic, partly expressed in his General Theory of Relativity where he discusses gravitational waves that speed across the universe at the same swiftness that light travels.
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As you may or may not know, that aspect of his theory proved correct in September 2015, when scientists detected and measured gravitational waves with light waves that hit the Earth from two black holes colliding to join as one, millions of years ago. Einstein's understanding convinced him that everything in the universe existed because of a shared, common and simple geometrical foundation.
Mathematics' Role in ToE
Like the simplicity of Einstein's Special Theory of Relativity expressed in mathematical form, E = mc2, physicists hope to find another eloquent equation that links everything in the universe back to a single, universal field. Since Einstein posited his ideas on the unified field in the decades before he died in 1955, physicists, following in his footsteps, still seek a straightforward equation that links the four known forces – gravity, electromagnetism, and the strong and weak nuclear forces – to that universal field, also known as the quantum field. What Einstein called the Unified Field Theory, physicists today call the "The Theory of Everything," abbreviated as ToE.
Since the beginning of the universe over 1.4 billion years ago, scientists and physicists have identified four forces that, when combined, serve as the universe's single source of energy. These four forces include the gravitational force, the power that attracts objects to the Earth; the electromagnetic force, which includes light and expresses in multiple frequency bands like the individual bands of colors of the rainbow; and the strong and weak nuclear forces, accountable for the atoms that make up all the known elements in the cosmos.
The pursuit of ToE by Einstein, and now other theoretical and quantum physicists since his passing in 1955, is to find one mathematical formula and principle that links everything together at a fundamental level. Einstein's main thought was to prove that the electromagnetic and gravitational forces are nothing more than two different expressions of one single unified field. Mathematicians know that math formulas exist in nature, music and art, and that math underpins everything in this physical reality human beings experience on Earth. The hunt is on to discover one mathematical formula that ties everything together.
Current Progress on the ToE
To link the four forces together to explain ToE, scientists in the 1970s first mathematically linked the electromagnetic force, which directs light behavior and atomic structure, to the weak nuclear force that underpins the method by which particles decay. Then they wanted to find a way to link them to the strong nuclear force, which combines smaller particles like quarks to protons and neutrons in atomic structures. Gravitational force they left alone because they don't yet have a formula for it – but they're getting close given the observations in September 2015.
The problem is that each force expresses itself differently, and combining them in a single theory is difficult. Think of it like the ancient fable from India of the three blind men and the elephant. Each blind person touched a different part of an elephant's body, thinking it a separate object. The man who touched the tail described a rope, the man who touched the leg described a pillar, and so on. Because they could not see, they did not know that the elephant was singular, not separate objects. Physicists posit that everything arises out of the unified field, but they just haven't found the mathematical formula that consistently represents everything, including the individual expressions of force, without breaking down at the particle level.
With the measurement of gravitational waves in 2015, scientists may soon discover a mathematical equivalent to express the activity of the gravitational force, which puts them well on the way to connecting the four forces together in the Theory of Everything.
What Physicists Hope to Prove
With the opening of a new window into the cosmos by the measurement of both light and gravitational waves, which travel at exactly the same speed, theoretical physicists might soon have a gravitational formula that makes sense in ToE. But the problem isn't the gravitational force; the drawback exists in the weak nuclear force, in how protons decay. Theorists successfully combined the weak and electromagnetic forces in the electroweak theory, which suggests that they both exist as a single collaboration, but only at high levels of energy like at the beginning of the universe. However, the union unfortunately dissipates when energy drops below a specific boundary established by the electroweak theory.
Physicists are still trying to find ways to observe these infinitesimally small particles and how they affect proton decay. For example, take the discovery of the Higgs-Boson particle; scientists predicted it existed long before they discovered it, but they had no way to measure it until 2012 at CERN's hadron collider in Switzerland. Since that time, scientists have also observed and verified the existence of a new particle, the pentaquark, in 2015 at the CERN facility as well.
Once scientists can observe and measure these and smaller particle interactions, or find new particles that define and quantify proton decay, they might just uncover the formula that explains everything about how the universe works, sooner rather than later.