The closest anyone has come to unifying everything has been Edward Witten's M Theory.
In the early 1990s, string theory was in a bit of a theoretical pickle. For decades, theorists had poured their hearts and minds into the idea that the fundamental building blocks of reality are tiny, vibrating strings. This was a potentially revolutionary idea, capable of uniting all the forces of nature and all the building blocks of matter into a single, harmonious picture.
The pickle, however, was that there were five independent candidates for string theory, each one looking radically different than the others. Which one was right?
The five different string theories had a few commonalities. For one, they all involved strings. They also all required our universe to have 10 total dimensions: the usual three spatial dimensions, one for time and six more compact dimensions that are tiny and curled up on themselves at submicroscopic scales.
And in all the theories, the ways strings vibrate give rise to the richness of our physical world, from the forces of nature to the building blocks of matter to physical constants themselves. But when it comes to physical theories, details matter, and the five competing string models differed in the details. Some theories only had closed loops of strings, while others allowed open, wiggling strings. Some theories only allowed vibrations to travel in one direction on the strings, while others allowed both. And some theories were combinations of other theories.
For reference, in case you're curious, the names of the five string theories are: Type 1, Type IIA, Type IIB, SO(32) heterotic, and E8xE8 heterotic.
They obviously couldn't all be correct descriptions of nature, but which one was the "real" string theory, and which were the phonies? The problem was (and still is today) that string theory isn't complete — there's no such thing as the final equations of string theory, something that could be printed on a t-shirt, that describes the theory in the same way that we have the Einstein's theories or the Maxwell equations for electromagnetism.
We only have approximations that we hope — but can't prove — are close to the actual theory. And so the five string theories represent five different approximations, with no way of being able to decide which one is best.
And then 1995 happened, when prominent theoretical physicist Edward Witten gave a talk at the annual string theory conference. In the talk, he offered a radical suggestion: perhaps the five string theories weren't so different after all.
It turns out that there are interesting connections, called dualities or symmetries, among the five theories. For example, something we don't know about strings is how strongly they like to interact. But if you take, say, Type 1 string theory and ramp up its interaction strength, you end up with the weaker version of SO(32) heterotic.
And there's more. Sometimes strings can wind around a tiny, curled-up dimension a certain number of times with a certain momentum, but the duality of that has the number of windings and the momentum flipped. Type IIA and Type IIB string theories are related by such a duality.
These dualities suggest that the five string theories are all related, somehow, and are probing something much, much deeper. That deeper thing can be guessed at by following all the dualities. By attempting both dualities on the five string theories, sometimes you get links to one of the other five, and sometimes you get dualities to somewhere new.
What is that "somewhere new"? Edward Witten suggested calling it "M-theory", with the "m" open to interpretation (e.g., "mother," "mystery" or "membrane") until such time as we actually understand it.
M-theory is like an uber-theory of strings, showing how all five string theories are really just small corners of a much larger, and much more mysterious, theory. We used to think of the five string theories as separate planets, with our theoretical and mathematical explorations confined to little islands on those planets. But M-theory revealed that all those islands actually shared the same, much larger, planet all along.
One curious feature of M-theory (the little that we know about it, that it) is that what we consider string theory appears to be just a low-energy approximation of the real deal. And that real deal requires not 10 but 11 dimensions in our universe.
What's more, the fundamental object of reality is no longer the string but the d-brane. "Brane" is just a fancy word for multidimensional vibrating things, with the letter "d" signifying the dimension, giving us everything from 1-branes (strings) to 2-branes (sheets) to 3-branes (blobs) and more.
For the most part, these branes lie low and mostly just act like strings, with the eleventh dimension not playing much of a role in the grand cosmic symphony.
Beyond that, there isn't much known about M-theory. String theorists usually work in one of the five usual regimes, since they've been so well studied for decades, and the additional dimension and the introduction of branes makes the already-fiendish mathematics of string theory that much worse. Still, theorists continue to probe at the edges, hoping to someday give a full name to the "m" in M-theory.
See:
https://www.math.toronto.edu/mgualt/Morse Theory/FloerWittenMorse.pdf
See:
https://www.space.com/string-theory-11-dimensions-universe.html
Witten's original paper on eleven dimensions, 'HETEROTIC AND TYPE I STRING DYNAMICS FROM ELEVEN DIMENSIONS' by Petr Horava and Edward Witten may be found here:
https://arxiv.org/pdf/hep-th/9510209.pdf
Excerpt below:
"We also wish to further explore the relation of string theory to eleven dimensions. The strong coupling behavior of the Type IIA theory in ten dimensions has turned out to involve eleven-dimensional supergravity on R10 × S1, where the radius of the S1 grows with the string coupling. An eleven-dimensional interpretation of string theory has had other applications, some of them explained in 3-5. The most ambitious interpretation of these facts is to suppose that there really is a yet-unknown eleven-dimensional quantum theory that underlies many aspects of string theory, and we will formulate this paper as an exploration of that theory. (But our arguments, like some of the others that have been given, could be compatible with interpreting the eleven-dimensional world as a limiting description of the low energy excitations for strong coupling, a view taken in [1].) As it has been proposed that the eleven-dimensional theory is a supermembrane theory but there are some reasons to doubt that interpretation,1 we will non-committally call it the M-theory, leaving to the future the relation of M to membranes."
See:
https://arxiv.org/pdf/hep-th/9510209.pdf
* Perturbation theory - In
quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical
perturbation for describing a complicated
quantum system in terms of a simpler one. The idea is to start with a simple system for which a mathematical solution is known, and add an additional "perturbing"
Hamiltonian** representing a weak disturbance to the system. If the disturbance is not too large, the various physical quantities associated with the perturbed system (e.g. its
energy levels and
eigenstates) can be expressed as "corrections" to those of the simple system. These corrections, being small compared to the size of the quantities themselves, can be calculated using approximate methods such as
asymptotic series. The complicated system can therefore be studied based on knowledge of the simpler one. In effect, it is describing a complicated unsolved system using a simple, solvable system.
See:
https://tok.fandom.com/wiki/Perturbation_theory_(quantum_mechanics)
** Hamiltonian function - also called Hamiltonian, mathematical definition introduced in 1835 by
Sir William Rowan Hamilton to express the rate of change in time of the condition of a
dynamic physical system—one regarded as a set of moving particles. The Hamiltonian of a system specifies its total energy—
i.e., the sum of its
kinetic energy (that of motion) and its
potential energy (that of position)—in terms of the
Lagrangian function derived in earlier studies of
dynamics and of the position and momentum of each of the particles.
The Hamiltonian
function originated as a generalized statement of the tendency of physical systems to undergo changes only by those processes that either minimize or maximize the abstract quantity called
action. This principle is traceable to Euclid and the Aristotelian philosophers.
See:
https://www.britannica.com/science/Hamiltonian-function
Given this new phase 11-dimensional phase of string theory, and the various dualities between string theories, we're led to the very exciting prospect that there is only a single fundamental underlying theory -- M-theory. The five superstring theories and 11-D Supergravity can be thought of as classical limits. Previously, mathematicians and scientists have tried to deduce their quantum theories by expanding around these classical limits using perturbation theory. Perturbation theory* has its limits, so by studying non-perturbative aspects of these theories using dualities, supersymmetry, etc. we've come to the conclusion that there only seems to be one unique quantum theory behind it all. This uniqueness is very appealing, and much of the work in this field will be directed toward formulating the full quantum M-theory.
Hartmann352