The elusive Theory of Everything is the Holy Grail of theoretical physicists across the world. Indeed, many scientists dedicate their entire careers and even their entire lives to doing their small part to find the Theory of Everything.
But what if our Universe refuses to be subject to such a theory? What makes scientists think that an all-encompassing theory that explains everything is even remotely possible?
Look at it this way: The theory of gravity describes the behavior of matter. Matter is made up of atoms. Atoms are made up of subatomic particles. And the behavior of subatomic particles is described by quantum mechanics.
This simple progression of links between gravity and quantum mechanics is intuitively obvious, but no matter how hard we try, we can't bring gravity and quantum mechanics together into a single theory. There's a broken link somewhere in this short chain connecting the two, and we just can't find it. It really is as if gravity and quantum mechanics are operating in two different universes with two separate sets of fundamental laws.
Except that they're not. They're operating on the very same matter in the very same Universe, and it's very difficult to believe that a natural link between them doesn't exist. All we have to do is find that link.
There have been several attempts to link the theories mathematically, but those have not worked out. Not at all. Not even remotely. But we keep trying.
Attempts have also been made to bring the two theories under the umbrella of String Theory, among others. This theory asserts that everything we see in our three-dimensional (plus time) Universe is comprised of, essentially, “shadows”, or intersections, cast by vibrating strings in a higher dimension. It's a beautiful theory that commands our attention for its elegance, its conceptual simplicity (despite its mathematical complexity), and its completeness. Despite the fact that String Theory has yet to produce any falsifiable predictions, the theory persists because of its sheer beauty. The main trouble is that the String Theory equations have an infinite number of solutions, but only one solution (presumably) will actually apply to and describe our Universe. Though we haven't yet found that one solution (if it exists), we have found several that come tantalizingly close. The good news is that these solutions do incorporate both gravity and quantum mechanics. But the bad news is that everyone knows that this is something of a contrivance. Just because you've created a Riemann tensor matrix with enough pigeon holes in which to stuff both gravity and quantum mechanics doesn't mean that you've actually linked them theoretically. When treated in this fashion, String Theory, with its resource of infinite solutions, becomes a something of a vending machine, ready to dispense whatever equations are required to describe the phenomenon of the day. And just because you can get cookies and potato chips from the same vending machine, that doesn't mean you've explained their combined existence with a single theory. But we keep trying.
More exotic approaches assert that gravity is leaking out of our Universe into other universes, (or into higher dimensions), or that it's leaking into our Universe from other universes (or from higher dimensions). This treatment essentially scales gravity's full magnitude – conveniently unobservable in our Universe – to something more amenable to the equations we use to describe other natural forces. But even then, we still end up with equations where inappropriate infinities and divide-by-zero errors are perplexingly numerous. But we keep trying.
How exasperating! It's like not being able to find the link between thunder and lightning when it's so obvious there's a connection!
Of course, it could be the case that we're simply wrong about there being a connection between gravity and quantum mechanics. Perhaps the Universe is so strange, so incomprehensible, that gravity and quantum mechanics, though they operate simultaneously on the very same matter, are absolutely not connected in any way whatsoever. Such a thing would defy logic and common sense. It's incomprehensible to us that a connection we can clearly see with our eyes wouldn't have some discernible, describable nature.
But if there's one thing scientists have learned, it's that there's no shortage of phenomena in our Universe that defy logic and common sense. And despite our presumptions, there is no universal law that requires everything about nature to be comprehensible. Indeed, the possibility that the Theory of Everything doesn't exist has occurred to every scientist who has given the matter even the most casual consideration. Why, then, do we not see scientists dedicating their careers to proving that the Theory of Everything does not exist?
The reason, of course, is that we simply can't explore the possibility that a Theory of Everything doesn't exist, since that would be proving a logical negative. It would be like trying to prove that leprechauns don't exist; it can't be done.
So our only alternative is to continue to do our best to prove that the Theory of Everything does exist, and we must do so under the auspicious cloud of uncertainty imposed by the fact that persistent failure on our part is not sufficient proof to the contrary. Are we on the right track, or are we digging for earthworms on the Moon? Unfortunately, the only way to tell is to keep digging. If we find a worm, we'll have our answer. But if we never find a worm, we'll never have an answer. Yes, it's exasperating, but it's also a lot of fun. Where else but in science can you dedicate your entire career to looking for something that may not exist, never find it, and still be held in high regard by your peers and employer?
So does the Theory of Everything exist? If I had to bet, I'd bet that, yes, the Theory of Everything does exist. Would I bet this way because I feel it in my gut or because I can't fathom the alternative? No, not at all. I'd bet this way because betting against proving a negative is ALWAYS the smart bet to make. That way, you may eventually win. But even if you don't, you'll at least never lose.