Sutter is an astrophysicist at SUNY Stony Brook and the Flatiron Institute, host of Ask a Spaceman and Space Radio, and author of Your Place in the Universe. What's next for cosmology after landmark gravitational wave discovery?.Images: Peering back to the Big Bang & early universe.Einstein's theory of relativity explained (infographic).The response from string theorists is something called the Landscape, a multiverse of all possible universes predicted by the various manifolds, with our universe as just one point among many.Īnd that's where string theory sits today, somewhere on the Landscape. So we have no mathematical technology for following the chain, from specific manifold to specific string vibration to the physics of the universe. The trouble is that string theory isn't done - we only have various approximation methods that we hope get close to the real thing, but right now we have no idea how right we are. Unfortunately, string theory can't give us an answer, at least not yet. So only one manifold can give rise to the world as we experience it. Since the ways that strings vibrate determine how they behave up here in the macroscopic world, each choice of manifold leads to a distinct universe with its own set of physics. And each possible configuration will affect the ways the strings inside them vibrate. That's a lot of different ways to wrap those extra dimensions in on themselves. It turns out that when you need six dimensions to curl up on themselves, and give them almost any possible way to do it, it … adds up. But there isn't one unique manifold that's allowed by sting theory. With further mathematical insight, it was found that the extra six spatial dimensions needed in string theory have to be wrapped up in a particular set of configurations, known as Calabi-Yao manifolds after two prominent physicists. And if those dimensions are wrapped up on themselves, then every time you move around in four-dimensional space, you're really circumnavigating those extra dimensions billions upon billions of times.Īnd those are the dimensions where the strings of string theory live. It's so small that we couldn't possibly hope to directly probe it with our high-energy experiments. If an extra dimension (or dimensions) is really that small, we wouldn't have noticed by now. He found that if this fifth dimension existed and was responsible in some way for electromagnetism, that dimension had to be scrunched down, wrapping back around itself (just like in Kaluza’s original idea), but way smaller, down to a bare 10^-35 meters. Still, a couple of decades later another physicist, Oskar Klein, tried to give Kaluza's idea an interpretation in terms of quantum mechanics. In retrospect, this was a bit of a red herring. It looked like adding dimensions could potentially unify physics. The equations of relativity don't really care about the number of dimensions it's something you have to add in to make the theory applicable to our universe.īut then Kaluza added a special twist to that fifth dimension, making it wrap around itself in what he called the "cylinder condition." This requirement made something new pop out: Kaluza recovered the usual equations of general relativity in the usual four dimensions, plus a new equation that replicated the expressions of electromagnetism. And he found something especially interesting when he added a fifth dimension to the equations - nothing happened. Thankfully, string theorists were able to point to a historical antecedent for this seemingly radical notion.īack in 1919, shortly after Albert Einstein published his theory of general relativity, the mathematician and physicist Theodor Kaluza was playing around with the equations, just for fun. How can the string theory's requirement for extra dimensions possibly be reconciled with our everyday experiences in the universe? Curled up and compact We're pretty sure that if the universe had more than four dimensions, we would've noticed by now. But when we look around the universe, we only ever see the usual three spatial dimensions plus the dimension of time. In other words, the strings don't just wiggle, they wiggle hyperdimensionally.Ĭurrent versions of string theory require 10 dimensions total, while an even more hypothetical über-string theory known as M-theory requires 11. This is because our usual space-time doesn't give the strings enough "room" to vibrate in all the ways they need to in order to fully express themselves as all the varieties of particles in the world. But for the math to work, there have to be more than four dimensions in our universe.
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