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"Technically you need the extra dimensions. At first people didn't like them too much, but they've got a big benefit, which is that the ability of string theory to describe all the elementary particles and their forces along with gravity depends on using the extra dimensions."
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Explore more quotes by Edward Witten
"But the beauty of Einstein's equations, for example, is just as real to anyone who's experienced it as the beauty of music. We've learned in the 20th century that the equations that work have inner harmony."
"I wouldn't have thought that a wrong theory should lead us to understand better the ordinary quantum field theories or to have new insights about the quantum states of black holes."
"As far as extra dimensions are concerned, very tiny extra dimensions wouldn't be perceived in everyday life, just as atoms aren't: we see many atoms together but we don't see atoms individually."
"One of the basic things about a string is that it can vibrate in many different shapes or forms, which gives music its beauty."
"Having those extra dimensions and therefore many ways the string can vibrate in many different directions turns out to be the key to being able to describe all the particles that we see."
"In Einstein's general relativity the structure of space can change but not its topology. Topology is the property of something that doesn't change when you bend it or stretch it as long as you don't break anything."
"There was a long history of speculation that in quantum gravity, unlike Einstein's classical theory, it might be possible for the topology of spacetime to change."
"Spreading out the particle into a string is a step in the direction of making everything we're familiar with fuzzy. You enter a completely new world where things aren't at all what you're used to."
"As of now, string theorists have no explanation of why there are three large dimensions as well as time, and the other dimensions are microscopic. Proposals about that have been all over the map."
"As for the forces, electromagnetism and gravity we experience in everyday life. But the weak and strong forces are beyond our ordinary experience. So in physics, lots of the basic building blocks take 20th- or perhaps 21st-century equipment to explore."
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