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. Edward Witten American Mathematician More Edward Witten Quotes 0

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. Edward Witten American Mathematician More Edward Witten Quotes 0

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. Edward Witten American Mathematician More Edward Witten Quotes 0

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. Edward Witten American Mathematician More Edward Witten Quotes 0

Even before string theory, especially as physics developed in the 20th century, it turned out that the equations that really work in describing nature with the most generality and the greatest simplicity are very elegant and subtle. Edward Witten American Mathematician More Edward Witten Quotes 0

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. Edward Witten American Mathematician More Edward Witten Quotes 0

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. Edward Witten American Mathematician More Edward Witten Quotes 0

If I take the theory as we have it now, literally, I would conclude that extra dimensions really exist. They're part of nature. We don't really know how big they are yet, but we hope to explore that in various ways. Edward Witten American Mathematician More Edward Witten Quotes 0

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. Edward Witten American Mathematician More Edward Witten Quotes 0

It's indeed surprising that replacing the elementary particle with a string leads to such a big change in things. I'm tempted to say that it has to do with the fuzziness it introduces. Edward Witten American Mathematician More Edward Witten Quotes 0

On the other hand, we don't understand the theory too completely, and because of this fuzziness of spacetime, the very concept of spacetime and spacetime dimensions isn't precisely defined. Edward Witten American Mathematician More Edward Witten Quotes 0

One of the basic things about a string is that it can vibrate in many different shapes or forms, which gives music its beauty. Edward Witten American Mathematician More Edward Witten Quotes 0

Quantum mechanics brought an unexpected fuzziness into physics because of quantum uncertainty, the Heisenberg uncertainty principle. Edward Witten American Mathematician More Edward Witten Quotes 0

So when you ask me how string theory might be tested, I can tell you what's likely to happen at accelerators or some parts of the theory that are likely to be tested. Edward Witten American Mathematician More Edward Witten Quotes 0

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. Edward Witten American Mathematician More Edward Witten Quotes 0

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. Edward Witten American Mathematician More Edward Witten Quotes 0

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. Edward Witten American Mathematician More Edward Witten Quotes 0

You have that one basic string, but it can vibrate in many ways. But we're trying to get a lot of particles because experimental physicists have discovered a lot of particles. Edward Witten American Mathematician More Edward Witten Quotes 0