What is a knot in physics?

In quantum physics, a knot may be regarded as the orbit in spacetime of a charged particle. One way of calculating the Jones polynomial in quantum theory involves using the Chern-Simons function for gauge fields. The term “knot” as it is used by mathematicians is abstracted from this experience just a little bit.

What is knot theory used for?

Knot theory provides insight into how hard it is to unknot and reknot various types of DNA, shedding light on how much time it takes the enzymes to do their jobs.

What are knots in space?

A knot is an embedding of the circle (S1) into three-dimensional Euclidean space (R3), or the 3-sphere (S3), since the 3-sphere is compact. Two knots are defined to be equivalent if there is an ambient isotopy between them.

Is DNA a knot?

Just like any long polymer chain, DNA tends to form knots. Using technology that allows them to stretch DNA molecules and image the behavior of these knots, MIT researchers have discovered, for the first time, the factors that determine whether a knot moves along the strand or “jams” in place.

How do you know if knots are equivalent?

1. Without detaching the ends of your pipe cleaner, can you make your knot look like someone else’s knot in your group? In math, we say two knots are equivalent or are the same knot if you can move the strands around to make one look like the other one.

Can knots exist in 4D?

Unknotting a knot in 4D A knot is a closed curve in space. It is quite easy to see that in four dimensions, there are no nontrivial knots. You would not be able to tie a shoe in four dimensional space.

Can knots exist in higher dimensions?

Knots can be considered in other three-dimensional spaces and objects other than circles can be used; see knot (mathematics). Higher-dimensional knots are n-dimensional spheres in m-dimensional Euclidean space.