Can someone explain to me....?

Question

Uncertainty principle and butterfly effect?

Thanks.

Answer 1

In quantum physics, the Heisenberg uncertainty principle is the statement that locating a particle in a small region of space makes the momentum of the particle uncertain; and conversely, that measuring the momentum of a particle precisely makes the position uncertain.

In quantum mechanics, the position and momentum of particles do not have precise values, but have a probability distribution. There are no states in which a particle has both a definite position and a definite momentum. The narrower the probability distribution is in position, the wider it is in momentum.

Physically, the uncertainty principle requires that when the position of an atom is measured with a photon, the reflected photon will change the momentum of the atom by an uncertain amount inversely proportional to the accuracy of the position measurement. The amount of uncertainty can never be reduced below the limit set by the principle, regardless of the experimental setup.

A mathematical statement of the principle is that every quantum state has the property that the root-mean-square (RMS) deviation of the position from its mean (the standard deviation of the X-distribution):

The butterfly effect is a phrase that encapsulates the more technical notion of sensitive dependence on initial conditions in chaos theory. Small variations of the initial condition of a dynamical system may produce large variations in the long term behavior of the system. So this is sometimes presented as esoteric behavior, but can be exhibited by very simple systems: for example, a ball placed at the crest of a hill might roll into any of several valleys depending on slight differences in initial position.

The term "butterfly effect" itself is related to the work of Edward Lorenz, based in Chaos Theory and sensitive dependence on initial conditions, first described in the literature by Jacques Hadamard in 1890[1] and popularized by Pierre Duhem's 1906 book. The idea that one butterfly could have a far-reaching ripple effect on subsequent events seems first to have appeared in a 1952 short story by Ray Bradbury about time travel (see Popular Media below), although Lorenz made popular the term. In 1961, Lorenz was using a numerical computer model to rerun a weather prediction, when, as a shortcut on a number in the sequence, he entered the decimal .506 instead of entering the full .506127 the computer would hold. The result was a completely different weather scenario.[2] Lorenz published his findings in a 1963 paper for the New York Academy of Sciences noting that "One meteorologist remarked that if the theory were correct, one flap of a seagull's wings could change the course of weather forever." Later speeches and papers by Lorenz used the more poetic butterfly. According to Lorenz, upon failing to provide a title for a talk he was to present at the 139th meeting of the American Association for the Advancement of Science in 1972, Philip Merilees concocted Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas as a title.

Although a butterfly flapping its wings has remained constant in the expression of this concept, the location of the butterfly, the consequences, and the location of the consequences have varied widely.[3]

Answer 2

Very simple.

Some things in life are very unsteady, such as a pencil ballancing on it's tip on your finger, or a house of cards.

There is no way of telling when the sleightest breeze could cause things to crash or what direction the pencil will fall.

Many years ago a weather man wanted to use a computer to make weather predictions, but found that the tiniest of rounding errors could mean the difference between a hot day or a blizzard.

Imagine if you will a room full of dominos or mouse traps. If one domino falls or one trap goes off (unless things are arranged very carefully) there is no way of predicting exactly what things will look like after.

The butterfly effect refers to the fact that unstable systems such as the weather [where the margin of error is greater than the (stability or predictability)] a small change like the wind off a butterfly's wings in China can lead to a domino of effects eventuating in an extra tornado in Cansas.

There is a more mathematical definition but you can look that up yourself if interested.

Answer 3

The butterfly effect basically states that a very small change can lead to an enormous change.

It is often used in regards to weather. If two fronts meet at exactly the right time, it can cause a hurricane in a densly populated area, if they meet a split second before or after that hurricane will move out to sea harmlessly, or not happen at all. Someone (if you care google it to find out who) said that the period of time  for the devistating hurricane was so small that it could be altered by having a butterfly flap it's wing.