Physique Quantique/

Quantum Physics

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Uncertainty

Table of Contents:

Introduction

Position

Velocity

Classical Uncertainty

Heisenberg's Uncertainty Principle

What obeys the Uncertainty Principle and why?

Position

Before we start talking about the Uncertainty Principle, it is important to understand three concepts: position, velocity and uncertainty (in the classical sense). Lets start with position. Position is where something is in space, the point in space it occupies at any given moment. It can be represented by directional coordinates (North, South, East, West ...), distances (20 meters left of a certain point), time (20 minutes past a certain point), a coordinate on a grid, etc. We'll be most interested in the latter of these examples, because it is the one that is used in quantum physics. Position can change (in fact, it does every time something moves). In the image (right), we can see a variation in position. The point moves from its initial position (in blue) to another position in space (green). Numerically speaking, it goes from the coordinate (1, 2) to the coordinate (3, 3). This change, or variation in position, can also be represented as a +2 movement on the x-axis (two places to the right) and a +1 movement on the y-axis (one place towards the "top"). The point now has a new position after a movement in space. In this example, the movement was two-dimensional, but in real life, it could also be three-dimensional.

Velocity

Velocity is a measure of the speed and direction of an object. Therefore, if an object is travelling south at 20 Km/h, its velocity is 20 km/h south. In the quantum world, velocity can be thought of as an object's "future trajectory" (as long as no outside force interacts with it). Think of it as "where an object is going and how fast it's going there". If an object has velocity, it means that it is in movement and is therefore constantly changing its position.

Uncertainty

Uncertainty, in the traditional sense, is a type of "margin of error". It is used to measure the degree of accuracy of a result. For example, if I measure the length of a line on a piece of paper with a ruler, I can only give a measurement as precise as my ruler. Say the smallest measurement on the ruler is 1 cm. In this case, it is impossible to say whether an object is 7.2 cm or 7.8 cm long with certainty. All I can do is guess. On the other hand, if my ruler has 1 mm measurements, I can say with certainty that the very same object measures 7.2 mm, but I don't know weather it measures 7.22 mm of 7.28 mm and so forth. Uncertainty is what I have to guess at, what I don't know, what I can't measure. In the traditional sense, uncertainty is measured in the same units as the units used to measure. Thus, if I'm measuring something in millimeters, my uncertainty is +/- 0.5 mm.

Heisenberg's Uncertainty Principle

In quantum physics, the word uncertainty
takes on an entirely new meaning, which we owe to
Mr. Werner Heisenberg. Heisenberg's uncertainty principle states that the
more precisely you know an object's velocity, the less precisely you know the
object's position. The opposite is also true. This roughly means that if you
know exactly which position an object occupies in space, you have no idea of
what its velocity is. Say we apply this principle to an electron. (See image,
left) We know the velocity of the electron, which is to say its orbit around
the nucleus of the atom. According to the
Uncertainty Principle, the more precisely you know an object's velocity, the
less precisely you know its position, So if we extrapolate from this idea,
we find that if we know exactly the velocity of an object (the uncertainty of its velocity is 0%), we have
no idea of its position (the uncertainty of its position is 100%). This means that it could be anywhere within its projected orbit (linked to its velocity). There is a
certain probability that it is at any given point at any given time, but it is impossible to determine with certainty where it is.
The opposite is also true. Lets back up a little. On the image, Atom A
represents the traditional view of an atom.
Each electron has a known position and a known velocity. Atom B, on the other
hand, represents an Atom to which we have applied
the Uncertainty Principle. Only one electron is represented. For complex
mathematical reasons, we can predict that the electron is within the
"orbit" that we have predicted for it, but like in
the image, it could be at any point within that orbit at
any moment. We don't know where. If we were to know the position of the
electron (say we take Atom A and apply the Uncertainty Principle to it), we
don't know its velocity. This is the basis of Heisenberg's Uncertainty
Principle. The smaller the uncertainty for one parameter (either
position or velocity), the larger the uncertainty for the other.

What obeys the Uncertainty Principle and why?

In every day life, in the macroscopic world, Heisenberg's Uncertainty Principle doesn't apply. In fact, when you see a car, you can calculate relatively precisely both its position and its velocity at any given moment. But that isn't how it works in the quantum world ... why? It's actually quite simple. In our lives, we measure the objects around us with photons (light), different waves or other particles. All these things are so small relative to what they are measuring that they don't influence it. But at the quantum level, photons and waves become very large. So large, in fact, that they influence what they are measuring. When they "collide with" what they are measuring, they change its position (if they are measuring its velocity) and inversely if it is it's position that they are measuring. To illustrate this, lets imagine that we are giants, and rather than detecting photons in order to see, we detect flying cars. Say we want to measure another car, which is travelling with a certain velocity and has a certain position at each moment. If we measure this car with another car (assuming that they don't harm each other when they bump into each other), when they collide, the state of the car that we are measuring (be it its position or its velocity) is changed. Therefore, we don't know much about the parameter that we didn't measure. Since there is no way to calculate how much the measuring of one parameter has influenced the other, we find that the Uncertainty Principle applies. Therefore, we find that anything that is small enough to be influenced by what we use to measure it is subject to the Uncertainty Principle.

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