Wave Particle Duality and Uncertainty Principle


The wave-like nature of light explains most of its properties:

1. Reflection/refraction

2.Diffraction/interference

3.Doppler effect

But, the results from stellar spectroscopy (emission and absorption spectra) can only be explained if light has a particle nature as shown by Bohr's atom and the photon description of light.
This dualism to the nature of light is best demonstrated by the photoelectric effect, where a weak UV light produces a current flow (releases electrons) but a strong red light does not release electrons no matter how intense the red light.


Einstein explained the photoelectric effect by assuming that light exists in a particle-like state, packets of energy (quanta) called photons. There is no current flow for red light because the packets of energy carried by each individual red photons are too weak to knock the electrons off the atoms no matter how many red photons you beamed onto the cathode. But the individual UV photons were each strong enough to release the electron and cause a current flow.

It is one of the strange, but fundamental, concepts in modern physics that light has both a wave and particle state (but not at the same time), called wave-particle dualism.

De Broglie Matter Waves:

Perhaps one of the key questions when Einstein offered his photon description of light is, does an electron have wave-like properties? The response to this question arrived from the Ph.D. thesis of Louis de Broglie in 1923. de Broglie argued that since light can display wave and particle properties, then matter can also be a particle and a wave too.

One way of thinking of a matter wave (or a photon) is to think of a wave packet. Normal waves look with this:
having no beginning and no end. A composition of several waves of different wavelength can produce a wave packet that looks like this:


So a photon, or a free moving electron, can be thought of as a wave packet, having both wave-like properties and also the single position and size we associate with a particle. There are some slight problems, such as the wave packet doesn't really stop at a finite distance from its peak, it also goes on for every and every. Does this mean an electron exists at all places in its trajectory?

de Broglie also produced a simple formula that the wavelength of a matter particle is related to the momentum of the particle. So energy is also connected to the wave property of matter.

While de Broglie waves were difficult to accept after centuries of thinking of particles are solid things with definite size and positions, electron waves were confirmed in the laboratory by running electron beams through slits and demonstrating that interference patterns formed.

How does the de Broglie idea fit into the macroscopic world? The length of the wave diminishes in proportion to the momentum of the object. So the greater the mass of the object involved, the shorter the waves. The wavelength of a person, for example, is only one millionth of a centimeter, much to short to be measured. This is why people don't `tunnel' through chairs when they sit down.



Uncertainty Principle:

Classical physics was on loose footing with problems of wave/particle duality, but was caught completely off-guard with the discovery of the uncertainty principle.

The uncertainty principle, developed by W. Heisenberg, is a statement of the effects of wave-particle duality on the properties of subatomic objects. Consider the concept of momentum in the wave-like microscopic world. The momentum of wave is given by its wavelength. A wave packet like a photon or electron is a composite of many waves. Therefore, it must be made of many momentums. But how can an object have many momentums?

Of course, once a measurement of the particle is made, a single momentum is observed. But, like fuzzy position, momentum before the observation is intrinsically uncertain. This is what is know as the uncertainty principle, that certain quantities, such as position, energy and time, are unknown, except by probabilities. In its purest form, the uncertainty principle states that accurate knowledge of complementarity pairs is impossible. For example, you can measure the location of an electron, but not its momentum (energy) at the same time.
Mathematically we describe the uncertainty principle as the following, where `x' is position and `p' is momentum:

This is perhaps the most famous equation next to E=mc2 in physics. It basically says that the combination of the error in position times the error in momentum must always be greater than Planck's constant. So, you can measure the position of an electron to some accuracy, but then its momentum will be inside a very large range of values. Likewise, you can measure the momentum precisely, but then its position is unknown.

Also notice that the uncertainty principle is unimportant to macroscopic objects since Planck's constant, h, is so small (10-34). For example, the uncertainty in position of a thrown baseball is 10-30 millimeters.

The depth of the uncertainty principle is realized when we ask the question; is our knowledge of reality unlimited? The answer is no, because the uncertainty principle states that there is a built-in uncertainty, indeterminacy, unpredictability to Nature.

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