Waves, particles, and duality

Waves

There are two main types of waves, mechanical waves and electromagnetic waves: and these are the main ways that energy moves from point A to point B: in other words, all waves transport energy as they travel.

Mechanical waves need a medium for energy to be transferred through - they can not travel through a vacuum. Mechanical waves, include ocean waves, seismic waves, or sound waves for instance - i.e., sound needs water or air to vibrate through. The fact that sound cannot travel through space, is probably a good thing concerning the Sun, as the noise given off by the Sun has been estimated to be around 100db, and if it could travel through space to Earth, it would be as loud as a mechanical hammer - all day-long, every-day… Mechanical waves can be both longitudinal (which is basically a compression or compaction being transmitted through a medium) or transverse waves.

Electromagnetic waves, such as visible light, do not need a medium - they can travel through the vacuum of space, but they can and do travel through mediums, and are effected by mediums - such as water, or air for instance - where they can be slowed-down, absorbed, reflected or refracted for instance. Electromagnetic waves are only transverse waves, and therefore, can also be polarised.

Although these forms of energy are different, they can all be represented as waves, as they all exhibit wavelike properties.

A wave can be defined as a disturbance propagating through space - which usually transfers energy. A single periodic wave, can be visualised in the image to the right.

A few properties that characterise a wave: Hertz (Hz), is the number of full wavelengths (λ - in meters) that pass a particular point (Point A in the image to the right) every second (s). It holds that the shorter the wavelength, the higher the frequency (ν - in Hertz) - they are inversely proportional - and as all forms of electromagnetic radiation travel at the speed of light (c: 3 x 108 m/sec (or 300 million metres per second) - the relationship is described in the formula c =  λν (same as λ x 1/T or λ x f).

Period (T) is the number of seconds per oscillation, and as frequency is the number of oscillations per second; frequency (f) = 1/T.

The second image to the right shows two waves with the same wavelengths, but different amplitudes (heights). With mechanical waves, amplitude normally means more energy (larger oceans waves carry more energy than smaller ones), however with electromagnetic waves, it describes more brightness, but not more energy, as will become clearer shortly.

Light Intensity (brightness) reduces the further away from a light source (just like gravity), the lit object(s) are from it. As shown in the image to the right, there is an inverse relationship to the square of the distance (inverse-square-law). Light must spread out over a larger surface area from the point source, over increasing distances, resulting in the reduction of brightness over a distance. For instance, the light intensity from the Sun on Mercury is estimated to be 9126 Watts/m2 (on average), compared to the greater distance to Earth, which receives ‘only’ 1367 Watts/m2. And so the threefold increase in distance, between these planets and the Sun, results in an approximate ninefold decrease in light intensity on Earth.

Light also redshifts if the light emitting object is moving away from the lit object (or viewer). Which is how scientists have proven that the universe is expanding.

The fourth image to the right, illustrates two waves with the same amplitudes (A), but with different wavelengths (λ). As all electromagnetic waves travel at the same speed – the speed of light (in a vacuum) – the number of waves (per second) that travel past point A depends on the wave length. This number is known as frequency (Hz), and so the shorter the EM wavelength the higher the frequency, and the higher the energy; and inversely, the longer the wavelength the lower the energy.

Electromagnetic radiation, can therefore, be described by its wavelength, amplitude (brightness), frequency, and period. But what is actually waving up and down?

These wave images, are not attempting to show photons flowing through space on a wave. Instead, the wave, is the oscillation of the value of the electric field (and magnetic fields as we will be showed later), as the photon travels through space at the speed of light.

Particles

Photons

Physicist Max Planck found that EM Radiation is not continuous - like the line in the wave image shown previously, instead energy is transferred in individual “packets” - or particles (of the size hv, ‘h’ being the Planck constant), oscillating as a wave. This was the discovery that light is both wavelike and particle-like - depending on the scale it is viewed at.

This “packet” became known as a ‘photon,’ and as described in the previous section on the transfer of energy through the Sun, photons interact with atoms and molecules, by being absorbed or emitted, or breaking molecules, or changing the energy properties of atoms and their electrons. Just as atoms can absorb photons, by energising outer electrons to a higher orbit; atoms (or molecules) that loose energy, also emit photons. The energy lost or gained by the atom or molecule, is directly proportional to the frequency of the photon, shown in Planck’s famous equation: E = hv. ‘E’ being the energy of the photon emitted or absorbed, and h being Planck’s constant, given in Joules (J).

Energy is microscopically deposited in discrete amounts - on a macroscopic scale it looks like a smooth continuous wave, but at the view of an electron, light deposits discrete - specific size chunks: which means they are quantised - they have clear quantities.

Photoelectric Effect

With the understanding that atoms absorb and emit energy only as discreet quantities (quanta), it was also proven with the photoelectric effect, that EM Radiation only travelled in quanta too; and so quantum physics was born.

An experiment first made by Hertz in 1887, showed that blue light could eject an electron (once ejected, is called a photoelectron) from a material (in this case potassium); but, red light couldn’t, even if the intensity (the amplitude) hitting the material was increased, and for long periods of time.

This went counter to classic wave (mechanical) theory  that understood that the ‘bigger’ (the higher amplitude of) the wave, irrelevant of its’ frequency (wavelength), it should heat up an electron until it was eventually freed from the metals surface. But the opposite was happening.

Einstein proposed correctly that, in fact, EM Radiation was actually travelling in quanta (photons), and not in continuous waves. And so, the photons have, like the wave, a specific frequency (wave length), but as a short ‘pulse’ or ‘packet’ their amplitude is better thought about in the numbers of photons; for instance, increasing the amplitude, increasing the number of photons travelling through space, it doesn’t generate (at least visually) a higher single wave. And so, unlike mechanical waves, EM waves do not increase in height with increased amplitude, and so a weak photon will not be able to knock an electron out of a metal, until the mimimim frequency is reached (threshold frequency), irrelevant of how many have been directed at it. And when the minimum threshold is met, electrons will be released, and an increase in intensity (more photons) will now release more electrons. This proposition, that was built on the work by Planck, was finally verified in experiments by Robert Millikan in 1916.

A standard 100-Watt light-bulb, for example, emits around 1020 photons per second.

Wave-Particle Duality

The Double Slit Experiment

One famous experiment that shows how light is (also) a wave, is Young’s Double Slit Experiment.

The first image to the right showed what the experiment would (should) show if light was indeed purely a particle (the orange dots): those particles that travel through the slits would predominately group very close to each other on the light detector screen inline with the slits.

The second image shows a light source on the left, which in modern experiments could be a laser, The laser is shone at a screen, which again, has two very small slits in it. The two holes are really close together - about the same distance apart as the wavelength of the laser light (making it possible for one single light ‘beam’ to be shone through both holes, to guarantee they are in phase). The orange arrows represent the light as waves (photons), and the larger orange curves represent the peaks of the photon waves, from a imagined top view. Beyond the light blocking screen, is the cavity, with a light detector at the back.

The second image shows how, the light that does goes through the slits, diffracts (bends), and spreads out, splitting into two new waves. The two new waves interfere with each other. As can be seen in the third image to the right: when a wave peak meets another wave peak, it creates a wave with a greater amplitude (more brightness) - known as a constructive wave; and when a wave peak meets a wave trough, they effectively cancel each other out (darkness) - known as a destructive wave. And so when the wave reaches the light detector screen, there is an unexpected wave pattern (known as an interference pattern) of particles, with the greatest intensity in the middle where there is the most constructive waves crossing prior to reaching the light detector screen, and effectively dark patches where the destructive waves have cancelled out the light.

More modern experiments have shown that there are even stranger things going on, like when a single photon (or electron) is fired at a time; the overall pattern after time on the light detector screen looks like the original interference pattern… is the electron predicting the future interference - or is it splitting in two and interfering with itself - or?