Dictionary tag: W

• All waves have shared characteristics such as height (amplitude), peaks (crests), direction of movement, rate of oscillation (frequency), and distance between peaks (wavelength).
• Electromagnetic waves travel at a constant speed (the speed of light) in a vacuum but more slowly though transparent media.
• Electromagnetic waves are generally invisible to the human eye, except within the visible part of the spectrum which is between approximately 400 and 700 nanometres.
• Our eyes can’t detect electromagnetic waves outside the visible part of the spectrum, whether the wavelengths are longer (as in radio and microwaves) or shorter (as in ultraviolet, X-rays, and gamma rays).
• Although we cannot see most electromagnetic waves, we can perceive some of them in other ways. For instance, infrared waves are felt as heat, and electric current (which produces electromagnetic waves) can cause a buzzing sensation in a wire or cause electrocution.

Wavelength & frequency

• The wavelength of electromagnetic waves can vary greatly, from extremely long radio waves, sometimes measured in kilometres, to very short gamma rays, measured in picometres (there are a trillion picometres in a metre (10^12).
• The frequency of electromagnetic waves can also range from extremely low (1 cycle per second equals 1 hertz  ) to extremely high, such as a quadrillion cycles per second, which equals 10^15 hertz (10^15).

• A wave diagram provides a visual representation of how a wave behaves when it interacts with various different media or objects.
• The purpose of a wave diagram is to illustrate optical phenomena, including reflection, refraction, dispersion, and diffraction.
• Wave diagrams can be useful in both theoretical and practical applications, such as understanding the basics of the physics of light  or when designing complex optical systems.
• Wave diagrams are not limited to light; they can also be used to represent other types of waves, such as sound or radio waves.

• A wave function provides information about the probable state of a system. It depends on factors such as the coordinates of the particles within a system (for example, position or momentum). It calculates the probability of finding the system in a particular state.
• Wave functions are used to determine the probability of various outcomes in quantum experiments.
• A wave function, in the context of quantum mechanics, must encapsulate a wealth of information about a quantum system, including its possible states, probabilities, and how it evolves over time:
  • Position and Momentum: The wave function must provide information about the possible positions and momenta of particles within the system. This information is crucial for predicting the outcomes of measurements.
  • Superposition: It should be able to represent the idea that a quantum system can exist in a superposition of multiple possible states. This means that the system can simultaneously occupy different states with certain probabilities until observed.
  • Probability Amplitudes: The wave function encodes probability amplitudes, which are complex numbers that determine the likelihood of finding the system in a particular state upon measurement.
  • Time evolution: It should be able to evolve over time, allowing for the prediction of how the system’s state will change over the course of time.
  • Observable properties: The wave function must account for the possible values of observable properties (such as energy, angular momentum, etc.) and their corresponding probabilities.
  • Normalization: It must satisfy the condition of normalization, meaning that the total probability of finding the system in any possible state must equal 1.
  • Boundary conditions: For specific physical systems, the wave function must satisfy appropriate boundary conditions that reflect the constraints imposed on the system (e.g., within a finite box or in a specific potential field).
  • Interference and entanglement: It should be capable of describing interference effects between different states and, in the case of multiple particles, account for entanglement, where the states of particles become correlated.
  • Wave function collapse: When a measurement is made, the wave function must be capable of undergoing a transition from a superposition of states to a single, definite state, in accordance with the process of wave function collapse.
  • Completeness and orthogonality: In certain mathematical formulations of quantum mechanics, wave functions must form a complete and orthogonal set to be used as a basis for representing quantum states.

Wave Function Collapse

Wave function collapse is a phenomenon in quantum mechanics where the act of making a measurement on a quantum system causes it to transition from a superposition of multiple possible states to a single, definite state.

• Prior to measurement, a quantum system can exist in a superposition of states, meaning it simultaneously occupies multiple possible states with different probabilities – these are described by the wave function. However, when a measurement is made, the wave function collapses, and the system assumes one of the possible states with certainty.
• Wave function collapse illustrates the profound influence that observation has on the behaviour of quantum systems.
• In the context of quantum mechanics, “observation” refers to the act of making a measurement or carrying out an experiment to gain information about a quantum system. When we observe a quantum system, we are attempting to determine one of its properties, such as position, momentum, energy, etc.
• The interpretation of wave function collapse is a subject of ongoing debate among physicists, with various interpretations positing different explanations for the phenomenon.

• All electromagnetic waves have common characteristics like crests, troughs, vibrations, wavelength, frequency, amplitude, and propagation direction.
• As a wave vibrates, a wave cycle can be seen as a sequence of individual vibrations, measured from one peak to the next, one trough to the next, or from the start of one wave cycle to the start of the next.
• While a wave cycle refers to the path from one point on a wave during a single oscillation to the same point on completion of that oscillation, wavelength is a measurement of the same phenomenon but in a straight line along the axis of the wave.
• Wavelength refers specifically to the horizontal distance between equivalent points in a single wave cycle, such as the distance between two consecutive crests or troughs.
• In contrast, a wave cycle encompasses the entire up-and-down movement of the wave, including the horizontal distance (wavelength) and the vertical displacement.

• Wave-particle duality refers to the phenomenon where entities like light can exhibit characteristics of both waves and particles.
  •  Electromagnetic radiation, including light, is often described using wave properties. However, when it interacts with matter, it behaves like particles.
  •  A photon is a quantum of electromagnetic radiation and represents the smallest discrete amount of light energy.
  • When a photon is absorbed by matter, the energy becomes localized at specific points. This phenomenon is termed ‘wave function collapse.’ It describes the transition of a quantum system from a superposition of states to a definite state upon measurement.
  • Wave-particle duality is a fundamental aspect of quantum mechanics and applies to all particles, not just light. Particles like electrons also exhibit wave-like and particle-like behaviour.
• The double-slit experiment is an experiment in quantum physics that demonstrates the wave-like behaviour of particles, including photons and electrons, and is a key illustration of wave-particle duality.

Concepts used to describe light as waves and particles can be paired to illustrate the wave-particle character of light

Wave concept	Particle concept	Explanation
Frequency	Energy	Frequency is related to the energy of a photon. Higher frequency light corresponds to higher energy photons. This is described by Planck's equation E = hf, where E is energy, h is Planck's constant, and f is frequency.
Wavelength	Momentum	The wavelength of a wave is inversely proportional to its momentum. This is described by the de Broglie wavelength formula λ = h/p, where λ is wavelength, h is Planck's constant, and p is momentum.
Wave speed	Momentum	The speed of a wave is related to its momentum through its frequency and wavelength. For light, the speed of propagation (c, the speed of light) is equal to its frequency times wavelength (c = λf), which is also related to its momentum as described above.
Amplitude	Intensity	The amplitude of a wave determines its intensity, which is related to the brightness or energy density of light. Higher amplitude corresponds to higher intensity.
Period	Lifetime	The period of a wave is the time it takes for one complete cycle. In the context of light particles (photons), their "lifetime" refers to the duration of their existence before they are absorbed or undergo a different process.
Phase	Quantum state	Phase refers to the position of a point in a wave cycle, and it can be related to the quantum state of a particle. In quantum mechanics, a particle's state is described by a complex-valued wavefunction, and the phase of this wavefunction is significant in determining probabilities and interference patterns.

These pairings are all based on the wave-particle duality of matter, which states that all objects have both wave-like and particle-like properties.

The specific pairings in the table can be derived from the following equations:

• E = hf (Planck’s equation describes the relationship between the energy of a photon and its frequency.)
• p = h/λ (de Broglie wavelength equation describes the relationship between the momentum of a particle and its wavelength.)
• p = mv (momentum equation describes the relationship between the momentum of a particle and its mass and velocity.)
• I = 1/2 cε_0 E^2 (intensity equation describes the relationship between the intensity of an electromagnetic wave and its electric field.)

where:

• E is energy
• f is frequency
• p is momentum
• m is mass
• v is velocity
• λ is wavelength
• I is intensity
• c is the speed of light
• ε_0 is the permittivity of free space. The permittivity of free space, also known as the electric constant, is a fundamental constant of nature. It is a measure of how easily an electric field can penetrate a vacuum.

The equation E = hf tells us that the energy of a particle is proportional to its frequency. This means that the higher the frequency of a particle, the more energy it has. This is why high-frequency radiation, such as gamma rays and X-rays, is so dangerous.

The equation p = h/λ tells us that the momentum of a particle is inversely proportional to its wavelength. This means that the shorter the wavelength of a particle, the more momentum it has. This is why high-energy particles, such as protons and electrons, can be used to accelerate other particles to high speeds.

• A wavefront is a conceptual tool used in the study of waves, including electromagnetic waves like light. It refers to the locus of all points that are in phase with each other along the wave at a given instant. In other words, it represents the leading edge of a wave as it propagates through a medium.
  • Sources that emit light in all directions, known as point sources, generate spherical wavefronts.
  • Lasers, which produce a narrow beam of parallel rays, create waves with flat wavefronts.
  • An electromagnetic wave with a flat wavefront is known as a plane wave.
• In addition to plane waves and spherical waves, there are also cylindrical waves which are produced when a point source is extended along a straight line.
• The shape of the wavefront can be influenced by interaction with different mediums or obstacles, such as when:
  • Refraction causes the path of light to bend as it crosses the boundary between two transparent media.
  • Dispersion causes light to separate into its constituent wavelengths, each of which bends to a different degree as it crosses the boundary between two transparent media.
  • Diffraction causes light to bend around the edges of obstacles into regions that would otherwise be in shadow.
• The concept of wavefronts applies not only to light but also to other types of waves such as sound waves or water waves.

More about wavefronts

• Wavefronts are typically used to describe the behaviour of waves in classical physics, where waves exhibit properties such as interference, diffraction, and refraction.
• While wavefronts are often associated with the behaviour of light, which can exhibit both wave-like and particle-like properties, they are a description of the wave nature of light rather than individual photons.
• At the quantum level, the behaviour of individual photons is described differently, often using concepts such as wave functions in quantum mechanics.

• While wavelength can be measured from any point on a wave, it is often simplest to measure from the peak of one wave to the peak of the next, or from the bottom of one trough to the bottom of the next, ensuring the measurement covers a whole wave cycle.
• The wavelength of an electromagnetic wave is usually given in metres.
• The wavelength of visible light is typically measured in nanometres, with 1,000,000,000 nanometres making up a metre.
• Each type of electromagnetic radiation – such as radio waves, visible light, and gamma waves – corresponds to a specific range of wavelengths on the electromagnetic spectrum.
• As energy increases, frequency also increases and the wavelength decreases. Therefore, shorter wavelengths correspond to higher energy levels, and longer wavelengths correspond to lower energy levels.

Wavelength & the Visible Spectrum

• The visible part of the electromagnetic spectrum consists of a range of wavelengths that correspond with all the different colours we see in the world.
• The visible spectrum, which spans wavelengths from approximately 400 to 700 nanometres, is commonly described in terms of bands of colour—red, orange, yellow, green, blue, indigo, and violet.
• However, these divisions are somewhat arbitrary since the spectrum is continuous, and the exact wavelength boundaries between colours is subjective.
• Humans don’t see the wavelengths of visible light directly but do see the specific colour associated with each wavelength and the colour produced when different wavelengths mix.
• Within this visible spectrum, each colour corresponds to a single wavelength of light.
• The concept of colour is a perceptual property, not a property of light itself.
• It’s how our brain interprets the wavelengths of light that reach our eyes. The perceived colour (hue) of a light stimulus is dependent on its wavelength.
• A colour produced by a single wavelength is known as a pure spectral colour.

Wavelength & Colour

• A light that we perceive as white is a combination of many different wavelengths of light across the visible spectrum. When these wavelengths containing red, green, and blue mix and reflect off a neutral-coloured surface, they appear white to our eyes.
• Light sources in nature rarely emit a single wavelength. They typically emit a mixture of many wavelengths that combine to create the colour we perceive upon reflection. The wider the range of wavelengths present in the light source, the less saturated (more diluted) the reflected colour will appear. In other words, light with a mix of many wavelengths tends to appear lighter or closer to white.
• Wavelengths of visible light are typically measured in nanometers (nm). While the human eye cannot distinguish every single possible wavelength within the visible spectrum (between 400 nm and 700 nm), it can differentiate a vast range of colours within that spectrum.