# When light speed changes?

##### Index of refraction

In this Wired article, there’s a useful recap of how and why the speed of light changes in various mediums.

• Wired > “What an iPhone Lidar Can Show About the Speed of Light” by Rhett Allain (Aug 12, 2022) – Why does light travel slower in a material than it does in a vacuum?

Classically, the speed (velocity) of light depends on the index of refraction of the medium.

If you look at a material like glass, it has an index of refraction with a value of 1.52. … That means that when light is in glass, it travels with a speed that’s only 0.66 [1/1.52] times as fast as in a vacuum, with a value of 1.97 x 108 m/s.

… air in our atmosphere … 1.000273 [STP], … Water … 1.33. Diamond … 2.417 …

Using this information, Allain (associate professor of physics at Southeastern Louisiana University) demonstrates how his iPhone’s Lidar shows an apparent indentation in the wall behind a glass container partially filled with water.

So, why is the speed of light slower in various mediums?

COMMON MISCONCEPTIONS

.1. … when light enters something like glass, it is absorbed by the atoms in the glass and then re-emitted some very short time later, and this delay causes the light to travel slower. But it’s easy to see that this is wrong. Although atoms can indeed absorb light and then re-emit it, this process doesn’t preserve the original direction of the light. If this was true, the light should scatter – and that doesn’t happen.

.2. … light goes through the glass, hitting atoms and bouncing off, before eventually making its way through the material. This bouncing would cause the light to take a longer path than it would in a vacuum, where it has no atoms to bounce off. …

In this case, a light beam entering glass would also spread out as it travels through the material, due to more “collisions.” … But in order to form an image, light beams have to move through the material in predictable ways and not randomly scatter. If the light had actually scattered, you would only see a diffuse glow, instead of being able to see an image.

THE CORRECT EXPLANATION (cf. Wiki‘s)

The first thing to understand is that light is an electromagnetic wave. … An electromagnetic wave has both an oscillating electric field and an oscillating magnetic field, … as described by Maxwell’s equations. This interaction between the fields is what allows light to travel through empty space.

When the oscillating electric field from a light wave interacts with atoms in a material like glass, it causes a disturbance in the atoms. This disturbance at the electron level means that those atoms also produce an electromagnetic wave. However, the electromagnetic wave from the atoms will be out of phase with the light that entered the glass. When two waves are out of phase, their peaks are at slightly different times. The combination of the original electromagnetic wave along with the wave from the excited atoms produces a new wave – one with a slower speed.

##### Beating the speed of light

This “Big Think” article is a useful recap about light and the cosmic speed limit. The medium matters.

In particular, I was interested in how science communicator Ethan Siegel navigates the “is it a wave or particle” legacy language. He says: “Light, you have to remember, is an electromagnetic wave. Sure, it also behaves as a particle …”

• Big Think > “The only way to beat the speed of light” by Ethan Siegel (July 20, 2022) – No, not with popsci tachyons or wormholes.

#### Prisms (dense medium) and rainbows

… when light travels through a medium — that is, any region where electric charges (and possibly electric currents) are present — those electric and magnetic fields encounter some level of resistance to their free propagation [e.g., in water it’s speed is only 0.75 of that in the “empty” vacuum of space].

If the frequency stays the same [from one medium to another], however, that means the wavelength must change, and since frequency multiplied by wavelength equals speed, that means the speed of light must change as the medium you’re propagating through changes [as evident by beam bending].

The frequency of all light remains unchanged, but the wavelength of higher-energy light [e.g., blue vs. red] shortens by a greater amount than lower-energy light.

#### Accelerated particles and Cherenkov radiation (a “shock wave” of visible light)

… the most interesting fact is this: particles that move slower than light in a vacuum, but faster than light in the medium that they enter, are actually breaking the speed of light [over short distances sans collisons].

[As an example] The Cherenkov radiation that results, produced so long as the particle “kicked” by the neutrino exceeds the speed of light in that liquid … [1]

Image (in article) caption: Here, a calcite crystal is struck with a laser operating at 445 nanometers, fluorescing and displaying properties of birefringence. Unlike the standard picture of light breaking into individual components due to different wavelengths composing the light, a laser’s light is all [practically?] at the same frequency, but the different polarizations split nonetheless.

##### Notes

[1] More specifically, as Wiki describes.

Cherenkov radiation is electromagnetic radiation emitted when a charged particle (such as an electron) passes through a dielectric medium at a speed greater than the phase velocity (speed of propagation of a wavefront in a medium) of light in that medium.

Phase (info carrier wave) vs. group (envelope wave) velocity – add (superpose) waves to get a wave packet.

• George Mason University > Physics > “Phase and Group Velocity

Dispersion is when the distinct phase velocities of the components of the envelope cause the wave packet to “spread out” over time. The components of the wave packet (or envelope) move apart to the degree where they no longer combine to complete the envelope.

## 3 thoughts on “When light speed changes?”

1. John Healy says:

Laser pulse tricks in plasma – getting the peak of the pulse to travel faster than c. A collective “dance” vs. solo interaction.

When (laser) “pulses of photons within narrow frequencies” pass through optical media (rather than individual photons), the interference between those photons creates a wave (beat) with a group (‘wave of waves’) velocity that varies from the phase velocity.

• Science Alert > “Physicists Broke the Speed of Light with Pulses Inside Hot Plasma” by Mike McRae (02 September 2022) – Using optical wave mixing (ion-acoustic response), US physicists have demonstrated variable group wave velocity – higher or lower than c – of laser pulses in streams of plasma.

(quote) Researchers have been playing hard and fast with the speed limit of light pulses for a while, speeding them up and even slowing them to a virtual stand-still using various materials like cold atomic gases, refractive crystals, and optical fibers.

But impressively, last year, researchers from Lawrence Livermore National Laboratory in California and the University of Rochester in New York managed it inside hot swarms of charged particles, fine-tuning the speed of light waves within plasma to anywhere from around one-tenth of light’s usual vacuum speed to more than 30 percent faster.

The overall effect was due to refraction from the plasma’s fields and the polarized light from the primary laser used to strip them down. The individual light waves still zoomed along at their usual pace, even as their collective dance appeared to accelerate.

References

• Rochester Institute of Technology > classes > physics > “Phase and group velocities” by Michael Richmond (teaches both physics and astronomy courses and runs the RIT Observatory; acts as liaison between RIT and the WIYN 0.9m telescope at Kitt Peak).

Lecture outline

The principle of superposition
Travelling waves with different frequencies
What if the waves travel through a dispersive medium?
Two choices for tracking the motion of a wave
Which velocity should we use?
A relationship between group and phase velocities

This rit.edu lecture used images from this YouTube video:

• YouTube > meyavuz > “Group Velocity / Phase Velocity Animation – Case 1: Group Velocity larger than Phase Velocity” (Jan 20, 2013)

Description: Here, we demonstrate the group and phase velocity phenomena as observed when two signals with different temporal and spectral frequencies (wavelength) are added to each other. The addition creates time varying constructive and destructive interferences along the space and time. The resulting wave packet travels with the so-called group velocity which – in the above case – is faster than the phase velocity. The wave packet envelope is shown in magenta color in dashed lines. Note that in this particular case, both group and phase velocities are positive.

An important interpretation of group velocity is that it represents the velocity at which the energy or information is conveyed along a wave (see Wikipedia for further details).

2. John Healy says:

Here’s an article about 2d “low dimensionality” Cherenkov radiation – an effect of the “interaction between free electrons and light waves traveling along a surface” aka an “optical shock wave.”

A new experiment that “explores the quantum-photonic nature of electron radiation.” In which, for the first time, “the quantum description of light is essential to explain the experiment results.”

I’ve added [ ]’d text for clarification and brevity. The term “particle” is, as always, shorthand for localized excitation in a quantum field.

Unlike other experiments, “interaction efficiency (also called the coupling strength)” was such that “every electron emitted radiation.”

• Phys.org > “First observation of the Cherenkov radiation phenomenon in 2D space” by Technion – Israel Institute of Technology (January 18, 2023)

(caption of article’s visualization) A single free electron [a quantum particle of the electron field] propagates [at a specific velocity, only a few tens of nanometers] above the special layered structure [a photonic-plasmonic surface] … During its movement, the electron emits discrete packets of radiation called “photons” [quantum particles of the electromagnetic field]. Between the electron and the photons it emitted, a connection of “quantum entanglement” is formed.

In this context, [indirect evidence of] “entanglement” means correlation between the properties of the electron and those of the light emitted, such that measuring one provides information about the other [as a “relationship between electrons and the radiation they emit”].

The breakthrough achieved by the Technion researchers links this phenomenon [Cherenkov radiation] to future photonic quantum computing applications and free-electron quantum light sources [“efficient electron-driven radiation sources“].

3. John Healy says:

I’ve enjoyed Paul Sutter’s articles over the years on key topics and ideas in physics. While his latest overview article (below) addresses an important topic about light, I’ve reservations about his presentation.

There’re no real visualizations for each model of the interaction between photons and a material like glass. Just some zen-like images. Not even a depiction of a molecular lattice of glass or water. Or how wave delay entails reduced speed (as manifested when light beams bend / refract).

Perhaps there’s the hope that readers will look deeper into terms like refraction, interference [“resistence” in a classical sense]; force carrier, phonon, polariton [interaction in a quantum sense] … Seek insight into all the hand-wavy explanations.

Also, I’d like to see clarification of the individual and collective (ensemble) interaction of “photons” – how:

“Photons can act individually, but when enough of them get together, they display all of the same properties as electromagnetic waves.”

That is, the distinction between light beams (of some electromagnetic frequency range) and single photons (as wavepackets of specific frequencies). Without that, the classical metaphors fall flat (without images either).

And there’s no mention (however slight) of quantum field theory.

I do like his use of the words “mess” and “nasty.” But not the metaphor of “slamming” – “the photons of the incoming light slamming into the material.” But he does stay mostly with the term interacting.

Maybe readers will be interested in learning more about Richard Feynman as well. And virtual particles, eh. A teaser for his podcast.

And check if Sutter addresses the misconceptions noted by Rhett Allain in my post above. As well as Allain’s correct explanation (involving superposition).

• Space.com > “How does light slow down?” by Paul Sutter (July 24, 2023) – There are three ways to look at the phenomenon of light slowing down as it passes through a material like glass (or water or air), corresponding to different models of light (as a traveling packet of energy).

All of these explanations have strengths and weaknesses, but all of them are powerful tools for understanding this fascinating interaction.

1. Waves (Maxwell’s classical waves of electricity and magnetism)

When these waves encounter a material like glass or water, they see [interact with] a whole bunch of charged particles … atoms, which have protons and electrons [which] respond to [incoming] electromagnetic waves … by wiggling [vibrating] along with them.

But moving charged particles also create electromagnetic waves of their own. The result is a giant mess, with the original electromagnetic waves interfering with all the waves generated by all the charged particles in the material (and there are a lot [gazillions!]). Thankfully [hand-wavy characterization], most of those waves, except the waves traveling in the original direction of the light, cancel each other out. But because the waves generated by the particles are a little delayed, the entire ensemble moves more slowly.

2. Particles (yes, an unqualified use of the term) – photons

Those charged particles [in the material’s atoms] can absorb those [incoming] photons and emit their own, because that’s what charged particles do [in quantum fields]. But these photons are a little different. In physics, they’re known as virtual photons [which mediate the electromagnetic force in the interaction].

So all of these charged particles start emitting copious [unlimited?] amounts of virtual particles, and once again, there’s a giant, confusing mess. Feynman [hand-wavy characterization] … developed a technique of averaging out all of the possible paths that those photons can take … leaving behind only the ones traveling in the original direction of the light. But all of those interactions come at a cost: It takes time for an electron to absorb and reemit a photon, and those delays add up. [Is this like bumper-to-bumper cars on the freeway? Or relaying a ball from the outfield rather than one long throw?]

3. Polaritons – “fake” or quasi particles (the combination of a photon with a polar excitation in a material)

To help physicists grapple with the complexities of all the kinds of vibrations that are constantly racing through materials, they proposed an entity known as a phonon [a collective excitation in a periodic, elastic arrangement of atoms or molecules – lattice waves as emergent phenomenon].

When photons and phonons get together [interact], they create [via strong coupling] something new: a polariton. … These polaritons … travel more slowly than the speed of light.

In this view, it’s not light that’s passing through a material, … but a new object, a polariton, passing through. This view is especially useful, because in many situations, it’s very easy to discard all the cumbersome math of conflicting waves or bouncing photons and just deal with a straightforward, simple entity that already encodes all the information you need.

Light goes in, a polariton travels through and light goes out.

Notes

Re Paul Sutter’s article on why light changes speed and reviewing my post “QFT – fields and wave packets.”

Cf. Wiki > Group velocity

So, “particles” as wavepackets, “a short “burst” or “envelope” of localized wave action that travels as a unit” [Wiki].

So, wavepackets are superpositions. Thinking of “group” velocity as that of the superposition – the envelope of the wave packet. Phase velocity as that of the superposed components.

(In a non-dispersive medium, there is no difference between phase velocity and group velocity.)

Wiki’s dramatic example is that of group and phase velocity going in opposite directions.

Wiki: The group velocity of a wave is the velocity with which the overall envelope shape of the wave’s amplitudes – known as the modulation or envelope of the wave—propagates through space.

Wiki image caption: A superposition of 1D plane waves (blue) each traveling at a different phase velocity (traced by blue dots) results in a Gaussian wave packet (red) that propagates at the group velocity (traced by the red line).

• Wiki > Wave packet

Significance in quantum mechanics > Quantum mechanics describes the nature of atomic and subatomic systems using Schrödinger’s wave equation. The classical limit of quantum mechanics and many formulations of quantum scattering use wave packets formed from various solutions to this equation. Quantum wave packet profiles change while propagating; they show dispersion.