# To what extent can speed of light be reduced? [duplicate]

Light slows down upon entering different transparent objects, and the ratio is taken as refractive index of the object. If light can be slowed down, then is there a limit up to which it can be slowed down? If yes, then what is the minimum speed?

• possible duplicate physics.stackexchange.com/q/87561 Jul 13, 2016 at 12:38
• If you consider coherent spin excitations as manifestation of a "trapped" photon (which isn't much different from what happens when light moves through a dielectric anyway), then you can, in some sense, stop a photon entirely... at least in the sense that the "same" (in the quantum sense, that coherence is maintained) photon that entered the medium in question comes out when it is later released -- see : extremetech.com/extreme/…
– J...
Jul 13, 2016 at 13:56
• Are you talking about refractive index specifically, or about the speed of photons? If the latter, they always move at c. Refraction is modelled on the wave theory of light, in which photons aren't considered at all - the wave front does move slower, but the photons don't. And should a set of two mirrors that bounce the same bit of light a billion times before letting it out count as "slowing down light" for your purposes? :) Jul 13, 2016 at 14:00
• If you consider repeated absorptions and reemissions, according to image.gsfc.nasa.gov/poetry/venus/a11354.html light taking 100000 years to travel 696000 km from the core to the surface of the sun travels at 0.2 mm/s. Jul 13, 2016 at 18:15
• I asked a very similar question not too long ago and received an interesting article. dailymail.co.uk/news/article-2380028/… Jul 13, 2016 at 20:48

The short answer is that there is no known theoretical strictly positive lower bound to the speed of light. Any positive number, no matter how small, is possible, although limits are set for each candidate material, as I explain at the end of my answer.

One has to be pedantic to understand the lack of limitation to a more generalized "speed of light". From this pedantic standpoint, true light has only one possible speed, namely $c$. Now we need to understand that the electromagnetic disturbance that one sees in an optical material is not pure light but a quantum superposition of electromagnetic field states and excited "atom" states (where I use the word atom to mean any atom / molecule that interacts with the light). What this means is that the dispersion relationships and thus the group velocity for the disturbance changes from $c$ owing to the coupling between the light and atom states. A rough analogy is that the disturbance becomes slowed because light is absorbed by atoms, which linger in excited states a short time before re-emitting light, thus slowing the disturbance propagation down.

The more the superposition is dominated by the atom states, the slower the disturbance propagation will be. Slower pulses are achieved by (1) longer effective lifetime of each light-atom interaction, (2) higher interaction cross sections (3) density of interacting atoms. As the interaction cross section increases without bound, each emitted photon is almost certainly going to interact with the emitting atom's nearest neighbor. This means that the limiting speed for that particular material will be of the order of the atom lattice spacing divided by the interaction lifetime. An interaction lifetime of $1{\rm ns}$ with a $0.3{\rm nm}$ lattice spacing will give a propagation speed of the order of $30{\rm cm\, s^{-1}}$.

• How appropriate would an analogy to sound propagating slower than the object creating the disturbance be? I realize when we're dealing with quantum physics our analogies tend to break down, but I'm trying to visualize what you're describing here. Jul 13, 2016 at 15:50
• I think absorb/re-emit is inaccurate and misleading. (Other than that one sentence I think the answer is excellent) Jul 13, 2016 at 15:51
• @JDługosz, what's wrong with absorb/re-emit? Is there some simple mental model that I can replace it with? I would be very happy, for example, with a lattice-hopping model of the kind you see in introductory condensed matter textbooks. Jul 13, 2016 at 18:56
• Lay explainations of refraction are sharply criticized for using that explaination. I don't recall the killer reason but it's been discussed here before, I think. Jul 13, 2016 at 20:34
• @JDługosz The explanation is simply the group velocity change that arises from the coupling between the two quantum systems - EM field and matter. The eigenstates of the separate system are replaced by eigenstates of the interacting one. One can't, I believe, get simpler than that. Jul 13, 2016 at 22:14

How the light slows down in a matter, it depends on the recipe of its refractive index. For common, ordinary materials it is in the range of 1-3.

Bose-Einstein condensates have an extreme refractional index, even millions or billions. In a BEC with a refractive index of $10^9$, the speed of light is only $30~\mathrm{cm/s}$.

Here is a relative old article from 1999 about the slowing of the light to around $50 ~\mathrm{km/s}$. There are recent results significantly improved even this.

The same scientist stopped the light later only two years and made it "restartable".

The answers given here make me wonder, because I sense in here perhaps a misunderstanding. Or maybe I'm wrong, which might be more likely. :-)

The answers here refer to distances light travels. But as far as I understood, light is never slower than 299 792 458 m/s. I guess it may "look" like from a point of reference that light has slowed down, when a event happened, e.g. travelling on a warped Raumzeit. My belief is, that you have to take "Raumzeit" into account, which Einstein described in the Relativitätstheorie a couple of decades ago. Slowing down means losing energy. But "losing" energy is just a redshift in the frequency, but light is still on the same fast pace, as before.

So I would suppose, that light does not slow down. I don't say I'm right, but maybe this is a hint.

• +1 You are strictly speaking correct (as I discuss in the second paragraph of my answer), but what the OP is actually referring to is the speed of the electromagnetic disturbance in material, which is a quantum superposition of light and excited matter states. Jul 13, 2016 at 14:04
• Sorry my Fault. 😉
– Semo
Jul 13, 2016 at 15:10
• It's a failure of casual physics jargon - when saying "the speed of light" physicists can either mean "the constant c, which limits the velocity of photons in a vacuum" or "the velocity at which a photon can travel through the material under test". This ambiguity can usually only be resolved by context. Jul 13, 2016 at 20:51
• Not Nice. Downvoting without giving a hint, what to improve is... useless.
– Semo
Jul 15, 2016 at 5:51

## How would you define speed?

### In case it has a direction:

The maximum slowdown you can get is 2C, this is achieved by using a mirror.

### In case it is defined by the time taken to get from A to B

In case you would define speed by looking at the width of an object, where the light enters at point A, and leaves at point B, the following can be derived:

• The object may be a black box
• Inside the black box, there are 4 mirrors, the light initially moves north, then hits the first mirror at a 90 degree angle and is reflected east. Many kilometers to the east, the light hits another mirror at a 90 degree angle and is reflected north. After 1 meter, the light hits another mirror and is reflected west. Close to the first mirror it hits the fourth mirror, and is reflected north.

Now the resulting speed through the object can be made arbitrariliy slow (but positive) by moving the second and third mirror further back.

This example is somewhat contrived, but if I recall correctly, a laser actually uses a similar concept. (Keeping light 'in' for a while, and thus slowing it down by this definition.)

### Otherwise

For other definitions, I would say the existing answers should suffice.

• I asked for speed not velocity. You seem.to be confused,and lasers Dont slow down speed of light even for a second...I therefore mentioned refraction in my question. Jul 13, 2016 at 13:53