# Alongside a light ray (in another medium)

It is a said fact that the speed of light is insurmountable. But can the validity of this fact be questioned in another medium?

If I pass a beam of light in, say water (here the light speed is reduced) and travel alongside it, then my dynamic mass will not become infinite and I will be able to notice some effects, right?

So can somebody please explain if this is correct or not? And what will I be experiencing while travelling at intermediate speed(Between c and and the same in an optically denser medium)?

Please do consider my ideas of a visual boom (in analogy to a sonic boom). Also, will there be any imposable physical restrictions barring such FTL motion in a non vacuum medium(such as disintegration at the atomic scale due to high speed collisions or friction holding me back)?

Yep, it's possible to move in a medium faster than the phase velocity of light in that medium.1

An example of the effects of this is Cherenkov radiation, emitted when a charged particle moves faster than the phase velocity of light in certain mediums. It is emitted in a roughly conical shape:

Here, $n$ is the medium's refractive index (which describes how much light is "bent"), $t$ is time, and $\beta$ is the particle's speed divided by the speed of light. Some simple algebra and trigonometry can give the calculations for the various quantities.

The comparison with a sonic boom is an apt one, and is commonly used.

1 Be careful to distinguish phase velocity from group velocity; this could be the result of your confusion.

• The problem is the OP's confusion about what is meant by "speed" of light. So you should compare this to the group velocity. – imallett Sep 6 '15 at 20:11

The significance of $c$ is not the speed of light, it is the maximum speed a cause effect relationship can propagate. This comes to mean a speed that is observed to be the same by all inertial observers, as I explain in my answer here. It is experimentally found that the speed of light is equal to $c$, because the speed of light has this transformation behavior between inertial frames (always the same) and, from basic symmetry considerations, there can only be one such speed. The experimental result that light travels at $c$ means, amongst other things, that light has no rest mass.

Now let us look at light in a medium. This is not the same thing as light; it is a quantum superposition of photons and excited matter states. There is a quasiparticle for this superposition and it is called a polariton (or several other names such as exciton, plasmon and so forth, depending on the exact nature of the superposition), it travels at some speed less than $c$, namely $c/n$ where $n$ is the medium's refractive index and you can indeed boost to a frame wherein such a disturbace is at rest relative to you.

This particle does have rest mass. Indeed see my answer here where I calculate that the rest mass of light - excited matter state superposition quantum is about 3.6 millionths of the mass of an electron at optical wavelengths for windowpane glass ($n=1.5$). That is, a few electron volts, or of a very similar magnitude to the total energy of the incoming optical photon from a frame at rest relative to the medium (but it's not the same, since total energy is not a Lorentz invariant).

• Is it a valid argument,that the force of colliding particles in the medium will prevent any non zero rest mass particle from accelerating to such speed? – Abhinav Sep 7 '15 at 6:31
• @user2511145 No: the point is that these quasi particles, as I calculate in my other answer, have a nonzero rest mass and move at that speed. Now there may be practical problems going through the medium alongside these particles (very definite colliding force) - see xkcd's Relativistic Baseball "what if" - but there is no theoretical bar on it if you could overcome this force: you could, for example, ride outside the block of glass at $c/1.5$ and see stationary regions of excitation in the glass. – Selene Routley Sep 7 '15 at 8:15
• @WetSavannaAnimal aka Rod Vance: "you could, for example, ride outside the block of glass at $c/1.5$ and see stationary regions of excitation in the glass" -- Note however the possibilities of refractive index values below unity, $n \lt 1$, or of group speed being greater than than signal front speed. – user12262 Sep 7 '15 at 10:05
• @user12262 Indeed. Although for my example the relevant speed is the signal speed, mostly (but not always) well represented by the group velocity, but never by a less-than-unity phase velocity. – Selene Routley Sep 7 '15 at 10:19

It is a said fact that the speed of light is insurmountable. But can the validity of this fact be questioned in another medium?

Specifically, it is said that the signal front speed, $c_0$, is the upper limit of any speed value referring to the exchange of a signal; by definition and the meaning of "front" referring to the very first observation of any signal indication under consideration.

This holds regardless of the value of refractive index, $n$, measured in the experimental region; and therefore

• independent of the value(s) of phase speed, $c_0\left(\frac{1}{n}\right)$, and

• independent of the value(s) of group speed, $c_0\left(\frac{1}{n} + k\frac{d}{dk}[~\frac{1}{n}~]\right)$.