If we accept the summary of the experiment, the laser pulse should emerge from the 6 cm cell in 0.2 ns, but it emerges 62 ns earlier than expected. The claim is that this is over 300 times c. But this is a faulty claim. The expected time is clearly +0.2 ns, while the claimed arrival time is -62 ns. So, even if we accept the claims, the difference in arrival times dictates a negative ratio. Even if we allow infinite propagation velocity, the pulse cannot exit the cell before it enters. The idea that time runs backwards is false.
Here's the explanation. Everybody knows that if you keep adding energy to a particle, it will speed up less and less for the same increment. The limit to velocity turns out to be c. However, that does NOT make it an absolute limit. Observable, measurable velocity is the cosine projection of a faster velocity. It is known as Proper velocity. Although it is the ratio of Proper length to Proper time, Proper length is measured in the co-moving frame while Proper time is measured in the relatively moving frame. That makes the physics definition of Proper velocity an improper derivative, something which is disallowed in mathematics. Physics is less logical, and only downgrades Proper velocity to a mathematical trick or convenience that facilitates some calculations.
Nevermind that Proper velocity is the 3-velocity term in 4-velocity, which is Lorentz Transformable, or that Proper velocity times invariant mass is ALWAYS momentum. It is Newtonian momentum at low speeds, but relativistic momentum at high speeds. It is valid for all velocities, and Proper velocity ranges from -infinity to +infinity. We will dispense with the false premise that Proper velocity is not real. Technically, that's actually true, but not in the sense that it is not physical. It is not real, because it is complex, both real and imaginary components. It does exist, and it is more than real. We can only measure cosine projections of time and distance. Since they both transform the same way, their ratio seems to be invariant in magnitude for both the stationary and moving observer. Truth is, even though both observers agree on the magnitude of relative velocity, they are both wrong. What they observe and measure is the cosine projection of Proper velocity.
As Proper velocity approaches infinity, its cosine projection asymptotically approaches c. The limit of the cosine projection is just c. But as the cosine projection that maps to infinite Proper velocity, it is hardly an absolute limit. However, the mapping between Proper velocity and its Newtonian projection is an isomorphism, and every element in each set is uniquely paired with one element from the other set. Every Proper velocity from -infinity to +infinity maps to an observable velocity from -c to +c. It is impossible to travel faster than c, because there is no corresponding Proper velocity faster than infinity. Similarly, time dilation asymptotically approaches zero as Proper velocity approaches infinite. There is no Proper velocity greater than infinity to push the time backwards. Even at infinite Proper velocity, time just freezes.
The summary states that the index of refraction varied sharply with frequency. This appears to be a resonance effect, which results in a negative index of refraction. It concerns me that the velocity of the rotating frame is quite likely non-relativistic in magnitude, but the relativistic correction factor, although small, is missing. c+v is problematic, but γc+γv is not. Because γc+γv is the sum of the 4-velocity components (γc-γv is the complement, the difference). These two combinations are the coordinates in eigenvector spacetime. It is a property of the eigenvector coordinates that their product is a relativistic invariant. (γc+γv)(γc-γv) is γ²c²-γ²v² = γ²(c²-v²) = γ²c²(1-β²) = c², the same relativistic invariant as in Minkowski spacetime.
The individual factors can also be expressed as γc+γβc and γc-γβc, which are (γ+γβ)c and (γ-γβ)c which are the same as e^w c and e^-w c. Clearly, their product is also c². The exponential is an eigenvalue of the Lorentz matrix, and the modified velocity is the result of a squeeze mapping. The Lorentz matrix is a pure diagonal matrix with the two eigenvalues on the main diagonal, and the velocity vector is the transpose of [c,c]. It is the nature of eigenvectors that a squeeze mapping scales each coordinate by inverse factors, so their product is invariant with respect to w, the rapidity. It also means that the column vector itself is also invariant with respect to w. Eigenvector spacetime preserves the area defined by a point on a hyperbola and perpendiculars to the two eigenvector axes. Since the eigenvectors are defined by Σ=ct+r and Δ=ct-r, they represent the worldlines of photons. Coordinates in eigenvector spacetime are measured by light rays, and are ALL invariant with respect to relative velocity. All Lorentz transforms are then the product of eigenvalues and invariant coordinates. In eigenvector space, this experiment confirms that the speed of light is invariant in two directions simultaneously.
Since there is no mention of eigenvalues, eigenvectors or complex geometry, I seriously doubt the conclusions offered by the experimenters.