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Consider this situation:

You are in the subway and you realize that this subway is somehow travelling in 99.9999% of the speed of light. The vehicle is travelling through a tunnel that is dimly lit. The question is: would it be possible to see the light in the tunnel if you look out in the window?

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According to SR (special relativity) a moving observer measures a radiation frequency shifted if compared to the original frequency of the source. If the moving observer is approaching the source, it will experience a blueshift, instead if going away a redshift.

Coming to the passenger in the subway, because of the velocity very close to $c$, he/she will experience a blueshifted frequency by a factor of $1414$ looking ahead and a redshifted frequency by a factor of $0.0007$ looking behind, times the light frequency in the tunnel. In either case the measured frequency would be out of the frequency interval perceived by the human eye.

To answer to the question the passenger would see a dark tunnel.

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According to Einstein's special theory of relativity the light from the tunnel would still be traveling at the regular speed of light relative to you so I don't see why you would have any problem seeing the light from the tunnel.

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The subway train will indeed be hit by light, but it will be hard to see the lights through the window.

The problem in seeing the tunnel light is relativistic aberration, that the angle of the light is changed by your relative velocity. The formula is $$\cos(\theta_2)=\frac{\cos(\theta_1)+\beta}{1+\beta\cos(\theta_1)}$$ where $\beta =v/c$. $\theta_1$ is the incident light angle, $\theta_2$ the perceived angle (where 0 degrees is forward). As you speed up, most light will arrive from the front - the "searchlight effect".

If you have lights at regular intervals along the tunnel there will be some lights far behind you that get a perceived angle of $\pi/2$ just outside the window, so you will indeed see some lights. However, they will be far behind you so their intensity will be low: the near lights will be shining on the front of the train.

Light angles and intensities for $\beta$ 0.5 and 0.999999. Plot of light angles and intensities for $\beta$ 0.5 and 0.999999. The circles denote individual lights at coordinates $(x,1)$ seen from the origin, with area proportional to the intensity $1/r^2=1/(1+x^2)$. For $\beta=2$ the brightest light just outside the train is seen at 60 degrees angle, while for the faster train nearly all light comes from the front and will be hard to see from inside the train.

In addition, there will be redshifting/blueshifting making lights behind you redshifted, so the light apparently just outside may be impossible to see if it has a spectrum with little ultraviolet light.

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