# What happens when light moves perpendicular to a moving object?

Imagine the folllowing situation: A coherent light source is attached to a car such that the emitted light beam path is "being crossed over" by the car i.e. the long parallel light beams are struck by the moving car such that their path wrt exach other is a 'X'. Say the car is going at a speed of 3000m//s and the coherent light source is attached to the car. do the light particles experience doppler shift? do they photon get absored by th car body? does the path of the photons change in any velcoity due to a gain in momentum? what about the angle of being hit - does it influence any of the above properties of light particles?

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Your question is not clear. If the light source is attached to the car, how will the car cross the beam? It will be always a delta(t) behind the beam and cannot be hit by it or hit it. –  anna v Jun 13 '11 at 14:36

## 1 Answer

I am guessing that the setting you are talking about is the following: You have a reference frame where the x axis is horizontal and the y axis is vertical and there is a stream of photons moving along the y axis. Then there is a car moving on the x axis with some velocity u, heading to the stream of photons. And the question is, what will the driver see? What will be the angle of attack of the photons and what will be their energy?

This is a standard special relativity exercise. First of all, the Doppler formula doesn't apply in this case. The correct way to handle this problem is to calculate the four-momentum of the photon in the first reference frame and then transform it to the frame of the car. The time-component of the four-momentum will give you the change in energy of the photon and the ratio of the spatial components (x and y) will give you the angle of attack where you will notice that there is an aberration effect.

Specifically, the energy will be increased by a gamma factor ($E'=\gamma E$) and the angle of attack will be

$$\tan\theta'=\frac{1}{\gamma \beta}$$

where $\gamma$ and $\beta$ are the parameters for the frame of the moving car. Of course the speed of the photons is always the speed of light $c$.

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