Einstein as a speed devil - science puzzle
| How fast should you drive towards a red traffic light to see it appear as green? |
|
Explanation
To calculate the speed for which the traffic light appears to become green, it is necessary to apply Einstein's relativity theory. One can show that
L/L_0 = (1 - v/c)^(1/2) / (1 + v/c)^(1/2)
In this formula, L_0 is the wavelength of the red traffic light and L the observed wavelength of somebody who drives with speed v towards the traffic light. The speed of light c = 300,000 km/s.
If you solve this equation with L = 500 nm and L_0 = 700 nm, you will find that v/c = 0.32. Hence if you are driving with about 300 million km/h (0,3 times the speed of light), you will see a green traffic light.
L/L_0 = (1 - v/c)^(1/2) / (1 + v/c)^(1/2)
In this formula, L_0 is the wavelength of the red traffic light and L the observed wavelength of somebody who drives with speed v towards the traffic light. The speed of light c = 300,000 km/s.
If you solve this equation with L = 500 nm and L_0 = 700 nm, you will find that v/c = 0.32. Hence if you are driving with about 300 million km/h (0,3 times the speed of light), you will see a green traffic light.
|
|