What would happen if you drove your car close to the speed of light and turned on the headlights?
Category: Physics Published: April 30, 2013
By: Christopher S. Baird, author of The Top 50 Science Questions with Surprising Answers and Assistant Professor of Physics at West Texas A&M University
Light in vacuum always travels at the same speed c, exactly 299,792,458 meters per second, no matter how it is created or in what frame it is observed. If you drove a car close to the speed of light relative to the ground (neglect air effects) and turn on the headlights, light would leave your headlights at speed c the way it always does. To you in the speeding car, the light would be traveling away at speed c. Your friend at rest on the ground would also measure the light traveling at speed c. How is that possible? When a frame of reference goes very fast (close to the speed of light) relative to a rest frame, its time slows down as observed by someone in the rest frame. This relativistic effect is known as time dilation. Additionally, the space of a moving reference frame, and the objects in that space, become contracted in the direction of motion relative to the rest frame. This relativistic effect is known as length contraction. The moving car actually gets squashed front to back. But this contraction does not hurt you or the car because it is space itself that is contracting, so the car experiences nothing different. Note that these effects are caused by the relative motion. To you in the car, you see your car as at rest and therefore it looks normal, it is not squashed and does not have its clock running slow. In fact, to you in the car, your friend on the ground is the one that is moving and therefore you see him as length-contracted and time-dilated. Because relativistic effects are caused by relative motion, as soon as the car slows down, your friend would see its length and time return to normal.
Einstein's theory of Special Relativity, which has been mainstream science for over a century, is essentially a mathematical formulation of length contraction, time dilation, and the speed of light in vacuum being the same in all frames. As non-intuitive as it may seem, length contraction and time dilation always manage to guarantee that the speed of light is the same no matter what frame we are viewing it in. To your friend on the ground, the light coming out of your car's headlights would be traveling at c relative to the ground, and the car itself would be traveling close to c. To your friend, this would make it look like the light is having a hard time getting away from car, and is nearly frozen relative to the car. Physically, what is going on is that time itself in the car's frame of reference as observed by your friend on the ground has slowed so much due to time dilation that the light is indeed taking a long time to get away from the car as seen by your friend on the ground. This does not mean that the light has slowed. Light always travels at c. It just means that the car is doing a good job keeping up with the light as observed from the ground.
What would happen if the car traveled exactly at the speed of light in vacuum and turned on its headlights? Objects that don't have exactly zero mass can never travel exactly the speed of light in vacuum. On the other hand, objects with exactly zero mass always travel at exactly the speed of light in vacuum and cannot travel at any other speed. Getting any object with mass at exactly the speed of light requires an infinite amount of energy and is therefore impossible. The closer the car gets to traveling at speed c relative to the ground, the slower its time progresses relative to the ground, so the more its light would seem frozen in the headlamps.
A few practical notes need to be made. In real life, a car driving on the earth's surface could never come anywhere close to the speed of light. The intense air friction and frontal air pressure would heat and vaporize a car long before it reached the speed of light. The Stardust sample return capsule was the fastest man-made object to ever travel through earth's atmosphere. The Stardust capsule had a peak speed of 12,400 m/s (28,000 mph), which is only 0.004% the speed of light in vacuum, but this speed still generated a peak temperature of 4700° F (2600° C). Getting a space ship traveling close to the speed of light in the near vacuum of space is much more feasible, but even then the sparse space dust starts to cause problems at such speeds.