If 2 cars are traveling at the speed of light and the one in the back turns on its headlights, would the car in front be able to see them? Why or why not?

There is a problem with the question as stated.  It is not possible for objects with mass to travel the speed of light.  So, technically the question has no answer.  But, if we were to restate the question slightly we would obtain some interesting results. If 2 cars are traveling nearly the speed of light and continue to get closer and closer to the speed of light, what happens when the car in the back turns on its headlights?

 Two cases need to be considered.  The first is what happens in the reference frame of the cars?  Since the cars are not moving relative to each other,  they could be treated as not moving at all.  Then the light always takes the same time to catch the car in front.  For example, if they are 300,000 km apart then the light will always take one second to catch up.

 The more interesting case is when one considers a frame at rest relative to the cars.  In this case, two things happen.  First, the rest observer measures the distance between the cars to be shrinking the faster they go.  Second, the rest observer measures the time it takes the light to go from the rear car to the front car to take longer the faster they go.

 To find out how much we use the Lorentz transformations, Lr = Lm / g and Tr = gTm.  Here Lr , Lm , Tr and Tm are rest frame length, moving frame length, rest frame time and moving frame time respectively.  g equals 1 / ( 1 - v2/c2)˝ where v is the speed of the moving frame and c is the velocity of light.  For example if they are going  99% the speed of light,  the observer measures them to be 43,320 km apart, but the light takes 7.09 sec to travel the distance.

 So, in the limit, the cars would be infinitesimally far apart and the light would take forever to get from the back car to the front car.

Submitted by J.(Texas, USA)
(September 29, 1997)

You might also be interested in:

What are the retrograde motions of planets in the sky?

It depends on what kind of motion you are talking about. When seen from the north pole of the celestial sphere all planets orbit around the Sun in a counter-clockwise or direct path. Most planets also...more

How do Astronauts Live in Space?

Almost everyone has a question or two about living in space. What do astronauts do in space? How do they do everyday things like eat, sleep and go to the bathroom? Well, this is our attempt to answer...more

How far is the Earth from the Sun, the Moon and all the other planets? How far are all of the planets from the Sun? Do you know of a software that tracks the planets in real-time?

There is a really neat internet program called Solar System Live that shows the position of all of the planets and the Sun for any given day. If you go to that page, you'll see an image similar to the...more

Is it really true that man never really walked on the Moon?

The picture of the American Flag (the one put there by the Apollo astronauts) is waving (or straight out) in the wind. How could that be possible if there is no atmosphere on the Moon? Was it some sort...more

How many planets orbit the sun?

I was wondering if there is a new planet? Are there planets (a tenth planet?) after Pluto belonging to our solar system? What are the names of the new planets discovered in the solar system? Are there...more

According to Stephen Hawking, any object with an energy which equals Plank's energy has to become a black hole.

If that is so, the energy released during the Big Bang must have created many such black holes. Therefore most of the Energy of the Big bang must have disappeared in that form. Then how did the Universe...more

Windows to the Universe, a project of the National Earth Science Teachers Association, is sponsored in part is sponsored in part through grants from federal agencies (NASA and NOAA), and partnerships with affiliated organizations, including the American Geophysical Union, the Howard Hughes Medical Institute, the Earth System Information Partnership, the American Meteorological Society, the National Center for Science Education, and TERC. The American Geophysical Union and the American Geosciences Institute are Windows to the Universe Founding Partners. NESTA welcomes new Institutional Affiliates in support of our ongoing programs, as well as collaborations on new projects. Contact NESTA for more information. NASA ESIP NCSE HHMI AGU AGI AMS NOAA