# Who hits the wall first: the light beam or light traveller?

1. Dec 21, 2015

### aboro

I am trying to understand in non-mathematical terms the meaning and physical reality posed by Einstein’s law which tells us that the speed of light is the same relative to all observers.

I start with a basic hypothetical: Observer A observes B riding a motorcycle that is traveling at 50 mph past A. There is a brick wall located X number of feet in front of B. B throws a ball in the same direction he and his bike are traveling. We know that by adding the velocities of B and the ball, the ball is traveling at 60 mph relative to A. We also know that A and B will mutually agree that the ball hit the brick wall before B and his bike did.

Assume that A observes B straddling a beam of light. I assume it is correct to say that A is observing B to be traveling at the speed of light. Now, let’s assume that B, while riding on his motorcycle which is itself traveling at the speed of light, takes out a flashlight and aims a beam of light in the same direction he and his bike are traveling.

Question 1: Is it correct to conclude that B is observing the beam moving away from him at the speed of light? If not, then what is B actually observing about the beam of the flashlight? Will he beam from his flashlight enable B to see any objects in front of him?

Question 2. Will B observe the beam from his flashlight hit the brick wall before he and his bike hits the wall? If yes, how is that possible since B ability to make such an observation would mean that the flashlight beam is traveling faster than he and his bike are.

Question 3: What is A seeing? Stated differently, will A see the beam of the flashlight hit the brick wall before B and his bike hits the wall? Or will A see B, the bike and the beam of the flashlight hit the wall at precisely the same time?

2. Dec 21, 2015

### Chalnoth

If B is traveling at the speed of light, then B cannot have any notion of the passage of time: zero time will pass for B from the time B starts to move at the speed of light to the time B stops. So even if it were possible for B to travel at the speed of light (only massless particles travel at the speed of light), it wouldn't be able to shine any photons at all because no time would pass for B.

3. Dec 21, 2015

### aboro

Clalnoth, does this mean that from B's perspective, he thinks his flashlight does not work because it emits no light?

Given your answer, am I right in assuming that A does not see the beam of light at all and that from his (A's) perspective, B and his bike will strike the wall at the same time and without A ever knowing that there was another, albeit unobservable, collision involving the beam of the flashlight hitting the brick wall?

4. Dec 21, 2015

### Chalnoth

From B's perspective, he doesn't have time to think anything. He only sees the start and end of the journey. Nothing in between.

5. Dec 22, 2015

### Staff: Mentor

This is impossible. See below.

No; B can't travel at the speed of light in the first place. No observer can. See below. Please don't feed misconceptions.

No. There is no such thing as "B's perspective". An object traveling at the speed of light cannot have a "perspective"; the concept is not even well-defined. We have a FAQ on this:

So your thought experiment is based on an incorrect premise and is therefore not valid.

6. Dec 22, 2015

### Mister T

Did you really mean to indicate that you wanted to understand this in non-mathematical terms? Because you're using math! In you example I suppose you mean that the ball moves relative to B at a speed of 10 mph? It turns out that adding 50 to 10 to get 60 is an approximation that works so well for speeds that are slow compared to light speed that it's usually assumed to be a fact. At high speeds, though, it doesn't work.

As others have pointed out, no, that's not a possibility. If B sees the beam of light travelling at speed c he can't possibly straddle it. If he chases after it trying to catch it he will forever see it recede from him at speed c. Likewise, A will also see the light beam recede from him at speed c.

B will observe the beam from a flashlight he carries hit the wall before him. A will also observe that same beam hit the wall before B hits it. They will not agree, though, on the time it takes the beam to travel from B's flashlight to the wall. They also won't agree on the distance the light beam travels. But they will agree that the ratio of the distance to the time is c.