Need a physicist to help with this one...

[SkyHog]

My brain is hurting trying to understand this one. I'm sure there's an explanation in the Theory of Relativity that I am missing, as this is mostly a Relativity issue.

Assumptions:
1. There are 4 viewpoints: A, B, C, D
2. Light always travels at the speed of light
3. Nothing travels faster than the speed of light within a system

Note - if any of the assumptions above are incorrect, then the entire premise is incorrect, so I need to make sure I understand that part first.

So here's the setup. We have a giant onlong cement box on a flat bed truck (or any other movable surface). Inside the cement box, we have a directional light source. This light source is positioned at viewpoint A, on one end of the box, and it is pointed to the other side of the box at the furthest distance (viewpoint B). It is safe to say that the light travels from viewpoint A to viewpoint B at the constant speed of light.

Outside the box, there is a sensor that is tripped when the light is sent from viewpoint A, which displays on viewpoint C. There is another sensor that is tripped when the light is received at viewpoint B, which displays on viewpoint D. Essentially, this serves as a form of measurement of the speed of light. The delay caused by the transmission from A-C and B-D is irrelevant because it is constant between the two (i.e., it always takes 5ms to get from A-C and 5ms to get from B-D).

So - that said, the box is on a stationary truck, light leaves A and hits B, and is measured outside the box as "the speed of light."

Now, the truck starts moving at a very high speed, and the light is measured again.

My hypothesis: it measures at the speed of light, still, because to viewpoint A, and to viewpoint B, the light is traveling at the speed of light. However, because the truck is moving, from outside the box, the light has traveled a further distance than it had originally, and therefore, the light traveled at a speed faster than the speed of light, right?

Its a matter of relativity, that within the box, the light traveled the same distance in the same time, but outside the box, it traveled a longer distance in the same time....

What am I missing?

Edit: A diagram to follow:

Code:

C D
*-----------------------*
*| A B |*
*-----------------------*
O O

 

[Jim Logajan]

Assumptions:
1. There are 4 viewpoints: A, B, C, D
2. Light always travels at the speed of light
3. Nothing travels faster than the speed of light within a system

Note - if any of the assumptions above are incorrect, then the entire premise is incorrect, so I need to make sure I understand that part first.

Point 2 should say that the speed of light in an inertial frame (i.e. unaccelerated) will always be measured the same speed. So if you measure the speed of a photon emitted from a passing truck, you get a speed c relative to your reference frame. A person inside the truck also gets c in their reference frame.

Point 3 is just a consequence of point 2 when you go work the math to make point 2 possible in all cases. Things like relative time and distance get affected.

So - that said, the box is on a stationary truck, light leaves A and hits B, and is measured outside the box as "the speed of light."

Now, the truck starts moving at a very high speed, and the light is measured again.

My hypothesis: it measures at the speed of light, still, because to viewpoint A, and to viewpoint B, the light is traveling at the speed of light. However, because the truck is moving, from outside the box, the light has traveled a further distance than it had originally, and therefore, the light traveled at a speed faster than the speed of light, right?

It isn't clear to me which way the truck is moving in this frame of reference. If in the direction of A to B, the same direction as the light, then at the instant that the light is emitted from point A, the length of the truck in our reference frame is, according to Lorentz contraction, L = L0*(1 - V*V/C*C)^(1/2) where V is the speed of the truck, C is the speed of light, and L0 is the original length of the truck.

Suppose L0 = 1, C = 1, and V = 0.5. Then L = (1 - 0.25)^(1/2) = 0.866. (Using arbitrary units for simplicity, where C = 1.)

The truck appears to us to be 86.6% of its original length. Point B no longer can line up with point D when point A lines up with point C. With point B located 0.866 units to the right at the instance A and C are lined up, and B is traveling rightward at a speed of 0.5 while light is also traveling that same direction at 1.0, how long before the light reaches B?

 

[Jim Logajan]

Yes, the truck is moving the same direction as the light. Are you saying that the distance from A to B gets shorter when the truck is in motion?

Yes. Such a shortening is known as Lorentz contraction. First devised by Dutch physicist Lorentz (and independently by Irishman FitzGerald, so also known as Lorentz-FitzGerald contraction) in 1892 to explain the result of the Michelson-Morley experiment. It was later shown that the same equation could be derived from Einstein's postulates.

To a person in the truck, the distance between A and B appears unchanged at 1. But to the truck person the distance between C and D appears to be shorter because those points are traveling at high speed to the left!

 

[Jim Logajan]

In the 70's a bunch of scientists actually proved this by sending an atomic clock either into orbit or onto a concord (I can't remember which), after some time of moving really fast, the atomic clock on the fast moving platform was some small amount slower than on on the earth.

You are probably referring to the Hafele-Keating experiement.

The GPS satellites have been validating the special and general relativity for the last 20+ years. The designers have to take into account special and general relativity - if they did not, the difference in clock rates would cause positional accuracy to drift by up to 10 km per day!