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If a mass is moving at a fraction of the speed of light, would light radiated from the rear of the mass have a light velocity slower by its sources fractional speed?
- Ron Oliver (age 62)
Las Vegas, Nevada
That's one of the two obvious guesses one might make.
Your guess is that light travels at a speed fixed with respect to its source. The other one would be at a speed fixed with respect to some medium. It turns out that, weird as it may sound, light travels at a fixed speed with respect to everybody. That seems impossible only because we have incorrect intuition about how space and time coordinates change as you change viewpoints.
(published on 05/30/12)
Follow-Up #1: Relativistic Measurements with Light
Hello I was hoping someone could shed some light on a hypothetical problem I have come up with while trying to wrap my head around the 'special theory of relativity'.
Just to simplify things lets say light moves at 10m/s (We are just scaling down so I dont have to type in 6 digits for every velocity)
So let's imagine there is a ship "Fast" moving at 9m/s (90% C), It passes a stationary ship "Still" (Or moving towards him at equal velocity, it does not matter it's the same thing right?) which shines a light beam parralell to to ship A's path right as it passes.
Ship "Still" will observe the light beam to overtake ship "Fast" by 1m/s.
Ship "Fast" will observe the light overtake him at 10m/s. (Becasue according to the theory, light moves at 100%C for all observers)
So after 11 secconds by ship "Still"s point of view, ship A will have travelled approx 100m but the light will have travelled 190m.
Ship B will see the light reach approx 110m as ship "Fast" reaches 100m.
So at the end there is a discrepancy between the two ships by 80m.
Can somone explain to me how time slowing down for either observer makes up for this gap in distance?
- Isaac (age 21)
Adelaide, SA, Australia
Great question. People are often confused by how speed of light is constant relative to different moving object. But in fact, you were right that speed of light is constant relative to any object moving at a constant velocity.
I'm not sure where that 190m comes from, but you're right that at first glance the combination of distances looks peculiar.
It's often said that "time slows down for the moving observer" but that's misleading. Each observer is moving, according to the other one. Whether the time between events is bigger or larger depends on how the events are moving with respect to each observer. Phrases like "at the end" assume that the different observers agree on what events are simultaneous, but actually they don't.
What we usually do in problems like this is just to carefully write down the t and x coordinates in each frame, using the Lorentz transforms.(http://en.wikipedia.org/wiki/Lorentz_transformation) When "A" sees "B" go by a marker fixed at distance 0.9ct away, the light has gone distance ct, as you say. As "B" goes by that marker, he says the time elapsed since A went by him is about 0.44t. [0.44 ≈ sqrt(1-0.92]) He sees the light then as 0.44ct away, and the distance from A to the light as ~0.84ct. You find it all comes out consistent.
Hope this helps,
Lingyi and Mike W.
(published on 10/03/13)
Follow-up on this answer.