Another thread discussed how the speed of light is constant thus a car moving at the speed of light can still operate headlights normally.
Frankly, this doesn’t seem to make much sense to me. Admittedly, I am very naive about this subject, but I think of it like this: I observe a cannon shoot a projectile at 500 mph. If the cannon is then mounted on a train moving forward at 500 mph, it makes sense that the projectile appears to move 1000 mph with respect to me, the observer.
How can something moving at the speed of light project forth photons moving at the speed of light? Shouldn’t the photons be moving at twice that speed?
Similarly, couldn’t you measure your speed through the universe by shining a light at mirrors in several directions and comparing how long it takes for the light to bounce back?
That was my example in that other thread and it wasn’t posed too well since I cited a car going the speed of light which adds a lot of complications. However, if you look at a car going 0.95c (95% speed of light), an observer in the car will see the headlights work normally (light travelling at the speed of light relative to the car). Your cannon example is true for a cannon, but the same does not apply to light.
As my bungling in those threads made clear, I’m not qualified to explain this in any detail. Personally, I’ve really enjoyed Stephen Hawking’s work, particularly “The Universe in a Nutshell” which covered the basics of relativity well.
A hundred years ago, these were the exact questions that physicists were struggling with. Very exact measurements had conclusively proven that the speed of light is constant, not affected at all by the speed of the person doing the observing. Also, our understanding of things like Maxwell’s equations, which describe electromagnetic fields and how their waves propagate, hinted that the speed of light is constant for all observers too.
So this really smart guy named Albert just started from there, with the assumption that the speed of light is constant for all observers, and derived what such a world would be like. He came up with the theory of Special Relativity, and later General Relativity. In this world, you can’t just add speeds - instead, one observer will not agree with another observer about the passage of time itself. Wild and kooky stuff, but it’s held up pretty well for the last hundred years as the way that the universe actuall behaves.
Relativity says that measurements you make of stuff going on inside your own frame of reference (say, a car), which we’ll say is moving at a constant speed with respect to another frame of reference, are different than measurements of your system taken from within the other system. There are all kinds of equations that describe how these differences work. Spatial dimensions and the rate at which time passes changes, and these differences get pretty big near the speed of light. For example, someone standing on the ground measuring your car as is passes will find that it is a little bit shorter in the direction of motion than you if you take the same measurement (because your ruler is a little shorter, too). And in the time it takes for your watch to click one second, the guy on the ground measured just a smidgeon longer than a second. So, as said above, no matter what your speed you will always measure the speed of light (in a vacuum) as being the same. You will find that your measurement of the speed of the light coming out of your headlights is the same as the speed of light coming out of the red light you just ran.
(BTW there is a doppler effect, but shifting the frequency is not the same as changing the speed.)
By the same token, how can a boat sluicing through the water not produce waves in the front that travel at the boats speed PLUS the “normal” propagation speed of waves in water ? That doesn’t happen either. The medium through which the waves travel governs the speed of propagation.
The cannon example only works because the speeds are much less than light. And even then it’s only approximately correct. The actual velocity addition formula is w = (u + v)/(1 + uv/c[sup]2[/sup]). This is approx equal to u + v, when u and v are small compared to c. When u and v get large compared to c, the difference grows. If you have a cannon that shoots at c/2 and place it on a rocket moving at c/2, the projectile will not move at c, but rather at 4c/5.
Also note that if u or v is set equal to c, the addition formula gives c.
Ok, this makes sense now, thanks. If I’m sitting in the car, then the light seems to project forth from the headlights as usual. But if I’m outside the car, then it would appear that the light does not stream forth. However, I’m also experiencing time differently.
You got the right idea son but yo’ in a heap o’ trouble if you was goin’ c in that car o’ yours. We got speed limits around these parts.
If the car is going c-(1 meter per hour) then as an observer you would see the beam of light going at the speed of light, with the car slowly losing distance to the front of the light beam. If the car were going c, then you wouldn’t see any light emitting, but then again, the car would have contracted infinitely in the direction of motion and the driver would have experienced infinite time dilation. So let’s not go there.
its like a horizon… its not so weird… say you and your freind decide you want to touch the horizon… so you go out to a big feild and run at it. you run and run… and are always the same distance from it… and your freind… who is running twice as fast as you shockingly sees the horizon moveing away at exactly the same distance! even if you went in a bullet train you would see the horizon at the same distance from you.