How do I do the 'video-in-video' effect?

Can someone explain to me how the doppler effect can have any effect on light, considering special relativity?

• This has been bugging me for quite some time, probably since I first read that scientists think the universe is expanding faster and faster because the light we see from galaxies far away, has a longer wavelength than we expect. This is fine, if you blame it on the doppler effect, but not (in my mind anyway) if you consider special relativity. I haven't heard anyone address this issue, but if a planet is moving away from us at great speed, the light would reach us far BELOW the speed of light, and it would look red-ish, right? The other way around, it would reach us much faster than the speed of light (if we are closing in on the other planet), and it will look blue-ish, so to speak. The thing is, though, if the planet was moving towards us at great speed, we would have to experience time slower, so that the light won't reach us at 400 000 km/s, but 299 000, as it should (approximately the speed of light, if I remember correctly). To visualize this, if we are experiencing time slower when the light reach us, it would have a slower frequency, right? Imagine a ball bouncing. Now imagine we slow down time, it would bounce slower, (lower frequency). Therefore, the planet moving towards us would look red-ish, contrary (quite opposite in fact) to what we would expect from the doppler effect. If I haven't taken any wrong turns here, I think this little thought experiment clarifies why I believe the red-ish hue *proves* that the gravity of the "universe" is in fact slowing the expansion down, and not accelerating it. But maybe I'm stretching it too far, and special relativity actually cancels any doppler effect out. But I am never the less curious to why this is never addressed. Oh, and by the way, I'm sixteen. So feel free to shoot this down, just please explain why I'm wrong.

• Answer:

  This is a great question for only being 16. The concept of special relativity is very difficult to understand but the fundamental principle that Einstein states is that the speed of light is always the same for every observer independent of speed. I know that is difficult to grasp and I completely understand your question. However that only scratches the surface of relativity. Light travels at 3x10^8 m/s. The only way this can make sense for all observers at different speeds is if the concept of distance and time are not constants. So to answer your question, the doppler effect does not apply to light since it's speed is always constant. So without getting too technical, if a planet was traveling toward you, simple newton laws would tell you that the light would reach your eyes faster than the speed of light but that's not true; it still hits you at 3X10^8 m/s. To make things simple let assume the planet is exactly 300,000,000 meters away from your perspective (obviously not possible, but it's simple). You will see its light in 1 second. However, somebody on that planet would see it differently. They would think at that same moment, that the distance is less and also that your concept of time is too fast. So in result, they would also see light leaving their planet at the same speed of light but hitting the earth sooner because the distance is shorter and their concept of time is slower. I probably confused you, but relativity is not easy to explain.