The solar system is moving, is the Light of the sun moving faster than the theoretical speed of light?
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It's true that the speed of light is constant no matter what speed at which you or the source is moving. This is a fundamental postulate of relativity, and there is no explination. It's just accepted because our experiments indicate that it is true. You used the formula "lights speed + X = actual speed" this type of velocity addition is called "Galilean". It turns out that speeds don't actually add that way. Far out.
Where is the rest of the energy? Good question. The frequency of the light you observe from the sun DOES depend on how fast you and it are moving. The energy of each photon is given by E = hf, where f is the frequency of light.
Disclaimer: I don't study physics. I've read some Stephen Hawking. I'm not an expert, just a decently knowledgable layman.
I believe that the answer is the distortion of space at high velocity. For sake of making my calculations easy, let's say that the solar system is moving at exactly .5c (half the speed of light) with respect to you.
First, the local case. Earth is 8 light-seconds from the sun, from Earth's frame of reference. So, if something happens to the light of the sun - say, it flashes purple - the light reaches the Earth 8 seconds later. Someone on Mars (in the same frame of reference, more or less) would see the sun flash, and 8 seconds later, see the flash reflected off the earth. This is fine, because that person sees the sun and the Earth as being 8 light-seconds apart in space.
Now, let's go back to your frame of reference. If you see the sun flash, and 8 seconds later, you see the earth reflect the flash, that's a problem - because from your perspective, the earth is 16 light-seconds away from where the sun flashed! That would require the light to to travel at 2c - twice the speed of light. And that's impossible.
But, from your perspective, the Earth isn't 8 light-seconds away from the sun. Because they're moving at .5 c, they're half as far apart - space warps at very high speeds. So the earth doubles its distance from the sun before the light reaches it, but that's OK, because the earth was only 4 light-seconds away from the sun to begin with, in your frame of reference.
If this sounds counterintuitive - it is. If this sounds wrong - it might be. I'm no physicist. But, with my meager understanding of relativity, I think this is how our elegantly weird universe works.
no. It seems like it would because of relativity, but it is a special circumstance because the speed of light is actually "the universal speed limit." Not even light can travel faster than it. If it was lets say sound, then the sound waves would be moving at X speed plus the speed of sound, as would any other object. But just not light. We are not sure why this is the cutoff, but it makes sense mathematically. In the Lorentz transformation formula 1/sqrt(1-v^2/c^2) where sqrt is square root, v is a velocity something is traveling at, and c is the speed of light, and ^2 means squared. Normal objects will follow this and according to this transformation, time, space, and mass are all warped by this same factor. Such as if you were to say t'=t/sqrt(1-v^2/c^2) where t' is the time that passes for a stationary observer, and t is the time the traveling object experiences. If you plug in velocities, you can see that this is negligable unless you get velocities very very close(like 95%) to the speed of light, But anyway, the reason nothing, not even light can go faster than this, is that you plug in a number greater than light for v, then you will have a number greater then 1 once you divide, meaning 1 minus that number would give you a negative number under the square root, which is impossible. Therefore, nothing, not even light can travel at the speed of light. The reason timing may seem off for things as described by another answerer would have to do with the fact that length is also distorted by velocity by this same factor. In fact,it has been observed in certain tiny particles coming to the earth's surface. These particles have a certain lifespan before they become unstable and decay. They are also moving at a certain speed. (which is very fast; close to the speed of light.) You should simply be able to calculate v=d/t (velocity=distance/time) to find out how far they would travel. However, they somehow travel farther than that. When this calculated distance is put into that formula, we come up with the correct distance they actually travel!
Excellent question. Please hear me out. In reallity, light would be travelling faster than 299,792,458 M/S. Practically, it is not. Think of it this way. If you were in an airplane travelling 500 miles per hour, and threw a baseball up the aisle at 50 miles per hour, did you just throw a 550 mile per hour fast ball. No, but in reality, the total velocity of the ball was 550 MPH. The universe is like the airplane, and light like the ball. This is the difference between total velocity and sectional velocity. If you threw the ball backward in the plane at 50 mph, you actually threw the ball 450 mph forward, since the plane is travelling 500mph. If the plane was travelling 50 mph, your ball would still fly back the plane, but it's actual velocity would be zero. Somewhat complicated, but very interesting once you understand the principle behind it.
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