Lighthouse,
I think you're starting to understand what we are conveying. Some of this is redundant for you, I'm sure, I just want to reinforce what we are trying to say. It should only take you a few seconds to skim over.
Stepping back away from the car analogies, imagine a space ship floating in space. There are no roads. There are no signs. There is only your space ship and yourself (and a stationary observer we will encounter in a moment). Now, you turn on your boosters and accelerate to 50% of the speed of light.
As soon as you pass the stationary observer, he fires a large gun right along side of you, which fires a projectile at 50% of the speed of light. As you look out your rocket ship window, you see the projectile traveling along side you. How fast is the projectile traveling
relative to you? Recall that you're traveling at 50% the speed of light. We know that the projectile is traveling at 50% the speed of light as well, so
relative to you the projectile is stationary. In other words, if we subtract the projectile's velocity from your velocity, we are left with 0 (0.5c - 0.5c = 0). If you were to look out your window, you would see the projectile appearing to hover stationary beside you because you're both traveling the same speed. Relative to a stationary observer, the projectile is traveling at 50% the speed of light, but
relative to you, it's velocity is 0. Makes sense, right?
That is precisely
not how light behaves. Imagine the same scenario with a laser instead of a gun. As you pass a stationary observer, he shines a laser right beside you. How fast is the light beam relative to you? Conventional wisdom says that light's velocity - your velocity = 50%, thus the light's velocity would be about 50% faster than your speed. But that's not we've discovered. We've discovered that if you were to look out the window, light would appear to pass you as if you weren't even moving! It passes by you at the full speed of light
faster than you.
In simple mathematical terms: (speed of a photons passing you) - (your speed)
always equals the speed of light; i.e. light always behaves as if your velocity is stationary.
The implications of this are phenomenal. It means that the stationary observer and the moving observer
will not agree on how long it takes light to reach a certain distance -- and this is the basis for time dilation.
This strange, counter-intuitive property of light has been verified over and over experimentally.
Lighthouse said:
If something was moving at 100,000,000 m/s right alongside a light beam that was traveling at 300,000,000 m/s the light would still be traveling at 300,000,000 m/s, but why would it not be traveling 200,000,000 m/s faster than the thing right next to it? How is it that the light would still travel at 300,000,000 m/s faster than the other thing?
Bingo. Why does it do that? I don't know why. I don't know that anyone can tell you why it behaves this way. All that we know is that it
does behave that way.
Lighthouse said:
The only reason a good imagination would be necessary is if you need to imagine something. And you only need to imagine something if it isn't real.
A good imagination is necessary to picture anything our brains and brains are not equipped to conceptualize. It's easy to become conceited and think that those things we encounter in our every day life
are all there is. But our place in the universal scale is just a tiny point on a vast continuum. We can picture things like the earth, trees, cars, people, ants, and gravity. But there exists a whole other world of things and laws at an atomic scale -- atoms, electrons, quarks, neutrinos, brownian motion, wave-particle duality, etc., that the human mind can never truly conceptualize -- because we never encountered them directly. We exist at a different scale. Likewise, there exist a whole universe of things bigger than we can ever picture. The size of galaxies, the number of stars, the distances between galaxies, black holes, cosmic expansion, pulsars, etc. Our brains are ill-equipped to deal with these phenomena, and so a good imagination is necessary to conceptualize these things. That doesn't mean they don't exist.