[Coda]

Originally Posted by Potironette

(I was confused by "Actually, it's that higher frequencies make it less likely to have a collision, and higher frequencies mean lower wavelengths." Isn't blue light a higher frequency than red light..?)

I think I actually meant to say "more likely" there and I messed up during one of my edits to the text.

Another way to think about it is that shorter wavelengths means there's less of a gap between the crests of the waves, so there's a greater probability that one of those crests will intersect with the target.

But why is it that sometimes the sky is pink or orange? Surely both the sunlight and the nitrogen in the sky stay the same?

Nope, there's more sky between you and the sun as the sun approaches the horizon -- think about two concentric circles and a line passing between a point on the inner circle and a distant point. That means the blue light is getting scattered even further, leaving the redder shades of light to pass through to where you can see them.

At night is it dark blue just because there's less light?

Yup, got it in one.

Does the sun having more energy cause it to have lots of blue wavelengths? Similar to how the blue bit of the fire is hotter--is that even related?

Bingo, got it again! This goes back to the discussion of blackbody radiation. Objects that emit light because of how hot they are follow a very predictable pattern.

Why does Newton's first law require a coordinate system to be constructed? And what does "relative rest" mean?

The first law is inertia, that is, an object won't change velocities unless a force acts upon it. A consequence of this fact is that -- in the absence of external forces -- you can pick any object you want, call it the center of your universe, define its velocity as zero, and judge the velocity of everything else relative to it.

The classic example is riding in a car. From your perspective inside the car, the seat, the steering wheel, the radio knobs, and the doors aren't moving -- they have a velocity of zero. You look out the window, and everything is moving backwards at 90mph. From the perspective of the cop on the side of the road, the street has a velocity of zero, and you're breaking the law. Newton's first law says that both of these descriptions are equally valid.

Why does it matter that the photon doesn't rest? Or does it mean that for some reason the first law requires there to be a moving photon to be compared to a not moving photon--which doesn't happen? And since photons are always moving at c...waves of light are basically how the photons are moving?

The second guess is closer.

If you pass a slowpoke going 70, then you, the slowpoke, and the cop agree that there's a 20mph difference in your velocities. (The cop still thinks you're breaking the law.)

The cop has a radar gun. After all, that's how he knows you're going 90mph faster than he is, and how he knows the slowpoke is going 70mph faster than he is. If he took off in his cruiser and got up to 100mph so he could catch up with you, the radar gun would say that you were going -10mph, and the slowpoke was going -30mph.

So far, so good. But here's where things get weird...

No matter who's measuring it, EVERYONE -- you, the slowpoke, the cop -- agrees that the radar beam coming out of that gun is going at the speed of light, c.

Not c - 70. Not c - 90. Just c. All the time. Always.

Even the alien spacecraft zipping by the planet at 0.3c sees the beam going c, not 0.7c. (The cop isn't going to try to write the alien a ticket. It gets off with a warning.)

So because photons always travel at c no matter how you look at them, you can't measure the velocity of things relative to the photon. Oh, sure, you can try, and you can get a number, and that number might even seem reasonable -- if the alien were in a drag race with a laser beam, the judge at the finish line would say that the laser beam was going 0.7c faster. But unlike you and the slowpoke, where everyone agreed you were going 20mph faster, the alien thinks the laser is going 1.0c faster than it.

The space police don't write speeding tickets; the interstellar speed limit is c, and you can't break it. On the other hand, drag racing a laser beam is reckless, so the cop comes up to the race at 0.5c. He thinks he's going roughly 0.2c faster than the alien (not EXACTLY 0.2c, but that's a lecture for another lesson), and he thinks the laser is going 1.0c faster than him, so the cop thinks that the laser is outrunning the alien by 1.2c. The cop doesn't have to write a speeding ticket for the laser, though, for the same reason it's not illegal to pass someone going 140mph relative to them on the highway.

So the judge, the alien, and the space cop disagree on how much faster the laser is than the alien.

That's why Newton's first law breaks down at relativistic speeds: when you're going that fast, then things look like they're going varying speeds relative to each other even if there AREN'T forces acting on them.