Understanding Velocity & Relativity: A Physics-Fling

[Ultermarto]

Ever since, err, hmm. I'm not entirely sure when it happened, but recently I've been on a physics-fling, and I've been trying to get a better grip on the mathematical side of physics, towards the goal of eventually understanding relativity and quantum mechanics beyond the point of "Stuff slows down when it speeds up" or "The electron goes through both slits and interacts with itself!". Even though I excelled at maths back in secondary school, it was an awful school, so as of now my grips on areas like calculus are ... well, they never really told us what that was. So equations don't exactly sink in. (But earlier, I completely understood the W1/w2 = d2/d1 lever principle. That's a big deal for me.)

One thing I do understand is relative speeds, as in the classical ones. Right now my velocity relative to the ground beneath me is 0, but that ground is orbiting the sun pretty damn fast, and the sun is thought to be orbiting the center of the milky way even faster, and since I am included in all of these motions, I could be said to have any of their velocities, depending on what you're comparing me to. Meanwhile, the bits and pieces I read about relativity talk about the speed of light and how we can't exceed it (because if we ever reached it, for some reason, our mass would become infinite). But in what way am I not traveling very very fast, at least at something that compares to the speed of light, right now, as the Earth orbits the sun and galaxies are driven apart by space at, as I understand it, close to the speed of light? And then again, am I really traveling at any velocity, or is the universe just moving around me at speeds close to light? Ho do the laws of physics check on my movement through space, with no true frame of reference, and say "He's traveling at 1/2 the speed of light, better increase his mass and slow the passage of time for him"? How do scientists look at our civilizations here on Earth, decide that velocities here are 0, and that if we add 300,000,000 meters of delta-v weird stuff will start happening?

Or does the weird stuff only happen with respect to the people back on earth, whilst a theoretical asteroid planet zooming through the solar system at the same speed will see our spacecraft fly by in the expected way?

Or maybe it has something to do with light always hitting us at the same speed?

Please help me.

 

[Nugatory]

One thing I do understand is relative speeds, as in the classical ones. Right now my velocity relative to the ground beneath me is 0, but that ground is orbiting the sun pretty damn fast, and the sun is thought to be orbiting the center of the milky way even faster, and since I am included in all of these motions, I could be said to have any of their velocities, depending on what you're comparing me to.

Right you are... and accepting that might be the single hardest part of special relativity.

Meanwhile, the bits and pieces I read about relativity talk about the speed of light and how we can't exceed it[STRIKE] (because if we ever reached it, for some reason, our mass would become infinite)[/STRIKE]. But in what way am I not traveling very very fast, at least at something that compares to the speed of light, right now, as the Earth orbits the sun and galaxies are driven apart by space at, as I understand it, close to the speed of light?

Forget the struck-out part above; it's misleading enough to be unhelpful.

Instead, you have to mate your correct understanding that speed is relative with another somewhat counterintuitive fact: The speed of light is c for all observers regardless of their relative motion. For example, if you are moving at .5c relative to me, and I send a light signal in your direction of motion:
1) You will consider yourself to be at rest while I am moving in one direction at a speed of .5c relative to you and the light signal is moving in the other direction at a speed of c relative to you.
2) I will consider myself to be at rest while you are moving in one direction at a speed of .5c relative to me and the light signal is moving in the same direction at c.

For more information and the equations, you can google for "relativistic velocity addition".