New Flashlights Now At TWICE the Speed of Light!

[LostAngeles]

This came up amongst some of us students before our Calculus II class started and unfortunately, none our physics is quite up to snuff on this.

You've got two particles being launched at each other in a particle accelorator. When they pass each other, by the theory of relativity, would the other particle appear to be going faster than the speed of light to the first?

Likewise, if you had two flashlights end-to-end and shone them both, then would the resulting photons percieve each other as going at twice the speed of light?

We ended up swirling around the main points of, "It makes sense that they would, but they can't go faster than the speed of light," "Yes, but this is quantum physics and logic doesn't quite work the same here," and, "Are we even thinking of this right?"

[Ziggurat]

Originally posted by LostAngeles
This came up amongst some of us students before our Calculus II class started and unfortunately, none our physics is quite up to snuff on this.

You've got two particles being launched at each other in a particle accelorator. When they pass each other, by the theory of relativity, would the other particle appear to be going faster than the speed of light to the first?

Likewise, if you had two flashlights end-to-end and shone them both, then would the resulting photons percieve each other as going at twice the speed of light?

We ended up swirling around the main points of, "It makes sense that they would, but they can't go faster than the speed of light," "Yes, but this is quantum physics and logic doesn't quite work the same here," and, "Are we even thinking of this right?"

No, they don't approach each other faster than c in their reference frame, and no, this has nothing to do with quantum effects. The problem is that you're thinking in Galilean terms: that is, when you change coordinate systems to a moving reference frame, velocities just add. This makes a lot of sense, and it seems to match our everyday experience. The only problem is that it doesn't describe the real world. Velocities don't simply add. At low speeds, the difference is unnoticeable, but near c, it's VERY important. I'm in a rush so I can't post more details, but basically, you're correct that relativity doesn't allow for faster than c motion, but you're missing WHY that's the case, and how you go about figuring out how fast the particles in your accelerator would see each other approach.

[roger]

No, you are not! :)

First, it is not quantum physics that applies in this domain, but relativity.

Second, the speed of light is absolute. You cannot add, say 0.75 SOL + 0.75 SOL and get 1.5 SOL. The speed of light is absolute in all reference frames.

Let's explain that in simple terms. Take a flashlight, and point it at you while you are standing still. The photons are coming at you at the speed of light. Now, start walking towards the flashlight. They are still coming at you at the SOL. Now run. Still the SOL. Get yourself up to 0.5 SOL. They are still coming at you at SOL.

Yes, this is not intuitive, but it is how the universe works.

And this is where you get some whacky, wild results. You've probably heard about time slowing down when you travel the speed of light, or of things looking distorted? Well, the easy way to explain this is that for the speed of light to measure the same no matter your speed, something 'has to give'. Time actually slows down at high relative speeds, so you end up measuring the photons moving at the speed of light.

Do you see? Intuition tells us that time is the constant, and that the speeds should vary, but what really happens is that the speed is constant, and time varies. we don't experience this in daily life because we aren't moving at relativistic speeds.

Note: real physicists will scoff at the looseness and inaccuracies above, but the idea is to give you a flavor of what is going on.

Einstein's book "Relativity" is a very gentle, yet through introduction to all this. all you need is basic algebra to understand the book, and there isn't much of that. It's mostly reasoning, thought experiments, etc. It's one of the best books of the 20th century, in my opinion. Accessible to high school students, yet utterly changes our understanding of the world.

[Dilb]

One of the best explanations of a relativity paradox that I've read is this puzzle (http://www.greylabyrinth.com/puzzles/puzzle.php?puzzle_id=puzzle181). It's a very nice, easy to visualize explanation of why having a constant speed of light means that information must be limited to the speed of light, or paradoxes occur, and how simultaneous events in one reference aren't simultaneous in other frames.

For all the fancy (actually really simple) math, and something that actually relates to the original problem, the second image here (http://landau1.phys.virginia.edu/classes/109/lectures/srelwhat.html) explains why time dilation occurs, assuming you accept the speed of light as constant.

[Matabiri]

Originally posted by Dilb
One of the best explanations of a relativity paradox that I've read is this puzzle (http://www.greylabyrinth.com/puzzles/puzzle.php?puzzle_id=puzzle181).

These videos (http://www.anu.edu.au/Physics/Searle/) are also rather funky.