Wednesday, August 25, 2010

Ask a Geek - Special Relativity, Part 2

Eek! Quick, quick--I must get in another blast of that sweet, sweet special relativity before bed.

I mentioned in my last geek-post that as a body starts moving faster (close to the speed of light), its mass increases. This is part of why humans are unlikely to ever personally experience some of the weirder effects caused by special relativity. To accelerate a body takes energy, and the amount of energy depends on the mass of the body. The larger the mass, the more energy it takes to speed it up.

And therein the problem, because if your mass increases with speed, then it takes ever more disproportionate amounts of energy to speed up even faster.

Theoretically, it would take an infinite amount of energy to speed a body with mass up to the speed of light. It takes obscene amounts of energy even to get close to that speed. With tiny particles, we can do it, but the cost of something like the Large Hadron Collider tells you it isn't easy, even then.

So how does light manage to travel at the speed of light?

First, I'll mention something that I plan to discuss more when I do my post on quantum mechanics: elementary particles can be thought of as either a wave or as a particle. In my discussion of special relativity so far, I've talked about light as a wave. Now I'll talk about it as a particle.

The smallest portion of light is a particle called a photon, and unlike many other particles we know of, the photon has no mass.

But wait--how can something with no mass even exist?

Short answer: because of an amazing loop-hole in the laws of physics.

A body with mass cannot be accelerated to the speed of light because that takes too much energy. The photon, however, has no mass so it can move at the speed of light. But something with no mass shouldn't be able to exist.

However! Remember how in the last geek-post I said that the faster you move, the more time slows down for you? What I didn't mention is that if you move at exactly the speed of light, time stops for you.

The reason the photon doesn't poof out of existence is because it doesn't experience time. It moves at the speed of light, and therefore it never ages. It can't stop existing because it can't undergo any sort of change.

You'll also remember from the last geek-post that I argued light can't appear to slow down or stop, or the changing electric and magnetic fields that create the wave would also stop and then the light would cease to exist.

Now we've got a completely different argument for that same thing. Light can't slow down or stop because if it did, then the photon would start to age and would immediately poof out of existence because it has no mass.

It's like something that isn't real but manages to exist because of a loop-hole. The universe is a strange and beautiful place, eh?
The last thing I'll talk about with regard to special relativity is the symmetry of it.

Say you're sitting on a train moving at close to the speed of light. You zip past someone who is standing still.

How is this different than if your train was standing still and the other person was the one zipping past?

The truth is that it's no different, and that leads to some mind-bending conclusions.

Remember how time slows down for a person who is moving? A person who is standing still will look at the person who is moving and think they are operating in slow motion.

However, the person who is moving will observe the rest of the universe (including the person standing still) to be moving in slow motion! The person in motion can argue that they're the one who is really standing still.

Special relativity is symmetric. If you are in motion, you will observe the world outside to be behaving as if it's in motion, not you.

This gives rise to the famous Twin Paradox. Consider what would happen if you sent one half of a set of twins (let's call her Rupinder) out on a rocket ship travelling close to the speed of light.

Rupinder's twin Mandeep is sitting on Earth. On the flight out, Mandeep will observe Rupinder to be acting and aging in slow motion. He will think he's growing older than his twin.

But Rupinder will also be observing Mandeep to be acting and aging in slow motion! She will think he is the one getting older!

There's no way for these two to tell who is in motion and who is standing still just by looking at the other twin or taking measurements. This leads to the question of who is really going to be older when Rupinder stops travelling and comes back to Earth. Thus, the "Twin Paradox".

There's actually no paradox. Mandeep is going to be older when Rupinder comes back.

You see, I haven't been very precise about stating when these odd predictions of special relativity are valid. It turns out they are only valid for people and objects travelling at constant speeds.

In order to come back to Earth, Rupinder has to decelerate, stop, then turn around and accelerate again. In other words, she has to stop moving at a constant speed.

When she does that, the universe gets a chance to bring her reality and Mandeep's reality back into sync. That happens again when Rupinder slows down and stops upon reaching Earth.

As long as she is travelling at a constant speed, then what she sees and what Mandeep sees are equivalent, and neither one of them can tell which of them is in motion and which is standing still (unless they let what the rest of the universe is doing influence their decision.) Acceleration and decelerate break that symmetry, however.

General relativity was Einstein's attempt to bring acceleration into the picture. Special relativity--which is what I've been talking about here--only applies in the special cases where acceleration doesn't occur or isn't important to the problem. Einstein came up with both theories, but general relativity is where the math really started to get ugly.

And so, that's where I'll stop talking. :-)


Again, have you any questions? Anything you would like clarified? I'd be happy to discuss this more in the comments!

Author website: J. J. DeBenedictis

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