Saturday, July 23, 2011

The Five Most Mind-Blowing Implications of Special Relativity

5. Loss of Absolute Space

In the olden days, before the earth cooled, people tended to believe in absolute space. If you drove for fifty miles, you had driven fifty miles, and that was it. You didn’t have to worry about what you were driving from or to, only that you had traveled a fixed distance. Natural, right?

The problem is, relativity means that everything is relative. You may be driving for 20 miles by your odometer, but the way you know that you’re moving is because you’re passing objects (pedestrians, trees, road-rage-crazed bastards in sports cars). Take away your frame of reference, put your car in deep space away from any gravity wells or other physical objects, and you’ll have no way to tell whether you’re moving*.

It gets better. Let’s say you find another car out in the abyss, and let’s also say it’s moving at 150 mph. To you, the other car is the one that’s moving, and you are stationary. But to the other driver, your car is hurtling along at 150 mph, and their car is floating innocently in space. Who’s right?

 Special relativity says that you’re both equally justified in claiming that the other car is moving, and what’s more, there’s no possible way to tell (without one of you turning on your engine and introducing your own acceleration) who’s right. The question of who’s right has no answer. In other words, you’re not measuring your velocity by some constant of space; you’re measuring it by your reference points, which are entirely relative.
Thanks for the illustration, Cousin Jerry!
4. Time Isn’t Absolute Either

Take the cars that I mentioned before. If you add huge clocks on top of them (I’m shamelessly borrowing from Brian Greene’s The Elegant Universe here, but only because there’s not really another way to illustrate this), both you and the other driver will observe your clock ticking slower than their own. The faster the relative motion between the two observers, the more the clock will appear to slow down. Again, there’s no way of telling which is which (in part because it’s hard to establish that events are taking place simultaneously) because you can both make the same claim to each other, and both be essentially correct.

This same effect happens in a different way, when you’re close to a large body and caught in its gravity well. If your car was orbiting the Earth and the other car was far away from the Earth, your clock would run slower than theirs because of the time-dilating effect of gravity. This time, because you’re introducing the outside force of gravity, it acts as a frame of reference; thus, both of you would agree that your clock is running slower than Driver 2’s.

3. The Faster It’s Going, The Shorter It Gets

I’ll save the buildup for this one and just say: the faster your vehicle is moving, the shorter it will appear to an observer perpendicular to the vehicle’s direction of motion. The vehicle will contract in the direction that it’s moving, in an effect called Lorentz contraction. The driver won’t notice; from her point of view, the vehicle will have the same dimensions it had previously. But to an observer, the vehicle will get marginally shorter as it increases speed.

Now, when I say marginally, I mean incredibly small; until you get up to half the speed of light, the difference is an infinitesimal fraction of an inch. But it occurs with every vehicle that moves at speed, relative to an observer. At 99% of the speed of light (hat tip, Wikipedia), an observer would see the vehicle as having almost no length at all.

2. Space and Time are One

This means, by the way, that the difference between “farther” and “further” is totally irrelevant, since they’re referring to the same thing. You may brandish this information in front of your English professors the next time they correct you. There’s a load of cool shit involving general relativity (which implies that spacetime is curved) and quantum physics, which holds that supposedly smooth spacetime is actually wildly chaotic on insanely tiny scales, but… oh, all right.

In general relativity, gravity is a consequence of spacetime. A massive body will create a sort of dip in spacetime, which means that lighter-mass objects will fall into the “dip” and orbit around the edges. It’s analogous to one of those things they have in airports and museums, where you put the coin in the top and it spirals around to the bottom, except that it takes place in a sphere around the massive body instead of just a funnel. Don’t ask me how to visualize it, I have no idea.
Like this, but we're sinking into the fabric in every direction simultaneously.
1. e = mc^2

Mass and energy are equivalent and can be changed back and forth; mass can become energy and vice versa. That sunlight hitting the ground outside could become a solid block of coal under the right energies, and we (people) could evaporate into electromagnetic radiation under the right energies. If that doesn’t blow your mind, nothing will. And this is a totally proven concept; it is applied every day in nuclear reactors, as mass (in the form of U-235) is changed into energy that powers our cities. I find this absolutely unbelievable.

*Acceleration changes the equation, but in a situation that's not influenced by an outside force, you'll have no way to tell. Also, windowless box: if you're inside of one, you'll have no way to tell whether the acceleration you feel is from your motion or from being near a gravitationally attractive body. Acceleration and gravity feel exactly the same.


alexandros trivyzas said...

Nice summary of it all!
Thanks for the compilation!

Glenn McMann said...

2. Space and Time are One
Actually the best way to think of this isn't the whole fabric or trampoline thing creating a funnel. A more accurate representation would be to make a 3D grid and the mass (planet, star, etc) warps this 3D grid towards itself at all points with extra bodies (Moons for example) reside just outside the bent threshold so that both are pulling on the same points of the 3D grid which causes stationary (or most ways stationary when considering our moon is moving further away from us ever so slowly) orbit.

Hope that helps the details on that point.

Andy said...

Thanks for the clarification, and for reading! If I am compelled to ever make a picture of a large mass's effect on gravity, I will remember your comment.

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