Monday, April 28, 2008

Einstein's twins explained (Edited)

A little over a month ago, I tried to figure out the twin paradox. I just couldn't wrap my brain around it - I kept coming to a different conclusion than Einstein, and no one seemed capable of telling me why I was wrong. I've done some reading since then, and I finally feel I get the concepts involved.
  • Here's the scenario, to make sure we're all on the same page. Start with two twins, Adam and Bob. Adam hops on a rocket ship and takes off a velocities approaching the speed of light. Bob stays home. After several years of streaming straight away, Adam reverses the rocket and comes back to earth. He finds that nearly twice as much time has occurred on earth in his absence. When he left they were both 20, but now Adam is 30 and Bob is 40.
What puzzled me was why Einstein would say that's how it works. To my layman's point of view, it seemed to be the opposite of what Relativity says. As I understood it, the earth was traveling relative to the rocket at the same rate that the rocket was traveling relative to the earth. As I imagined it, both would age the same rate, and picture time dilating around the other. "I'm normal, he's the weird one!" they would say, and the net result would be that no one would truly age differently thanks to the curvature of time-space.

I was wrong. But a search of the internet failed to explain how or why. The only explanation I could find was on wikipedia, but it was poorly written and involved math I couldn't really follow. It also failed to summarize what the math meant in any sort of useful real-world meaning. And then it name-dropped "blueshift" and "relativistic doppler effect" which really don't have anything non-tangential to do with the scenario. They even put in some triangular doppler-effect diagrams that actually amount to a red-shifted herring.

Having since opened an actual book, I now get it, and am somewhat amazed that there appears to be no resource on the net that explains it in simple terms. Several allude to it, but don't put the heart of it in the big bold print like I do below. So that no one else outside the hallowed halls of academia needs to go through the mind-wrenching relativity gymnastics and blisteringly dry reading that I have done these past couple weeks, here's the gist...
  • Special Relativity only applies to inertial frames of reference. It doesn't apply to frames of reference that are accelerating (or decelerating, if you care to distinguish them, which Physics doesn't) relative to themselves. Further, Relativity only applies to the "Laws of Physics" it doesn't bound "specific phenomena within the environment" such as the side effects or results generated by the physical laws.
Consider the difference between the laws that define how sound is transmitted, and the specifics of any one sound you've heard. Relativity applies to the laws of sound, but it doesn't guarantee that two people will hear the same sound or interpret the sound in the same way. Time is defined by physical laws, but the aging process is a result of time. Aging is more like a specific sound.
  • Further, acceleration can break the symmetry between frames of reference. You see, two things distort time-space. That's speed, and gravity. Travel at velocities approaching the speed of light, and time and space dilate. Get close enough to something big, and time and space dilate. But gravity (aka G-Force) can also occur because of changes in velocity relative to your own motion - and you don't have to get anywhere near the speed of light to measure that force.
That's still too abstract and not quite down-to-earth enough. So, rather than sticking Adam in a rocketship, let's put him in a car.

Rather than being an astronaut, Adam's just a guy driving round town. To make it interesting, let's say he's hoping to find good deals on crystal vases at antique stores. He's found a couple, and now has a few vases sitting in his passenger-side seat. This will matter later.

Meanwhile, unknown to him, his twin brother (separated at birth, I guess) Bob owns an antique store across town. As Adam drives towards Bob's store, Adam is moving relative to Bob and Bob is moving relative to Adam, so time dilates equally, inversely, and relatively. So far, so good, and that's where I was getting stuck.

Adam's driving around, when, out of the corner of his eye, he spots an antique store he'd never noticed before. He slams on the breaks so as to not just speed past the store. Now the two brothers are no longer moving relative to each other. Both were moving. Both are now not moving. But only one decelerated. Relative to his own former speed, Adam has slowed down. Bob has not.

We even have evidence to back it up. Adam's car now has shattered remains of crystal vases in it, broken from the lurch and impact caused by sudden deceleration. The vases in Bob's shop, however, remain intact and positioned just as they were (relative to Bob) before Adam hit the breaks. Only Adam experienced that G-force (gravity) caused by his sudden stop.

And that gravity does something other than just break crystal vases - it dilates time. So, there's an extra time-distortion that only Adam has experienced. If Adam's acceleration were fast enough, he'd age far more slowly than Bob. It's weird. If I'm understanding it all correctly, moving near-light speeds stretches or dilates time, and accelerating or decelerating contract it. Both A & B get time-stretched by their relative speeds, but only Adam get time-squished by rocketing and braking.

In other words, the Twin Paradox is not caused by moving at speeds near the speed of light. It's caused by accelerating quickly. This is fundamentally different than how it's represented in TV, Movies and Novels. While there's a good dozen places on the web that state the paradox has something to do with shifting inertial frames of reference, none I've seen do a decent job of pointing out the crux of the matter, which is revealed in those oversized letters at the start of this paragraph.

Now, in a car, the accelerations not fast enough, and our technology's not precise enough, to really generate a measurable difference. But experiments have been done using long flights of supersonic planes to prove this all really works. Two clocks were synchronized, and one was put on a plane. At the end of a long and fast flight the clock on the plane was a running a couple nanoseconds fast compared to the one that was left on the ground.
  • Same thing happens to clocks at different elevations, because of the diminishing of the force of the earths gravity field over distance. If you synchronize two atomic clocks, and put one at sea level and the other in a penthouse of a skyscraper in Denver, they'll slowly get out of synch because one is closer than the other to the source of gravity.
Now then, as I said I'm a layman, with no real Science classes beyond high school. So, if anyone spots flaws in what I've written above, please chime in.

All this reading brought up some other questions in my mind, and I'm not sure I'll ever understand the math behind it well enough to answer them. Here's five thoughts I'm curious about:
  1. To what extent does the rate of acceleration influence this time-squishing? How much impact can Adam have on his aging by gunning the engines vs slowly easing into it?
  2. What about if neither were in earth's gravity well? What if they took a ship together to the edge of the universe, where gravitic forces where minimal, and then their ship split apart like Voltron and the halves accelerated into independent tours of the circumference of the universe? How much impact would that have on the equation?
  3. Let's say Bob slowly accelerates to 70% of light speed, feeling minimal g-force, and Adam guns it to get maximum survivable acceleration, and a top speed of 95% of light. What does this do to their ages? How do they compare to their previously-unmentioned triplet, Charlie, back on earth? Mass-related gravity, acceleration-related G-Force, both seem to trump c-fractional velocity, but does real gravity trump the pseudo-force?
  4. Why the heck do they call G-Force a pseudo-force? I'm more than a little nervous that there's some scientific treatise that refutes and redefines all this, and it just has yet to be read by myself or the relevant wikipedia editors.
  5. Do fighter pilots really live fast, die young, and leave a good looking corpse?

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