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Relativity – Introduction

March 20, 2012

Physicists don’t say things like “Polonius wasn’t a caricature of Lord Burghley.” They are protected from the more egregious blunders by skeptical experimenters who test all the theories. Effectively, physicists get to “look in the back of the book,” or, if you like, they get to “ask God what the answer is.”

So it is probably actually true that if you put mom on a spaceship and send her off at just under the speed of light, when she gets back, she’ll have aged only a few years while decades will have passed on Earth. You might wind up older than your mom! This particular experiment hasn’t been tried (yet), but physicists have good reasons for saying they know what would happen. I wouldn’t bet against them. Where they go wrong is in claiming that we understand it. We don’t. Even Einstein didn’t understand it.

In 2000 words or less, you can catch right up with Einstein. Ready? Set. Go!

Throwing Things in a Speed-Limited Universe

Speeds add. Suppose you are standing in the back of a pickup truck going at 20 mph and you see a street sign 100 feet in front of the truck. If you can throw a rock at the modest speed of 15 mph and if you throw it forward while the truck is moving, the rock will be going at 35 mph.  It will make a satisfying clang when it hits the street sign. Or imagine you are traveling at 80 mph in the truck and you “gently” toss the rock out of the truck – if it hits a street sign, it will do a lot of damage because it still has the 80 mph from the truck.

So don’t be tossing objects out of speeding pickups, okay? Glad we could clear that up.

Let’s switch to an airplane. If you are flying in an airplane at 599 mph and walk briskly (say, at 4 mph) toward the front of the plane, you will be going at 603 mph. If you throw a baseball at 50 mph toward the front of the plane, it will be a blistering 649 mph fastball. If you shoot a B.B. forward at 599 mph, it’s actual speed will be 1198 mph.

We don’t need Einstein yet. Sure, people on the plane say the baseball goes 50 mph and people on the ground say it goes 649 mph, but this minor difference in perspective is not relativity. Everyone agrees on how much time it takes the baseball to hit the wall (a second or so) and that’s all that matters to physicists.

But what if there’s a universal speed limit? There’s no obvious reason for any limit on speed, so you may need to eat some hallucinogenic mushrooms before you can accept this idea. (Having a Ph.D. in physics doesn’t make the idea seem any less crazy to me – pass the ‘shrooms please.) Okay, imagine that nothing in the universe can ever go faster than 600 mph no matter what. Now if you fly on a plane going 599 mph, you can’t walk toward the front of the plane at 4 mph because that would break the speed limit. Obviously, this is going to cause some problems.

In this speed-limited universe, weird things happen. The B.B. is absolutely not allowed to go anywhere near 1198 mph. The best it can manage is a speed just under 600 mph. But even rounded up to 600 mph, the B.B. bizarrely creeps toward the front of the plane at 1 lousy little mph. That is, the speed of the B.B. relative to the plane is only 1 mph; even though it was shot out of a gun, it takes more than a minute to travel across a 100-foot airplane cabin.

All three of our speeds must fit into the narrow space between 599 and 600 mph. The baseball is now a very special kind of pitch we might call a superslowball; it reaches the front of the cabin more than seven minutes after being thrown. And the person trying to walk at 4 mph gives new meaning to the idea of a leisurely stroll: he doesn’t get to the forward lavatory for almost an hour and a half.

But – and now it gets even stranger – since everything on the plane slows down to obey the speed limit, including people’s thoughts, no one notices anything amiss. People on the plane say, “We shot a B.B. into the front wall and played catch and walked around and everything seemed fine.” But then they get a bit of a shock. Their transatlantic flight that was supposed to require 6 hours of cruising is mind-blowingly over in 20 minutes: “We’ll be landing now,” says the pilot. “What’s going on?” say the passengers. “We can’t be there yet!”

But they are. They’ve traveled across the Atlantic Ocean in 20 minutes (for them) and arrived in Europe 6 hours later right on schedule. One person wearing a heart monitor confirms that his heart only beat 1200 times during the flight. The speed limit was never broken by the plane or by any object moving on board the plane, BUT they somehow covered a distance of almost 3600 miles in 20 minutes (on their watches). A little girl who was on the plane says, “OMG, the ocean must’ve shrunk while we were on the plane and then expanded when we landed, WOW!”

(Years later, when the little girl gets a degree in physics, she learns that this phenomenon is called “length contraction” and that it goes hand in hand with “time dilation,” but the phrase, “expanded when we landed,” still trips off her tongue like a song when she is hired by the airline to help bring passengers “up to speed” on the experience of flying close to the universal limit.)

That’s Einstein’s theory of relativity. There’s nothing fancy, nothing difficult to understand: if there’s a universal speed limit, everything on a plane traveling close to the limit has to move slowly to avoid going “too fast.” That’s all there is to the theory from a conceptual standpoint. No one knows how there can be a speed limit to the universe. All we can say, and all Einstein said, is that there is apparently a speed limit whether we like it or not.

In the paper Einstein wrote while his boss at the patent office wasn’t looking, he figured out the mathematical details of how his hypothetical speed limit would have to work. Basically no matter what speed you add to 599 mph, you have to get a speed at or below 600 mph. So 599 + 4 equals 599 and a fraction; 599 + 50 equals 599 and a bigger fraction; 599 + 599 equals almost 600; and 599 + 600 equals exactly 600. Pretty crazy, but there is math that will do that and it’s no fancier than ninth grade algebra. If you are Einstein and if you don’t care about the entire physics establishment and if you have nothing to lose and if you are willing to assume there is a speed limit, then you figure out the math of this new universe, send your paper to the physics journal, and get back to work before the boss catches you.

Of course, Einstein used the speed of light as the speed limit rather than 600 mph. So on a ship traveling at the speed of light minus one mile per hour, a laser mounted on the tail of the ship may be fired forward, but the beam goes at the speed of light and no faster. Since the beam travels only 1 mph faster than the ship, it creeps toward the front of the ship at a decidedly unhurried pace. If the ship is a mile long, it takes an hour for the laser beam to reach the front of the ship. But a solid hour on the one hand is virtually instantaneous on the other hand. On the ship, the laser beam shoots to the front and out into space at the speed of light as all good laser beams should. No mere illusion, this apparent contradiction could exist, Einstein reasoned, only if he was willing to give up everything he thought he knew about space and time.

So he did. He was like that. Lasers and B.B.’s and baseballs, walking and heartbeats and even thoughts – and time itself if there is such a thing – must go slow or there can be no speed limit. The operation of any clock – whether it’s one that goes tick-tock or a clock based on radioactive decay or even a ball bouncing once per second – is affected in exactly the same way. By applying a mathematical correction to all measurements of time and to all motion, Einstein was able to “explain” what would happen on a spaceship. He did not tell us how time could slow down or even clear up what this thing called time was exactly beyond saying it is what a clock measures. He wasn’t keeping secrets; he simply didn’t know. Don’t be mad.

A Crazy Idea Turns 100

More than a century ago now some patent clerk no one had ever heard of had a mathematically consistent theory about a speed-limited universe. Big deal. The journal editor who published Einstein’s paper figured (quite reasonably) that his theory was almost certainly wrong. The editor let the paper through anyway because even a wrong but carefully-constructed theory is an interesting thing for physicists to kick around. Nowadays, interesting ideas take much longer to propagate in the physics community partly because journal editors are far, far more conservative. But this was 1905.

Seventeen years later, when Einstein received a Nobel Prize, the committee still couldn’t bring itself to mention relativity because there was a lingering thought that the theory might be as crazy as it sounded: publishing a paper that may be wrong is one thing, awarding a Nobel Prize quite another. The Nobel committee’s caution was neither surprising nor excessive. Once particle accelerators were invented however, relativity could be tested and even the most skeptical of the skeptics became convinced. Today, most physicists say we understand it all perfectly well; the implication is that there is no mystery. The scientists are kidding themselves, mistaking impressive experimental evidence for real understanding.

The most obvious way to test relativity is to try to make a B.B. go faster than the speed of light. B.B’s are kind of big so we have to settle for electrons. At first, electrons behave just like cars – the more gas you give them, the faster they go. But then . . .  you push the electron more and more and it looks at you and says, “that’ll be fine, thanks.” At 99.99% of the speed of light, you angrily triple the amount of energy you are putting in, dimming the lights of your entire city – and you get another 9 plus a lot of irate phone calls. You can (and we do) triple the energy input again and again and again – all you get are more 9’s, just about one more each time you triple the energy exactly as Einstein predicted.

But wait. If we go back to the plane example, we see that the passengers can shoot a B.B. into the front wall or throw a baseball hard into the front wall of the cabin thereby causing substantial damage to the wall. But the B.B. and baseball actually approach the wall very slowly which means they should not damage the wall. Aha! Einstein must be wrong because the  the damage is there and is undeniable. How are the physicists going to explain that one? Gotcha!

Believe it or not, they have an answer. At speeds close to the speed limit of the universe, objects get heavier. That’s right, they magically acquire more mass. The B.B. and the baseball did all that damage because they were extra heavy. Einstein’s equations say an electron traveling at 99.9999% of the speed of light has 700 times more mass than usual. According to Einstein, when you crash together two relativistic electrons, you should get a shower of hundreds of particles big, medium, and small.

Right. Sure. You collide two marbles and get showered by bowling balls. Total nonsense . . .

Of course, it happens just as Einstein predicted. The particle showers are indeed spectacular. In fact, all of the trillions of heavy and light, exotic and ordinary, stable and unstable, expected and unexpected particles created in collisions at accelerators every day just appear out of thin air – energy is magically turned into matter according to a prediction made before particle accelerators were even imagined.

Physicists next tried speeding up unstable (radioactive) particles to see if their internal “clocks” would go in slow motion. We don’t know how unstable particles decide when to decay into other particles but they do decay on a schedule and that schedule is slowed down exactly as Einstein predicts. Same goes for clocks on airplanes. Put a super-accurate clock on an airplane, fly it around the world, and it comes back behind by the number of nanoseconds predicted by relativity. Clocks on GPS satellites are thrown off by thousands of nanoseconds per day due to relativity. But even a 100 nanosecond error would be unacceptable (here, “unacceptable” means the following: your passenger jet coming in for a landing misses the runway). But don’t worry, the the GPS are routinely adjusted for relativistic effects.

Do You Believe in Psychics?

Imagine if someone who claimed to be psychic put a prediction in a sealed envelope and wrote “open at 2:15 pm tomorrow” on it and handed it to you. At 2 pm the next day, you have finished shopping at your regular grocery store, but on the way home realize you forgot to buy Pop-Tarts, so you stop at the Ultimart where you buy the all important pastries and, while counting your change, you bump into a tall, thin man which causes you to drop a 1958 penny, a 1963 nickel, and a 1967 quarter heads up on the floor. You happen to notice the three dates when you pick up your change. You then open the sealed envelope and it says, “At 2:10 pm tomorrow you will go to the Ultimart to buy Pop-Tarts where you will bump into a tall, thin man . . . blah, blah, blah, . . . and a 1967 quarter.” You are amazed but remain skeptical. Over the next few months, the psychic provides 10 more accurate, detailed predictions. Then he tells you, the person who doesn’t believe in psychics, to go buy a lottery ticket at the Ultimart. Guess what? Now you believe in psychics. He may be wrong about the lottery ticket, but his previous predictions have been so impressive that nothing is going to come between you and your destiny. You’re grabbing your car keys before the guy even finishes talking . . .

We haven’t tried it with a person yet so we don’t know for certain that you can actually effectively travel into the future (there’s no going back) by traveling at relativistic speeds, turning around, and coming home. Physicists believe it simply because all of the testable predictions have been both incredibly detailed and repeatedly confirmed. These same scientists are dying to find deviations from relativity – no one’s going to win a Nobel Prize just for confirming the theory – but so far no dice (the superluminal neutrinos recently seen turned out to be a loose wire).

Someday, someone will actually climb into a ship and travel at nearly the speed of light for 20 years of our time, reach a star about 20 light years from here, turn around, and come home, taking another 20 years for the return trip. If the physicists are correct, this person will, while on the ship, experience life as usual except that the star that seemed to be 20 light years away when she started the trip from Earth, will, as soon has the ship is up to speed, seem to be only a couple of light years away. The traveler will arrive at this “close” star in only 2 years or so of her time, slow down, stop, and see Earth 20 light years away. She will marvel at how she managed to travel 20 light years in only 2 years.

When she gets back into her ship and gets back up to high speed, the return-trip distance will again appear to be only 2 light years. The traveler will arrive on Earth having aged 4 years plus a bit more for the speeding up and slowing down parts of the trip; meanwhile, 40 years will have passed on Earth.

Would this really happen? You know everything you need to know to form an opinion. And your opinion is as good as anyone’s. Pay your money, take your choice, volunteer for the first relativistic trip – you’ll get to see the future. Maybe.

P.S. Note that I haven’t explained how it was that Einstein was able to guess that the speed of light was a universal limit. In a certain sense it doesn’t matter, since he was right. But it is an interesting question for a future post. TK

P.P.S. I also haven’t explained why people on the ship observe Earth clocks ticking faster (they have to since time on Earth passes faster than time on the ship). You can read my paper in the November 2006 issue of Foundations of Physics Letters but I recommend waiting for the relevant post. TK

From → Physics, Relativity

  1. When on the ground in my backyard I see an airliner in flight, it appears to be moving rather slowly. But I know from experience (having flown in airliners) that the actual airspeed is about 600 MPH. So what is seen from the ground is a matter of perception, not reality.

    When that airliner I’m flying in makes its descent, something happens to the passageways of my ears: by the time we reach groundlevel I am deaf. If I hold my nose and blow, there are noises in my head and I can hear again.

    So human perception is a function of how the human body is constructed; I KNOW the plane is flying at 600 MPH — how I see it from the ground doesn’t change the reality.

    I assume that I get deaf during descent because my body has trouble adjusting to changes in altitude, cabin pressure, whatever. I assume the “perfect” clock, being a mechanical device, has flaws in its construction which prevent it from working perfectly at high speeds.

    I am pleased that Einstein, like me, didn’t understand his own theory. I bet that, like me, he thought there must be some other explanation as to why it works. Maybe some day someone will come up with it.

    • Thanks for the comments. I revised the post to explain better why physicists don’t regard relativity as a matter of perception.

  2. Well I guess I don’t have to spend the weekend fignuirg this one out!

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