Putting the science in fiction - Dan Koboldt, Chuck Wendig 2018
Relativity and space-time
Sometimes, it really is rocket science
By Dan Allen
In the 1800s, life was good. Steam engine-riding folks in Europe were all in on the new electromagnetics of James Clerk Maxwell, and soon Guglielmo Marconi would send sound over wireless waves in the ether.
But there were two dirty little secrets that threatened to destroy that idyllic steam-powered world of the late nineteenth century. Queen Victoria herself, if she knew them, would have kicked the bucket—or at least fallen off the fantastic flushing toilet of Thomas Crapper.
These two great puzzles, when solved, opened to us the power of the atom and gave birth to the nuclear age, effectively obliterating the steam era—much to the chagrin of all the steampunk fans who still fantasize about it.
One of these dirty little secrets was the “ultraviolet catastrophe.” The solution to this conundrum came from combining a bit of math from Niels Bohr and Albert Einstein’s idea of the photon, giving birth to the funky modern science of quantum mechanics.
The other dirty little secret was the electromagnetics of moving objects. (Eek, it didn’t work!) And it was all because of this little (huge) problem called the speed of light.
The steampunk world
To figure out what this special relativity business is all about, let’s put on our riding goggles and take a brisk ride in a bouncing buggy back in time to the late 1800s.
To a scientist of this era, things were simple. Wiggling charges created electromagnetic waves in the ether. Everyone’s properly calibrated pocket watches and ivory cane measuring sticks agreed, even if they were moving past each other fast enough to kick up dust from the cobblestones (all while wearing dapper waistcoats and top hats, of course).
The fundamental premise of the pre-Einstein world was that events that happen at the same time for me, happen at the same time for everyone—a world good enough for Galileo Galilei and Isaac Newton.
There is one teensy little problem. With those rules, when you happen to move past electrical charges that are being accelerated (like by an antenna), the charges generate electromagnetic waves before they are even moved—wait, what?! That is because by riding on a train you can get your flashlight to shine at the speed of light plus forty-five leagues per hour, so causality breaks down.
I will spare you the math. It’s bad, and when you’re done with three pages of it, you get equations that are nonsense. So … if you like a world where none of the rules make sense, consider yourself a steampunk scientist! Smoke your pipe with no thought of lung cancer, ride a steamboat across the Channel, and use some burning magnesium for your photograph flash. The speed of light—poppycock!
How Einstein saw the world
It all began when Albert A. Michelson and Edward W. Morley flabbergasted, flummoxed, and discombobulated themselves and the whole scientific world by accidentally proving there is no unseen “ether” in which everything in the universe is suspended, like some kind of cosmic Jell-O fruit salad. Shortly after, Einstein decided that a few ideas had to change.
The first postulate or premise of Einstein’s ether-less universe was that everybody experiences the same laws of physics regardless of their frame of reference. It is a reasonable assumption, given that there is no “stationary” ether that we move through. Einstein simply abandoned the idea that there is some magical “north pole” or other fixed object in the universe that we can say is “not moving.” At the time, this was quite a cheeky thing to do and the height of impropriety.
What this means is that if I shine a flashlight, the beam shoots out from my flashlight at the speed of light, as expected. If a planet or star or galaxy whizzes past at close to the speed of light, it doesn’t matter. Or, by the same token, if I whiz past a planet at close to the speed of light, my flashlight still sends out light at the speed of light. The big idea is it doesn’t matter if you are sitting still or moving. In fact, according to relativity you can’t even know whether I’m moving past you, or vice versa!
It is very fair. Everything about Einstein’s work has that pragmatic feel to it. That never-failing “simple, easy, works for everyone” math expunged all the great quirkiness of science of the steam era.
But wait, there’s more!
Postulate number two (and this is the kicker) is that everybody measures the same speed of light, regardless of whether they are in a box with a fox, or on a boat or in a train.
Special relativity
That last point had some interesting implications. It meant Einstein had no choice but to relate the experiences of people moving past each other using a kind of transformation worked on by brainiacs with names that started with L: Hendrik Lorentz, and Joseph Larmor (and some people’s names that don’t start with L, such as Woldemar Voigt and Henri Poincaré). This “Lorentz transformation” is the basis of special relativity and is one of the great hammers that struck down our romantic and mysterious world of the 1800s and took us into the nuclear age of mutually assured destruction and TV advertisements.
The first conclusion is that the universe is like a picture with a width axis and a length axis. All the dimensions of space are like one axis. And the second axis is another kind of distance: time. All events take place somewhere in this “picture” called space-time. The distance between two events is measured along both time and distance, like the distance between two pixels in a photograph being a combination of horizontal and vertical distances. Now, you can stretch one axis on a picture and distort it without changing the details of the picture. This is what happens when we convert happenings in one reference frame to another. Length and time get stretched in each picture to make the total space-time distances the same.
Is the speed of light mysterious and mystical? No, it is just the scale factor our universe uses to relate time and distance. Time has units of seconds, so we scale it by the speed of light in units of meters per second or miles per hour to change it into a distance. It is not mysterious at all. Even worse (steampunk fans flee while there is still magic in the world), the speed of light is the same for everybody. You see, unfortunately for philosopher friends, relativity is not about things being relative, like my morals vs. yours. It is about absolutes. There is one speed of light for everybody, all day, all the time, ever. Not very romantic at all.
So, what does it all mean?
The implications of space-time
Distances in space-time are constant for observers having a picnic in the countryside as well as those riding first class on steam trains. Unfortunately, that has some consequences for pocket watches and ivory-handled measuring sticks and canes. If we didn’t allow these space-time “pictures” to be distorted, when we shine a light from a lantern on a steam train, that light moves at the speed of light plus some—which Einstein made illegal. Instead, to move from my reference frame watching the train go by to the reference frame of the brakeman holding the lantern, I have to distort my measurements of distance and time in just the right way so we agree.
Now, the distance between two points in two warped pictures may be the same, but that doesn’t mean the X and Y axis values are the same. For example, up two and over one is the same distance as up one and over two. One observer may see events as having more X (spatial distance), while the other observes events as having more Y (time). But only this space-time distance, the combination of distance and time, is conserved. That means if we watch a horse race and start and stop our pocket watches to time the race, and you are on a train and I am not, our measurements simply don’t match up. And that is okay. The Lorentz transformation will settle whose pocket watch is running fast—no gentlemen’s duel necessary.
Our space-time pictures in our respective “reference frames”—the one on the ground and the one moving along at a heady clip down the track—work just fine for each of us. But when we examine each other’s space-time picture, we find it distorted relative to our own, liked a warped woodcut of an idyllic Victorian family with perfectly behaved children and a mother soon to die from tuberculosis.
Events are no longer simultaneous for everyone. You say the revolver shots in the duel happened at the same time, but when I move past at close to the speed of light, I see them happen at different times. My clock runs slower than yours, and strangely things aren’t so far away as they used to be when I looked at them before I caught the express trolley.
Of course you’ve all heard this before, and most of us think it sounds mystical: time dilation, the effect of slower time when you get close to the speed of light; and length contraction, the idea that distances to objects ahead of you appear shorter when you head toward them at speeds close to the speed of light.
But it gets worse. Moving electrical charges or currents generate magnetic fields, right? So if I move past some charges, it’s the same as a current moving past me. There has to be a magnetic field. Thankfully relativity changes your electric fields into my magnetic fields and vice versa in a wonderfully symmetric way that makes the whole math simple enough to express all four of Maxwell’s equations of electromagnetics in a single (matrix) equation.
What happens at the speed of light
Without going into the math, which starts out not too bad then gets a little woolly, like food left out of the icebox, the idea is this: There is a parameter called γ (gamma), which starts out a 1 (things act like steam era objects), then as you get close to the speed of light, γ gets bigger and bigger and goes to infinity as you approach the speed of light. This gamma factor is what we plug into the Lorentz transformation, like a sort of cosmic currency exchange for measurements. That parameter tells me how to stretch your universe picture (space-time) to make it agree with mine on the timing of events and the measuring of distances. It is that simple.
But it’s also really cool. When moving at the speed of light, time stops relative to other reference frames because you’ve stretched space-time infinitely, so the distance between any two times is immeasurable. Now, stretching space-time that much would require an infinite amount of energy, which is why you can’t reach the speed of light if you have any mass at all.
We can see this concept of stretched or “dilated” time with subatomic particles that are generated by cosmic rays in the outer atmosphere. We know their lifetimes because we can make them on Earth, too. They should decay and disappear before they reach the surface of Earth, even travelling at close to the speed of light. But they actually make it to Earth’s surface to mess with our electronics just fine. How is that possible?
When those particles are generated moving at close to the speed of light, they look down at Earth and say, “Not so far, I’m gonna make it.” Now, if we on Earth could see into their internal clockwork mechanisms as they flew by, we would notice that their system is running slow. So we say, “Well, of course they made it. They were decaying slowly.” One worldview has a tall picture, and the other a short and wide one. In both pictures the particles make it to Earth.
That is how Ender Wiggin in the Ender’s Game novel series by Orson Scott Card managed to outlive everyone from his era, by traveling at close to the speed of light most of the time. His internal clock ran slower, along with all his electronics, to avoid violating the speed of light. His picture was “stretched,” spreading out the distance between points in time for him. He moved from one point to the next and then the picture was squished again when he returned and stopped. He traveled a greater distance across space and a shorter distance across time—fair enough? (Incidentally, you can move across the picture and back in space, but only in the forward direction in time. Otherwise, the math hits the fan and you are back where we started with steampunk non-causality and things happening before they are caused.)
So, the next time your dinner party discussion about Franco-Prussian relations is interrupted by an Orwellian machine that abducts you and heads out into space, you’ll find that the distance to the star you are headed for is much shorter than it appeared from Earth. But when you get back to Earth after only a few months journeying among the stars, you will find that everything has changed, Rip Van Winkle. You are suddenly in the digital age. Thankfully, your tightly wound pocket watch still works.