Michael Strauss: Our universe is too vast for even the most imaginative sci-fi

As an astrophysicist, I am always struck by the fact that even the wildest science-fiction stories tend to be distinctly human in character. No matter how exotic the locale or how unusual the scientific concepts, most science fiction ends up being about quintessentially human (or human-like) interactions, problems, foibles and challenges. This is what we respond to; it is what we can best understand. In practice, this means that most science fiction takes place in relatively relatable settings, on a planet or spacecraft. The real challenge is to tie the story to human emotions, and human sizes and timescales, while still capturing the enormous scales of the Universe itself.

Just how large the Universe actually is never fails to boggle the mind. We say that the observable Universe extends for tens of billions of light years, but the only way to really comprehend this, as humans, is to break matters down into a series of steps, starting with our visceral understanding of the size of the Earth. A non-stop flight from Dubai to San Francisco covers a distance of about 8,000 miles – roughly equal to the diameter of the Earth. The Sun is much bigger; its diameter is just over 100 times Earth’s. And the distance between the Earth and the Sun is about 100 times larger than that, close to 100 million miles. This distance, the radius of the Earth’s orbit around the Sun, is a fundamental measure in astronomy; the Astronomical Unit, or AU. The spacecraft Voyager 1, for example, launched in 1977 and, travelling at 11 miles per second, is now 137 AU from the Sun.

But the stars are far more distant than this. The nearest, Proxima Centauri, is about 270,000 AU, or 4.25 light years away. You would have to line up 30 million Suns to span the gap between the Sun and Proxima Centauri. The Vogons in Douglas Adams’s The Hitchhiker’s Guide to the Galaxy (1979) are shocked that humans have not travelled to the Proxima Centauri system to see the Earth’s demolition notice; the joke is just how impossibly large the distance is.

Four light years turns out to be about the average distance between stars in the Milky Way Galaxy, of which the Sun is a member. That is a lot of empty space! The Milky Way contains about 300 billion stars, in a vast structure roughly 100,000 light years in diameter. One of the truly exciting discoveries of the past two decades is that our Sun is far from unique in hosting a retinue of planets: evidence shows that the majority of Sun-like stars in the Milky Way have planets orbiting them, many with a size and distance from their parent star allowing them to host life as we know it.

Yet getting to these planets is another matter entirely: Voyager 1 would arrive at Proxima Centauri in 75,000 years if it were travelling in the right direction – which it isn’t. Science-fiction writers use a variety of tricks to span these interstellar distances: putting their passengers into states of suspended animation during the long voyages, or travelling close to the speed of light (to take advantage of the time dilation predicted in Albert Einstein’s theory of special relativity). Or they invoke warp drives, wormholes or other as-yet undiscovered phenomena.

When astronomers made the first definitive measurements of the scale of our Galaxy a century ago, they were overwhelmed by the size of the Universe they had mapped. Initially, there was great skepticism that the so-called ‘spiral nebulae’ seen in deep photographs of the sky were in fact ‘island universes’ – structures as large as the Milky Way, but at much larger distances still. While the vast majority of science-fiction stories stay within our Milky Way, much of the story of the past 100 years of astronomy has been the discovery of just how much larger than that the Universe is. Our nearest galactic neighbour is about 2 million light years away, while the light from the most distant galaxies our telescopes can see has been travelling to us for most of the age of the Universe, about 13 billion years.

We discovered in the 1920s that the Universe has been expanding since the Big Bang. But about 20 years ago, astronomers found that this expansion was speeding up, driven by a force whose physical nature we do not understand, but to which we give the stop-gap name of ‘dark energy’. Dark energy operates on length- and time-scales of the Universe as a whole: how could we capture such a concept in a piece of fiction?

The story doesn’t stop there. We can’t see galaxies from those parts of the Universe for which there hasn’t been enough time since the Big Bang for the light to reach us. What lies beyond the observable bounds of the Universe? Our simplest cosmological models suggest that the Universe is uniform in its properties on the largest scales, and extends forever. A variant idea says that the Big Bang that birthed our Universe is only one of a (possibly infinite) number of such explosions, and that the resulting ‘multiverse’ has an extent utterly beyond our comprehension.

The US astronomer Neil deGrasse Tyson once said: ‘The Universe is under no obligation to make sense to you.’ Similarly, the wonders of the Universe are under no obligation to make it easy for science-fiction writers to tell stories about them. The Universe is mostly empty space, and the distances between stars in galaxies, and between galaxies in the Universe, are incomprehensibly vast on human scales. Capturing the true scale of the Universe, while somehow tying it to human endeavours and emotions, is a daunting challenge for any science-fiction writer. Olaf Stapledon took up that challenge in his novel Star Maker (1937), in which the stars and nebulae, and cosmos as a whole, are conscious. While we are humbled by our tiny size relative to the cosmos, our brains can none the less comprehend, to some extent, just how large the Universe we inhabit is. This is hopeful, since, as the astrobiologist Caleb Scharf of Columbia University has said: ‘In a finite world, a cosmic perspective isn’t a luxury, it is a necessity.’ Conveying this to the public is the real challenge faced by astronomers and science-fiction writers alike. Aeon counter – do not remove

UniverseMichael A. Strauss is professor of astrophysics at Princeton University and coauthor with Richard Gott and Neil DeGrasse Tyson of Welcome to The Universe: An Astrophysical Tour.

This article was originally published at Aeon and has been republished under Creative Commons.

Pi Day: “Was Einstein Right?” Chuck Adler on the twin paradox of relativity in science fiction

This post is extracted from Wizards, Aliens, and Starships by Charles Adler. Dr. Adler will kick off Princeton’s Pi Day festivities tonight with a talk at the Princeton Public Library starting at 7:00 PM. We hope you can join the fun!

For more Pi Day features from Princeton University Press, please click here.


Tfts56[1]Robert A. Heinlein’s novel Time for the Stars is essentially one long in-joke for physicists. The central characters of the novel are Tom and Pat Bartlett, two identical twins who can communicate with each other telepathically. In the novel, telepathy has a speed much faster than light. Linked telepaths, usually pairs of identical twins, are used to maintain communications between the starship Lewis and Clark and Earth. Tom goes on the spacecraft while Pat stays home; the ship visits a number of distant star systems, exploring and finding new Earth-like worlds. On Tom’s return, nearly seventy years have elapsed on Earth, but Tom has only aged by five.

I call this a physicist’s in-joke because Heinlein is illustrating what is referred to as the twin paradox of relativity: take two identical twins, fly one around the universe at nearly the speed of light, and leave the other at home. On the traveler’s return, he or she will be younger than the stay-at- home, even though the two started out the same age. This is because according to Einstein’s special theory of relativity, time runs at different rates in different reference frames.

This is another common theme in science fiction: the fact that time slows down when one “approaches the speed of light.” It’s a subtle issue, however, and is very easy to get wrong. In fact, Heinlein made some mistakes in his book when dealing with the subject, but more on that later. First, I want to list a few of the many books written using this theme:

  • The Forever War, by Joe W. Haldeman. This story of a long-drawn-out conflict between humanity and an alien race has starships that move at speeds near light speed to travel between “collapsars” (black holes), which are used for faster-than-light travel. Alas, this doesn’t work. The hero’s girlfriend keeps herself young for him by shuttling back and forth at near light speeds between Earth and a distant colony world.
  • Poul Anderson’s novel, Tau Zero. In this work, mentioned in the last chapter, the crew of a doomed Bussard ramship is able to explore essentially the entire universe by traveling at speeds ever closer to the speed of light.
  • The Fifth Head of Cerberus, by Gene Wolfe. In this novel an anthropologist travels from Earth to the double planets of St. Croix and St. Anne. It isn’t a big part of the novel, but the anthropologist John Marsch mentions that eighty years have passed on Earth since he left it, a large part of his choice to stay rather than return home.
  • Larris Niven’s novel A World out of Time. The rammer Jerome Corbell travels to the galactic core and back, aging some 90 years, while three million years pass on Earth.

There are many, many others, and for good reason: relativity is good for the science fiction writer because it brings the stars closer to home, at least for the astronaut venturing out to them. It’s not so simple for her stay-at-home relatives. The point is that the distance between Earth and other planets in the Solar System ranges from tens of millions of kilometers to billions of kilometers. These are large distances, to be sure, but ones that can be traversed in times ranging from a few years to a decade or so by chemical propulsion. We can imagine sending people to the planets in times commensurate with human life. If we imagine more advanced propulsion systems, the times become that much shorter.

Unfortunately, it seems there is no other intelligent life in the Solar System apart from humans, and no other habitable place apart from Earth. If we want to invoke the themes of contact or conflict with aliens or finding and settling Earth-like planets, the narratives must involve travel to other stars because there’s nothing like that close to us. But the stars are a lot farther away than the planets in the Solar System: the nearest star system to our Solar System, the triple star system Alpha Centauri, is 4.3 light-years away: that is, it is so far that it takes light 4.3 years to get from there to here, a distance of 40 trillion km. Other stars are much farther away. Our own galaxy, the group of 200 billion stars of which our Sun is a part, is a great spiral 100,000 light-years across. Other galaxies are distances of millions of light-years away.

From our best knowledge of physics today, nothing can go faster than the speed of light. That means that it takes at least 4.3 years for a traveler (I’ll call him Tom) to go from Earth to Alpha Centauri and another 4.3 years to return. But if Tom travels at a speed close to that of light, he doesn’t experience 4.3 years spent on ship; it can take only a small fraction of the time. In principle, Tom can explore the universe in his lifetime as long as he is willing to come back to a world that has aged millions or billions of years in the meantime.

 

Was Einstein Right?

This weird prediction—that clocks run more slowly when traveling close to light speed—has made many people question Einstein’s results. The weirdness isn’t limited to time dilation; there is also relativistic length contraction. A spacecraft traveling close to the speed of light shrinks in the direction of motion. The formulas are actually quite simple. Let’s say that Tom is in a spacecraft traveling along at some speed v, while Pat is standing still, watching him fly by. We’ll put Pat in a space suit floating in empty space so we don’t have to worry about the complication of gravity. Let’s say the following: Pat has a stopwatch in his hand, as does Tom. As Tom speeds by him, both start their stopwatches at the same time and Pat measures a certain amount of time on his watch (say, 10 seconds) while simultaneously watching Tom’s watch through the window of his spacecraft. If Pat measures time ∆t0 go by on his watch, he will see Tom’s watch tick through less time. Letting ∆t be the amount of time on Tom’s watch, the two times are related by the formula

where the all-important “gamma factor” is

The gamma factor is always greater than 1, meaning Pat will see less time go by on Tom’s watch than on his. Table 12.1 shows how gamma varies with velocity.

Note that this is only really appreciable for times greater than about 10% of the speed of light. The length of Tom’s ship as measured by Pat (and the length of any object in it, including Tom) shrinks in the direction of motion by the same factor.

Even though the gamma factor isn’t large for low speeds, it is still measurable. To quote Edward Purcell, “Personally, I believe in special relativity. If it were not reliable, some expensive machines around here would be in very deep trouble”. The time dilation effect has been measured directly, and is measured directly almost every second of every day in particle accelerators around the world. Unstable particles have characteristic lifetimes, after which they decay into other particles. For example, the muon is a particle with mass 206 times the mass of the electron. It is unstable and decays via the reaction

It decays with a characteristic time of 2.22 μs; this is the decay time one finds for muons generated in lab experiments. However, muons generated by cosmic ray showers in Earth’s atmosphere travel at speeds over 99% of the speed of light, and measurements on these muons show that their decay lifetime is more than seven times longer than what is measured in the lab, exactly as predicted by relativity theory. This is an experiment I did as a graduate student and our undergraduates at St. Mary’s College do as part of their third-year advanced lab course. Experiments with particles in particle accelerators show the same results: particle lifetimes are extended by the gamma factor, and no matter how much energy we put into the particles, they never travel faster than the speed of light. This is remarkable because in the highest-energy accelerators, particles end up traveling at speeds within 1 cm/s of light speed. Everything works out exactly as the theory of relativity says, to a precision of much better than 1%.

How about experiments done with real clocks? Yes, they have been done as well. The problems of doing such experiments are substantial: at speeds of a few hundred meters per second, a typical speed for an airplane, the gamma factor deviates from 1 by only about 1013. To measure the effect, you would have to run the experiment for a long time, because the accuracy of atomic clocks is only about one part in 1011 or 1012; the experiments would have to run a long time because the difference between the readings on the clocks increases with time. In the 1970s tests were performed with atomic clocks carried on two airplanes that flew around the world, which were compared to clocks remaining stationary on the ground. Einstein passed with flying colors. The one subtlety here is that you have to take the rotation of the Earth into account as part of the speed of the airplane. For this reason, two planes were used: one going around the world from East to West, the other from West to East. This may seem rather abstract, but today it is extremely important for our technology. Relativity lies at the cornerstone of a multi-billion-dollar industry, the global positioning system (GPS).

GPS determines the positions of objects on the Earth by triangulation: satellites in orbit around the Earth send radio signals with time stamps on them. By comparing the time stamps to the time on the ground, it is possible to determine the distance to the satellite, which is the speed of light multiplied by the time difference between the two. Using signals from at least four satellites and their known positions, one can triangulate a position on the ground. However, the clocks on the satellites run at different rates as clocks on the ground, in keeping with the theory of relativity. There are actually two different effects: one is relativistic time dilation owing to motion and the other is an effect we haven’t considered yet, gravitational time dilation. Gravitational time dilation means that time slows down the further you are in a gravitational potential well. On the satellites, the gravitational time dilation speeds up clock rates as compared to those on the ground, and the motion effect slows them down. The gravitational effect is twice as big as the motion effect, but both must be included to calculate the total amount by which the clock rate changes. The effect is small, only about three parts in a billion, but if relativity weren’t accounted for, the GPS system would stop functioning in less than an hour. To quote from Alfred Heick’s textbook GPS Satellite Surveying,

Relativistic effects are important in GPS surveying but fortunately can be accurately calculated. . . . [The difference in clock rates] corresponds to an increase in time of 38.3 μsec per day; the clocks in orbit appear to run faster. . . . [This effect] is corrected by adjusting the frequency of the satellite clocks in the factory before launch to 10.22999999543 MHz [from their fundamental frequency of 10.23 MHz].

This statement says two things: first, in the dry language of an engineering handbook, it is made quite clear that these relativistic effects are so commonplace that engineers routinely take them into account in a system that hundreds of millions of people use every day and that contributes billions of dollars to the world’s commerce. Second, it tells you the phenomenal accuracy of radio and microwave engineering. So the next time someone tells you that Einstein was crazy, you can quote chapter and verse back at him!