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So I get to thinking about things. And a recurrent theme with me is the size of the universe, interstellar distances, and how humanity will one day—and other intelligent beings perhaps sometime sooner—cross them.
According to our current thinking about the nature of space and time—or “spacetime,” if you will—we physical beings cannot travel faster than light.1 Supposedly, the nearer you approach light speed, or c, the more massive yourself and your ship become and the slower your onboard clocks tick until, finally, at c, you and the ship weigh an infinite amount and time stops for you. That would be a problem, especially since you also have to carry fuel to move that mass—at least with our current propulsion technologies. And if time has stopped, how are you accounting for your speed toward your destination? But I digress …
Popular science fiction tropes to deal with this—so that humanity and other beings can conquer and maintain interstellar empires that don’t quickly become temporally distorted and dissociated—include both wormholes and warp drives. Wormholes presumably punch through the “fabric” of space that appears to be crumped up like a giant wad of papier-mâché, so that one place and another are not actually separated by vast interstellar distances but actually lie side-by-side through interdimensional space. This presumes, of course, that the entire universe we see around us is crushed up to a thing about the size of a walnut. But I digress …
Warp drives, popularized by the Star Trek television franchise, allow that those two places are indeed far apart, but that you can get from one to the other without violating the light-speed limit by collapsing the “fabric” of space ahead of the ship while simultaneously expanding it behind. You do this by creating a “warp bubble” around the ship. My best analogy for this—since it’s kind of hard to envision space itself collapsing and expanding2—is someone walking on an elastic sidewalk.
From my home in the Bay Area to the state capitol in Sacramento is a distance of about seventy miles. Walking at a steady pace of four miles per hour—my maximum sustainable speed—I could get there in about twenty hours, allowing for one or two rest stops along the way. I have long legs, so my stride is a bit longer than three feet, heel to toe, but I can’t move my legs any faster than my normal, determined pace of about two strides per second, or say, six feet per second, to complete the trip in any less time.
But suppose I could somehow, magically, draw together or compress the sidewalk and the ground beneath it that lies in front of me, so that each of my three-foot strides might cover, say, thirty feet. And as soon as I had placed that forward foot and lifted my rear foot, the sidewalk expanded again to unclench the concrete and soil behind me. My legs wouldn’t be moving any faster; I myself would not be exceeding my walking speed limit of about four miles per hour. But with a ten-to-one advantage in ground coverage, I could make the trip to Sacramento in two hours without getting out of breath. If I could compress the sidewalk by 300 feet per step, and expand it again behind me at the same rate, I could walk to the city in twelve minutes without even breaking a sweat.
I would be warping the sidewalk and the ground under it in the same way the starship Enterprise creates a warp bubble to collapse and expand the space around it.
With my walking pace, we have known points of contact with the ground—my heel coming down, my toes pushing off—at a steady pace of three feet per step, six feet per second. So we can easily determine how much the sidewalk has to collapse and expand to achieve a reasonable travel time. If I were moving much slower—say, hobbling with a cane—we would need to collapse larger and larger amounts of sidewalk but do so at a slower rate than once per half-second, to make that twelve-minute trip of seventy miles. Conversely, if I were a seasoned marathoner, running three times as fast as a brisk walking pace, or about twelve miles per hour, we would need to take smaller bites of sidewalk but collapse and expand them at a much higher cycling rate.
What’s left out of the Star Trek story is how fast the Enterprise can travel between the stars without warp effects. The alternative to warp dive in the narrative is “impulse drive,” which is presumably some kind of mass-reaction thrust. But the stories told around the ship’s adventures never exactly correlate the capabilities of either drive with distances traveled. Sometimes a modest speed at warp drive covers light years in a matter of minutes; sometimes much longer. Sometimes a hefty fraction of impulse drive will take them halfway across a solar system in a minute or two; sometimes much shorter distances—say, to close with an enemy vessel a thousand kilometers away—in the same time.
Various official and unofficial “manuals” created either by the show runners or the fans attempt to quantify these fantasy speeds. One reference says that maximum impulse speed is one-quarter of light speed, or 167,000,000 miles per hour. So, without the benefit of warp drive effects, the ship could travel the 93 million from Earth to the Sun in about half an hour. Or the 365 million miles, on average, between Earth and Jupiter in about two hours and eleven minutes. So, to maneuver within orbital distances around a planet or to close within range of an enemy a hundred kilometers away, the ship would need to operate at the barest fraction of impulse drive. Not tenths but hundredths or thousandths of the available thrust.
All of which—and given that these fantasy speeds are extremely slippery—makes me wonder how much of the fabric of space does the starship’s warp bubble need to collapse and expand to appreciably speed up its maximum non-warp speed. If the bubble extended for just a hundred feet around the ship, or even a couple of thousand feet, it would have to cycle extremely fast to make any decent headway on an interstellar flight. I mean, it would be collapsing and releasing that much space in terms of microsecond or even nanosecond cycling, over and over again. Otherwise, the ship’s maximum 167-million-mile-per-hour speed would simply overrun the bubble.
Or the ship’s warp bubble would have to take in a lot of space. If the Enterprise is reputed to be a kilometer long, and moving at even a fraction of its top impulse speed, say, fifty percent, or 83.8 million miles per hour—or 23,285 miles per second (37,474 kilometers per second)—then it would have to collapse a volume of space about 37,500 times its own length each second just to keep pace with itself. To increase this natural, non-stressful impulse speed by a factor of ten, it would have to collapse 374,740 kilometers of space ahead of its bow. That’s just a little less than the distance from Earth to the Moon, which is 384,400 kilometers. And even that wouldn’t be a very high “warp factor,” because at ten times half-impulse speed, the ship would travel to the nearest star, Proxima Centauri—a distance of 4.22 light years, or 40 trillion kilometers—in about 3.4 years.
To obtain the warp speeds needed to represent travel times in the Star Trek world, the Enterprise would have to be collapsing volumes of space roughly equivalent to our solar system. Either that, or the ship would be collapsing and expanding smaller volumes at much higher cycling rates—so high that the warp field would probably destabilize any “structure” such a volume of space might have and reduce any interstellar dust and gas captured in that volume to blazing quarks.
Early in the Star Trek narrative, the ship had to travel far outside a planet’s gravity well before engaging its warp drive. That story element seems to have since been dropped from the telling in later series—again, the show’s distances and speeds are slippery things. But still, if a ship that was traveling even close to a near-Earth orbit engaged its warp drive at even the lowest factors described above, it would severely damage the fabric of the planet and play havoc with the Moon’s orbit.
But the question of the ship overrunning the warp bubble presents a conceptual puzzle, doesn’t it? The warp drive serves no purpose as a travel enhancer if the starship merely sits in the middle of a bubble while space pulsates around it: contracting and relaxing ahead of the bow, expanding and then retracting behind the stern. Just as I must step across the wrinkled, compressed concrete of the sidewalk to take advantage of that thirty- or three hundred-foot contraction, so the starship would have to cross the region of collapsed space ahead of it in order to put all that collapsed space behind it. If I’m walking in the open air and only the sidewalk is contracting beneath me, then my body is not affected by the compression. But for the starship, all of space is collapsing around it. Presumably this collapse would also affect the fabric of the ship’s hull and the people inside. So how does the ship survive that ultimate disruption? But perhaps I digress …
As things stand in our real, non-fantasy physics, we can’t begin to imagine grappling directly with the “fabric” of space—if such a thing even exists—or how we might make it collapse by so much as a cubic centimeter. My bet is that doing this kind of roughhouse to so small a volume would still require immense amounts of energy. To collapse a volume stretching from Earth to the Moon would take more energy than you could get from any conceivable matter-antimatter reaction. And to collapse the volume of even a medium-sized solar system would be playing with energies reserved for the gods.
Space is really, really big. Manipulating it in any significant way to travel between the stars will take unheard-of energies and a physics we can’t yet begin to understand. … Maybe it would be simpler just to punch through a wormhole to the other side.
1. Neither can energy elementals or beings of pure thought, according to the theory of relativity. But for now we’ll concentrate on carting our physical, protoplasmic bodies to the stars.
2. As I’ve said numerous times before, I don’t think our physics or mathematics really understands or accurately describes space, time, and gravity. For which see, once again, Fun with Numbers (I) from September 19, 2010, and (II) from September 26, 2010.