The Promise of Star Travel

UnknownThere are still a lot of True Believers in technology, and one theme, though it is getting a bit long in the tooth, is the idea of humankind going to the stars and founding grand galactic empires of the sort we starry-eyed science-fiction fans devoured in our youth.

Many True Believers also see space travel to nearby star systems as a potential solution to the problems we face with resource shortages and climate change on Earth. I’d like to put that prospect into some perspective with a little basic (and perhaps some not-so-basic) physics.

The nearest star system to our own is Alpha Centauri, which is 4.37 light-years distant. For those of you who aren’t in-the-know, a light-year is the distance light travels in one year, which is roughly 9,461,000,000,000 kilometers. There are about fifty stars within 16 light-years, and the number goes up rapidly from there. So if we can go some 20 light-years on a tank of fuel, we have quite a few tourist attractions to visit, some of which just might feature something more interesting than the universe’s largest ball of lint. But we absolutely must be able to travel 5 light-years on one tank of fuel to make it to the nearest rest stop.

How long does it take to travel five light-years? Well, it takes light itself five years. But light moves at — as you might guess — the speed of light. The laws of physics as we know them tell us that you can’t make matter move at the speed of light. In fact, here’s the magic formula, from Einstein’s special theory of relativity, that illustrates the problem:

E = (\gamma - 1)mc^{2}

m is the mass, c is the speed of light, and E is the relativistic kinetic energy of the moving mass. Because of the well-known law of conservation of energy, if you want to get the speed, you have to pay for the ticket in terms of energy — you have to put in at least this much energy to get it to go that fast, and that’s assuming nothing is wasted on, say, heat or light or anything else that bleeds away. The whole trick lies in the value of gamma, which is the rather daunting Lorentz factor:

\gamma = \frac{1}{\sqrt{1 - \frac{v^{2}}{c^2}}}

As you can see, if the velocity of the object is the speed of light (v = c) this becomes one divided by the square root of zero, which turns out to be … well, infinite. So the kinetic energy of a mass moving at the speed of light is infinite, and the ticket price is way out of our budget.

But 90% of the speed of light isn’t infinite. In that case, the Lorentz factor is:

\gamma = \frac{1}{\sqrt{1 - \frac{(0.9c)^{2}}{(1.0c)^{2}}}} = \frac{1}{\sqrt{1 - 0.81}} \approx 2.294

At half the speed of light, this drops to a paltry:

\gamma \approx 1.155

At half the speed of light it takes about nine years to get to Alpha Centauri — not counting acceleration and deceleration, which would roughly double that, so let’s call it a twenty-year one-way journey. At half the speed of light, time-dilation is still pretty tame, and would apply mostly to the middle portion of the trip, at maximum velocity: it will only shave a few years off our crew’s subjective experience of time aboard ship.

Let’s look at how much energy this twenty-year voyage to Alpha Centauri takes.

E = (1.155 - 1)mc^{2} = 0.155mc^{2} \approx (14\times10^{15} \textrm{J/kg}) \times m

where mass, m, is measured in kilograms, and E comes out in Joules. Now 1015 Joules is called a Petajoule, which is a lot of energy. This much energy is usually compared to nuclear explosions, such as the Tsar Bomba, the 50 megaton nuclear test explosion that qualifies as the largest nuclear test ever performed. That rang in at 210 Petajoules.

It takes 14 Petajoules to get one kilogram moving at half the speed of light. One kilogram is a little over two pounds. So it takes the full energy content of a good-sized nuclear explosion to get half a bag of flour moving at half the speed of light.

Please note that I’m not saying that a nuclear bomb will fling a half-bag of flour into space at half the speed of light. I’m saying that if you took all the energy released by a nuclear bomb, packed it into a rocket engine, and released that energy in a controlled fashion over a reasonable period of time without wasting any of it on heat or ejection mass, it would be enough energy to get a half-bag of flour moving at half the speed of light.

A half-bag of flour isn’t very interesting.

The lunar lander from the Apollo missions, a little metal box enclosing 160 cubic feet (about 5 x 5 x 6), weighed nearly 5000 kilograms. To get that up to half the speed of light would take around 70,000 Petajoules, or the energy released by 333 of the largest nuclear bombs ever tested, all tightly focused on accelerating the lander and not blowing it to smithereens.

Of course, you’ll need another 333 nuclear bombs to slow down again at the end of your flight.

We’re talking now about a little box barely bigger than a somewhat roomy coffin for two, in which our intrepid explorers are going to spend twenty years in the middle of the biggest nighttime nowhere the mind can imagine.

As I recall, the lunar lander was not equipped for a twenty year journey. Our intrepid explorers will definitely run out of beer and pretzels. And after twenty years in the dark, Scrabble gets old.

Something the size of a cruise ship sounds a little more reasonable. I don’t know if you can pack a cruise ship with enough pretzels and beer to keep a crew alive for twenty years with no layovers, but let’s say you could. A smallish cruise ship like the Titanic will weigh in at somewhere around 40,000 metric tons, or 40,000,000 kilograms. Modern cruise ships are much larger. To get the Titanic moving at half the speed of light would require about 560 Zettajoules, and the same to slow it down at its destination.

Now we’re talking some serious energy. Total modern worldwide energy consumption is about a half a Zettajoule per year. So pushing a cruise liner the size of the Titanic to half the speed of light would take … let’s see … something a bit over a thousand years’ worth of the total modern industrial energy consumption of the entire Earth.

This is modern energy consumption, not what the world consumed a thousand years ago when the fastest war machines were chariots. Assume that we could keep our current rate of energy consumption going for a thousand years, but instead of consuming it, we instead all use candles and horse-drawn carts and plows and store every bit of our industrial energy in a big battery that can (somehow) release its stored energy directly into motion with no waste heat.  If we did this, we could set out on a twenty-year journey to Alpha Centauri a thousand years from now.

Oops, make that two thousand years from now, because they will need a second battery to slow down.

Of course, you can’t just slap the Titanic with 560 Zettajoules and crank it right up to half the speed of light. Well, I suppose you could — but you’d have a bright spray of subatomic particles instead of a starship. No, you have to spread it out over time.

Let’s assume we spread our 560 Zettajoules over half the flight (then the other 560 during the second half). Five years is about 157,000,000 seconds, so we’d be burning about 3.6 Petawatts continuously. That’s a rather big light bulb. The entire earth receives about 174 Petawatts from the sun. So we’re taking roughly two percent of the Earth’s total energy influx from the sun, and applying it toward accelerating a single ship the size of the Titanic. That’s a magnifying lens about 1000 miles in diameter, focusing the energy of the sun down to a point less than 200 feet in diameter (the keel of the ship). Did you ever use a magnifying lens to burn paper as a kid? Well, it’s like that, only more so.

Of course, we’re already assuming that we can convert all that energy directly into kinetic energy, and none of it into heat, so this giant magnifying glass isn’t going to turn the Titanic into the world’s biggest vaporized ant. If we did use it to heat the Titanic instead of moving it, the Titanic would reach a temperature where the energy radiating from it would balance the energy we’re putting into it. That’s what makes hot steel or a light bulb glow. This is governed, to first approximation, by the Stefan-Boltzmann formula for blackbody radiation:

\frac{P}{A} = \sigma T^{4}

or

T = \sqrt[4]{\frac{P}{\sigma A}} = \sqrt[4]{\frac{3.6 \times 10^{15}}{(5.67 \times 10^{-8}) \times (2500)}} = \sqrt[4]{2.540 \times 10^{19}} = 71,000^{\circ}\textrm{K}

That means an area the size of the keel of the titanic (2500 square meters) raised to 71,000 degrees Kelvin, will put out 3.6 Petawatts of power as radiant energy; or, conversely, that an area the size of the keel of the Titanic, wired up to 3.6 Petawatts in open space, will heat up to 71,000 degrees and glow.

That’s pretty darn hot. Since steel melts at around 1700 degrees Kelvin, this means we have to keep the power that gets wasted as heat less than:

P \le \sigma A T^{4} = (5.67 \times 10^{-8}) \times (2500) \times (1700)^{4} = 1.18 \times 10^{9}\textrm{W}

That means that we can afford to waste on heat only a tiny fraction of the power we’re using to drive the Titanic across the void, specifically:

ratio = \frac{1.18 \times 10^{9}}{3.6 \times 10^{15}} = 0.00000033

So let’s sum this up. To move a modest “colony ship” the size of the Titanic, fitted out for a twenty-year voyage to the nearest star, it will require a fuel source equivalent to 2000 times the current industrial energy consumption of the entire earth — fuel that can somehow be packed aboard the Titanic without taking up all the space for food, water, and crew, and without exploding spectacularly if you give it a hard look — and spend it with 99.999967% efficiency to accelerate the ship, where that tiny fraction of waste heat keeps the low-carbon steel thruster nozzles just barely below melting point for the entire twenty-year journey.

Based on physics as we know it — including a wee bit of pure science fiction in the form of a thruster that doesn’t eject mass and is 99.999967% efficient — interstellar travel is not even close to possible.

That leaves the slow route, or the magic route.

The slow route involves colony ships much larger than the Titanic — they would be self-sufficient colony worlds, really — that can support a human society for centuries at least, and probably more like thousands of years. We’d propel these out of the solar system using the same gravity slingshot that the Pioneer satellite used, and they’d never get close to any appreciable fraction of the speed of light.

There is a whole riot of problems with this concept, the worst being the human problem. We’ve had only a handful of cultures on the Earth that have lasted a thousand years without breaking down in social disorder and civil war, and that’s while living in the lap of terrestrial luxury where you can get shot in the leg and make your way to some farmhouse where you can at least pass on your genes through the lonely farmwife before you succumb to gangrene. We’re talking here about a self-contained ecosystem where every watt of energy, every ounce of food, every drop of water, every breath of air requires ultra-careful management, where population must be strictly controlled, and where even a minor war means that everyone dies. Gravity slingshots aren’t accurate, and there isn’t going to be a lot of energy for maneuvering: the odds that such a colony mothership would ever pass close enough to another star to be captured by it, much less warmed by it, are practically zero.

The slow route is not a plan for colonizing the universe. It’s an extremely expensive and wasteful form of execution by exile.

The magic route involves pure science fiction in the form of warp drives, wormholes, teleportation, and the like. That is, speculations about ways that the universe might work that could perhaps be exploited to sidestep the problems of a straightforward approach.

I can’t say whether any of these things are possible or impossible. But there are a couple of guiding principles to keep in mind.

The most important is that the conservation of energy is the devil you have to pay, one way or another.

One of the more entertaining concepts of space travel was in E.E. Smith’s Lensman series, where it was accomplished using the “inertialess” space drive: this was a kind of force field that would suppress all of the inertial mass in objects under its influence. The lightest thrust would then make the largest spaceship move at a speed that exactly balanced the thrust of the engines against whatever frictional resistance the ship encountered from stray hydrogen atoms in deep space, and since the ship had no inertial mass and thus no momentum or kinetic energy, the speed of light was no barrier at all. Nor were collisions of any concern, since ramming into a rock would merely cause the ship to stop instantly without jarring anything inside or even scratching the paint.

The downside came when the inertialess drive was shut off, because then the original inertial mass, including all its original momentum and kinetic energy, was instantly reasserted. The spaceship and everything in it would return to the inertial rest-frame (as relativistic physics terms it) of its point-of-origin.

At this moment, anyone reading this on their computer is rushing eastward at around 1000 miles per hour, following the turning surface of the earth. The earth itself is moving around the sun at roughly 65,000 miles per hour. The sun is whipping around the galactic center at about 486,000 miles per hour.

Whether we have an inertialess space drive, a warp drive that somehow pulls a spaceship along by its own bootstraps with very little energy input, a wormhole, or some kind of teleportation device, the moment we shut down the device, the transported object is going to return to the inertial rest-frame it started from — unless we apply enough energy to change its rest-frame momentum. That’s the consequence of moving the object for free.

So if you were to teleport to a planet on the opposite side of the galaxy, you’d find yourself moving at roughly 972,000 miles per hour relative to the landing platform. If that happens to be up, you’ll make a spectacular Roman candle as you tear through the atmosphere — otherwise, you’re going to leave a substantial divot.

The only way to avoid this is to apply at least enough energy to the transported objects to get them to sync up with the place they are going. In E.E. Smith’s terms, you have to “match intrinsics.” Nothing, other than wishful thinking, is going to get around at least that much — unless, of course, what we think we know about the physics of the universe is just completely and utterly wrong.

It’s possible that we could apply this energy through the wormhole itself, a bit like slipping a greased pig into a nylon tube and then whipping the tube so that the pig shoots out the other end at high velocity — hopefully with its skin still on. But the final velocity of the pig is still going to be related to the energy we put into whipping the wormhole: the bigger the pig, the more the energy required. So how much energy is this?

Well, 972,000 miles per hour is nothing like half the speed of light. In fact, it’s only 0.32% the speed of light, and the energy to accelerate a single 200-pound person (or pig) to this speed is:

E = (\gamma - 1)mc^{2} = (\frac{1}{\sqrt{1 - \frac{v^{2}}{c^{2}}}} - 1)mc^{2} = ((1 + \frac{1}{2}\frac{v^{2}}{c^{2}} + \frac{3}{8}\frac{v^{4}}{c^{4}} + ...) - 1)mc^{2}

E \approx \frac{1}{2}mv^{2} \approx (95 \times 10^{9} \textrm{J/kg})(90 \textrm{kg}) \approx 8.6 \times 10^{12} \textrm{J}

That’s about 14% of the energy released by the nuclear bomb dropped on Hiroshima, which isn’t completely unthinkable. If you can apply it in some way that doesn’t vaporize the passenger.

Of course, this is unreasonably expecting to teleport all the way to the other side of the galaxy, which is moving the opposite direction relative to us at galactic velocities. Transporting ourselves to something closer, say Mars, would not be nearly as bad. It moves around the sun at about 54,000 miles per hour, as compared to Earth’s 65,000 miles per hour, so during a Mars solar opposition, you’d only have to use enough energy to slow the person by about 11,000 miles per hour. Low-earth orbit requires a change in velocity of about 20,000 miles per hour, so our magic space drive would make an Earth-Mars commute about half as expensive as putting an astronaut into orbit. During a Mars solar conjunction — when Earth and Mars are on opposite sides of the sun — it’s a bit more difficult, since we have to overcome a 119,000 mile per hour difference, so you’d probably just wait for the next opposition, which happens roughly every 26 months.

Even a New York City to Los Angeles teleport isn’t free. Not only do you move more slowly in NYC than in LA (because NYC is closer to the north pole and thus closer to the axis of the earth), you’re moving in different directions in space because of the difference in longitude. The computation is a little tricky, but the landing platform in LA is moving due East at

\frac{2 \pi \times 4000 \textrm{mi} \times \cos 34.1^{\circ}}{24 \textrm{hr}} = 867 \textrm{mph } \bold{LA East}

The sending platform in NYC is moving due East at

\frac{2 \pi \times 4000 \textrm{mi} \times \cos 40.7^{\circ}}{24 \textrm{hr}} = 793 \textrm{mph } \bold{NY East}

However, “due East” is not the same direction for the two cities. Relative to the platform in LA, our New Yorker is moving

793 \textrm{mph} \times \cos 44.25^{\circ} = 568 \textrm{mph } \bold{LA East}

793 \textrm{mph} \times \sin 44.25^{\circ} = 553 \textrm{mph } \bold{LA Down}

When he steps onto the platform in LA, he’s going to be moving at a relative velocity of

\sqrt{(867-568)^{2} + 553^{2}} = 629 \textrm{mph}

slightly northwestward and mostly straight down. Ouch.

The LA to Bombay commute is, of course, much worse, since LA and Bombay are moving in roughly opposite directions fast enough for the traveller to cause a sonic boom on arrival. Wear a helmet.

The other problem with warp drives and wormholes is the gravity gradient. You need a fierce gravitational gradient to make a warp that will move anything bigger than an electron — which takes a lot of energy to produce — but fierce gravity gradients produce tidal forces that can tear apart even atomic nuclei. Indeed, if Hawking’s theories about small black hole evaporation are correct (and they seem to be) the gradients can actually rip apart vacuum.

It’s not something you want to put a finger into.

Wormholes in particular are purely speculative, and are related to the question of where stuff goes when it falls into a black hole. Most likely, it stays in the black hole. But there are speculations that it might come out “somewhere else,” and if it does, it’s possible that the distance through the wormhole is less than the distance around the wormhole. On the other hand, the distance through might be longer. Or it might dump you into an unformed protouniverse where you get to be its Big Bang.

Odds that anyone will enjoy the trip through a wormhole are vanishingly small.

I want to state again that I have no idea if there are ultimately ways to get to distant stars. What I do know is that based on what we know or think we know right now, there’s no reasonable way to get to another star: the brute-force approaches are impossible, the speculative approaches are impractical even if possible, and if there is a practical way to do this, no one with any grasp of physics has any idea where or how to start working on the problem.

This entry was posted in General.

2 comments on “The Promise of Star Travel

  1. Rita says:

    Hi Joe – I had this exact same question, and surprisingly I got an answer from a space traveller from another star system that is hanging out on Earth. I was very surprised he had managed to get here, and I asked him how it was done. His answer was that as you have pointed out, it’s impossible to get matter to travel those distances, so you want to travel with only your consciousness. As you know there are only two fundamentals that exist, matter/energy and consciousness, and consciousness goes all the way down

    “Getting
    matter or energy (anything physical) out of purely non-physical
    ingredients would be just as inexplicable as the mainstream scientific
    claim that non-physical mind or consciousness “emerges” from purely
    physical ingredients in the brain.” ~Christian de Quincey

    So how does one travel with the ‘speed of thought”? I’m still working on projecting consciousness to a place I can ‘see’…. never mind another star system! What I could gather from my conversation with the star traveller was it’s an advanced consciousness thing, and humans won’t be able to do this until they evolve to a more mature state of consciousness.

    Did you ever see the movie K-Pax? when I saw this, I thought immediately that the author of that book must have spoken to somebody like Prot, because I got a lot of the same information from my friend. What Prot did was use a physical body that was vacated by it’s human. Other thoughts I’ve had is like Rupert Sheldrake’s ‘morphic fields’, consciousness carries memory, and a pattern of organization, so if the consciousness is adept creating a physical body from the zero point field, for example…. they would generate a body to physically manifest, though I imagine it’s a lot easier to just show up as consciousness, and experience other worlds like a ghost!

    Like

    • Aha! Yes, I was actually going to follow up this post with something like that, down the road. You beat me to it! 🙂

      At that level, we are no longer talking about the sense-observed unconscious (or subconscious) regularities that comprise “physics,” and quite a few very odd things could and can and do happen. But you can’t study those things the same way you study rocks and stellar spectral signatures.

      I liked K-Pax.

      I actually have a post underway talking about some of this stuff. We’ll see when it reaches air. 🙂

      Like

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s