“No matter how these issues are ultimately resolved, Centauri Dreams opts for the notion that even the back of a cereal box may contain its share of mysteries.” I wrote that line in 2005, and if it sounds cryptic, read on to discover its origins, ably described by Christopher Phoenix. I first encountered Christopher in an online discussion group made up of physicists and science fiction writers, where his knack for taking a topic apart always impressed me. A writer whose interest in interstellar flight is lifelong, he is currently turning his love of science fiction into a novel that, he tells me “incorporates some of the ideas we talk about on Centauri Dreams as a background setting.” Today’s essay examines the ideas of a physicist who dismissed the idea of interstellar flight entirely, while using a set of assumptions Christopher has come to challenge.

by Christopher Phoenix


“All this stuff about traveling around the universe in space suits — except for local exploration which I have not discussed — belongs back where it came from, on the cereal box.”

Over fifty years ago, physicist Edward Purcell penned the boldest dismissal of interstellar flight on record in his paper “Radioastronomy and Communication Through Space”. In that paper, Purcell uses the elementary laws of mechanics to refute the possibility of starflight in total. There are many people, of course, who share his belief that we will never reach the stars.

Keeping a firm grounding in the laws of physics is absolutely necessary when researching interstellar travel. A healthy skeptical attitude can help keep researchers honest with themselves. Certainly, not everything we imagine is possible. Nor can we hope to ever reach for the stars if we do not keep our feet firmly planted in reality.

However, sometimes such extreme skepticism deserves some healthy skepticism itself. Even though Purcell’s equations aren’t wrong, he didn’t prove that starflight belongs back on the cereal box. Instead, he defines the problem of interstellar travel in such a way that it seems to be insurmountable.

Radioastronomy and Communication Through Space


Before we begin, I want to quickly introduce Purcell and this paper. Edward M. Purcell made important contributions to physics and radioastronomy. He shared the 1952 Nobel Prize in Physics for discovering nuclear magnetic resonance (NMR) in liquids and solids. Later, Purcell was the first to detect radio emissions from neutral galactic hydrogen, the famous “21cm line”. Many important developments in radioastronomy resulted from his work.

“Radioastronomy and Communication Through Space” was the first paper in the Brookhaven Lecture Series. These lectures were meant to provide a meeting ground for all the scientists at Brookhaven National Laboratory. In this paper, Purcell argued that traditional radio SETI, not interstellar travel, is our only way of learning about other planets in the galaxy.

Image: Edward Mills Purcell (1912-1997). Credit: Wikimedia Commons.

Purcell builds to his conclusion in three sections. The first section discusses then-recent discoveries in radioastronomy. Purcell tells how astronomers mapped the galaxy by observing radio emissions from neutral galactic hydrogen (the 21cm line). He notes in particular that we gathered all this information by capturing an astonishingly tiny amount of radio energy from space. Over nine years, the total amount of radio energy captured by all 21cm observatories added up to less than one erg (10-7 J).

The paper then jumps from radioastronomy to more speculative topics. In the second section, Purcell takes on the idea of interstellar travel and runs some calculations on relativistic rockets. He concludes that interstellar flight is “preposterous”. In the final section of his paper, Purcell argues that radio messages can be sent between the stars for relatively little energy cost, while the energy required for interstellar travel is unobtainable.

I shall primarily discuss the second part of this paper, where Purcell argued against the possibility of interstellar travel.

“This is preposterous!”

From the start, Purcell considered fast interstellar travel as our only option. Purcell noted that relativity is not the obstacle to reaching another star within a single human lifetime. We cannot travel faster than light. However, if a we travel at speeds close to that of light, time dilation becomes an important factor, reducing the amount of time that passes for us on our trip. You will age much less than your friends back home if you travel to the stars at relativistic speeds.

This is perfectly correct, in my view, so far as it goes. Special relativity is reliable. The trouble is not, as we say, with the kinematics but with the energetics… Personally, I believe in special relativity. If it were not reliable, some very expensive machines around here would be in deep trouble.

The problem, Purcell says, is building a rocket capable of carrying out this mission. He develops this argument by examining a particular example flight.

Let us consider a trip to a place 12 light years away, and back. Because we don’t want to take many generations to do it, let us arbitrarily say we will go and come back in 28 years earth time. We will reach a top speed of 99% speed of light in the middle, and slow down and come back. The relativistic transformations show that we will come back in 28 years, only ten years older. This I really believe… Now let us look at the problem of designing a rocket to perform this mission.

So, Purcell has defined the problem in a certain way. The starship must fly to another star and return to Earth within a human lifetime. To do so, it will reach a top speed of 99% the speed of light (C) in the middle of the voyage. The craft is a rocket, and it must carry all its propellant from the beginning of the trip. It cannot refuel anywhere. To reach 99% C within a short amount of time, the rocket must maintain an acceleration of one g for most of the trip.

Having laid out the starting assumptions for our trip, Purcell uses the relativistic rocket equation to calculate the amount of propellant the rocket will require to complete the trip. Remember that rockets are momentum machines. They throw a certain mass of propellant out the back, and the reaction force pushes the rocket. When that propellant is all gone, only the payload remains and the rocket has reached its final speed.

A rocket engine’s performance is determined by its exhaust velocity (Vex). This is the velocity at which propellant leaves the engine as measured by the rocket. The higher the Vex, the more efficiently the rocket engine uses propellant. Engineers refer to rocket efficiency as specific impulse (Isp). A rocket’s specific impulse is determined by its exhaust velocity.

If you have a rocket of a certain Vex, and you want to accelerate it to a certain maximum velocity (Vmax), physics imposes a certain relationship between the initial and final mass of the rocket. Engineers call this ratio a rocket’s mass ratio. This relationship is shown by the rocket equation. Unfortunately, if our Vmax is much larger than our Vex, mass ratios increase exponentially. This is because the rocket must not only accelerate the payload, but also all the as-yet unused propellant. To go faster, you need more propellant, but you need more propellant to carry that propellant- and so on.

So, our next problem is choosing an engine. We want to travel close to the speed of light, so we need an engine with the highest exhaust velocity (and thus highest Isp) possible. Chemical rockets have much to low a Vex to do this- they would require an unimaginably large amount of reaction mass to approach the speed of light. We need a far more powerful engine.

One type of engine that could perform far better than chemical rockets is the nuclear fusion rocket. So, Purcell first proposes using idealized nuclear fusion propellant. In this case, the rocket’s initial mass must be a little over a billion times its final mass to reach 99% C. A ten ton payload will require a ten billion ton rocket at the start of the journey. This is simply too much mass!

We need something far more potent. Purcell turns to idealized matter-antimatter (M/AM) propellant. Again, we assume the fuel is utilized with perfect efficiency. Matter annihilates with antimatter, and the resulting energy is exhausted as massless electromagnetic radiation (gamma rays), giving us a Vex of C. We can’t beat that.


Image: VARIES (Vacuum to Antimatter Rocket Interstellar Explorer System) is a concept developed by Richard Obousy that would create its own antimatter enroute through the use of powerful lasers. Credit: Adrian Mann.

The situation is vastly improved by M/AM propellant. To reach 99% C, the rocket’s initial mass must be only 14 times its final mass. But we must also slow down at the destination, and slowing down requires just as much effort as accelerating in the first place. After that, we must turn the ship around and return to Earth.

So, during the course of our flight, the rocket shall undergo four accelerations. On the trip away from Earth, the rocket will accelerate to 99% C, and then decelerate back down to rest at the destination star. After turning around, it will accelerate back to 99% C on the trip home and then decelerate back down to rest at Earth. To do this, the rocket must start with an initial mass 40,000 times its final mass. To send a ten ton payload on this round trip will require a 400,000 ton rocket, consisting half of matter and half of antimatter.

The starship must accelerate at one g for most of the trip. At the outset of its journey, this rocket must radiate 1018 watts of radiant energy to accelerate its 400,000 tons of mass at one g. This is a little over the total power that the Earth receives from the sun. Only this energy is in gamma rays, which presents a shielding problem for any planet near the ship. In addition, once the rocket achieves relativistic velocities, cosmic dust and gas present a shielding problem for the ship itself. At these speeds, even tiny specks of matter will behave like pinpoint nuclear explosions, and individual protons will be transformed into deadly cosmic rays.

Purcell concludes that these calculations prove that interstellar flight is “preposterous”, in this solar system or any other.

Rigging the game

There isn’t anything wrong with Purcell’s calculations. The problem is that Purcell wants to take this one set of calculations and prove that any form of interstellar travel is impossible. This isn’t very fair, since the starting conditions he picked in his example lead to his pessimistic conclusions. Let’s examine these assumptions.

Purcell’s first assumption is we must travel at 99% C. Why must we travel so fast? Even to complete a trip to a nearby star within a human lifetime, you can travel slower than that. Purcell is committed to these extreme relativistic speeds in order to take advantage of time dilation and complete the round trip in a decade.

If we are willing to travel much slower, perhaps 10% C, or even 1% C, and let multiple generations of crew make the trip, the difficulties are greatly reduced. At slower speeds, propulsion requirements are far more reasonable, and deadly collisions with cosmic dust would be easier to defend against.

Of course, there are many very difficult challenges to solve before we can launch such a ship. The travelers must recycle all their air and water, grow their own food, and build a stable society able to last for centuries. Some form of artificial gravity must be provided to prevent muscle and bone loss in microgravity. The habitable sections of the ship must be shielded from cosmic rays. But none of these represent hard physical limits arising from the laws of mechanics and nothing else.

This is all assuming humans are making the trip. Slow travel is made even easier if humans do not make the trip, just as we have done with our current robotic exploration of the solar system.

The second assumption is the starship must return to Earth. Particularly if we must carry all the propellant we use from the outset, a round trip mission is far more difficult than a one-way trip. But why must the starship return to Earth? There are many interesting missions that do not require the spacecraft to return to Earth. A colonizing expedition does not have or even want to return. Neither does a robotic probe. A fly-by probe like Daedalus doesn’t even need to carry propellant to slow down at the destination.

Purcell’s third questionable assumption is an interstellar vehicle must carry all its energy and reaction mass on board from the start of the trip. Is this really true? Think about in-situ resource utilization. An interstellar expedition could mine propellant from planetoids encountered at the destination. We can use propulsion systems that use the resources present in space, like gravitational assists, solar sails, or even interstellar ramjets. Granted, gravitational assists and solar sails could not get you anywhere near relativistic speeds, but they could work for slower travel.


Image: A Bussard ramjet in flight, as imagined for ESA’s Innovative Technologies from Science Fiction project. Credit: ESA/Manchu.

If the natural resources of space are not sufficient, there are other options. Rockets carry all their energy and reaction mass from the start. Beam-rider propulsion systems are an alternative that leave heavy engines, energy sources, and propellant back home. One such craft is a photon sail pushed by a laser. Another is a spacecraft propelled by a stream of relativistic pellets, each transferring momentum to the craft. As a cursory read of Mallove and Matloff’s excellent book The Starflight Handbook shows, we are not limited to rockets only.

Ultimately, Purcell’s conclusion that all speculation about interstellar travel belongs back “on the cereal box” simply doesn’t hold air in the space vacuum.

SETI vs interstellar travel?

Purcell’s paper underscores an unfortunate split in the ranks of scientists. Many scientists interested in SETI maintain that interstellar flight is simply not feasible for any civilization. They argue that we don’t need to physically travel to other planetary systems in order to learn about the rest of the universe. We need only turn our radio telescopes to the sky and search for broadcasts from more advanced civilizations. If we find them, these advanced civilizations will hopefully tell us everything we want to know. We might even find that mature civilizations in space have formed a galactic community of communicating societies. Perhaps they might allow us to join the conversation once we demonstrate enough maturity to engage in interstellar radio communications. This an exciting possibility, if a bit idealistic, and SETI deserves our support.

However, it is important to realize it is not an either-or question. We can research interstellar travel and carry out SETI searches at the same time. Even if SETI searches find communicative aliens to talk to, that will not negate the usefulness of interstellar travel. We will still need interstellar flight to investigate the countless solar systems where such civilizations are not present, and starflight is absolutely necessary for interstellar migration. But it seems like some SETI supporters don’t see it that way.

Denying starflight has become a fundamental tenant of the SETI worldview. It speaks directly to the question of whether it might be dangerous to contact alien civilizations. Many SETI supporters claim that we don’t have to worry about this question. If we assume interstellar travel is impossible, no civilization in space can physically threaten another. As Purcell claims in his paper:

It [communicating with ETI] is a conversation which is, in the deepest sense, utterly benign. No one can threaten anyone else with objects. We have seen what it takes to send objects around, but one can send information for practically nothing. Here one has the ultimate in philosophical discourse – all you can do is exchange ideas, but you do that to your heart’s content.

In my opinion, this is the real reason why Purcell argues so vehemently against the possibility of interstellar flight. In order for communication with ETI to be completely safe, interstellar travel must be impossible for any civilization anywhere in the universe. Contact with ETI becomes more complicated if there is a possibility of encountering them or their technology physically. Of course, we can’t be entirely sure messages from ETI will be entirely harmless either, if they contain instructions or information that might pose a danger.

I suspect that Purcell’s pessimistic arguments against starflight were driven more by his desire to believe that discourse with aliens comes without risks than a genuine interest in the future of space travel. Whatever the disposition of aliens, we can’t allow our personal hopes and dislikes to bias our conclusions. While interstellar travel is very difficult, we can already conceive of ways that a sufficiently motivated civilization could reach the stars.