The Bergenholm remains a fascinating piece of technology.

I intend to write a blog post about the various technologies that have worked their way into science fiction to allow us to reach the distant stars in more than 1000 human lifetimes. There are several of them: hyperspace, subspace, jump ships, warp bubbles, wormholes, even merely assuming Einstein was just wrong, and a few of my own: space rarefaction (especially the infinite-gradient case), space stratification, negative-inertia corridors, and that as yet unnamed technology that not only whisks Tim, Wendy, and Two halfway across the universe but bumps them a century into the future.

Aside from my own flights of fancy, there is one that I've seen in only one fictional universe,  and it is one that has intrigued my curiosity ever since I first read of it when I was in high school, decades ago.  I'm referring to Edward E. "Doc" Smith's inertialessness, implemented by the ubiquitous and mysterious device called the "Bergenholm", named after the cryptic figure who explained how to make it work.

The premise is that it completely neutralizes the inertia of matter, rendering it massless, or "free". In that state, an object such as a spaceship instantly attains the velocity at which friction against the rarefied gas of space exactly matches its propulsive force, which in the Lensman series amounts to thousands of tons. It is presumed that this balancing velocity is many thousands or millions of times the speed of light.

Smith doesn't stop there.  He introduces the concept of "intrinsic velocity", claiming that the conservation of momentum is never actually violated because when the Bergenhold shuts off, the ship immediately goes "inert" and assumes the velocity and momentum that it had the instant it was switched on.  This in turn leads to complications and subtleties that stretch across the six volumes as a way of life for space-farers. Any rendezvous in space must necessarily include "matching intrinsics."

It's all a very interesting proposition, but as I recently re-read the series as I am compelled to do periodically, I was struck by a few more inconsistencies on top of the ones I already knew about. Here, with no disrespect for Smith intended, as he remains the father of the space opera, here are the ways the Bergenholm drive doesn't quite ring true.

1. It would alter the fundamental properties of the universe

All amateur physicists and most science fiction fans know that as velocity increases, so does mass, so that at the speed of light, an object's mass is infinite.  It is obviously impossible to accelerate it any further.  This might be true, but it's only one aspect of the situation, one that is easy to visualize for the non-scientist.  At heart of the matter is that the laws physics has to be the same for everyone, or the universe has some serious problems.

The speed of light turns out to be related to the magnetic permeability (μ₀) and electric permittivity (ε₀) of free space by the relationship:

Since these are the two most fundamental constants upon which electronics operates, not to mention our nervous systems, we had better not mess with them.  For physics to keep working, the speed of light must not only remain a constant, but the speed of every photon of light in a vacuum must be the same constant for every observer.  Look at it this way.  You see a beam of light about to pass you by (at the speed of light, of course) and

you decide to follow it.  You go faster and faster, but no matter how fast you go, in order for your iPod to still play, the light has to still pass you by at the speed of light.  You're up 99.999% of the speed of light.  How fast does that beam pass you by? You got it: at the speed of light.  If it were otherwise, all of the electronics on the ship would quit working and you would die.  What happens if we actually exceed the speed of light? Well, at the  very least, physics breaks down, and you're in a heap of trouble.

Some of the other hypothesized faster-than-light drives, including the one that NASA is really exploring, get around this by never exceeding the speed of light in local space.  The Bergenholm inertialess drive, unfortunately, breaks the law.

2. It relies on windings and armatures

Smith never completely explains how the Bergenholm works, which is understandable because it's a fictional device, and if he did we'd be able to build one.  Like all good science fiction writers, however, he drops come clues.  He talks of electrical windings and uranium armatures, all of which sounds very much as if he envisioned it as something akin to a motor.  As both scientist and engineer, this concept presses my credibility right to the limit.  I'd have preferred him be less detailed.

3. It violates the conservation of energy (part 1)

Although Smith does address the conservation of momentum with his intrinsic velocity, he completely ignores the conservation of energy.  Momentum is given by p=mv, so we can easily see that when mass goes to zero, so does momentum.  OK.  But kinetic energy is given by K=½mv², so when mass goes to zero, so does kinetic energy.  Where, pray tell, does that energy go?  Most of the time, when either kinetic or potential energy "disappears", it becomes heat.  This is related to the Second Law of Thermodynamics, but let's not go into too much detail about that.  As a net result, we should expect that when a 20,000-tons spaceship traveling at 1000 km/s switches in its Bergenholm, it would instantly puff up into a cloud of incandescent vapor.  Or would it?  Let's look into how that would play out.

4. It violates thermodynamics

According to the kinetic theory, the temperature of matter is related to the average kinetic energy of its molecules.  But wait!  The molecules that make up the ship (not technically molecules, but the same logic applies) have no mass, therefore no kinetic energy, therefore they are at absolute zero.  Let's skip the fact that the crew would be frozen solid, because that's part of the same picture.  Not only does the gross kinetic energy of the ship disappear, so does all the energy associated with its temperature.  Just were, then, would it go.

I had thought of throwing in a bunch of equations like

but this isn't really a treatise on thermodynamics. Suffice it so say that in order for that much energy to vanish without violating thermodynamics, the entropy of the system would have to decrease abruptly, without doing the math, probably to a negative value.  The problem is, negative entropy is impossible by either the Boltzmann or Gibbs definition.  And even if it weren't, for a closed system to decrease its entropy at all violates that pesky Second Law of Thermodynamics.  There is no way for it to work.

5. It violates the conservation of energy (part 2)

We looked at kinetic energy, now let's look at potential energy.  If you switch on a Bergenholm on the surface of Earth, fly to Valeria with almost three times Earth's gravity and turn it back off, what happens? Forget about matching intrinsics for the moment.  Well, you're suddenly at a much lower gravitational potential energy than you had on Earth and even if you can postpone the conservation of energy as he does with momentum, it has to go somewhere. It can't go into kinetic energy because we also have to conserve momentum.  This is just another way that energy has to disappear, which takes us back to the last two problems above.  Only there's more.  If you go the other way, from Valeria to Earth, energy has to suddenly appear from nowhere.

Incidentally, in one of my unfinished works, I use this to advantage.  To conserve gravitational potential energy after entering hyperspace from low Earth orbit, you have to come out at the same energy level, i.e., probably near an Earth-sized planet.

5. You wouldn't be able to breathe

Even if you didn't freeze.  The pressure of a gas depends on the inertia of molecules.  Take that away, and no matter how much you gasp for breath, air is not going to seek out your lungs.  You'd effectively be in a vacuum.  In the first successful trial of the inertialess drive, either Rodebush or Cleveland (I forget which one it is without looking it up) drifts across the cabin until the tip of one his hairs touches the bulkhead. Drifts?  With what?  There is no inertia.  But somehow they could still breathe. Blood might well pump OK, as the molecules of liquid are pretty much in contact, wherein forces are communicated primarily by Pauli exclusion, but that would do you no good if you can't get oxygen into your lungs.

6. It requires absolute space

The most fundamental concept of Einstein's General Theory of Relativity is that there are no absolute positions and no absolute times.  Everything is relative; that's why it's called relativity.  You're out in the middle of space and go free.  You stop, but what do you stop relative to?  Anywhere in our galaxy, that's easy; you stop relative to the gas in space, even though it's not much.  You're blown around by interstellar winds.  But this argument doesn't get around the basic problem.

Let's say you're so far out in space between superclusters that molecules of gas are thousands of miles apart. You go free.  Now, what do you stop relative to?  In order for stopping to even be meaningful in that case, there has to be some absolute concept of position.  This requirement was actually built into the notion of "intrinsic velocity" to begin with, even though I didn't mention it until now, because in a relative universe there is no such thing.  There is only relative velocity.  I'm not saying that absolute space is impossible, but in that case, we would have to go back 100 years and rewrite all of physics from the ground up.

7. It violates symmetry

This is the toughest one of all to explain without getting nauseatingly mathematical, but I'll try.  If you're a mathematician or a masochist — believed by many to be the same thing — check out the Euler–Lagrange equation. OK, to put the heart of the matter into words, if a generalized coordinate does not appear in a Lagrangian equation of motion, then the first moment of that coordinate is invariant, or constant.  If we're looking at the conservation of momentum, the generalized coordinate is position and its first moment is momentum. The similarity in the words moment and momentum is no accident. To get less mathematical again, it is the fact that every point in space is identical that results in the conservation of momentum.  This is actually really, really cool stuff if you're a physics geek, and is codified in Noether's Theorem.  Also, that every direction is the same that leads to the conservation of angular momentum and that every time is the same that leads to the conservation of energy.

So what happens the instant you switch on the Bergenholm?  Mass disappears and so does momentum; we've covered that.  Momentum experiences a discontinuity at that point, and so by the very basics of what constitutes motion, there must be a discontinuity in linear space.  With the Bergenholm on, when the ship is free, it is arguable that it is no longer in the same space that it was before. I don't mean the same place in space, I mean the same space.  Where you would go, I have no idea.  Technically, I suppose, another universe, which would wreck havoc with their detectors and communications.  But the whole thing bears a striking mathematical similarity to both my space stratification drive and negative-inertia corridors.

Let me reiterate that these observations are in no way intended to disparage Smith.  He was a visionary.  It's hard to find any feature of modern science fiction he didn't pen in the early days of pulp fiction: defensive screens, faster-than-light travel and communication, atomic blasters, all the way up to the sun gun, planetary mass negaspheres (there is some bad physics there, too), parallel universes, and mental telepathy.  About the only things he missed were teleporters and computers. He laid the basis for Star Trek, Star Wars, 2001: A Space Odyssey, and pretty much everything else.  And let's not forget that the Lensmen were part of my inspiration to write, and a huge part of the inspiration for my own space opera series.

What have you found in science fiction that doesn't quite ring true?