NASA is renowned for doing really difficult stuff. You want to drop a Mini-sized lander on Mars using a sky crane? Well, NASA will do that for you. There is a view of NASA as staid and conservative but, on the whole, I think the agency is full of innovative problem solvers, albeit sometimes crippled by political oversight.

The side-effect of being innovative is that some rather strange and unphysical ideas sometimes escape from NASA. This probably explains the Helical Drive.

Twisting the laws of physics

The basic idea of the Helical Drive, according to the author of that link, is simple. Imagine that you have a mass in a cylinder that is oscillating back and forth. Every time the mass hits the end of the cylinder, it will impart some momentum, accelerating it. Because the mass sequentially collides with each end of the cylinder, the net force is zero, and the only outcome is that the cylinder gets a massive headache.

But, what if—you're going to love this—you could magically increase the size of the mass when it was traveling in one direction and decrease the mass when it was traveling in the other direction? If the velocity of the mass is kept the same, the force imparted at one end would be greater than at the other. You would have a net force: the cylinder would continuously accelerate in one direction.

Now we just have to fill in the magic part: how do we magically change the mass? The answer here is special relativity. If something is moving at close to the speed of light, its mass will increase. Indeed, the closer the object is to the speed of light, the larger its mass.

So, the answer, apparently, is simple. If we use a very strong magnetic field along the length of the cylinder, then alpha particles (helium atoms with the electrons stripped off) will start to corkscrew around the field. An accelerator in one section can accelerate the ions to as close to the speed of light as possible, while in a different section a countering accelerator will slow them back down. At each end, the ions reflect, imparting momentum to the cylinder.

Even better, the energy lost in accelerating the ions can be recovered when you slow them down, so it's nearly free acceleration (it is not a perpetual-motion machine in that sense, anyway). To put this in perspective, the author modeled this using magnetic fields of about 13T. The accelerator requires 160MW of power, which the author hopes to recover from the particles when they slow.

Conservation of momentum should not be ignored

Now, the author argues that because the inertial mass grows nonlinearly with speed, there is an average acceleration in one direction. Even better, this difference increases as the peak particle speed gets closer to the speed of light. Unfortunately, the Universe just doesn't quite work like that.

So, let's just state up front: this drive won't work. The problem is that, even though the author does a very nice simulation, he has left out the fields that do the accelerating. When we accelerate ions using a magnetic or electric field, the ions push back on the field. There is an equal and opposite force exerted on the electrodes and coils that produce the fields, and those just happen to be in the spaceship, too.

In the first step, where we accelerate the mass to a high relativistic speed, we also accelerate the cylinder in the opposite direction. Now, in special relativity, we don't conserve energy and momentum separately. Instead, they are conserved together. If you only consider momentum (and not energy), then you will find net forces everywhere due to inertial mass changes—things get heavier as they approach the speed of light. This is exactly what the author has found. If you consider energy and momentum simultaneously, those forces will suddenly disappear.

This is where the increase in inertial mass comes from in the first place: energy is sucked out of the field and turned into mass. When the particles are slowed, that mass is given up as photons in the field, which slow the cylinder as they are absorbed. What is the net force? Zero, 0N of force.

Now, my issue with this idea is not that it doesn't work. And my issue is not that NASA has people who spend time wondering about ideas like this—the author's job title includes the word "manager," so the more time he spends on this, the less damage he can do managing. My issue is that the last set of bullet points in the last slide tell the entire story.

• Basic concept is unproven • Has not been reviewed by subject-matter experts • Math errors may exist!

Yes, and the author works at an organization full of physicists who are subject-matter experts. I can't decide whether the moral of the story is that you should talk to people who know things before publishing anything or that, if you can't figure out where the momentum has gone, you don't understand what you are modeling.