Self-Accelerating wavepackets: What are they and can they impulse a spaceship?

Question

Nature today published a (paywalled) article that mentions 'Self-accelerating Dirac wavepackets'. They claim that they behave in a similar fashion as the diffractive tricks of polarized beams that have light twist in a direction, but in this case with charged particles (A previous article by some of the authors on the same subject)

Now, on the media article (unfortunately I don't have access to the original paper, although I might end up buying a copy in a few days if I don't find someone to borrow a copy) they say that this happens due to 'uncertainty principle' and that the 'acceleration is compensated by larger position uncertainty in the opposite direction'.

I don't understand very well what that means, but I suspect what it means is that it cannot be used to accelerate a spaceship

What is your interpretation of the claims in the article? is this just useless for space propulsion? If as they also claim in the media article, the acceleration is indistinguishable from acceleration due to EM fields, I don't see why it wouldn't, but it wouldn't be the first time that quantum physics troll our expectations

Edit: It seems that the question boils down to what counter-force is exerted by the beam on the holographic mask grating used to generate the wavepacket, and how such counter-force would compare to a similar electron beam without any grating

Answer 1

These quantum states were predicted already in 1979 by Berry and Balazs for photons (called Airy beams), shown experimentally in 2007 by Christodoulides et. al. and have had lots of applications since then. It is also a phenomena general to wave equations and not specific to the Schrödinger or Dirac equations.

The authors find a solution to the Dirac equation (a wave equation for spin-1/2 particles) which is a quantum-mechanical superposition of an infinite number of plane waves, all related to each other by a relativistic boost.

The resulting composite wave exhibits interference which results in a probability density (of charge) that looks like it's accelerating.

The key point is that with the setup in this paper, any boosted observer (observers moving at different velocities) interacting with the particle, will see the exact same wave-shape, and furthermore the wave-shape locally at the observer will look like it is accelerating, i.e. interacting with a force, even though it's not. This directly means their solution conserves the composite wave shape through any velocity, which means it looks like acceleration.

I'm sure the math of it for once actually is more intuitive than the description :)

You can see this paper by Voloch-Bloch from 2013 on arXiv (free) which describes an experiment generating a "self-accelerating" electron beam (called an electron Airy beam), by preparing the quantum state by sending the electrons through a special nanoscale hologram.

The newer Nature article adds on this by showing that properties of their superposition also exhibits relativistic length-contraction and time-dilation and the article goes to length to show that all properties actually make it look exactly like the particle feels a force (which is not there) in a relativistic context (twin paradox etc) even in a flat space. It's a pretty thorough exhibition of how relativistic effects can arise through carefully prepared initial quantum states. The article also shows that the particle picks up a phase as if it passed through a potential, similar to the Aharonov-Bohm effect.

The particle still conserves energy and momentum and particle number - and you should never say no, but I would be surprised if there is a way to accelerate a whole spaceship with this in an obvious way. Would be pretty cool though..

Edit: I guess the electron in the curved trajectory does transfer lateral momentum, which means the waveshaping device should rebound. See the comment section. There is probably more to be said here..