I've read that even in a "perfect" vacuum, matter exists in the form of virtual particles that spontaneously pop into existence only to be immediately annihilated. This suggests to me that it might be possible to use these particles during their short existence as a propellant by accelerating them before they annihilate. Problem is, this seems to violate the conservation of momentum because the virtual particles would immediately cease to exist after their mass is accelerated to create momentum.

My question is this: what would be necessary in order to get around the conservation of momentum issue here?


My question is this: what would be necessary in order to get around the conservation of momentum issue here?

There's two options.

Photon Truster

This is the more conventional of the two options, and ignores virtual particles.

E=mc^2 is often mistakenly described as the energy you get by converting mass into energy. This isn't really what it says. It says that energy and mass are equivalent. That's why it's known as the Mass-energy equivalence. Even E=mc^2 is only the special case for mass at rest, but there's no need to get into that.

You can rearrange the equation to read m = E/c^2. This means energy, for the purposes of calculating momentum, has mass. If you fire enough high energy photons out the back of a spacecraft you will get thrust. This is known as a photon thruster or photon rocket.

Photon thrusters are extremely inefficient. Because c^2 is very large, like 9e16 m^2/s^2, the thrust is very, very, very low. 1 GJ, roughly the energy in a lightning bolt, has the rest mass of about 10 micrograms. You're better of using that energy to fire out a small amount of mass at very high speed; then you have an ion thruster, one of the most efficient thrusters currently available.

But as efficient as they are, even ion thrusters will run out of mass. So long as there's energy available, like from solar panels, you can get thrust out of a photon thruster. Over a long enough time it can add up to something noticeable. Photons from waste heat bouncing off the inside of the craft in an unbalanced fashion is what caused the Pioneer Anomaly.

RF resonant cavity thruster aka EmDrive

The infamous EmDrive being tested at NASA is supposed to work with no reaction mass and a higher efficiency than a photon thruster.

enter image description here

They did measure a thrust in a vacuum and at different orientations ruling out a lot of errors. It did pass peer-review; Measurement of Impulsive Thrust from a Closed Radio-Frequency Cavity in Vacuum.

The hype on this got out of control, so let's reign it in. No, NASA did not prove the EmDrive works, but they did eliminate a lot of potential conventional explanations. The paper claims to have observed a thrust of about 1.2 mN/kW in a vacuum (which is very, very low), at different orientations, and at different power settings. They don't speculate on why, but they do note it's about two orders of magnitude over what they'd expect from a photon thruster.

The 1.2 mN∕kW performance parameter is over two orders of magnitude higher than other forms of “zero-propellant” propulsion, such as light sails, laser propulsion, and photon rockets having thrust-to-power levels in the 3.33 – 6.67 μN∕kW (or 0.0033 – 0.0067 mN∕kW) range.

There's any number of non-crackpot conventional and unconventional explanations including pushing off of "quantum vacuum virtual plasma" but other physicists say that's not possible.

Most physicists are EXTREMELY skeptical that this actually works. Because the thrusts involved are so low, because existing quantum theory is so successful, and because the error bars on this experiment are so high, their money is on experimental error.

enter image description here

Here's a bunch of physicists and rocket scientists on the EmDrive.

We won't really know until it flies in space, even then I expect physicists to remain very skeptical and call for more experiments to eliminate all error.

But hey, probably good enough for a sci-fi story!

  • $\begingroup$ I was getting all ready to make nasty comments about using the EmDrive in a hard science article till I read the last line. Patience, is, as always, a virtue. +1 $\endgroup$
    – kingledion
    Mar 3 '17 at 18:01
  • $\begingroup$ @kingledion Yeah. That its passed peer-review by NASA in a vacuum chamber elevates it well above the usual quackery, though the headlines have blown the findings WAAAAY out of proportion. I'll link to the actual published paper. $\endgroup$
    – Schwern
    Mar 3 '17 at 18:06

You don't need mass to have momentum

Photons are mass-less particles that have momentum. As @b.Lorenz points out in the comments, the do have a relativistic mass, since they have energy and by relativity energy is equivalent to mass. But they do not have a classical mass.

The particles that you are talking about popping into existence seems like the electron-positron pair that form from high energy gamma photons. Since the photons are required to produce this pair, any momentum you could get from them would also be in the photons that formed them (due to conservation of momentum).

So, if you want to use a 'reaction mass' that you don't have to carry with you then you want to use the photons themselves as the 'reaction mass' for your thruster. I talk about the various aspects of a photonic thruster in this post, in an equation-oriented way.

The advantage of the photons is that the relativistic mass/energy of the photons that is expended in firing them is the same as the relativistic mass/energy needed to impart the photons their momentum in the first place. That means, if you are using a fusion reactor, the mass of the waste product particles involved in fusion will be lower than the mass of the fuel for the fusion by the same amount as the mass/energy transferred to the photons (minus efficiency losses).

  • $\begingroup$ Not that I assume this is the same thing but would it be similar to a Dyson Bladless Fan?. It seems to follow a similar concept that pushes air without having a blade or mass to do so but I am probably totally off base and why it is a comment XD $\endgroup$
    – ggiaquin16
    Feb 23 '17 at 21:02
  • $\begingroup$ Yeah, the Dyson fan would be a very simple way of describing this, only instead of operating on air, it would operate on virtual particles. $\endgroup$
    – Adam
    Feb 23 '17 at 21:47
  • $\begingroup$ Your statement about photons having momentum, but not having mass is only partially correct. Their rest mass is 0, but since they carry energy, they have relativistic mass too. So if the spaceship uses it's onboard energy source (Fission or fusion or antimatter reactor, simple fire or anything you want) to emit photons, it's mass will decrease by h*f/c**2 kg for every photon. $\endgroup$
    – b.Lorenz
    Feb 24 '17 at 20:04
  • $\begingroup$ @b.Lorenz You are certainly right. From the prospective of the perspective (punny?) interstellar traveler, this is a good thing, however. you still don't need to effectively bring any fuel mass with you. The same mass that you use to generate the energy is your reaction mass as well. $\endgroup$
    – kingledion
    Feb 24 '17 at 20:11

I think you got a wrong grasp of the theory: in vacuum pairs of particle and antiparticle are created and immediatly annihilated. Momentum is conserved here. The only known (but not yet proven) mechanism that materializes these virtual particles it's the event horizon of a black hole: any pair which materializes on the horizon is separated by the gravitational pull. The half within the horizon falls into the black hole, the half after the horizon can escape the black hole as a real particle. This is called Hawking radiation.

Therefore it looks pretty unpractical to have a black hole in a starship to propel it.

  • $\begingroup$ There's also the Casimir effect, but this isn't of much help either $\endgroup$ Feb 25 '17 at 9:41
  • $\begingroup$ In Star Trek didn't the Romulans have singularities propelling their ships? $\endgroup$
    – Willk
    Feb 26 '17 at 0:56
  • $\begingroup$ @Will, I think the tag hard-science rules out the Star Trek thingy $\endgroup$
    – L.Dutch
    Feb 27 '17 at 6:18

Apply a mechanism that induces a physical effect on the vacuum that causes sufficient numbers of the virtual particles to emerge moving in the same direction. Assume the virtual particles have a component of motion. If the particles are charged and if the chamber in which the virtual particles are moving in a collimated flux, can apply an electromagnetic field to decelerate the charged virtual particles.

Basically it is a gigantic particle accelerator that instead of accelerating the virtual particles "steals" momentum from them.

The process of polarizing the emergence of virtual particles from the quantum vacuum is a purely hypothetical concept. Hypothetical to the point of calling it a fiction as there is no known physical mechanism to justify or explain it. But it could pass muster in science-fiction.

The scale and power of the linear particle accelerator required to transfer momentum from the polarized virtual particle flux is uncertain, but is presumably many orders of magnitude beyond anything that human technology can achieve in the foreseeable future.

The quantum vacuum is effectively a sea of virtual particles in all possible momentum states. Any propulsive system utilizing them would have to work by sequestering an excess of virtual particles to emerge with a momentum spectrum capable of acting as a propulsion system.

John Baez's FAQ on virtual particles deals with both momentum and energy conservation of virtual particles. This is explained in terms of quantum mechanical perturbation theory.

Some descriptions of this phenomenon instead say that the energy of the system becomes uncertain for a short period of time, that energy is somehow "borrowed" for a brief interval. This is just another way of talking about the same mathematics. However, it obscures the fact that all this talk of virtual states is just an approximation to quantum mechanics, in which energy is conserved at all times. The way I've described it also corresponds to the usual way of talking about Feynman diagrams, in which energy is conserved, but virtual particles can carry amounts of energy not normally allowed by the laws of motion.

This explained here in clearer terms:

The concept of virtual particles arises in the perturbation theory of quantum field theory, an approximation scheme in which interactions (in essence, forces) between actual particles are calculated in terms of exchanges of virtual particles. Such calculations are often performed using schematic representations known as Feynman diagrams, in which virtual particles appear as internal lines. By expressing the interaction in terms of the exchange of a virtual particle with four-momentum q, where q is given by the difference between the four-momenta of the particles entering and leaving the interaction vertex, both momentum and energy are conserved at the interaction vertices of the Feynman diagram.

Consideration of issues about virtual particles in relation to momentum and energy conservation is a good idea. However, quantum mechanics has definitively answered this: the conservation laws apply and aren't a problem.

Note: For those who care about this sort of thing: The hypothetical virtual particle propulsion system proposed above is undoubtedly a form of Maxwell's demon and would have all the usual problems associated with it.


Froning, H. D., Jr. (1980) “Propulsion Requirements for a Quantum Interstellar Ramjet”, Journal of the British Interplanetary Society, Vol. 33, No. 7, pp. 265-270.

Froning, H. D., Jr. (1985) “Use of Vacuum Energies for Interstellar Flight”, MDC paper H1496, 36th Congress of the International Astronautical Federation, October, Stockholm, Sweden.

Froning, H. D., Jr. (2003) “Investigation of a 'Quantum Ramjet for Interstellar Flight'”, MDAC paper G7887, AIAA/SAE/ASME 17th Joint Propulsion Conference, Colorado Springs, July, CO.

Froning, H. D., Jr. and Roach, R.L. (2002) “Preliminary Simulations of Vehicle Interactions with the Quantum Vacuum by Fluid Dynamic Approximations”, paper AAIA-2002-3925, American Institute of Aeronautics and Astronautics, Washington, DC.

Froning, H. D., Jr., Barrett, Terence W., and Hathaway, George (1998) “Experiments Involving Specially Conditioned EM Radiation, Gravitation and Matter”, paper AAIA-98-3138, American Institute of Aeronautics and Astronautics, Washington, DC.

Minami, Y. (2008) “Preliminary Theoretical Considerations for Getting Thrust via Squeezed Vacuum”, Journal of the British Interplanetary Society, Vol. 33, No. 7, pp. 315-321.

Fiction where the concept has been used:

Charles Sheffield, The McAndrew Chronicles (New York: Tor Books, 1983)

Arthur C Clarke, The Songs of Distant Earth (New York: Ballantine/Del Rey, 1986)


Perhaps you could attempt using "squeezed light" so you could use destructive quantum interference to cancel out the virtual particles in certain areas, thereby creating areas of "low pressure". This so called "pressure difference" of the energy being exerted by virtual particles in certain areas could be used to create a propulsion-like effect.

  • 3
    $\begingroup$ can you give more details or reference on how to squeeze light? $\endgroup$
    – L.Dutch
    Mar 3 '17 at 8:28
  • $\begingroup$ You need to note the rules for hard-science answers. For a normal answer, this does not address concervation of momentum. You can’t make a force that violates Newton’s 3rd Law. And light are “real” particles, not virtual: electromagnetic forces invoke virtual particles. $\endgroup$
    – JDługosz
    Mar 4 '17 at 20:09
  • $\begingroup$ But, welcome to Worldbuilding! Fill in your profile, stick around; browse the existing bank of questions and answers, and please do contribute again. $\endgroup$
    – JDługosz
    Mar 4 '17 at 20:11

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