Quantized inertia

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Quantized inertia (QI), previously known as the acronym MiHsC (Modified Inertia from a Hubble-scale Casimir effect), is a hypothesis about the origin of inertia, that has been characterised as pseudoscience. The concept was first proposed in 2007 by Mike McCulloch, a lecturer in geomatics,[1] claiming to provide an explanation for galaxy rotation curves without dark matter.[2][3][4][5] Since then, some of the problems it was initially proposed to solve have been solved by conventional physics, like the Pioneer anomaly.

Unruh radiation and horizon mechanics[edit]

There is an event horizon in the universe where light (and therefore any information) cannot and will never be able to reach an object, because the cosmic acceleration outpaces the speed of light: the cosmological comoving horizon.[citation needed] If the object accelerates in one direction, a similar event horizon is produced: the Rindler horizon.[citation needed] Anything beyond these horizons is outside the observable universe, and therefore can't affect the object at the center of the Rindler space.[citation needed]

The Rindler event horizon is effectively the same as the event horizon of a black hole, where quantum virtual particle pairs are occasionally separated by gravity, resulting in particle emissions known as the Hawking radiation. For a Rindler horizon produced by an accelerating object, a similar radiation is predicted by quantum field theory: the Unruh radiation.[citation needed] Due to the difficulty of measuring such tiny quantum background radiation seen only from the reference frame of an accelerated object, Unruh radiation has not been definitely observed so far, although some evidence may exist.[6]

Quantized inertia posits that Unruh radiation is the origin of inertia: as a particle accelerates, the Rindler information horizon expands in the direction of acceleration, and contracts behind it. Although being different in essence, this is a macroscopic analogy of the Casimir effect: a non-fitting partial wave would allow an observer to infer what lies beyond the event horizon, so it would not be a horizon anymore. This logical assumption disallows Unruh waves that don't fit behind an accelerating object. As a result, more Unruh radiation pressure (which acts through the volume of the mass, not only on its surface like the electromagnetic radiation pressure) hits the object coming from the front than from the rear and this imbalance pushes it back against its acceleration, resulting in the effect observed as inertia.[7][8][non-primary source needed]

There is another event horizon much farther away: the Hubble horizon. So even in front of an accelerating object, some of the Unruh waves are disallowed, especially the very long Unruh waves that exist if the object has a very low acceleration. Therefore, quantized inertia predicts that such an object with very low acceleration would lose inertial mass in a new way.[2][non-primary source needed]


Quantized inertia has been criticized as being pseudoscience by astrophysicist Brian Koberlein.[9]

Some of the problems it was initially proposed to solve have since been solved by conventional physics. One of these is the EmDrive, which claimed propulsion without any propellant. As of 2021, it appears that the EmDrive effect is solely due to experimental errors, such as heating and magnetic effects, rather than new physics.[10] Quantized inertia was also proposed to explain the Pioneer anomaly. As of 2018, the general scientific consensus appears to be that the problem of the Pioneer anomaly is completely explained by the recoil of thermal radiation from the spacecraft's power source.[11]

In 2019, a Romanian particle physicist performed a derivation of quantized inertia in which he claims to have found two errors in McCulloch's original work prior to 2013. He subsequently provides a new derivation showing different predictions.[12]

Current Experiments In Quantized Inertia[edit]

In 2017 the United States, Defense Advanced Research Projects Agency (DARPA) provided $1.3M in funding for a four-year study which aims to investigate quantized inertia[13]. As part of the DARPA grant, a number of experimental tests in various configurations were performed at the Dresden University of Technology. They reported no thrust and the results put strong limits on all proposed theories like quantized inertia by 4 orders of magnitude.[10]


  1. McCulloch, M. E. (21 March 2007). "Modelling the Pioneer anomaly as modified inertia" (PDF). Monthly Notices of the Royal Astronomical Society. 376 (1): 338–342. arXiv:astro-ph/0612599. Bibcode:2007MNRAS.376..338M. doi:10.1111/j.1365-2966.2007.11433.x. S2CID 5315184.
  2. 2.0 2.1 McCulloch, M. E. (20 May 2010). "Minimum accelerations from quantised inertia". EPL. 90 (2): 29001. arXiv:1004.3303. Bibcode:2010EL.....9029001M. doi:10.1209/0295-5075/90/29001. S2CID 118335505.
  3. McCulloch, M. E. (December 2012). "Testing quantised inertia on galactic scales". Astrophysics and Space Science. 342 (2): 575–578. arXiv:1207.7007. Bibcode:2012Ap&SS.342..575M. doi:10.1007/s10509-012-1197-0. S2CID 119211930.
  4. McCulloch, M. E. (March 2017). "Low-acceleration dwarf galaxies as tests of quantised inertia". Astrophysics and Space Science. 362 (3): 57. arXiv:1703.01179. Bibcode:2017Ap&SS.362...57M. doi:10.1007/s10509-017-3039-6. S2CID 119437133.
  5. McCulloch, M. E. (September 2017). "Galaxy rotations from quantised inertia and visible matter only". Astrophysics and Space Science. 362 (9): 149. arXiv:1709.04918. Bibcode:2017Ap&SS.362..149M. doi:10.1007/s10509-017-3128-6. S2CID 13665174.
  6. Smolyaninov, Igor I. (24 November 2008). "Photoluminescence from a gold nanotip in an accelerated reference frame". Physics Letters A. 372 (47): 7043–7045. arXiv:cond-mat/0510743. Bibcode:2008PhLA..372.7043S. doi:10.1016/j.physleta.2008.10.061. S2CID 119050574.
  7. McCulloch, M. E. (March 2013). "Inertia from an asymmetric Casimir effect". EPL. 101 (5): 59001. arXiv:1302.2775. Bibcode:2013EL....10159001M. doi:10.1209/0295-5075/101/59001. S2CID 118357836.
  8. Giné, J.; McCulloch, M. E. (2016). "Inertial mass from Unruh temperatures" (PDF). Modern Physics Letters A. 31 (17): 1650107. Bibcode:2016MPLA...3150107G. doi:10.1142/S0217732316501078. hdl:10459.1/58386.
  9. Brian Koberlein (2017-02-15). "Quantized Inertia, Dark Matter, The EMDrive And How To Do Science Wrong". forbes.com.
  10. 10.0 10.1 Tajmar, Martin (2021-03-01). "Thrust Measurements and Evaluation of Asymmetric Infrared Laser Resonators for Space Propulsion". researchgate.net.
  11. Adler, Doug (2018-08-17). "How the Pioneer anomaly was solved". Astronomy.com.
  12. Renda, Michele (October 2019). "A sceptical analysis of Quantized Inertia". Monthly Notices of the Royal Astronomical Society. 489 (1): 881–885. arXiv:1908.01589. Bibcode:2019MNRAS.489..881R. doi:10.1093/mnras/stz2189. S2CID 199442424.
  13. Alan Williams (2017-09-17). "Scientists receive $1.3 million to study new propulsion idea for spacecraft". plymouth.ac.uk.