Wednesday, December 16, 2015

No, you don’t need general relativity to ride a hoverboard.

Image credit: Technologistlaboratory.
This morning, someone sent me a link to a piece that appeared on WIRED

The hoverboards in question here are the currently fashionable two-wheeled motorized boards that are driven by shifting your weight. I haven’t tried one, but it sure looks like fun.

I would have ignored this article as your average internet nonsense, but turns out the WIRED piece is written by someone by name Rhett Allain who, according to the website “is an Associate Professor of Physics at Southeastern Louisiana University.” Which makes me fear that some readers might actually believe what he wrote. Because he is something with professor, certainly he must know the physics.

Now, the claim of the article is correct in the sense that if you took the laws of physics and removed general relativity then there would be no galaxy formation, no planet Earth, no people, and certainly no hoverboards. I don’t think though that Allain had such a philosophical argument in mind. Besides, on this ground you could equally well argue that you can’t throw a pebble without general relativity because there wouldn’t be any pebbles.

What Allain argues instead is that you somehow need the effects of gravity to be the same as that of acceleration and that this sounds a little like general relativity, therefore you need general relativity.

You should find this claim immediately suspicious because if you know one thing about general relativity it’s that it’s hard to test. If you couldn’t “ride a hoverboard without Einstein’s theory of General Relativity,” then why bother with light deflection and gravitational lensing to prove that the theory is correct? Must be a giant conspiracy of scientists wasting taxpayers’ money I presume.

Image Credit: Jared Mecham
Another reason to be suspicious about the correctness of this argument is the author’s explanation that special relativity is special because “Well, before Einstein, everyone thought reference frames were relative.” I am hoping this was just a typographical error, but just to avoid any confusion: before Einstein time was absolute. It’s called special relativity because according to Einstein, time too is relative.

But to come back to the issue about gravity. What you need to drive a hoverboard is to balance the inertial force caused by the board’s acceleration with another force, for which you have pretty much only gravity available. If the board accelerates and pushes forward your feet (friction required), you better bend forward to shift your center of mass because otherwise you’ll fall flat on your back. Bend forward too much and you fall on your nose because gravity. Don’t bend enough, you’ll fall backwards because inertia. To keep standing, you need to balance these forces.

This is basic mechanics and has nothing to do with General Relativity. That one of the forces is gravity is irrelevant to the requirement that you have to balance them to not fall. And even if you take into account that it’s gravity, Newtonian gravity is entirely sufficient. And it doesn’t have anything to do with hoverboards either. You can also see people standing on a train bend forwards when the train accelerates because otherwise they’ll fall in dominoes. You don’t need to bend when sitting because the seat back balances the force for you.

What’s different about general relativity is that it explains gravity is not a force but a property of space-time. That is, it deviates from Newtonian gravity. These deviations are ridiculously small corrections though and you don’t need to take them into account for your average Joe on the Hoverboard, unless possibly Joe is a Neutron star.

The key ingredient to general relativity is the equivalence principle, a simplified version of which states that the gravitational mass is equal to the inertial mass. This is my best guess of what Allain was alluding to. But you don’t need the equivalence principle to balance forces. The equivalence principle just tells you exactly how the forces are balanced. In this case it would tell you the angle you have to aim at to not fall.

In summary: The correct statement would have been “You can’t ride a hoverboard without balancing forces.” If you lean too much forward and write about General Relativity without knowing how it works, you’ll fall flat on your nose.


  1. It's interesting that people don't naturally lean forward when they are learning to ski or ice skate. The natural reflex is to lean backwards away from your direction of motion, which as you explain is the wrong thing to do!

  2. "the effects of gravity to be the same as that of acceleration" To 14+ significant figures, no measurable observable violates the Equivalence Principle (EP). Chemistry offers an unmeasurable observable violating the EP given ECSK gravitation, "E" being Einstein. Source baryogenesis by dropping the other shoe. Look.

    "Dr. Allain's research interests are in the field of Physics Education Research" (SLU website). If you are in the tested 90th percentile in math, MIT or Caltech will slay you. Education is not at fault as runts are culled. Mediocrity is a vice of the doomed.

  3. A true hoverboard would likely make use of Maxwell-Einstein supergravity.

  4. Without
    Relativity, those boards seem to be relativly dangerous. :=(

  5. During the "Deflategate" (American Football) scandal, I read two articles (one at a national media site) by different physics professors who tried to calculate the expected change in football internal pressure due to a temperature change using the Ideal Gas Law, but without knowing (or at any rate, accounting for) the difference between gauge pressure (psig) and absolute pressure (psia). (Sorry for the English units, American Football has not gone metric.)

  6. @JimV P1/P2 = (k)T1/T2 (degrees absolute: kelvin, rankine, whatever). The van der Waals equation (atoms' finite size, moiety interactions) for greater accuracy. A football's internal pressure is gauge (scale not balance). Theory requires barometric correction, elastic deformation of the envelope, etc.
    When theory fails, engineering prevails. Measure it.

    Engineering solutions suffer reality deficit disorder (e.g., the Golden Gate Bridge versus Galloping Gertie). More studies are needed - penetrometer vs. pressure readings over a temperature span.

  7. @Uncle Al - I did use elastic as well as thermal deformation of the envelope in my calculation, as is common in engineering. (I am not highly confident of the expansion coefficients which I found online, but the effect was small, about 0.1 psi.) To do this you must include V1 and V2 in the equation, as well as auxiliary equations of deformation, which I did. My calculation disagreed significantly with the two by physics professors, but the major source of the difference was that they used the gauge pressure as absolute. Sometimes engineers are better at everyday problems (due to more experience in that realm). The physics professors used your equation, neglecting elastic and thermal deformation of the container.

    In the engineering analysis paid for by the NFL, actual tests of NFL footballs were made, as is usual in engineering studies.

    (I'm not sure what the point of your reply was, but it seemed to be critical. I'm not claiming that I know physics better than any physics professor, including the two I mentioned. I'm sure they could do lots of calculations that I cannot do. In the case above they made a common mistake which I thought was relevant to the original post. If my comment was offensive I am sorry and hope it gets deleted.)

  8. Hi,

    As far as I know the only thing you need GRT for is the GPS system (and Galileo, Glonass) as it includes (on-board) clocks corrections due to the altitude in the field. The initial series of GPS satellite had a switch on-board to enable or disable the correction.. because the engineers of the time did not believe GRT was field-proven (that was in the 1970s).

    Though I am not even sure GRT is needed because with E = m c^2 = h nu, and considering the Newton potential energy increase, you also get a different clock rate (which may miss a factor 2).


  9. General relativity works: Galaxy cluster delayed image gravitational lensing of SN Refsdal is accurately predicted, arXiv:1512.04654. GR cannot be complete. Falsify weak postulates.

    @JimV Football inflation resists ab initio theory. Semi-empirical approaches are splendid. However, semi-empirical is also 45 years of gravitation and particle theory failing to accurately predict. Reality is being modeled not understood. Strop Occam's razor. Observe trivially explanative outliers. Hoverboards are...Spaceballs (1987), Yogurt: "Moichandising!!"

  10. "Southeastern Louisiana University"

    Of course, there are many universities in the States, and not all have the high quality of European or good US universities. I don't recall Southeastern Louisiana University as being a leading centre of GR research. And normal-scientist-turned-crackpot Frank Tipler hails from Louisiana as well. Academic standards don't seem to be too strict down there.

  11. " the multiverse opponents [...] seem to be afraid that merely considering the multiverse an option discourages further inquiries, inquiries that might lead to better answers." that statement is very unbalanced since you fail to mention the self-serving, self-promotional and financial motivations of many of the leading multiverse proponents, especialy those who engage in 'pop-science' exposition. as you must know, opponents of the multiverse have a variety of reasons that are objective and based on the testability and usefulness of the multiverse concept. Scientists should deal with the ideas themselves rather than engaging in the amateur psychologizing of the motivations of the individuals involved.

  12. Naivetheorist,

    I think you posted your comment in the wrong thread. You won't have to look far to see that my statement is far from being 'amateur psychologizing'. Instead, it's a brief summary of the discussion. This isn't my argument - it's an argument that has often been raised.

    "“I consider such a view to be ‘giving up’ on finding a true scientific explanation,” says Princeton University theoretical physicist Paul Steinhardt."

    "The danger, if the multiverse idea takes root, is that researchers may too quickly give up the search for such underlying explanations. "

    "Friedan’s view can be usefully contrasted with that articulated at the “Strings2003” conference by David Gross, who closed his lecture by quoting Winton Churchill. Gross appealed to his fellow string theorists to: “never, never, never, never, never give up” (quoted in Woit 2007, p. 10). "

    (And probably some more. Google will tell you.)


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