Can kinetic energy be negative ?

At various places, including questions on this website itself, I have seen people say negative kinetic energy of a body. I don't really understand how something such as negative kinetic energy is even possible. To me, kinetic energy is $E_{kin}=\frac{1}{2}mv^2$. As far as I know, mass cannot be negative, and velocity is squared, so that has to be positive. So why/how is there something called negative kinetic energy? Also, when can potential energy be negative?

My question is a bit naive, but if someone could explain, it would be great.

  • $\begingroup$ Hey, can you link the PSE posts? I want to read about it too. As for potential energy, it is a matter of reference mostly. $\endgroup$ – frederick99 Apr 28 '17 at 14:14
  • $\begingroup$ @frederick99 I'll have to search for them. Also could you explain your views on negative potential energy. When you say matter of reference, you mean frame of reference? Could you give some examples where it is positive and where it is negative. $\endgroup$ – devb Apr 28 '17 at 14:28
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    $\begingroup$ @Nightshade Potential is just basically available energy relative to another state. Think of gravity for example. Often we define 0 gravitational potential energy as being at ground level. Now imagine digging a hole. You have managed to go below ground level. You could redefine the potential as 0 at this new lowest point, but that would require changing other work as well. It is just as accurate to say it has negative potential energy. It just means there is a state below your reference that is available. That said, I don't really see how that would apply to kinetic energy either. $\endgroup$ – JMac Apr 28 '17 at 14:33
  • $\begingroup$ @JMac yes thanks I think that clarifies my doubts about negative P.E. $\endgroup$ – devb Apr 28 '17 at 14:36
  • $\begingroup$ Something cannot have a negative kinetic energy. $\endgroup$ – DilithiumMatrix Apr 28 '17 at 14:44

This would be the case with the hypothetical negative mass, but there is no evidence such a thing exists in reality. But nevertheless, mathematically a negative $m$ is allowed in general relativity, see the reference Michigan Tech: Negative Mass video and presentation, so one can still play it through as a thought experiment.

Such a hypothetical negative mass would have a repelling gravity, so theoretically with a pair of positive and negative mass you could constantly accelerate both objects in the direction of the positive mass (because the positive mass would be repelled by the negative mass, while the negative mass would be attracted by the positive mass due to the equivalence principle).

The sum of the kinetic energies, negative and postive, of the system would always cancel out to zero, although almost travelling with the speed of light (the technical term for such an accelerating constellation of positive and negative mass objects is runaway pair).

Another weird thing is that if the negative $m$ particle would hit you, it would push you in the direction it came from, since due to the negative kinetic energy the momentum would be in the opposite side of motion.

  • $\begingroup$ This is pretty cool. Negative mass. Never even thought of that. Thanks. $\endgroup$ – devb Apr 28 '17 at 15:12
  • $\begingroup$ A research team at Washington State University has recently claimed that they successfully realized negative effective mass. $\endgroup$ – andars Apr 28 '17 at 19:10
  • $\begingroup$ Maybe a pseudo-particle could have negative mass. $\endgroup$ – Ralph Dratman Oct 28 '17 at 18:25

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