What happens if I accelerate air to the speed of light?

To be more specific I'd like to know what will happen if I do the following: some volume of air (just regular atmospheric air), I accelerate it to speeds comparable to the speed of light ($v\in [10^{-3},{1})c$).

To be even more specific: imagine we have one milligram of air as we accelerate this volume to the $v=0.2c$ spending $t=10^{-20}$ seconds of time. Let's imagine that we somehow were able to achieve this results under normal atmospheric pressure etc. The question is: what exactly will happen? I've calculated the approximate kinetic energy of air that we will get with this speed and it equals approximately $E_k = 1.852\operatorname{Gj}$, but I do not have enough knowledge to predict anything more than just 'explosion' or similar thing happening after.

Note: I'm looking for more or less simple answer without too much of insight, even though I will be really grateful if you could provide more explanation or link to the book/article that could help me understand what will happen.

Note: I've googled quite a bit before asking this question and found something that looked familiar to what I wanted: hypersonic gas flows. But after I've looked a bit more I understood that it is not what I want. I'm interested in very quick acceleration of small portion of the gas to the near-light speeds but not the continuous flow of gas even if it is also really fast.


closed as unclear what you're asking by Sebastian Riese, sammy gerbil, Kyle Kanos, Emilio Pisanty, Jon Custer Jun 12 '18 at 1:46

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  • $\begingroup$ If you mean acceleration to 0.2$c$ took just $10^{-20}$ seconds, then this is impossible. In that time light would only travel $3\times 10^{-12}$ m and an Oxygen atom is approximately $60\times 10{-12}$ m in radius (a photon would not be able to cross an Oxygen atom is such a small time, so no action could affect it on that time scale). If you meant it only traveled at that speed for $10^{-20}$ seconds then the distance involved is about 1% of the atom's size. $\endgroup$ – StephenG Jun 6 '18 at 17:13
  • $\begingroup$ @StephenG I've just put this number to make my question more understandable because asking "what will happen if air moving at $0.2c$ appears out of nowhere?" seemed too vague to me. So I chose this number as very small just to explain what I mean. If you could provide lover limit for the time that will make this question realistic I would correct it according to that number $\endgroup$ – Kamanji Jun 6 '18 at 17:30
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    $\begingroup$ what-if.xkcd.com/1 $\endgroup$ – Aaron Stevens Jun 6 '18 at 17:48
  • $\begingroup$ @safesphere Thanks, that's about as many details that I needed. If you wish to post your comment as an answer I will accept it. $\endgroup$ – Kamanji Jun 6 '18 at 17:57
  • $\begingroup$ Unclear. What kind of thing are you expecting to happen? Why do you think it might explode? What kind of explosion are you thinking of? $\endgroup$ – sammy gerbil Jun 6 '18 at 19:29

The moving air will collide with the static air in the atmosphere. The kinetic energy of the moving air will convert to both heat and the kinetic energy of the pushed molecules of air that were static. There will be a high pressure in the front and vacuum behind (until everything settles down). The pressure differences will create a loud supersonic "boom" just like with fighter jets. If you move enough air, say, downward, the effect would be like of a burning meteorite hitting the Earth. Tree branches will break, but the trunks still stand in the epicenter: https://en.m.wikipedia.org/wiki/Tunguska_event

The total energy of the explosion is defined by $E=(\gamma-1)mc^2$ where $m$ is the mass of the relativistic air, $c$ is the speed of light, and $\gamma=\dfrac{1}{\sqrt{1-\beta^2}}$ where in turn $\beta$ is speed of the moving air expressed as a fraction of the speed of light. In your example, $m=1mg$ and $\beta=0.2$, so $\gamma-1\approx 0.02$ and the mass converted to energy is $0.02mg$. This is $34,000$ times less than in the Hiroshima bomb, so your explosion would be equivalent roughly to $0.44$ tons of TNT or approximately $2$ thunder lightnings at once ($1.85GJ$ of energy, as in your calculations).

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    $\begingroup$ $v/c$ isn't rapidity, that's just speed in natural units. The equation for rapidity is $w=\tanh^{-1}(v/c)$, see en.m.wikipedia.org/wiki/Rapidity $\endgroup$ – PM 2Ring Jun 6 '18 at 19:02

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