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The other day, a friend of mine asked me this question:

If you had a sphere in the dead of space which contained a vacuum and through some mechanism began expanding that sphere with outward force uniformly in all directions across its outer surface, what would happen inside the sphere?

My initial thought was the sphere would expand at a rate corresponding to the elasticity of the spheres material, until it would eventually break. Until it does break, the vacuum would continue to exist with an increasing volume of vacuum. Nothing more would happen.

But is this correct? My intuition is that if there is "nothing" in the sphere to begin with, then there will be a larger volume of "nothing" as it expands. Can there really be "more" of a vacuum?

zero_dark_birdy
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  • I guess in classical view you get perfect vacuum both inside and outside all the time... This question starts to be really intriguing when quantum oscillations are taken into account and when the sphere expands rather fast. – dominecf Jun 11 '21 at 11:52

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Take a look at the force diagram. If the vacuum inside and outside is "pure," i.e. no particles at all, then there's nothing restraining the expansion other than the material of the sphere itself.

If you take "real" space, the vacuum contains on the order of one atom or particle per cubic cm (depending on location in space and the source quoted, this can differ by an order of magnitude). So now, given the rough temperature of 10 K, you can calculate the pressure-temperature-volume relationships using the same formulas as we use for Terran atmospheric statistical mechanics.

And as some wag commented, if you pull fast enough, quantum pair-formation might occur.

Carl Witthoft
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  • It is an interesting thought though. Is the idea that pulling very fast would make the material hot enough to kick particles into each other with more energy than the rest mass energy of nearby particles? I'm not exactly following why speed is a factor. – zero_dark_birdy Jun 11 '21 at 17:45
  • @zero_dark_birdy no, no matter how hot the shell material is, the "Doppler" value of atoms bouncing off it will not add to the atoms' energy. The quantum pair-formation occurs via Schwinger pair production (maybe) https://physics.stackexchange.com/questions/7388/critical-electric-field-that-spontaneously-generates-real-pairs – Carl Witthoft Jun 15 '21 at 15:32