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Consider a sphere with physical and chemical properties favorable to your solution (for example responsive to electric force or high heat capacity or anything). How would you compress it such that it remains a perfect sphere and simply faces a change in radius?

You can't extract material from inside, so obviously you'll need to increase its density. Hence we aren't considering the extent to which you can achieve the decrease in radius: you can assume something small like 1%.

I've been thinking and I've decided that the only way to achieve this is by applying the same force on all sides, but after this, I got stuck. Maybe placing it in a mold of the same shape and then applying the thermal expansion of the mold to shrink the ball? Are there any other interesting ways?

I'm considering this just as a thought experiment, with no concern for feasibility, so feel free to use unorthodox techniques.

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    $\begingroup$ What about increasing the external pressure? $\endgroup$ – Farcher May 26 '18 at 6:37
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    $\begingroup$ You can find plenty of materials that would shrink when cooled. $\endgroup$ – V.F. May 27 '18 at 2:28
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Here are a couple of methods:

1) you can immerse the object in a container of water and apply pressure to the container. the pressure will naturally distribute itself evenly about the object and squeeze it from all sides.

2) you can envelop the object with artfully-shaped pieces of high explosives and carefully set them off at the same instant. This technique was used in the Fat Man atomic bomb of WWII to compress a (subcritical) sphere of plutonium enough to make it go critical and start a chain reaction.

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  • $\begingroup$ Can you talk a bit more about the second part? That's what got me thinking about this question in the first place; I didn't fully understand the article which I read about it... though I've mentioned macroscopic in the question. $\endgroup$ – user191954 May 26 '18 at 6:49
  • $\begingroup$ it was called the implosion method and it was the reason the plutonium bomb was made to work. it took tremendous effort to figure out exactly how to shape the chunks of explosive into "lenses" that would precisely focus the crushing shock wave onto the sphere. Lots has been written about this in histories of the bomb project and I have photographs of implosion experiments in one of my books about atomic bombs- they are INCREDIBLE. $\endgroup$ – niels nielsen May 26 '18 at 7:05
  • $\begingroup$ How would the first method work? Won't the pressure be more at the bottom and deform the sphere? $\endgroup$ – Anurag B. May 27 '18 at 11:01
  • $\begingroup$ the difference would be small compared to the compression you are applying. if that difference is important, you could surround the sphere with air instead and compress that. $\endgroup$ – niels nielsen May 27 '18 at 16:07
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If you place a gas in a spherical balloon, place that balloon in a pressure chamber, and increase the pressure, its density will uniformly increase due to pascals law

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