$ε_0$ = 8.854187817 × $10^{-12}$ F⋅m$^{-1}$ (farads per metre)
What would happen if tomorrow vacuum permittivity change, I consider an example, into an hypothetical $ε_0$ = 8.85 × $10^{-4}$ F⋅m$^{-1}$ ?
How and in what manner nature laws change?
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Jack
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Why don't you think about it yourself? What quantities depend on $\epsilon_0$? – Avantgarde Mar 05 '19 at 00:22
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Possible duplicate of Why do universal constants have the values they do? – Mar 05 '19 at 00:48
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3I'm voting to close this question as off-topic because this is an open-ended What if... question that is explicitly off-topic, as described in [help]. – Kyle Kanos Mar 05 '19 at 02:15
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How and in what manner nature laws change?
Nothing about nature would change in the slightest. There would be no detectable change whatsoever in any experiment or measurement. What would change is only the SI units.
$\epsilon_0$ is a defined constant with an exact defined value in the SI unit system (until 20 May 2019). That means that the BIPM committee got together and voted on its value and definition. Since they could define it to the exact value that it has, they could also have defined it to be some other value, including one several orders of magnitude different.
All that would happen is a change in the size of the Ampere. Since you are increasing $\epsilon_0$ by a factor of $10^8$ then the Ampere would have to be smaller by a factor of $10^4$. Ammeters would need to be relabeled so that the 1 A readout said 10000 A instead, but nothing would change physically.
Dale
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I think you forgot something, When you say Since you are increasing $\epsilon_0$ by a factor of $10^8$ then the Ampere would have to be smaller by a factor of $10^4$ I think that change the metric of space. Because to preserve same physics you need to 'relabel' 1A as 10000A, that is, equivalentally, to say that you need to change distance between each pair of elements of a set – Jack Mar 05 '19 at 18:49