What Happens If We Change Just One Physical Constant?

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Lamdbaenergy
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So, I know that there are already three absolutely mandatory physical constants, like the gravitational constant, the Planck constant, and the speed of light. But what if you only changed the value of one constant? For example, if you changed the value of the gravitational constant to 4.4663 x 10^ -19, would other constants change too, or would they stay the same? In another case, you end up changing the light constant from 299,792,458 meters per second to only 45,643,111 meters per second. I'm pretty sure that would inevitably mean a drastic change in the strength of the electromagnetic force, but would it also lead to a change in pretty much all other constants, also?

One last thing, which constant would be the worst to change? Like, "destroy a universe" kind of worst?
 
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davenn said:
if the value could change, it wouldn't be a constant any more, aye

Alright, but what about values in other universes?