Some people suggest the idea of a multiverse with each universe having a unique set of laws of physics governing it, but not many delve deeper into this. I was wondering if it was even possible to imagine a universe that is different to ours in this regard.
The universe could share some of the laws from our universe yet still be different enough that it is not a matter of just tweaking a few digits of the gravitational constant or the speed of light. Also the universe with those set of laws should be able to sustain itself through the same period as our universe has been so far, meaning it shouldn't implode or instantaneously cease to exist the moment it is born.
Is it even possible to imagine this? If not, is this due to us having become so accustomed to the logic of our universe that we cannot come up with any such idea that does not exist here, or is it just that our universe happens to be the only possible one to exist, at least while maintaining the harmony between each law of physics and avoiding any paradoxes to occur?
Yes.
We are all very likely doing it now with most of what we believe to be the laws of physics. While they may seem to reasonably explain the phenomena we have been able to observe that represents such an infinitesimal fraction of the universe that the margin for error is astronomical.