If there is something that lies beyond, it's in the realm of the supernatural, which is beyond the realm of nature and science and, hence, not provable. You can't prove an afterlife doesn't exist just as I can't prove one does. Like a fish in a pond, you live and I live within a system and can't see outside that system or know if there's something that supercedes it.

There are some things we can't fully explain by science, for example, consciousness. It seems to be more than computational. I don't think even the best scientists fully understand it.

After I listened to patients describe near death experiences, I did some reading. There are many things we can't fully explain. Children who die and come back speaking of a brother they met on the other side they never knew existed. The child had died before their birth and they were never made aware of their existence.

There are many cases of people having knowledge of things upon death that they didn't when they were alive. University of Virginia has a department that studies these experiences. It's hard to explain them away.

Ultimately, everyone has to decide what they believe since it's impossible to prove one way or the other. By the way, you say I'm asking people to believe in something that exists outside of physical laws, but I'm not asking anyone to believe anything. It's an individual choice. :-)