Physical world: those things which can be observed, inspected and reasoned about by all potential observers, and to which all potential observers hold a similar understanding. Space, time, matter, energy, and their characteristics, behaviors and relationships are all things that fit this category. We can know what they are, and how they behave, separately and in combination.
Given a group of Homo sapiens in the world today, they will largely agree that objects fall towards the Earth, the sun shines in the sky during the day, water is wet, the Earth is relatively solid, and you shouldn’t let flames burn you. One hundred, one thousand or one million random people will almost certainly agree with these statements about the physical world. Anyone disagreeing with these trivial claims will find it nearly impossible to come up with a persuasive argument that something to the contrary is true. Therefore, we often refer to claims such as these as “facts”.
Note that we do NOT attempt to answer “non-physical” questions (purpose, meaning, emotion) when describing a physical world.
Mental world: an individually-held set of understandings, attitudes, beliefs about physical things (both external and internal to the observer), as well as understandings, attitudes and beliefs about what is, what has been, and what could be in the physical world, or in any imaginable world.
We also perceive pain, conceive of purpose, meaning, emotion in this world.
Some Differences:The physical world that we observe - Space, time, matter, energy, and their characteristics, behaviors and relationships - does not necessarily include all that there is. This is important to keep in mind. For example, physicists have models and hypotheses that somewhat predict the existence of “extra dimensions” , and (separately) multiverses. These are not observed in everyday life, and there’s no good reason for the layman to believe such things are true. Yet, physicists research and test these ideas because there are reasons to think that the models and hypotheses will lead to better understanding of our universe.
In the mental world, there are less reasons to constrain one’s thoughts to that which can be observed, measured and reasoned about. That’s where the idea that the supernatural exists first arises. There was a time when Homo sapiens didn’t have the mental and physical tools to explain phenomena that they observed, so entities with human or animal traits (since that was what they were familiar with) were imagined to explain the phenomena. In more sophisticated imaginations, these entities were explained to exist in a realm beyond the natural, presumably to address their hiddenness . The “supernatural” was thus born.
How does one reconcile the physical world with their personal mental world? I can’t speak for everyone, but
seems to be an effective rule of thumb.
“A wise man apportions his beliefs to the evidence.” ― David Hume
Conclusion: Nothing we observe today leads us to believe that a supernatural realm exists. No one has taken evidence to the National Science Foundation that resulted in a new understanding of the physical world. Faeries, ghosts, angels, demons and gods have no basis in fact. If they do, the evidence should be held up to scrutiny. So, it seems clear to me, and to hundreds of millions of others, that supernatural claims arise in the mental world, and vanish when held up to scrutiny in the physical world.
Believers cannot point to anything in the Physical World and demonstrate the existence of god. They can say “you can’t explain that“, or assert that such-and-such phenomena could only be the handiwork of god, but they can’t make a persuasive case that their assertions are probably true. They can’t take you to someone who can show any research and artifacts, or demonstrate any formulas and measurements that indicate that a deity is responsible for any feature of the universe. Their claims rely on the mental world. Without the mental world, their concepts have no existence.
In contrast, the non-believer can demonstrate physical facts, or take the believer to chemists, physicists, geologists, anthropologists, etc, who can demonstrate and explain features and phenomena in the world that most of us lack the time and tools to understand on our own. Sure, we can’t explain why the universe is here. “Why” questions are not the province of science. Science can tell you “what”. Still, scientists won't give you pat answers for what brought the universe into being, or what caused life to emerge from non-life, because their hypotheses about these haven't been tested and refined well enough to indicate a probable answer. They're working on it, though, with the intention of bringing us closer to the truth. Believers never do that. Their claims never hold up to scrutiny.
If that changes, it will be an interesting day.