“If the universe isn’t a closed system, this problem might go away. Perhaps the information wasn’t destroyed; it just went elsewhere.”
Matter can not be destroyed, it can be converted to energy. Energy can not be destroyed, it can be turned into matter.
The information exit out a white hole (big bang) to another universe. Our universe was created from a black hole in another universe pumping energy and matter into our universe.
Matter cannot be destroyed? That’s false.
Matter is not conserved. What is conserved is mass.
Take the sun. As hydrogen burns to form helium, the mass of the matter decreases. The sun radiates away infra red, visible light, x-rays, etc. They have mass. The total of the mass of the matter, and the mass of the radiation stays the same.
Take an atomic reactor. As the fuel burns, the mass of the fuel is decreasing (at a rate equal to the square of the speed of light, or 19.7 trillion Btu’s per pound in US Standard units.) In a typical 1100 mw reactor, the mass of the fuel drops by about 5 pounds a year.
But mass is always conserved. So where does the mass go?
In water cooled reactors, it goes into the reactor coolant water.
When you add energy to something (heating water, lifting a weight, tightening a spring, charging a battery), its mass goes up. So as the water circulates through the reactor and it heats up from about 570 to 630 deg F, its mass goes up. When it loses its heat by boiling off steam in the boilers, the mass of the cooling water goes back down again, The mass of the steam goes up when boiling occurs, so mass is always conserved.