There are at least two places in our universe where we know that we do not know what laws of physics to apply. Those two places are inside black holes and at the Big Bang. First, think about black holes, with an analogy:
Imagine: You take an encyclopedia, and you throw it in a fire...all of the information in that encyclopedia is gone, right? Not quite. If you could gather information about the current state of the ashes, collect all the light that was shown during the fire, gather the heat, and everything else, you could reconstruct the encyclopedia. Its not gone; its just very difficult to retrieve in practice, but retrieval is theoretically possible.
For a black hole the situation is very different. If you throw an encyclopedia into a black hole, the black hole will evaporate quantum particles that have nothing to do with the encyclopedia whatsoever. You cannot reconstruct the encyclopedia from the evaporations of the black hole. You might as well have thrown in something else.
This is a problem because it means that our universe has memory loss. It means that whatever a black hole has swallowed, would get inside, and never get back out, and we would never be able to understand the past of our universe. In other words, there are some things that are not retrievable at all...not just in practice but also in theory. That is, physics as we know it now, explains that there are some things that we can never know, not practically speaking, but even theoretically...that is, the laws of the universe are such that we cannot know certain things. This is non-unitarity, which means we cannot use physics to understand the history of what happened before. In a sense the information paradox says that Physics is limited in that it cannot give us a full history of our universe.
Obviously, scientists do not like this idea, and are working hard to solve it.
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should be preserved, not lost.
The implication of this problem is not just information loss, it is that we would have one domain in the universe where quantum mechanics does not work at all. There are still some scientists (maybe not this guy, I guess he is just making the subject interesting ) who use this black hole information paradox to attack QM.
Nothing is "forever unknowable."
This guy (a protege of Hawking) isn't saying that it is difficult or nearly impossible to know these things. He is saying that the laws of physics as we know them require that we cannot know these things. The information is lost not just to us, humanity. The information is lost to the universe itself. In other words, science states that science cannot know all things about the universe...again, not practically speaking (just give us enough time), but theoretically speaking (even an incredibly old species cannot learn all things).
Science states that the structure of the universe is such that not everything can be learned about it by science.
Now, having said that, we may yet develop theories which allow us to explain the situation better...who knows. But, for now, the best theories we have now say that we cannot know certain things...certain information is just beyond the ken not only of humanity, but of anything within the universe.
[Edit to add this: Don't get me wrong. Science is still the best thing we have to explain the physical universe. I'm not bashing science.]
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