The comment above was about the singularity, so “the rest” clearly does not include the singularity
I don’t think “no interpretable meaning in physics” is a reasonable description, though. In classical mechanics, sure, but we’ve got plenty of physics that doesn’t work in classical mechanics
Non-classical mechanics includes things like quantum physics and (depending on who you ask) special relativity. They feel extremely counterintuitive but they provide pretty reliable explanations for how things work. That infinite density doesn’t make sense in our regular understanding of the world doesn’t necessarily mean it’s not a useful model. That doesn’t mean it’s necessarily true, of course, but the fact that it seems weird isn’t really important. It might just be that physics inside a black hole permit for something that we can best describe as infinitely dense
Infinite density doesn’t seem “weird”, it is meaningless and indicates that our model incomplete and simply cannot make predictions beyond a certain point. You don’t look at an equation that divides by zero and think, “maybe someday this will make sense.” It will never make sense because it will always be undefined, and you need to start looking for your mistake.
You seem to be suggesting that there is a non-classical physical model that resolves the paradox. But you don’t claim that any such one exists. The physics inside a black hole might be different than here on Earth, but mathematics is not. There is no mathematical way to interpret the singularity, and so there can never be a physical interpretation. The model is meaningless deep inside a black hole. We will not know what happens until we develop a more complete model, not a better interpretation of this bogus prediction.
I am not suggesting that there is a non-classical model that accurately explains the inside of black holes, I am saying that due to our inherent lack of any evidence we should not be immediately discounting the models that work exceptionally well where we do have evidence just because they give us results that feel weird to us. Quantum superpositions were also widely rejected early on because they seemed impossible to meaningfully interpret, and yet now we can make computers do maths with them
You don’t look at an equation that divides by zero and think, “maybe someday this will make sense.” It will never make sense because it will always be undefined, and you need to start looking for your mistake.
This is like saying that the equation of velocity = distance divided by time doesn’t make sense because if you travel somewhere in zero time then you have to divide by zero. The equation is correct and has physical meaning, it just so happens that moving somewhere always takes some time. We can understand just perfectly what moving somewhere in zero time would be, we just don’t know of any way to make it happen. Loads of useful and practically-applicable equations have vertical asymptotes. Maybe there’s something that prevents the inside of a black hole from collapsing to an actual point. Maybe space-time really does just collapse inside the black hole. The model would still be useful and mostly accurate, just incomplete
You know, except for the actual singularity which has no interpretable meaning in physics
The comment above was about the singularity, so “the rest” clearly does not include the singularity
I don’t think “no interpretable meaning in physics” is a reasonable description, though. In classical mechanics, sure, but we’ve got plenty of physics that doesn’t work in classical mechanics
okay what does infinite density mean in avant-garde mechanics?
Non-classical mechanics includes things like quantum physics and (depending on who you ask) special relativity. They feel extremely counterintuitive but they provide pretty reliable explanations for how things work. That infinite density doesn’t make sense in our regular understanding of the world doesn’t necessarily mean it’s not a useful model. That doesn’t mean it’s necessarily true, of course, but the fact that it seems weird isn’t really important. It might just be that physics inside a black hole permit for something that we can best describe as infinitely dense
Infinite density doesn’t seem “weird”, it is meaningless and indicates that our model incomplete and simply cannot make predictions beyond a certain point. You don’t look at an equation that divides by zero and think, “maybe someday this will make sense.” It will never make sense because it will always be undefined, and you need to start looking for your mistake.
You seem to be suggesting that there is a non-classical physical model that resolves the paradox. But you don’t claim that any such one exists. The physics inside a black hole might be different than here on Earth, but mathematics is not. There is no mathematical way to interpret the singularity, and so there can never be a physical interpretation. The model is meaningless deep inside a black hole. We will not know what happens until we develop a more complete model, not a better interpretation of this bogus prediction.
I am not suggesting that there is a non-classical model that accurately explains the inside of black holes, I am saying that due to our inherent lack of any evidence we should not be immediately discounting the models that work exceptionally well where we do have evidence just because they give us results that feel weird to us. Quantum superpositions were also widely rejected early on because they seemed impossible to meaningfully interpret, and yet now we can make computers do maths with them
This is like saying that the equation of velocity = distance divided by time doesn’t make sense because if you travel somewhere in zero time then you have to divide by zero. The equation is correct and has physical meaning, it just so happens that moving somewhere always takes some time. We can understand just perfectly what moving somewhere in zero time would be, we just don’t know of any way to make it happen. Loads of useful and practically-applicable equations have vertical asymptotes. Maybe there’s something that prevents the inside of a black hole from collapsing to an actual point. Maybe space-time really does just collapse inside the black hole. The model would still be useful and mostly accurate, just incomplete