By definition, a manifold has a place where things go in, and other things come out. So yes, it does in fact logically follow. If its a manifold, then it logically follows that what goes in comes out.
You’re saying we know a bunch of stuff I’m not certain we know.
My understanding is that by definition, the singularity has infinite mass and infinite gravity, so there is no way it can gain mass; because infinity + 1 = infinity. It’s the very nature of infinities. You can have a number of infinities, but manipulating them arithmetically always yields infinity. 2 x infinity = infinity. 3 / infinity = infinity.
Like zero, it is more identity than number. 0 = nothing, infinity = everything.
So if you hope to have me follow your narrative, you’re going to address this assertion concerning increasing the mass of black holes first.
Almost nobody actually believes the singularity is real, it’s just what the math tells us – it’s where the math of GR breaks down, and a better theory of gravity would be needed to resolve it.
I’ve never heard a black hole described as a manifold, but then again I’m not sure exactly what a manifold is.
Also Idk what you are talking about nobody believing there’s an actual singularity; I don’t know what else you think is happening, or of what use the mathematics might be if it doesn’t approach some degree of accuracy as concerns the physical character of the phenomena
We know that GR predicts some things extremely well, and QM some things extremely well, but they fundamentally disagree. Both CANNOT be entirely correct, and black holes is the most notable case where one or both break down. (See the “black hole information paradox”.)
exhaust manifold on combustion engine takes raw cylinder exhaust gases in pipes that all come down and combine into a single larger pipe that connects to the input of a catalytic converter.
the plenum in your attic is a manifold. One big duct runs from your air handler into a box with several ducts coming from it, delivering air to each of the vents. the ducts and the plenum form a manifold.
In literature, it means ‘many and various’.
In mathematics, “a collection of points forming a certain kind of set, such as those of a topologically closed surface or an analog of this in three or more dimensions”
In Kantian philosophy, “the sum of the particulars furnished by sense before they have been unified by the synthesis of the understanding”
Origins: Old English manigfeald ; current noun senses date from the mid 19th century.
All from the wikipedia
They all have some descriptive relevance, but the one that really counts for us is the math one, suggesting the closed surface.
It wouldn’t surprise me though if it still worked; there are many examples of topologically closed surfaces that can still be traversed, if in unexpected ways. I’m thinking of another manifold, the klein bottle, and of course the mobieus strip.
the singularity has infinite mass and infinite gravity, so there is no way it can gain mass; because infinity + 1 = infinity. It’s the very nature of infinities. You can have a number of infinities, but manipulating them arithmetically always yields infinity. 2 x infinity = infinity. 3 / infinity = infinity.
Thank you for linking that! I knew I had read that they could be, but I couldn’t recall where. It might not have been Scientific American, but that’ll do XD
While clearly they can be, infinity == infinity is still true, If I recall.
Also, I’ve got some simple problems with that crate analogy, Scientific American or not; any crate with an infinite number of anything inside it cannot be emptied, it’s in the very definition of infinite. Consequently, neither crate will ever empty and the pairing will be an infinite pairing of apples and oranges.
Black Holes do not have infinite mass. We pretty much know how heavy the are, because we can measure their gravitational influence on surrounding matter. They just have enough gravity, that light can’t escape their gravitational pull. Infinite mass would also break a lot of fundamental physic laws, like conversation of energy.
3/infinity is 0. You probably meant infinity/3 is infinity.
According to my understanding, beyond the event horizon, gravity is infinite.
I am not a physicist - I’m a guy who read Prof. Hawking. Given the nature of llight vis a vis observation, inside the singularity, mass and gravity approach infinity.
Mass bends spacetime into gravity. Gravity bends light. Infinite mass > infinite gravity > stops light == singularity.
Note that things happening near the singularity are not the same as things that happen beyond the event horizon.
Density is infinite (or at least very high) and that creates the singularity. Mass is still finite. You don’t need infinite gravity to trap light as well, you can look into the calculation of escape velocities for that.
@exscape
@readbeanicecream
By definition, a manifold has a place where things go in, and other things come out. So yes, it does in fact logically follow. If its a manifold, then it logically follows that what goes in comes out.
You’re saying we know a bunch of stuff I’m not certain we know.
My understanding is that by definition, the singularity has infinite mass and infinite gravity, so there is no way it can gain mass; because infinity + 1 = infinity. It’s the very nature of infinities. You can have a number of infinities, but manipulating them arithmetically always yields infinity. 2 x infinity = infinity. 3 / infinity = infinity.
Like zero, it is more identity than number. 0 = nothing, infinity = everything.
So if you hope to have me follow your narrative, you’re going to address this assertion concerning increasing the mass of black holes first.
Almost nobody actually believes the singularity is real, it’s just what the math tells us – it’s where the math of GR breaks down, and a better theory of gravity would be needed to resolve it.
I’ve never heard a black hole described as a manifold, but then again I’m not sure exactly what a manifold is.
@exscape
@readbeanicecream
Also Idk what you are talking about nobody believing there’s an actual singularity; I don’t know what else you think is happening, or of what use the mathematics might be if it doesn’t approach some degree of accuracy as concerns the physical character of the phenomena
Here’s some reading about black holes singularities and whether they’re real or not:
https://www.pbs.org/wgbh/nova/article/are-singularities-real/
https://en.wikipedia.org/wiki/Gravitational_singularity#Interpretation
We know that GR predicts some things extremely well, and QM some things extremely well, but they fundamentally disagree. Both CANNOT be entirely correct, and black holes is the most notable case where one or both break down. (See the “black hole information paradox”.)
@exscape
@readbeanicecream
A couple examples of manifolds:
exhaust manifold on combustion engine takes raw cylinder exhaust gases in pipes that all come down and combine into a single larger pipe that connects to the input of a catalytic converter.
the plenum in your attic is a manifold. One big duct runs from your air handler into a box with several ducts coming from it, delivering air to each of the vents. the ducts and the plenum form a manifold.
In literature, it means ‘many and various’.
In mathematics, “a collection of points forming a certain kind of set, such as those of a topologically closed surface or an analog of this in three or more dimensions”
In Kantian philosophy, “the sum of the particulars furnished by sense before they have been unified by the synthesis of the understanding”
Origins: Old English manigfeald ; current noun senses date from the mid 19th century.
All from the wikipedia
They all have some descriptive relevance, but the one that really counts for us is the math one, suggesting the closed surface.
It wouldn’t surprise me though if it still worked; there are many examples of topologically closed surfaces that can still be traversed, if in unexpected ways. I’m thinking of another manifold, the klein bottle, and of course the mobieus strip.
Can’t infinities be different sizes, though?
@FfaerieOxide
@readbeanicecream @exscape
Thank you for linking that! I knew I had read that they could be, but I couldn’t recall where. It might not have been Scientific American, but that’ll do XD
While clearly they can be, infinity == infinity is still true, If I recall.
Also, I’ve got some simple problems with that crate analogy, Scientific American or not; any crate with an infinite number of anything inside it cannot be emptied, it’s in the very definition of infinite. Consequently, neither crate will ever empty and the pairing will be an infinite pairing of apples and oranges.
Black Holes do not have infinite mass. We pretty much know how heavy the are, because we can measure their gravitational influence on surrounding matter. They just have enough gravity, that light can’t escape their gravitational pull. Infinite mass would also break a lot of fundamental physic laws, like conversation of energy.
3/infinity is 0. You probably meant infinity/3 is infinity.
@Sodis
@readbeanicecream @exscape
According to my understanding, beyond the event horizon, gravity is infinite.
I am not a physicist - I’m a guy who read Prof. Hawking. Given the nature of llight vis a vis observation, inside the singularity, mass and gravity approach infinity.
Mass bends spacetime into gravity. Gravity bends light. Infinite mass > infinite gravity > stops light == singularity.
Note that things happening near the singularity are not the same as things that happen beyond the event horizon.
Density is infinite (or at least very high) and that creates the singularity. Mass is still finite. You don’t need infinite gravity to trap light as well, you can look into the calculation of escape velocities for that.