Thanks! Lots of information for me to learn about.
I assumed they can occupy the same space due to superposition principle, as waves could stack and modulate each other, sort of like wave A and wave B occupying the same space could produce a wave A+B
So a singular point would be the sum of all waves occupying the space.
But maybe gravity or spacetime itself is a recursive function and black holes are functions without a base case and there is no singular point, only non-terminating recursion.
Some ideas to funnel into AI so I can entertain myself hah
The world is made of two types of particle - fermions and bosons. A difference between them is that fermions can not occupy the same quantum state (the Pauli exclusion principle) while bosons can exist as superpositions. Matter is made of electrons, protons and neutrons which are fermions, while the forces are photons, gluons, W , Z and Higgs which are bosons.
There is a difference between "being in a superposition" and "occupying the same space". The uncertainty principle basically tells you that an electron is never in a defined place - it exists with some probability in many different places (technically it could be at a definite position, but only if it had completely indefinite momentum, and that's not physically meaningful given energy constraints).
Now, say we have an experiment where two different sources each fire one electron in some direction; and say the electrons have the same spin and other properties except for their initial position and momentum. We can meaningfully say that for a certain location between the two sources there is some > 0 probability for either electron to be there, so the amplitude of each electron's wavefunction at that position is > 0. However, that doesn't mean we can ever find both electrons at that same postion at the same time: the individual wavefunctions are just parts of the two-electron system's wavefunction, and, per the Pauli exclusion principle, that one will be 0 for any state of the form "electron A at position x and electron B at position x". So, for any position, you can find either electron there, but never both.
An additional wrinkle is that this only applies for two identical electrons. If the electrons have different spins, then they can actually be found at the same location at the same time. You can have a spin-up and a spin-down electron in the same place at the same time, but not two spin-up electrons. This is the fundamental property of fermions. However, you can have any number of identical photons at the same location - that's the fundamental property of bosons.
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Thanks! Lots of information for me to learn about.
I assumed they can occupy the same space due to superposition principle, as waves could stack and modulate each other, sort of like wave A and wave B occupying the same space could produce a wave A+B
So a singular point would be the sum of all waves occupying the space.
But maybe gravity or spacetime itself is a recursive function and black holes are functions without a base case and there is no singular point, only non-terminating recursion.
Some ideas to funnel into AI so I can entertain myself hah
The world is made of two types of particle - fermions and bosons. A difference between them is that fermions can not occupy the same quantum state (the Pauli exclusion principle) while bosons can exist as superpositions. Matter is made of electrons, protons and neutrons which are fermions, while the forces are photons, gluons, W , Z and Higgs which are bosons.
In a black hole though … who knows
There is a difference between "being in a superposition" and "occupying the same space". The uncertainty principle basically tells you that an electron is never in a defined place - it exists with some probability in many different places (technically it could be at a definite position, but only if it had completely indefinite momentum, and that's not physically meaningful given energy constraints).
Now, say we have an experiment where two different sources each fire one electron in some direction; and say the electrons have the same spin and other properties except for their initial position and momentum. We can meaningfully say that for a certain location between the two sources there is some > 0 probability for either electron to be there, so the amplitude of each electron's wavefunction at that position is > 0. However, that doesn't mean we can ever find both electrons at that same postion at the same time: the individual wavefunctions are just parts of the two-electron system's wavefunction, and, per the Pauli exclusion principle, that one will be 0 for any state of the form "electron A at position x and electron B at position x". So, for any position, you can find either electron there, but never both.
An additional wrinkle is that this only applies for two identical electrons. If the electrons have different spins, then they can actually be found at the same location at the same time. You can have a spin-up and a spin-down electron in the same place at the same time, but not two spin-up electrons. This is the fundamental property of fermions. However, you can have any number of identical photons at the same location - that's the fundamental property of bosons.