Parth G | When Quantum Physics and Relativity Compete Against Each Other to Keep Stars From Collapsing @ParthGChannel | Uploaded 2 years ago | Updated 11 minutes ago
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#degeneracypressure #quantum #neutronstar
In this video, we'll be looking at degeneracy pressure - a quantum mechanical effect that prevents the collapse of stars!
During the life cycle of a main sequence star, like our Sun, there are two major competing forces: the inward-acting gravitational force, and the outward-acting forces created by nuclear fusion in the core. In general, these forces are in balance because the star has a stable size.
However once all the hydrogen in its core runs out, the star has to start fusing helium. This continues until there is no more fusion fuel in the core. At this point, the gravitational forces dominate, causing the star to collapse into a white dwarf (for medium-sized stars).
A white dwarf is a dense bit of matter that is no longer radiating energy due to the lack of fusion. But why does a white dwarf not collapse down even further into a smaller region of space? We may think that electrostatic repulsion between the charged particles making it up have something to do with this. However stars are usually large enough that this electrostatic repulsion can be overcome by the strong gravitational forces.
The effect preventing this further collapse of white dwarves is in fact degeneracy pressure. To understand it, we start by remembering that every quantum system can be described by a wave function. This includes multi-particle systems. Also, electrons are all indistinguishable particles - we cannot tell one from another. This results in some very interesting properties, including that fermions (a category of indistinguishable particles) have an antisymmetric wave function. All this means is that when we swap two of the particles in the system, the wave function becomes negative of what it was before.
Finally, we recall that an electron wave function consists of a spin part and an orbital part. Due to the antisymmetric nature of the wave function, no two particles can have exactly the same spin and orbital parts. If they did, then we could swap those two particles and the wave function would remain the same - showing symmetric, or "boson" behaviour, not fermion behaviour.
This is why multiple electrons cannot occupy the same quantum states in an atom - it's Pauli's Exclusion Principle! If electrons are to occupy the same orbital state, then they must have different spins - and there are only two possible spin states, up and down. Therefore, each orbital state can only hold two electrons. And this is important because orbital spin states are closely related to where we can find electrons in space.
Within a white dwarf, the gravitational forces causing collapse force the electrons into lower energy states as they occupy a smaller region of space. But eventually, all the lowest energy states are occupied (remember, only 2 electrons per state). And many electrons have much higher energy than this because the lower states are full. So this creates a degeneracy pressure that prevents electrons from being placed into even lower energy states.
Another way to look at this is that the gravitational forces tend to force electrons into the same region of space - or the same orbital states. But this cannot happen for more than two electrons at a time, so the white dwarf cannot be compressed any further than a specific size!
This same effect is found in neutron stars too, because neutrons are fermions. And since neutrons are not charged, we know it's not the electrostatic repulsion causing the gravitational collapse to halt!
Videos linked in the cards for this video:
1) https://youtu.be/w9Kyz5y_TPw
2) https://youtu.be/skFU7pmBOys
Thanks so much for watching - please do check out my socials here:
Instagram - @parthvlogs
Patreon - patreon.com/parthg
Music Chanel - Parth G's Shenanigans
Merch - https://parth-gs-merch-stand.creator-spring.com/
Many of you have asked about the stuff I use to make my videos, so I'm posting some affiliate links here! I make a small commission if you make a purchase through these links.
A Quantum Physics Book I Enjoy: https://amzn.to/3sxLlgL
My Camera (Sony A6400): https://amzn.to/2SjZzWq
ND Filter: https://amzn.to/3qoGwHk
Microphone and Stand (Fifine): https://amzn.to/2OwyWvt
Gorillapod Tripod: https://amzn.to/3wQ0L2Q
Timestamps:
0:00 - Degeneracy Pressure, and the Force Balance in Stars
1:50 - White Dwarf - What Happens After Fusion Stops?
3:05 - Indistinguishable Particles and their Wave Functions
8:22 - Degeneracy Pressure in White Dwarves
#ad - This video was sponsored by Squarespace.
Go to Squarespace.com for a free trial, and when youre ready to launch, go to http://www.squarespace.com/parthg to save 10% off your first purchase of a website or domain.
#degeneracypressure #quantum #neutronstar
In this video, we'll be looking at degeneracy pressure - a quantum mechanical effect that prevents the collapse of stars!
During the life cycle of a main sequence star, like our Sun, there are two major competing forces: the inward-acting gravitational force, and the outward-acting forces created by nuclear fusion in the core. In general, these forces are in balance because the star has a stable size.
However once all the hydrogen in its core runs out, the star has to start fusing helium. This continues until there is no more fusion fuel in the core. At this point, the gravitational forces dominate, causing the star to collapse into a white dwarf (for medium-sized stars).
A white dwarf is a dense bit of matter that is no longer radiating energy due to the lack of fusion. But why does a white dwarf not collapse down even further into a smaller region of space? We may think that electrostatic repulsion between the charged particles making it up have something to do with this. However stars are usually large enough that this electrostatic repulsion can be overcome by the strong gravitational forces.
The effect preventing this further collapse of white dwarves is in fact degeneracy pressure. To understand it, we start by remembering that every quantum system can be described by a wave function. This includes multi-particle systems. Also, electrons are all indistinguishable particles - we cannot tell one from another. This results in some very interesting properties, including that fermions (a category of indistinguishable particles) have an antisymmetric wave function. All this means is that when we swap two of the particles in the system, the wave function becomes negative of what it was before.
Finally, we recall that an electron wave function consists of a spin part and an orbital part. Due to the antisymmetric nature of the wave function, no two particles can have exactly the same spin and orbital parts. If they did, then we could swap those two particles and the wave function would remain the same - showing symmetric, or "boson" behaviour, not fermion behaviour.
This is why multiple electrons cannot occupy the same quantum states in an atom - it's Pauli's Exclusion Principle! If electrons are to occupy the same orbital state, then they must have different spins - and there are only two possible spin states, up and down. Therefore, each orbital state can only hold two electrons. And this is important because orbital spin states are closely related to where we can find electrons in space.
Within a white dwarf, the gravitational forces causing collapse force the electrons into lower energy states as they occupy a smaller region of space. But eventually, all the lowest energy states are occupied (remember, only 2 electrons per state). And many electrons have much higher energy than this because the lower states are full. So this creates a degeneracy pressure that prevents electrons from being placed into even lower energy states.
Another way to look at this is that the gravitational forces tend to force electrons into the same region of space - or the same orbital states. But this cannot happen for more than two electrons at a time, so the white dwarf cannot be compressed any further than a specific size!
This same effect is found in neutron stars too, because neutrons are fermions. And since neutrons are not charged, we know it's not the electrostatic repulsion causing the gravitational collapse to halt!
Videos linked in the cards for this video:
1) https://youtu.be/w9Kyz5y_TPw
2) https://youtu.be/skFU7pmBOys
Thanks so much for watching - please do check out my socials here:
Instagram - @parthvlogs
Patreon - patreon.com/parthg
Music Chanel - Parth G's Shenanigans
Merch - https://parth-gs-merch-stand.creator-spring.com/
Many of you have asked about the stuff I use to make my videos, so I'm posting some affiliate links here! I make a small commission if you make a purchase through these links.
A Quantum Physics Book I Enjoy: https://amzn.to/3sxLlgL
My Camera (Sony A6400): https://amzn.to/2SjZzWq
ND Filter: https://amzn.to/3qoGwHk
Microphone and Stand (Fifine): https://amzn.to/2OwyWvt
Gorillapod Tripod: https://amzn.to/3wQ0L2Q
Timestamps:
0:00 - Degeneracy Pressure, and the Force Balance in Stars
1:50 - White Dwarf - What Happens After Fusion Stops?
3:05 - Indistinguishable Particles and their Wave Functions
8:22 - Degeneracy Pressure in White Dwarves
#ad - This video was sponsored by Squarespace.
