Parth G | We DON'T Understand Magnetism (According to Quantum Mechanics) - Aharonov-Bohm Effect by Parth G @ParthGChannel | Uploaded 3 years ago | Updated 3 hours ago
The first 1000 people to use the link will get a free trial of Skillshare Premium Membership: https://skl.sh/parthg06211
Scientists have often thought that magnetic (and electric) fields are fundamental quantities that relate to real, physical, observable things in the universe. And they are. But, it may be possible that their potentials are even more fundamental! #quantumphysics #quantummechanics #aharonovbohm #electromagnetism #magneticfields #electricfields
Hey everyone, in this video I wanted to discuss how a quantity initially created purely for mathematical convenience, ends up being a really important fundamental quantity in the study of quantum mechanics.
Magnetic fields (B) are used to describe how magnets interact with each other - both the creator of the field, and any magnet placed within the field. And these fields are thought to be fundamental quantities, neatly describing the behaviour of all magnetic objects. However, sometimes magnetic fields are not mathematically simple to deal with.
To overcome this issue, physicists made use of a neat math trick. They took an identity that states that the divergence of the curl of any vector must be zero, as well as the Maxwell equation that states that the divergence of any magnetic field must always be zero (https://www.youtube.com/watch?v=0jW74lrpeM0&t=6s) to define a "magnetic vector potential" (A). The relationship is that a magnetic field is equal to the curl of its vector potential.
Now vector potentials are often easier to work with mathematically, but they aren't uniquely defined ("gauge invariance"). If we have a certain B-field, this can be described by multiple related A-fields. But when given an A-field, we can uniquely find the corresponding B-field. This is important later.
When studying quantum mechanics, it turns out that the A-field can have a real, measurable impact on a system, despite only being considered a mathematical convenience. Importantly, this measurable impact has nothing to do with the corresponding B-field! This is because in a region of space where B is zero, but A is not zero, we can find the wave function of an electron being changed. Specifically, the phase of the wave function changes, and this can be measured using a particular type of double-slit experiment. This effect is known as the Aharonov-Bohm Effect.
In other words, we find that the magnetic vector potential can have a real-world impact WITHOUT any influence from its corresponding magnetic field. The Aharonov-Bohm effect is telling us that electric and magnetic fields are not the fundamental quantities that we initially thought, and their potentials are the fundamental quantities! This despite potentials only being created for mathematical convenience!
Caveat to the Aharonov-Bohm effect: It *may* be possible to describe the effect by purely dealing with the magnetic field and not the vector potential, but this would involve having to give up the idea of locality - we would need nonlocal fields! (https://en.wikipedia.org/wiki/Principle_of_locality)
Timestamps:
0:00 - Magnetic Field Lines: Vectors for Magnetic Interactions
1:46 - Magnetic Fields vs Mathematical Convenience
2:17 - A Neat Trick for Defining Magnetic Vector Potential
4:00 - Sponsor Chat: Thanks to Skillshare, Check Out a Free Trial Below!
5:00 - Gauge Invariance, Uniquely Defining the Vector Potential
6:08 - B Fields are the Real Fundamental Quantity... Right?!
6:45 - Passing an Electron Near a Solenoid (Coil of Wire)
7:56 - Phase and the Aharonov-Bohm Effect
9:40 - Final Thoughts
Useful resources:
https://en.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect
https://en.wikipedia.org/wiki/Del
https://en.wikipedia.org/wiki/Phase_(waves)
https://en.wikipedia.org/wiki/Double-slit_experiment
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 (Canon EOS M50): https://amzn.to/3lgq8FZ
My Lens (Canon EF-M 22mm): https://amzn.to/3qMBvqD
Microphone and Stand (Fifine): https://amzn.to/2OwyWvt
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/
This video was sponsored by Skillshare #ad
The first 1000 people to use the link will get a free trial of Skillshare Premium Membership: https://skl.sh/parthg06211
Scientists have often thought that magnetic (and electric) fields are fundamental quantities that relate to real, physical, observable things in the universe. And they are. But, it may be possible that their potentials are even more fundamental! #quantumphysics #quantummechanics #aharonovbohm #electromagnetism #magneticfields #electricfields
Hey everyone, in this video I wanted to discuss how a quantity initially created purely for mathematical convenience, ends up being a really important fundamental quantity in the study of quantum mechanics.
Magnetic fields (B) are used to describe how magnets interact with each other - both the creator of the field, and any magnet placed within the field. And these fields are thought to be fundamental quantities, neatly describing the behaviour of all magnetic objects. However, sometimes magnetic fields are not mathematically simple to deal with.
To overcome this issue, physicists made use of a neat math trick. They took an identity that states that the divergence of the curl of any vector must be zero, as well as the Maxwell equation that states that the divergence of any magnetic field must always be zero (https://www.youtube.com/watch?v=0jW74lrpeM0&t=6s) to define a "magnetic vector potential" (A). The relationship is that a magnetic field is equal to the curl of its vector potential.
Now vector potentials are often easier to work with mathematically, but they aren't uniquely defined ("gauge invariance"). If we have a certain B-field, this can be described by multiple related A-fields. But when given an A-field, we can uniquely find the corresponding B-field. This is important later.
When studying quantum mechanics, it turns out that the A-field can have a real, measurable impact on a system, despite only being considered a mathematical convenience. Importantly, this measurable impact has nothing to do with the corresponding B-field! This is because in a region of space where B is zero, but A is not zero, we can find the wave function of an electron being changed. Specifically, the phase of the wave function changes, and this can be measured using a particular type of double-slit experiment. This effect is known as the Aharonov-Bohm Effect.
In other words, we find that the magnetic vector potential can have a real-world impact WITHOUT any influence from its corresponding magnetic field. The Aharonov-Bohm effect is telling us that electric and magnetic fields are not the fundamental quantities that we initially thought, and their potentials are the fundamental quantities! This despite potentials only being created for mathematical convenience!
Caveat to the Aharonov-Bohm effect: It *may* be possible to describe the effect by purely dealing with the magnetic field and not the vector potential, but this would involve having to give up the idea of locality - we would need nonlocal fields! (https://en.wikipedia.org/wiki/Principle_of_locality)
Timestamps:
0:00 - Magnetic Field Lines: Vectors for Magnetic Interactions
1:46 - Magnetic Fields vs Mathematical Convenience
2:17 - A Neat Trick for Defining Magnetic Vector Potential
4:00 - Sponsor Chat: Thanks to Skillshare, Check Out a Free Trial Below!
5:00 - Gauge Invariance, Uniquely Defining the Vector Potential
6:08 - B Fields are the Real Fundamental Quantity... Right?!
6:45 - Passing an Electron Near a Solenoid (Coil of Wire)
7:56 - Phase and the Aharonov-Bohm Effect
9:40 - Final Thoughts
Useful resources:
https://en.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect
https://en.wikipedia.org/wiki/Del
https://en.wikipedia.org/wiki/Phase_(waves)
https://en.wikipedia.org/wiki/Double-slit_experiment
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 (Canon EOS M50): https://amzn.to/3lgq8FZ
My Lens (Canon EF-M 22mm): https://amzn.to/3qMBvqD
Microphone and Stand (Fifine): https://amzn.to/2OwyWvt
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/
This video was sponsored by Skillshare #ad
