We DON'T Understand Magnetism (According to Quantum Mechanics) - Aharonov-Bohm Effect by Parth G

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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 ( • Let There Be Light: Ma... ) 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! (en.wikipedia.org/wiki/Princip...)
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:
en.wikipedia.org/wiki/Aharono...
en.wikipedia.org/wiki/Del
en.wikipedia.org/wiki/Phase_(...)
en.wikipedia.org/wiki/Double-...
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[@ParthGChannel]

Hi friends, thanks very much for supporting my channel! I'd also like to thank this video's sponsor. The first 1000 people to use the link will get a free trial of Skillshare Premium Membership: skl.sh/parthg06211 Also, I've made a follow-up video to this one, discussing potentials in more detail. In that one we look at the electric scalar potential! Check it out here if you're interested: kzbin.info/www/bejne/baPNcqerrN2le6M

[@baklolvlogger8413]

Sir please make a video explaining everything about standard model clearly 🙏🏻🙏🏻🙏🏻.

[@atiquakhan3218]

Thank you so so much I always wanted to know the quantum side of magnetism I love how your videos are very simple. Even after being an undergraduate, your content is always understandable

[@anilsharma-ev2my]

Nobel Prize ka business karwa do kuch to guzara ho jayega

[@anilsharma-ev2my]

Magnetic field are black holes ???????????since at cool temperature we got attraction and same thing happened in real black holes per second Ever wondered two ice cubes stick with each other Oxygen is ferromagnetic or paramagnetic

[@SidharthGat]

Hello, This is sidharth I'm currently pursuing mechanical engineering but want to shift to physics after my BE. Do you have any suggestions for me? How can I make this happen? Also, I was supposed to make a project as a part of my degree program for that I was thinking of choosing such topic that could reflect my ability at physics, as I don't have a traditional bachelor's degree in physics, which could help document my physics knowledge and improve my chances of getting admitted. But couldn't come up with a good enough topic which involves both physics, but can also be converted into a prototype (which is needed being part of an engineering program), Do you have any topic suggestions for me?

[@joeamrine7450]

You really are unusually talented at explaining complex topics.. if I could offer any advice (I was a TA for physics in undergrad) is to always underestimate the students knowledge, you literally can never dumb things down enough.. it’s a natural blind spot as an expert to forget which concepts are NOT common sense.. so constantly repeating and dumbing simplifying things down will always help students understand better.. great videos

[@stopthephilosophicalzombie9017]

I disagree. I think you should teach to the highest level possible and only dumb-down when necessary. "Dumbing down" of necessity means leaving out crucial details.

[@bxlawless100]

Dumbing down isn’t what’s needed. Simplifying a concept is. If you can’t explain something simply, you don’t understand it.

[@stopthephilosophicalzombie9017]

@@bxlawless100 Of course some concepts don't admit to dumbing down. I've started wondering of the value of "popular science". We live in a world of bad pop science and bad science purported to be good science. I'm not sure we are making much progress. Physics has stalled in fundamental discoveries for 40 years, and now we've got woke commies dictating policy in engineering and physics schools. Something has to give.

[@alexdagios28]

i'm a electrical engineer and you simply blew my mind, thanks for the amazing content Parth! this potential magnetic vector was always a bummer, never (until now) had thought about the relationship between electric potential and the vector A, very nice watch a video that makes me re-think about things that always were the basis of my knowledge and learn.

[@Qwerty-cb1ti]

Hi. as an electrical engineer myself I'd like to help you. To understand this you have to check what is available in English about Gennady Nikolaev. He solved the problems around this topic in the eighties. all the info is available in russian but since 2008 there is info in english also. Just try to grasp the notion of scalar magnetic field. Once you know that this component exists everything is obvious. Otherwise you have a series of paradoxes such as Aharonov-Bohm, Newton's third law violation in case of charges moving at right angles, Nikola Tesla's Colorado Springs akcievement (longitudinal EM waves in action) and many others.

[@sonarbangla8711]

I knew div and curl but didn't know they are important in QM. I am looking forward to the next video on this series, explaining the effect on QM (Aharonov-Bohm) effect. Does considering these effects help calculate the values of quantum states better?

[@JohnDlugosz]

You should look at how the electric and magnetic fields are really front and side views (so to speak) of a single underlying thing, when using special relativity. Consider that moving a magnet through a stationary coil and moving the coil past the stationary magnet in the opposite direction are just different descriptions based on your reference frame, so *must* have the same underlying physics. Yet you teach, classically, that the former is a changing magnetic field inducing an electric field which then affects charged particles in the wire; and the latter is an unchanging magnetic field with charged particles passing by. Where is the electric field in this reference frame? It only works because the electric field vs magnetic field is due to your choice of reference frame, thus the "real" physical thing that doesn't care about the different observers (who may be looking at it at the same time) must be something else.

[@Qwerty-cb1ti]

@@sonarbangla8711 Aharonov-Bohm can be explained in terms of clsssical physics. This is what Nikolaev did. No need for QM. QM just demonstrates that in classical physics there is a component of the magnetic field which is unaccounted for. This is the so called scalar magnetic field (divA)

[@woowooNeedsFaith]

@@JohnDlugosz *Yet you teach, classically, that the former is a changing magnetic field inducing an electric field which then affects charged particles in the wire;* Right. *and the latter is an unchanging magnetic field with charged particles passing by. Where is the electric field in this reference frame?* 1. Classically we would use Lorentz force to explain this induction, right? (Does this give rise for induced/apparent/actual electric field?) 2. In your example the magnetic field would have to be inhomogeneous, so charged particles would experience gradients of magnetic fields. Did you take this into account?

[@zmaz3898]

Just Amazing.... Finally I could complete my Masters from your channel 😅

[@Stasis247]

Masters in QF theory? Good job

[@zmaz3898]

@@Stasis247 Yup gonna take Grammy of QFT soon😄

[@Stasis247]

@@zmaz3898 amazing! Hope you do well! I want to study QFT too!

[@Stasis247]

@@zmaz3898 can I ask what age you started to study QFT? How long it took you to get your master’s? What were your high school grades like? Are you enjoying the studies? Asking cause I really want to study QFT but I need to get past a mental block that I’ve had the past few years and it’s really stopping me from learning

[@vampirethespiderbatgod9740]

@@zmaz3898 Congrats! This shows that one doesn't need the formal, tedious, text syllabus for everything. The learning is about how better we understand something. Paths to learn things are many.

[@takashitamagawa5881]

When classical electrodynamics is taught in a typical college physics class electrostatics is taught first and then the students are shown how magnetism arises from the fields of moving charges. But quite clearly all of magnetism can't be derived this way and quantum mechanics is involved in a fundamental way. Heck, even natural magnets (known for centuries) whose fields arise from the phenomenon of ferromagnetism can't be described without bringing in quantum mechanics and the idea of spin.

[@goodmaro]

This is why in that famous video Feynman told the interviewer, no, he couldn't explain to him how magnets work. Every partial answer leaves several "why"s that are as or more unintuitive than the original question.

[@jeffxanders3990]

Unless we acknowledge the ether. Ken Wheeler wrote the book on magnetism.

[@asdfniofanuiafabuiohui3977]

electric and magnetic fields are the same thing- electromagnetic fields, but from different observers. Thus you also need relativity (length contraction) to truely explain magnetism (such as electromagnets)

[@Chicken_Little_Syndrome]

@@asdfniofanuiafabuiohui3977 Many of us think this is the case. But the truth is many of us are wrong. Relativity is nonsense.

[@Chicken_Little_Syndrome]

Quantum mechanics explains nothing. It is mental misdirection.

[@Testgeraeusch]

Simple rule of thumb: electric potential links directly to the particle energy, if it has charge. Similarly, magentic potential A links directly to particle momentum, which is defined as... well, actually this one is a bit tricky since the only usefull definition of momentum uses the Lagrangian and most regular people don't know what that is... it is a mathematical extention of Newtons equation giving the same results based of a function L of space x, time t and velocity v. This function is typically suited for a Legendre transformation, which is replacing every dependency of v by a dependency on the slope of L with respect to v. And this slope is called momentum. For regular classical mechanics, the momentum is just p = dL/dv = m*v, for relativistic particles it is p = dL/dv = m*v/sqrt(1-v^2) and if the Lorentz forces should also arise in the equations of motion than the momentum includes a dependency on A. p = m*v/sqrt(1-v^2) - q*A where q is the charge and the units are Heaviside-Lorentz-cgs with c=1 (these have the same form as the SI units if you set epsilon0 = 1). The classical limit is just p = m*v - A and the total energy is no longer H = p^2/(2m) but instead H = (p - q*A)^2/(2m) and that is also the (kinetic part of the) Hamiltonian you have to use for the quantum models. And this is the direct link which makes A appear in all equations of motion, even though it never directly influences the paths taken by a classical object.

[@antonventer8532]

Very well explained man!👌

[@richardaversa7128]

Great video Parth - background well-explained, main concept is fascinating. Well done

[@00pehe]

Coincidently or not, I presented a seminar about the Aharonov-Bohm effect for my Quantum Mechanics class a month ago. Great video! :D

[@maus3454]

So far the best explanation about vector potential "A" I have seen. Keep on going the good work.

[@yonjarisgarcia821]

I cannot understand why this guy doesn't have more suscribers and view. He is just excellent explaining these extremly complicated topics as they were as simple as count from one to ten.

[@yeastinchampagne440]

Another anecdote on the unreasonable effectiveness of mathamatics

[@En_theo]

I don't think that maths are efficient because they're fundamentally "made" for this. We create rules that correspond more or less to a reality and so when the theory is right or close enough, there is no wonder that we get results. For example, in pure math 1+1 = 2 . But if I add speeds of two bodies (the famous Einstein's train with a light ray inside it) then we can't simply add the speed of the train and the speed of the light. Here, 1+1 does not = 2 . So you see, it's all about the preconceived ideas that we applied to the math that gives a result, and not the other way around.

[@yeastinchampagne440]

@@En_theo ofcourse you can't arbitrary put maths together to prove something but it is more about the capability of math and its logic to show reality when used correctly with physical quantities.

[@En_theo]

@@yeastinchampagne440 Then it's not the "unreasonable effectiveness of mathematics" that works, it's our ability to establish the correlation between several phenomenon. Maths are a handy tool to compensate the fact that our ape-brain can't handle data under a certain form. In some ways, math being an invention of man, we can say that there again it was our ability to establish the link between different concepts that created the efficiency of math. My point is, I see everywhere people talking about math as if it was universal concept in itself. It is not. It's a tool, it's very handy, but like every tool it has its limit and it's not universal.

[@yeastinchampagne440]

@@En_theo I agree with your point now. Thanks for giving new perspective.

[@En_theo]

@@yeastinchampagne440 Np, glad if it helped somehow :)

[@cihualocos]

Just finishing my electromagnetism course and watched this video, definitely blew my mind.

[@spinnymathingy3149]

But have you ever seen a magnetic field like this ? kzbin.info/www/bejne/pJysepeIf7-smNk

[@runs_through_the_forest]

@@spinnymathingy3149 however beautiful those holographic like images are, they are not really showing you the magnetic force nor the magnetic field lines, they show you an optical illusion, the only useful configuration would be a tank with ferrofluid evenly dispersed and one strong light behind the tank, while putting a magnet inside.. good info i found in video's by fractal woman..

[@chispun2]

More on this topic, please, I am loving it and feeling for the first time electromagnetism and it’s operators make sense

[@davidschroeder3272]

Thank you Parth, this is so much easier to follow than reading a dry textbook! The way you present all these physics topics takes the scariness out of learning. Years ago when I majored in electrical engineering and minored in physics (pre-internet) I felt overwhelmed by the abstractness of it. And when I came across the Aharonov-Bohm effect long after college I was totally perplexed. I'm just at the 4:10 mark in this video, but I know I'll understand this effect when I finish watching the video. All of your videos are absolutely awesome!

[@bxlawless100]

Parth You jumped into my KZbin suggestions and now i can’t live without you. 😀

[@stevenschilizzi4104]

Fascinating presentation - ideal for grasping the essentials *before* delving into the specifics if one is interested. Thanks again for your efforts, Parth!

[@gman9090]

Good video mate!

[@blackbear92201]

Awesome video - thanks for posting! :D

[@rajgupta759]

Beautifully explained. Thank you so much.

[@phonsefagan3754]

You are an amazing teacher! Bravo!

[@reigak6599]

Simply mind blowing. Great video.

[@KB08.a]

Amazing video. Please make more videos of this sort.

[@buckrogers5331]

Fantastic job on this. Thanks.

[@derherrdirektor9686]

Beautiful. We always heard of the vector potential in university, about the Lorentz-Calibration, that puts potential and vector potential into relation and that there are problems that are easier to be solved with the vector potential and some are only to be solved using the vector potential. But finally I've been enriched with some real world example. :)

[@mokhodadadi1087]

Amazing explanation!!

[@atharvadeshmukh6328]

Really like your stuff! Keep it up! Could you please release a series discussing, going a little deeper?? Please, it'll be really helpful! Thanks, and again keep it up! Something like physics version of 3blue 1brown

[@cyto3338]

Nice video Parth, Gauss and Maxwell would be proud!

[@AbuSous2000PR]

simple and easy to follow. many thx

[@gravitytutorials6537]

This is so intuitive. And you are so clear. Respect, Sir.

[@space-time-somdeep]

So beautifully explained

[@carlthorellstein53]

I was wondering if you could do a video on the space metric (g_ij) and how it works. I have been trying to find resources about it online, introducing it on an undergrad level, but I can't seem to find much. I love your videos, keep it up

[@SKARTHIKSELVAN]

Thanks for your efforts.

[@richardmoncure2744]

Thank you. This is first I've heard of this. It may be the missing link in my understanding of magnetism and of Maxwell's equations.

[@kuzy2276]

A few months ago all this would have gibberish, I just took a quantum physics and an Electromagnetic theory class, and this blew my mind. I'm about to go on a marathon now.

[@MatteoDeLeone]

Wuaho! I really like your video, bravo!

[@azharqayyum5474]

Well explained....

[@briann10]

I remember seeing Aharonov-Bohm effect describing resonace in aromatic hydrocarbons, I had no idea what electric potential was. The visual helps a lot.

[@ravigautam8685]

Thank you so much. You saved my lit of time.

[@borisvukcevic1454]

Fascinating

[@PaulJohnLeonard]

Great video. I would have liked to a video talking about the similarities between electric charge and the static voltage field (V) ; compared with ; current (moving charge J ) and the magnetic vector potential (A). That is if you treat the charge and current density as a 4 vector in space time (time+ 3 space coordinates) (p,J) then the integral form of the leads to the 4 vector of voltage and magnetic vector potential (V,A). That is the magnetic vector potential can be calculated in exactly the same manner as you calculate the voltage due to a charge distribution (high school physics) the source of A is the current vector. This integral form gives a unique value for the 4 vector (V,A) for a given frame of reference. The voltage field describes the potential energy between charges whilst the magnetic vector field describes the mutual momentum between moving charges. Things get interesting if you start moving the frame of reference. All of electromagnetic field theory and no mention of E or B !!!!

[@dutonic]

This was so good. This effect was always tough for me to understand in my quantum classes. But this really cleared things up.

[@gyro5d]

It's still Aether! e->~~~~~~~~~~...~~~~~~~~~~~~~~~

[@objective_truth]

Now I can better understand gauge fields, Thank you.

[@sobreaver]

Great video ! Thanks ! PS: useless details but I would say that your light setup has got me distracted a bit with mainly the red ring light being reflected in your glasses. Anyways, just a little something that might 'improve' your content.. good day ! :)

[@petrosmikh]

Great explenation.

[@ingitabanerjee9727]

Thank you make are very much informative as well as enjoyable videos you make. One request , can you please make a simple version of Gibb's Paradox as I cannot find anywhere in youtube where they have explained in simple terms.

[@geor664]

So now that you've opened my eyes, where should i go to expand on this knowledge, particularly at the interface of the applied. For example books & you tube? Another way of framing this question is, if i go down this path, does this change in understanding affect how interpret the application of electromagnetics, electrostatics and maybe optics? Or an i no better of, i just interpret the results through different coloured lenses?

[@Qwerty-cb1ti]

search for info in English of Gennady Nikolaev . He solved these paradoxes in the eighties.

[@ManfredVonRichtoffen]

Great video. Could you at some point explain what the covariant derivative is and its significance in physics?

[@shutupimlearning]

Mind=blown I thought this video was going to be about virtual photons mediating electromagnetism, but as usual theres always so much more to learn!

[@Amipotsophspond]

this was really good.

[@jockellis]

Doing magnetic particle inspections, I want to know if there is any way to determine how far out the gauss lines stray from the line between the two electromagnets formed by the feet of the yoke.

[@martinhsl68hw]

Great stuff! Collective Electrodynamics by Carver Mead is a work of genius which wised me up to the meaning of A

[@bassinnoor8318]

Bro your vedios are so good and interesting

[@captainhd9741]

Was this video based on recent discoveries or is this about something that is perhaps a few years old?

[@OssyaTheBrave]

Great video but GREAT closing music

[@abhijithrambo]

+1 for explaining the wavefunction as a mathematical description of what we know about the quantum state vs the more common "state of the physical system"

[@alyaaathirajasmine8716]

i'm a final year physics student at uni and i have an advanced quantum mechanics exam in 3 days. you're actually saving my degree with this video thank you so much!!!

[@5ty717]

Vaidman says the AB Phemonenom results from classical solenoid interaction within the quantum system and emphasizes the corrolary that local effects remain local in purely QM vector fields (excl spatial entanglement)

[@SquidKing]

im probably wrong, but i thought magnetic fields were technically infinite? as in their strength just got very very small (but not zero) as you moved far away from the magnet

[@piratesofphysics4100]

No. All the magnetic field lines can be bound within a small space. But electric field can't be. Electric field is infinitely large. I think the electric field of the electron somehow interacts with the localized magnetic field. And hence we noticed reasonable changes in quantum mechanical world

[@SquidKing]

@@piratesofphysics4100 thanks very much for clearing this up 👍👍

[@antonk.653]

@@piratesofphysics4100 This is wrong, magnetic fields can also extend infinitely in space. Just look at earth's magnetic field, pretty big for a weak magnet.

[@gcewing]

The magnetic field outside a solenoid is not exactly zero, but it can be made very small -- far too small to account for the observed effect.

[@jerwynjames8312]

@squidKing i do believe you are right and we are missing something here....zero really cant add up in maths unless it comes between or behind a value.... And taking into consideration the magnetosphere i really do believe your theory that the wave lengths do get infinity weaker but they never cancel out .. they just observe into the magnetosphere and sort of grounds out on the magnetosphere grid... That is my theory....

[@clavo3352]

WOW! except that I'm 65+ and close to braindead, I could almost understand this. My curiosity leftover from my youth helped me watch but ultimately I could feel my brain saying: "can't handle this super interesting stuff!" time to let go and let younger minds onto this educational ladder of knowledge. It's a great video! The graphics really help.

It seems 'tricks' invented, to have more simple math, but that often signals that there must be a "real-world" importance of that "trick" as well (possible hidden though and hard to figure out, specially at the first time).

[@charleshudson5330]

Nice video. I'm a physicist and I'm never surprised when a mathematically coherent entity turns out to have a physical counterpart. Nor was Dirac. Both solutions to his equation have physical significance. I met David Bohm in the mid-1970s and we discussed his 'quantum potential' in Bohmian Mechanics.

[@boiiwizzy7809]

SOng at the END , pls upload !!

[@Draginx]

Hey, parth! Could you make a video on tensors and how they are used in GR? Maybe the difference between contravariant and covariant and how the metric tensor is loosely used?? Thanks!

[@ManojKumar-cj7oj]

Much appreciated

[@gandelfy]

Eigenchris is great, Also check out the channel XylyXylyX, he has videos starting from basic Point-Set Topology builing up to GR, also Lie Groups/Algebras and some QM

[@RobManser77]

This would be good 👍🏻

[@ManojKumar-cj7oj]

@@kirkhamandy Thanks buddy😊 ! His tensor series is blowing my mind ❤️ And xylyxyly has the same quality

[@alwaysdisputin9930]

​@@kirkhamandy fuck eigenchris. Try his teachings experience the confusion & then stop. Try DrPHysicsA. Experience the clarity nearly everything explained very nicely eg his vid on blackholes. Then one can start to be in a position to decipher what the heck these other people are trying to say. I got a little bit of that with ParthG here. The compass bit very nice. The talk of curl & div was not. The solenoid diffraction bit was pretty good. Never watch PBS or Susskind IMO

[@palfers1]

That non-locailty caveat is interesting. You should make a video about it.

[@sayyestophysics1705]

Hello, I feel the concept is well explained and also quite clear, it does not make much sense to a normal person who is looking to explore physics. May be it's more suitable for a few university courses where the physics becomes abstract. However, I really don't understand what that abstractness really leads to or what it's practical relevance to technology is

[@tanvirfarhan5585]

pls explain pointing vector

[@philoso377]

Page 8:00 When we study physics through math, we give away our chance to comprehend nature (as most mathematical physicists do), in trading for a place on a fast lane. In this case B=0 implies the presence of magnetic field in a space where total B vector of it summed into (net) zero. Closed loop vector force isn’t physically zero or absence. A battery has potential difference also is net zero. It release energy upon a load. A spinning fly wheel in space possess energy is also net zero energy until we apply friction to generate heat. We use Lorentz force as a load to a B field to discern magnetic field of B=0. It is not too late to re-learn physics from rediscovering physics through interactions and experimentation. (As old school education did) If we never leave home only interact through the Internet soon we marry to a virtual wife to raise virtual kids and obey or legislate virtual law of physics through a bunch of equations. Not much difference from wingless bees live on honey in the comb. How sad.

[@Greg_Chase]

Absolutely wonderful perspective you have. Math was always just a shorthand to allow communication of a physical idea. Written music plays the same role. By demanding a true 'physical nature' description of Nature means more discovery, more "new physics" is possible. If the intellectual laziness remains the same, ie. if everyone only wants mathematical/theoretical physics because "I don't want to get my hands dirty doing experiments, I leave that for 'lesser' people to do the real work" ............ That is why the exact physical nature of gravity is not taught and is not sought. For example, we know that the alignment of 'magnetic domains', otherwise known as aligned electron spin orientation, in certain elements (iron, nickel, cobalt) results in the Vacuum manifesting a magnetic field in the immediate vicinity of that material. We have known this *physical nature* of the magnetic field for nearly 100 years. But absolutely no attempt has been made to pursue the physical nature of gravity. We know from the Cavendish experiment from the year 1798 that all collections of atoms - ie. all matter objects - will manifest a gravity field in their immediate vicinity. And we know that the electron is responsible for EM (electromagnetic) effects. That leaves the nucleus of the atom, which possesses 99% of the mass of the atom, to account for gravity. And NO ONE pursues this in physics, mainly due to the "intellectual momentum" of general relativity. You have a great attitude about Nature, and about physics, and it is people like you, I believe, who benefit humanity and the sciences in the most impactful way - asking questions from a non-common perspective. Good luck to you. . .

[@Silavite]

This story of a mathematical convenience turning out to have physical meaning reminds me Planck. He originally thought that the quantization of energy was a mathematical trick for figuring out an empirically correct blackbody radiation law. Little did he know that this assumption would open the door to quantum mechanics!

[@user-vg7zv5us5r]

6:20 No, magnetic vector potential component isn't meaningless. It tells that vector field has the property of magnetism. It's like telling what flows in your veins: blood or alcohol. The vector field provides a structure whereas with a vector potential we say what has been actually transferred by the means of that structure. In the end, we obtain a magnetic field "B" as a vector composition of structure ("nabla") and flowing substance (magnetic vector potential "A").

[@michaelransom5841]

This actually makes complete sense. aftercall, there is information you can gain about the field from the electron.

[@nileshkulkarni6196]

✋✋✋I have been asking this for a long time….😅 Will you please make a video on how newtons third law is supposedly violated when 2 charged particles move wrt each other and how it inspired Einstein to discover special relativity

[@recramorcenlemniscate7945]

1 question, does this also apply in fields where the magnetic &/or electric fields have been cancelled out by their antithetical field?

[@deusdat]

Can't understand how do you control A in order to observe the changes in the electron's wavefunction. When B is zero, what exactly determines A in an experiment ??

[@MusicEngineeer]

yes, indeed - good question! how did the A field get established?

[@00pehe]

Actually, the change in phase of the wave function depends only on the change of the vector potential A over a path (a line integral). Usually, these experiments are made comparing closed paths for the test particles. And by the mathematics, you can find that the vector potential has the form A' = A + ∇λ, where ∇λ is the gradient of some scalar function λ. From calculus you can show that the integral of the gradient of a function over a closed path is zero, so the "arbitrary" part of the vector A' doesn't affect the result of the change in phase.

[@deusdat]

Perhaps the idea is that the change in phase is a proof of A's actual physical existence inthe absence of B ??

[@00pehe]

Yes, that's the idea of the experiment, in case B is zero, A is the gradient of some scalar function

[@kevinoboyle8939]

And more support for the Pilot wave interpretation of QM

[@woowooNeedsFaith]

A Question (probably malformed because I have forgotten too much of this topic...): 9:15 - When you have (homogenous and constantly) changing magnetic field through region of space, you get (static) induced sourceless electric field. You can't (uniquely?) define electric potential along these closed loops of electric field, because its value depends on the path you take, right? Or could you simply define the potential to be imaginary quantity, and that way somehow get rid of this problem? Could you measure imaginary potential or would you be limited to measuring the real part only?

[@laliborio]

oh my gosh! Why have I taken so long to find your channel? T_T

[@slickwillie3376]

Interesting. Any ideas on how the electric scalar potential might be isolated from the E field so as to be tested?

[@markseidler3251]

Is the vector "A" the magnetic analog of electrical potential (voltage) "V" ? Like in a charged capacitor, it's not changing.

[@slickwillie3376]

Thinking about this mechanistically, and hydrodynamically, I like to imagine the B field as being a torque vector field. The A field becomes a flow field circulating around the B field. In this case, it is interesting (to me anyway) that if the B-field lines were discrete (a wild and crazy supposition) then they would repell one another due to the fluid dynamics of opposite flow turbulence. Likewise, when similar magnet poles are placed together, the same effect would cause the magnets to repell. Also, when opposite poles are placed facing each other, the torque circulations would be in the same direction, pulling the magnets together. Strange reasoning I know, but also a strange coincidence. Could the B-field lines be (real) discrete quantum vortex lines in a superfluid medium?

[@En_theo]

Maxwell first described the electromagnetic field as vortexes, and it seems to me that imagining fields as being a real stuff is the right way to take on these problems. I know that none managed to put up a theory that could describe space-time as a superfluid that would have all the properties we observe, but I'm sure it's just a question of time until we manage to achieve that.

[@dsdy1205]

You don't need the field lines to be discrete vortices, you can have an overall continuous corticity distribution analogous to a continuous B field, no field lines necessary.

[@En_theo]

@@dsdy1205 This works if you assume that quantum fields are discrete but that does not work well with GR. My point was that imaging fields as superfluid can work for one aspect of a theory but not for all theories.

[@bobann3566]

Your on the right track. Maybe Ken Wheeler of Theoria Apophasis may have some interesting insights for you.

[@En_theo]

@@bobann3566 Yes I have seen his videos, but he's sketchy at best. He does not explain well his idea, he's more about ranting than teaching.

[@jlpsinde]

Really cool

[@jesscorbin5981]

Can this help us explore the relationship between superconductivity and magnetism?

[@classictutor]

If the vector or scalar potential is more fundamental than the field (which could just be for mental convenience), is space itself be more fundamental than the particles themselves? Then what does that mean for Maxwell's equation if we don't start from particles but from space time? How do we put it all together?

[@edwardlewis1963]

understanding magnetism may be the key to understanding gravity. (because levitation can be demonstrated using magnetism) the vector A might be usefully viewed as more fundamental than the B field; while the way it was arrived at may paint it as a 'construct', one can look at it the other way around, as in not a complex construct, but a discovery of something less complicated

[@snehalatapanigrahi7270]

Can the Aharonov -Bhom Effect be applied to other fields too?

[@Qwerty-cb1ti]

no

[@JohnDlugosz]

Well, anything that's a "charge" that falls off with distance from a source gives you what's called a gradient field. And the curl of a gradient field is zero. Maxwell's observation that the divergence of a magnetic field is zero is synonymous with the fact that there are no magnetic charges. The fields we normally think of are those of _charges_ on particles. To get a similar effect, you would need to look at a secondary field induced by the motion of these charges, not the particles themselves. Now you can get an analogy of magnetism with gravity. What happens when you apply relativistic transforms to the color charge, I have no idea. You could certainly do the same thing as for the electric scalar potential, though, for any kind of charge. That is, mathematically. Whether it seems to mean anything physically is an interesting question.

[@mikhailmikhailov8781]

>sees the divergence of curl formula d^2=0 Diff forms are great) Also, non uniqueness of potentials being analogous to non uniqueness of indefinite integrals isnt just an analogy - it is mathematically an exact the same thing.

[@user-zj2ir9hg6n]

讚讚~這個影片有趣!

[@EnsignRho]

There are things called FIPs, Fundamental Infinitesimal Processors, which make up our universe. They are running software which is based on fundamental theories. When aggregated, systems emerge which produce fundamental particles. The networking nature of these FIPs explain why things interact the way they do. Only in certain message alignments do certain responses and their ability to read certain types of inputs exist. This interaction explains quantum effects, gravity, the speed of light, everything. It also explains why things like entanglement exists, with instantaneous awareness over a distance. It's because FIPs exist, and they are running a program executing digitally, but they exist physically and can communicate in their native domain without the limitations of the simulation. FIPs, baby! It explains everything.

[@solomonmason835]

For the multiple sets of magnetic potential, will they always equal the same thing when the magnetic field is zero? If not, how does the wave function decide which potential to react to? Would that mean quantum mechanics makes one of the set the actual magnetic potential?

[@renanmelo4903]

does the surface electrical charge of the solenoid influence the trajectory of the electron in the experiment?

[@davidwoods1337]

I've seen images of ferrofluid and iron filings that will point or align along field lines. However I don't understand why there are separate lines and not just a homogenous field. Why are there quantized lines?

[@mb-3faze]

At 8:00 , if there is current flowing in the solenoid coil, then B in that rectangular region will not be zero (?). There's even a purple magnetic field line in it . In this experiment, is there actually a current flowing? or is this the whole point - that there is a coil of wire which *could* produce a magnetic field but it is not doing so (no current flowing) and therefore B is zero (but A isn't).

[@cafebrasileiro]

Very good video, but A and Phi shouldn't be labelled as "fundamental properties". Because they are what physicists call "Gauge dependent properties", which means they vary according to the assumptions you make about your physical system (even though B and E remain the same). What puzzles me about the Aharonov-Bohm experiment, is that these quantities shouldn't have physical reality, but they seem to have. As a physicist myself, I rather state that probably something else is changing the phases, not the vector potential itself.

[@LuisAldamiz]

Wow!

[@exxzxxe]

Good job! You and followers of this channel may want to read "Gauge Fields, Electromagnetism and the Bohm-Aharonov Effect " by C N Yang- written as a follow-on to Freeman Dyson's article on Feynman's derivation of Maxwell's equations from commutator algebra and Newton's equations of motion. A bit mathematical, but doable.

[@adrianwolmarans]

This leads one to wonder, if the A field can be non-zero where the B field is zero, then how for does it extend away from the solenoid? And then, doesn't the curl of the A field being zero imply that either either the A field is zero in that region of space or it's uniform and irrotational, and if the last case is true, doesn't that imply the the A field would be non zero everywhere?

[@00pehe]

From electromagnetics, it's possible to show that, for a supposed infinitely long solenoid, the magnetic field is confined within it's interior, therefore it's null on the outside. But the vector potential is nonzero on the outside, extending infinitely away. It's also possible to show that the magnetic field is invariant if the vector potential is transformed as A -> A + ∇λ, where ∇λ is the gradient of some scalar function λ. Notice the the magnetic field is: B = ∇×(A + ∇λ) = ∇×A + ∇×∇λ = ∇×A (invariant wrt λ) So, if the magnetic field B is zero, A isn't necessarily zero, but rather the gradient of some arbitrary scalar function λ, which may or may not vanish on infinity.

[@bassinnoor8318]

Any explanation are in simple , understandable way

[@SidharthGat]

Hello, This is sidharth I'm currently pursuing mechanical engineering but want to shift to physics after my BE. Do you have any suggestions for me? How can I make this happen? Also, I was supposed to make a project as a part of my degree program for that I was thinking of choosing such topic that could reflect my ability at physics, as I don't have a traditional bachelor's degree in physics, which could help document my physics knowledge and improve my chances of getting admitted. But couldn't come up with a good enough topic which involves both physics, but can also be converted into a prototype (which is needed being part of an engineering program), Do you have any topic suggestions for me?

[@JohnDlugosz]

Something I find interesting is to use your mechanical engineering skills to replicate "classic" apparatus and experiments. With modern tools, materials, and understanding, it's straightforward to build something that was groundbreaking in the past; for example, the first cyclotron particle accelerator, I learned, was only 7 inches in diameter. When I was in high school, I considered that this could be replicated using modern parts quite easily. Now that's more EE than ME, but that's the kind of idea I wanted to share.

[@SidharthGat]

@@JohnDlugosz Thank you for your suggestion. I had considered working on cyclotrons, now I will reconsider that idea.

[@SidharthGat]

[ ] Cryo cooler [ ] Particle detector [ ] Cyclotron (particle accelerator) or velocity selector [ ] Space mapping [ ] Atom mass measurement [ ] Rectannas [ ] Tunneling diode [ ] Checking photon tunneling [ ] Verifying relativistic effects(time dilation and length contraction) [ ] Vehicle going faster than itspropulsion [ ] Branched idea from above, windmill faster than wind. [ ] GPS [ ] Time synchronization [ ] Satellite navigation [ ] Tripple pendulum [ ] Magnetic confinement (solenoid bottle) These are the topics that I currently have. But not aware of how financially feasible would these options be. We in a group of 4 might be able to arrange a few hundred USD together. Can anyone help me with that? Also you can suggest if you have any other good ideas.

[@neil6477]

There will be many opinions about what A could represent. My question is could it not be a time indepedant, undisturbed field? Being undisturbed it would not give rise to any magnetic event, hence B = 0. However A itself could not be 0 since it is obviously present. Equally an electron passing through the 'static', undisturbed field would cause time dependant changes, giving rise to a local magnetic event, hence inducing a phase change.

[@Nobody_114]

Could you please tell me under what conditions or equations is vector A !=0, but B=0?

[@Chris-gy3eh]

A=(x, y, z) would all give a non-zero A but zero B.