I was lost on the Aharonov-Bohm Effect and this video made me almost fully understand the fenomena. Thank you very much, your explanation was very very clear and dynamic with the support of the images. I only have questions with regard to the g(r) function, but that is just to go deeper on the effect. Overall I understand it a lot better. Seriously, thank you for the lecture and the helpful notes!
Thanks for taking the time for this video. 6:38 (1 dimensional) vector potential CAN be quantified but it requires access to time from past to present and future to present (i.e. at least 2 linear directions) and if time is equal in all directions, which it is NOT (i.e. no dimensional anchors or dimensional buoys nearby...) one can ballpark the potential by sliding the single time value across xyz placeholders with the known value relative to the rest of the equation variables, but don't take that to the bank for NIST calibrations lol. only recently are we developing the capability to start visualizing time in more than one linear measured value (i.e. it past to future and future to past). It is going to be some more years before time crystals and multidimensional gravity influences can be taken into account for adjacent spacetime and electrical/magnetic field phenomena calculations, to reverse engineer minute stuff like vector potentials and understand how to read and detect the metaphorical holes before the electrons arrive at those positions... but I have faith that those few of us who know what we are looking for will find it with the correct hard work and hand of Provenance to guide. "Ask and ye shall recieve. Knock and it shall be opened unto you." Something to liken it to would be on a macro level: freezing praesiodymium or niobium and watching it levitate. How high will it levitate? well that depends on environmental factors around it and temperature and core purity. Or calculating the exact paths of a air-ground lightning strike and then actually MANIPULATING it to be directed into an HV storage capacitor other than planetary water. It might seem impossible but with hard enough work it can be done. _At a subatomic level _*_even playing music in a room_*_ can impact how the particles flow in this and ajacent dimensions._ Farnsworth knew this general idea when he and George guys did the magnetic choke for the first electronic television tubes to stabilize the path. This would later be used extensively in particle accelerators and in theoretical optics as containment structures... and for the last 60 years they have been attempting to figure out how Philo did it before when he had the Mark III Fusor working. It took 60 years to reach fusion ignition again. Critics say absolute zero is not possible. It absolutely is, and Neil Degrass Tyson is incorrect. I respect the man as a scholar and professional, but he is incorrect on his video. Understanding the Aharonov-Bohm effect will be helpful in knowing and expressing how light will travel after it 'defrosts' from the stasis of absolute zero conditions, as well as programming the isolation fields of shield generators and containment fields of non-fixed-output power fusion engines.
This is excellent. I didnt realize that the experimental evidence was like a double slit. With the 2 paths traversing equal/opposite vector potentials A, does that also make it like an interferometer? Regarding the Forces explanation, i think your phase shift (from potential A, Wb/m) makes more sense when you consider the units in Schrod. Eqn term. (q/hbar, radians/Webber). I've seen that q/hbar*A term in Likharev's online book (Essential Graduate Physics, sect 6.4-6.5). It is discussed in the context of quantized flux in superconducting loops, where phase MUST be an integer multiple of 2*pi. Current in the loop generates flux A Wb/m and picks up A*q/hbar radians/m. The quantized flux just happens to be whatever value causes 2*pi phase shift. Sorry for going on at length. Been working at this math for awhile and some things are starting to click into place finally. Math is beautiful like that. Suddenly you can make leaps and predict things that are known to be factual/experimental- cool feeling.
A longitudinal Ampere force on the free electrons can definitely shift the phase of the electron particle-wave, even if such forces are very very small, such that one never notices an electron travel-time interval difference (from coil to screen) of the left passing electrons with respect to the right passing electrons. Experiments have been executed to measure the travel time interval of the free electrons, and it was concluded that all electrons travel in more or less the same time interval from coil to screen. But I think that in order to induce the AB effect, the longitudinal Ampere forces that act on the free electrons are too small to get a noticeable travel time interval change. Longitudinal Ampere forces also lead to the conclusion that the electromagnetic potentials are physical. Btw, starting with the electromagnetic potential gauge freedom, it has been shown mathematically that the phase of the quantum wave function has no physical meaning as well, however the AB effect contradicts this conclusion. Because of the shielding in the AB experiment, it has been observed that the magnetic field is zero outside the solenoid area, so instead of a phase-difference equation that depends on the absolute value of the magnetic field, B, it should depend on the the absolute value of the solenoid current, I, where the solenoid current induces a very small force on the free electrons that do not deflect the electron path (longitudinal Ampere force, parallel to the electron path), so this force cannot be a normal magnetic field or normal electric field.
Ian trying to remember if this effect is mentioned in the work on ring theory, which is fun to explore and beautiful if perhaps a bit too Lego brick, at least the bricks look right in principle. If I remember right, unequal phase speaks to the internal structure of the electron according to ring theory.
Makes sense. I thought that the charged particles would travel in a circular path, not a helical path, but it makes sense that it would be helical. Is it really helical? The right hand rule doesn't seem to indicate that. According to the right hand rule, the path should be in a plane orthogonal to the B field, implying a circular path, clockwise looking down the length of the magnetic field lines and counter clockwise facing the B field lines.
You're right that if the particle velocity is purely perpendicular to the magnetic field, then it would just go in a circle. It's helical if there is any component of its velocity parallel to the magnetic field.
The following link describes this pretty well: phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Book%3A_University_Physics_II_-_Thermodynamics_Electricity_and_Magnetism_(OpenStax)/11%3A_Magnetic_Forces_and_Fields/11.04%3A_Motion_of_a_Charged_Particle_in_a_Magnetic_Field
@@TheCynicalPhilosopher Thanks for that link. I saved it to my home screen for reference. If, then, there is a solar flare, along with a rapidly expanding magnetic field loop that seems to accompany one, and assuming protons are ejected from the sun's photosphere, along the magnetic loop outward, the protons might be greatly accelerated to the point of inertial escape from the confines of the loop, being slung outward away from the sun at high speed, and roughly in a similar direction. It may be that this travelling in roughly a similar direction aspect could lead to their respective motional magnetic fields resulting in a Birkeland current helix, but dunno. I'll have to simulate that with two or three particles I suppose, to find out. It does seem however, with respect to that article, that a cloud of plasma in space, traveling in roughly the same direction, and encountering a roughly uniform external magnetic field, would form a helical current. Still unsure how the force-free current would form, but getting there.
Slowing down the electrons on the far side of your diagrams, IS the obvious explanation. Moving magnetic flux lines CAN do that. Instruments saying 0 magnetic field are lying to you. If this is happening in the Bloch wall zone of the outer flow of the solonoid's torus, then this is evidence that there is a rapidly rotating horizontal component in the Bloch wall that is too fast for current magnetometers to detect.
If you can show that the Aharonov-Bohm effect is wrong or inaccurate or misinterpreted, I would suggest getting it published in a scientific journal. Great esteem awaits if you are successful. If I have simply explained it incorrectly, I would be happy to have you point out where I deviated from the theory.
Actually, doing a little looking around, you may have been scooped. The authors of the following papers seem to agree with you: "On the Role of Potentials in the Aharonov-Bohm Effect" by Lev Vaidman (2012) "Quantum Mechanical Inclusion of the Source in the Aharonov-Bohm Effects" by Philip Pearle and Anthony Rizzi (2017) "Quantizing the Vector Potential Reveals Alternative Views of the Magnetic Aharonov-Bohm Phase Shift" by Philip Pearle and Anthony Rizzi (2017)
Everything after a right-hand rule stops me, but somehow you all keep going. After a right-hand rule, you leave reality and cause behind. A cross product turns numbers perpendicular FOR NO REASON, so you skip KEY physics using it. Most professionals just ignore me, but some will scoff and say how rigorous and exact it is, even though they don't see the huge gap in understanding. Even worse, they will derive "cause" from the math AFTER the gap. Angular momentum does not "cause" the gyroscopic effect. That came from the math AFTER the right-hand rule. That's goofy. I have a video that illustrates the actual cause, and it's linear acceleration, NOT "angular" momentum. Most rote memory dependent people cannot see it, so peer review has made it my 20 year secret. Further, "The wheels on the bus go round and round." This song describes everything you see a bus do exactly like math does, but it is not an understanding of a bus. Wheels going round are coincidental, not causal. The variables in gravity math are coincidental, not causal. Gravity is clue #1 contaminated by math analogies such that we will NEVER really understand it. Accurately describing what you see it do is not an understanding! Modern science is more like a bandwagon on Facebook. Everyone is just doing what they were taught to do. If you question ANYTHING, it tends to fall apart, and then others ignore you. This is true top to bottom. Light-speed-constant-to-the-observer is a goofy declaration, not an observation. After pure faith, It is only true on paper after you "transform" your numbers, but a Doppler effect happens BEFORE you "transform" your numbers. That cannot be good. This says that there is a NON-transformed reality underneath left behind ignored by everyone. It does not disappear when you "transform" your numbers, and it works just fine. A transformation is based on a number between 0 and 1. It's not smarter than that. The fact that it works just creates fools.
