Why Snell's law and "phase velocities" in a dispersive prism when light speed is a constant and cannot be slowed.

Fluid dynamics and specifically pressure loss and flow rate reduction through a system of ductwork due to friction, turbulence, and leakage. Change in flow rate of open registers when other registers close. Does Bernoulli hold up or does the HVAC fan become a compressor that cannot overcome the resistance from the remaining open duct registers.

In high schools we are taught how to calculate the angular speed, time period of of revolution, orbital radius etc of an Electron considering it as a "particle" (Bohr's postulates), and also we can calculate the magnetic moment of the atom due to the moving electrons. But we also know that electrons does not exist in orbits, but rather something called Orbitals in the form of "elctron clouds" which describes the probability of finding an electron in it. Moreover, De broglie hypothesis states that orbiting electrons is associated with a stationary matter wave. So my question is that how all these things are related? Which one is true in practical life? Exactly in what form electrons exists in a stable atom?

How can we conclude that speed of electron in conductor is same as the speed of electron. Speed of current is nearly equal to light ( since it's a wave that travels) while speed of electron is nearly 1 cm/s , which is very less to compare for length contraction and theory of relativity should not play a role here. Could you elaborate it further.

@@kuldeepbhalodiya2559 You should study about drift velocity. Speed of dc current in a conductor is measurable and much much slower than the speed of light (even in superconductors). For example, the speed of an electron in room temperature, in a 12 gauge copper wire carring a current of 10A will approximately be 0.0508 cm/s.

@@fdsphone6854 Yes, but the point is that electromagnets and permanment magnets are everyday objects but have relativistic and quanutm mechanical foundations.

I can't see why it's wild.... nature is full of rules we barely scratch the surface, and even in this smallest atom there are already an insane number of those rules.

​@@douglasstrother6584the question is how to unify both phenomenon.😂😂😂😂

​@honumoorea873 but we're not. Quantum rules are linear. They are mathematically incapable, even in principle, of modelling a human (or even anything whose effects cross wide ranging areas of influence - e.g. membranes & potentials around complex structures like veins). That's like one of the central open problems with the whole quantum doctrine and the question about how the classical/quantum crossover could be defined.

plot twist: it's magic

dF = J in different inertial frames is mind blowing

same, as a high school junior

@@1dgram Wait how did you do it? the charges would be zero as mentioned in the video right?

@@varunh6342 Maybe I'd need to watch the whole video to fully understand your question, but there's an apparent length contraction in the parallel wire in the direction of motion along the first wire due to relativity. When you do the math for the electric force (coulomb attraction only) in that situation, taking into account the Loretz factor, you discover the magnetic force. It turns out that the electric and magnetic fields are different facets of the same electromagnetic field! It's an amazing feeling to have a hunch like that and see it work out perfectly in the math... I was wondering at the time whether it was only part of the story. It was also great going from having a confusion about the nature of magnetism (while trying to get an intuitive grasp of it in my Physics AP class) to it actually making sense to me.

WOw, thank you. Means a lot coming from another educator!

I hope you didn't teach this to your students. It's not even wrong.

Like Richard Feynmann famously said: "If you think you understand quantum mechanics, then you don't understand quantum mechanics." Science is the best tool we have at our disposal to understand reality as it is, even if it's contradictory to what our senses tell us. Our senses are flawed, that's why we build instruments and machines to "see" the world for us.

Exactly and also this fact along with other parts of science that are so unintuitive for me totally eliminates any possibility of God demons or anything spiritual cuz modern science is like 500 years old and that’s how long we’ve been able to mesure reality in ways isolated from ourselves and your intuition and we’ve discovered that none of this shit makes sense so the idea that the ultimate answer the key to reality is a God and theres a forever good place and a forever bad place and like that stuff at this point is terribly ridiculous to believe at this point but it makes so much sense to us that people continue to believe

​@@louisrobitaille5810 well it's a debate that the laws that we know shows reality as it is. In other words are we sure we learning about the laws as it is?

but if it were true, it would be the same with permanent magnets. Can it explain permanent magnets?

I'm guessing you didn't watch the video to then end?

​@@SongfugelIt's a point that is worth belabouring IMO, especially when most viewing a video like this haven't had a super rigorous introduction to the topic.

This does not invalidate the claim of there being only a singular field (i.e. the electric field and the magnetic field are one and the same, and not opposites or orthogonal to each-other).

For all we know, this might be the reason behind the magnetic forces/fields and the length contraction could be caused by the fermions' spins? Is this a rational hypothesis or complete nonsense? I have basically no knowledge when it comes to fields and particle spin but I know about general relativity and I'm very interested in anything QM/QFT/GR related.

​​@@WalterSamuelsThe EM field has 4 degrees of freedom. Without that context it is inaccurate to say there is only one field, because there is no single 3-vector field that can represent every possible EM configuration. This is related to the fact that, while you can Lorentz boost to eliminate the magnetic component at any single point, there are many fields (like a lone electrons EM field) that will always have both electric and magnetic components when you look at any region of space.

Wow, that’s very powerful Kishore!

​@@Mahesh_Shenoythe last question,how about the charge was not created, the net charge remained algebraicly the same,but due to contraction of space,more charge was experienced by the single electron

I don't get that the opposite is true in the other part of the circuit, sure the current is in the opposite direction, but length contraction as far as I know is only dependent on movement, not the direction of movement.

@@johnwythe1409 The positive charges in the opposite part of the wire will be length contracted the same amount as in the part we’ve been looking at, so nothing strange there. The same number of positive charges in both parts of the wire, just closer together. But the electrons in the opposite part of the wire will be moving upwards at twice the speed (in the RF of the single electron) and therefore their length contraction will be greater than that of the positive charges and so there will be more electrons in the opposite part of the wire. With that said, the electrons don’t magically jump to the other part of the wire just because we change reference frame. I’m guessing relativity of simultaneity comes into play here.

@@johnwythe1409 From the external electron's POV. Draw the diagram, you'll see what maxv.d.9391 is saying. ==========================================================================================================

@@christofferberg3840 I think you're fundamentally in the right, but I think in can be explained exclusively with relativity and its consequential length contraction. Basically, the moving electron perceives a modified charge density distribution (not homogeneous throughout the circuit, but polar, which doesn't mean the net charge is different from zero, just unevenly distributed) where the piece of wire closest to it in every moment of its movement is positive (what the video explains), whereas the opposite piece of the wire is negative (what you explain in the third sentence of your comment). I must say, the nature of magnetic fields escapes what I recall from my physics lectures and I should really recheck the theory of electromagnetism.

Also Chapter 6 of Purcell's 'Electricity and Magnetism,, the 2nd book in the Berkeley Course. By the way, I was pretty sure I have figured out myself that magnetic field is a relativistic correction to the Coulomb law until I remembered there was a chapter on that in the very handbook I used as a student. I don't think we discuses this issue in class but I might have seen it browsing the book.

@@arctic_haze Cool! Good to know.

Thanks @douglasstrother6584 -- I was thinking the same thing. Jackson writes in caution of Lorrain & Corson's derivation, saying in part (p. 578, sec. 12.2) "At present it is popular ... to attempt to derive magnetic fields and even the Maxwell equations from Coulomb's law of electrostatics and the kinematics of special relativity. It should be immediately apparent that without additional assumptions this is impossible... The confusion arises chiefly because the Lorentz transformation properties of force are such that a *magnetic-like force term* appears when the force in one inertial frame is expressed in terms of the force in another frame. It is tempting to give this extra force term an independent existence and so identify the magnetic field as a separate entity. But such a step is unwarranted without additional assumptions." He explains these and then refers the reader to Frisch and Wilets, Am. J. Phys. v. 24, p. 574 (1956) for an accurate derivation of Maxwell's equations using special relativity. Nevertheless, the fact that the Lorentz force law on a single charge can be derived from Coulomb's law and the Lorentz transformations shows how intimately connected Maxwell's equations are with special relativity. Remarkable.

@@spinhalflight8153 Maxwell's equations do not transfer between frames of reference without relativity and this was one of the reasons they were not that popular at first as we now believe. Lorenz knew how to fix this but did not believe himself in the physical reality of the transformation he derived which still has his name. We needed Einstein for that.

​@@spinhalflight8153It's extremely well-known how the two things are related. In graduate physics, you stop thinking of the electric and magnetic field separately, and learn the Faraday Tensor and 4-potential instead. The E and B fields all out as special cases in certain coordinate systems. This stuff is ancient classical work at this point, there is really no contention. Your author must be nit-picking some minor point about postulates, which is sort of silly in physics...I am a professional mathematician, and from a true logical point of view, nothing in physics is correctly derived from axioms...so why fight about the extent to which it is "incorrectly" done? Physics employs intuition more than pure logic, and that's OK, it would be incredibly slow to do it axiomatically.

I am glad you loved it 😊

I hope you get back into physics, I was in aerospace engineering and moved back to physics by emailing a professor now im starting a graduate degree.

I'm sorry about that :( . I hope you find joy in it and whatever must swing your way to get back in to physics does.

Thanks for explaining

What about if the circuit is broken at the opposite side? Then it would take a split second for the information of the breaking to travel and "inform" the electrons on our side. During this split second the electrons on the opposite side would have stopped however the electrons on our side will be still in motion. During this split second I almost want to say charge isn't conserved? It changes hence net change in charge ≠ 0, for a very short amount of time

⁠​⁠@@Krokodil986I’m sure this problem is likely solved by relativity of simultaneity. I don’t have the brainpower to work it out, but this is likely similar to the train going through a tunnel “paradox”.

@@jonschreiners5006 maybe it goes like this - Either way (whether the circuit is broken or complete) the total number of charges N doesn't change. It's like an elastic band being stretched at one side but compressed at the other. This "wave of compression" travels at the speed of light (along with the disturbance of the field, or perhaps marginally slower since electrons have mass and take time to accelerate) but N is still constant. Alternatively, taking into account relativity of simultaneity - Relativity is local and doesn't work on environments where the measurement takes less time than light would take to cross this environment. So we should count N not instantly but at the speed of light, as the "measurement/information" makes its way along the wire. This means it will travel along with the "compression wave" which informs the electrons of the sudden break in the circuit. So the density of charges inside each local section of the wire will be constant for the time it takes for the measurement to pass thru the wire, so net charge remains constant, as this "wave" (or whatever you wish to call it) affects electrons and protons at the same time. But this does mean that although observers will agree on total charge, they won't agree on specific numbers of electrons e and protons p, but only on the ratio e:p?

Thanks, Yogesh!

Time dilation is expertly explained (vulgarisation) on Science Clic (English) in his General Relativity playlist. You should definitely check it out 👀.

Glad to hear that! :)

Thanks, Pratham. There’s already a ton of amazing videos out there.

The dielectric field IS magnetism, when the dielectric field experiences loss of energy it manifests as magnetic effects :)

So great to hear that, Shaurya!

I also wonder how radio waves (Electro Magnetic radiation) can propigate through a vacume, if there is no M field.

Why would the electrons be closer together?

Hi, no it is not! From the point of view of a stationary electron, the length contraction applies only to the single moving electrons that are into the wires (because they are moving) and so they appears to be squeezed, not to the wire and neither to the distance between the electrons that are flowing, since the conductor is at rest also in the reference frame of the stationary electron! Only when we are into the reference frame of a single moving electron outside the wire we will see the wire (and thus the distance between protons) to be contracted because from our perspective the whole conductor is moving with respect to us (and thus it appears contracted)!

@@rickroller1566Because they would be moving relative to the single stationary electron outside the wire. Thus length contracted. Thus closer together.

⁠​⁠@@WonderUniverse_ I’m not sure I follow. “The length contraction only applies to the single moving electrons in the wires”. Not sure what you mean by “single moving” here, aren’t they all moving together? “They appear to be squeezed…”. Yes I agree, just another way of saying contracted. “… not to wires…” do you mean the stationary wire (ie positive ions) are not contracted, as yes I agree. “… and neither to the electrons that are flowing”. Lost me here, are you saying the flowing electrons haven’t contracted? I guess you don’t mean this as I thought you established above “the single moving electrons, which are in the wire, are contracted”. And just to make sure we are on same page, by “the conductor” do you mean the stationary wire / ions?

Ya true, electrons don't move with respect to electrons reference frame. But with proton refrence frame when proton is moving these proton see the electrons move away.

​@@ShivamVerma-hg2ivI am still confused. This idea of particles moving closer together suggests that they ate simply under some sort of compression force: they aren't; they are only 'closer together' because EVERYTHING is closer together in that reference frame, because the concept of length is different. What appears to be being said here is 'there are 100 protons on this side but, due to length contraction, there are 110 electrons on the other side', implying that the protons are now interacting with a larger number of electrons on 'the other' side ? Why would the ly interact like this, surely the various forces and fields between the two sites would 'fan out', leaving the original 1:1 correspondence.

same ! i honestly still feel like magnetism isnt actually a thing, and its just electric forces being distorted due to movement or quantum spin

So, with the circular wire what would happen? The radius of wire would decrease? (specifically the radius of wire сrystal structure, and the radius of space that holds electrons would stay the same, so these two spaces wouldn't coincide anymore). I'm afraid, as in all cases where Einstein is involved, there would be no clear and intuitive explanation for that.

@@AccelYT As Richard Feynmann famously said: "If you think you understand quantum mechanics, then you don't understand quantum mechanics." In other words, if something relating to quantum mechanics feels intuitive or seems to make sense, you're probably missing something important. In this case, it's special relativity applies at the quantum scale and particles.

@@AccelYTFirst of all, basically nothing is intuitive when it comes to SRT/GRT. Second, from the electrons perspective the entire structure containing the protons is moving and therefore appears to be clinched in the direction it is moving. If it looks like perfect cubes from the proton perspective, it's just a rectangular prism from the electron's view (squished in direction of movement). But you can't make an entire circuit in a straight line and with the curve there comes change in direction of the moving particles, which means acceleration, which in turn leaves the realm of SRT and requires GRT. And here I'm not confident to be able to explain this in the comment section. I could try with paper, crayons and cookie, but probably still fail. :3 What might help: look for relativity and why simultaneity ist not conserved when changing the reference frame.

@@AccelYTWire forms a closed loop, so from the reference frame of a moving particle, for each part of the wire that appears positively charged there would be another part of the wire that would appear to be charged negatively.

Sadly I know exactly what you mean

pseudo-force or pseudo-explanation?

but, the magnetic force is not a pesudo-force... the magnetic field is pseudo vector though! this question has been asked (and answered!) a relatively long time ago, the EM field definitely does exist, and if we try to assume either the magnetic or electric field to be fundamental, an illusion caused by relativistic phenomena, we can craft a theory, but we will not get it to be Lorentz convariant. there is also an I think simpler explanation as to why this does not work: our assumption is that, due to relativistic phenomena, there is a difference in charge density which causes an electromagnetic force. so let's see what we can derive from this: the force on a particle ought to be higher in a boosted reference frame, but we cannot say this because special relativity automatically assumes that the force on an object doesn't depend on the speed of the reference frame. so we cannot say that this is all one force, we see there is a new force. we can say that this force is the magnetic force. the electric and magnetic fields are both components of the electromagnetic field, they are different, have different properties, and most importantly: all of them do exist and are not illusions of relativism :)

Electricity is one force that splits into 2.

You are wrong magnetic force is not pseudo force it had energy so it must be real pseudo force are just introductie for relativistic transformation

true dat... relativity abstracted reality and our classical equations @@mehuldangar6660

heyhey, you likely aren't missing anything. I haven't looked at your case, but just from watching this video and skimming online I can tell that this is, for the better part, just wrong :/ it seems to assume and imply that the magnetic field does not exist, but that it is some sort of mathematical illusion, but this does not make much sense from the get-go, because the electric and magnetic fields indeed have different properties, and it immediately sticks out to me for example the different degrees of freedom they have. assuming that an electric field is fundamental, and that a magnetic field is an illusion, or otherwise, seems to always lead to a theory that is not lorentz convariant (but if you find any that are do lmk :) so, if we assume there is one electric field, we will not be able to apply the theory we get to all cases. and, if we assume there is only one magnetic field, we will also fail to apply the theory we come up with in other cases. this question has been debated, and the answer has been fully known to us for a relatively long time: there is certainly an electromagnetic field :)

Good question, If there were no magnetic field, how to explain 🧲 we find in nature, motors, generators....?

Thanks, Mahad :)

Nice!

Can you explain it to me?

From the electrons' Frame Of Reference (FOR), the protons are moving but they're not getting closer to each other. They're all moving at a constant rate so they stay at the same distance from each other. Same thing for the electrons from the protons' FOR. This changes ever so slightly for the electron outside the wire though. Just enough for it to feel an attraction towards the wire.

It’s an excellent question! Intuitively we know we will just see normal bright room, right? But why? Remember that there are both bright and dark spots. So, can you reason out from there? Yes, coherence is another importance but let’s assume your two bulbs are coherence sources!

@@Mahesh_Shenoy amha. Didn't see the picture.

@@Mahesh_Shenoy oh! You mean the room is bright because there are more constructive interference than destructive?

I once imagined this in a Single Mode FIber... Reflect the laser light back onto itself... The pulse has already left the laser. How can it destructively interfere when therre's no where else for energy to go? Maybe its like a giant tuning fork, and steadily leaks through the cladding ? - Ok - But what if I use a Maser in a super-conducting waveguide? (zero Loss !)

@@prathamsinha8266 I don’t think so! What happens if we a lot of tiny alternating dark and bright spots? Our eyes will average it out, no?

I am glad you enjoyed it, Adrita :)

Can’t believe how much love I get from you folks!

You know what? That’s the exact question I don’t have an answer too. I searched a lot, but just couldn’t find an answer for it. So kudos! Let me know if you find something!

That is the point: The electrons moving inside the wire make the distance between them shorter (Lorentz contraction) than that of the nuclei. Then the linear density of electrons would be higher than that of the nuclei, producing an effective electric field that the charge outside the wire would feel, no matter if it is moving or not. In synthesis, your explanation is not convincent.

@@carlosvazquez4401 Agreed. But, if you ignore that, for a while, and assume that the wire with running current has the same electron and positive charge density, then the math works out. You can derive the expression for the magnetic field using relativity and perfectly matches with the Bio-Savart and Lorentz force. But, why isn't there an electric field in the stationary reference frame is something beyond me. If I had to guess, then it could have something to do with the fact that electrons aren't moving in a straight line. There random motion maybe counteracting the whole contraction. But, when the charge starts moving and we jump into it's reference frame, the wire and the electrons inside ARE moving in a straight line. But, again, this sounds very shaky to me.

@@Mahesh_Shenoy ​ @Carlos Vázquez Phonons. Electron movement creates phonon counter-oscillations inside the wire also called as proton holes. These are not protons and contain the counter fields of many protons and electrons (azimuthal countering as you said electrons dont travel straight but with many helicities selecting the perfect spot against each other) dynamically changing due to moving electron for all electrons. These phonons counter the electron movement in a balanced wire thus cancelling the electric field in stationary ref frame relative to protons. More resistance the electron have less phonon dissipation inside the wire=less electric field to counter due to loss towards heat energy. These phonons dissipates perfectly in superconductors for example covering 100% of the energy thus electrons move without resistance still with 0 net charge feeling from stationary frame relative to protons. your question in video: where new protons/old electrons came from/gone to? my answer: when you move relative to protons, both protons and the distance between protons is contracted as the lab and earth and universe also contracted in that way (no new protons came still same number no problem as universe is contracted). But when you are stationary relative to protons and universe, thus electrons move compared to you only make electrons length contracted not the distance between them (animations are wrong). Thus when you start moving with the same speed with electrons making you move relative to protons and make you stationary relative to electrons only revert that contraction of each electron to its stationary form and doesn't change the distance between each electron. Thus no electron gone anywhere as they did not came in the first place but only change their lengths parallel to the movement direction they move without any change the distance between them. And proton concentration increases due to the universe concentration increases parallel to the movement direction so no protons came from anywhere as whole space is contracted. Good day

You are 100% correct!

Haha!

I can understand Hindi! Speak broken Hindi!

@@Mahesh_Shenoy Wow, sir that's really awesome..

You also😂