Comments by "Dr Gamma D" (@DrDeuteron) on "How Special Relativity Makes Magnets Work" video.

  1. You are wrong. In the cat frame the ions are contracted by gamma, while the electron are dilated by gamma ( see. Bells spaceship paradox). Note that g - 1/g = 1 - 1/g2 = 1- (1-v2)= v2 which is the factor that appears in the Lorentz transform of fields. When in doubt: DO THE LORENTZ TRANSFORM
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  2. because the problem stipulates that they don't, or else current carrying wires would be charged (they're neutral).
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  3.  @drslump9314  no, but I use his equations. I am in complete agreement with J. All fields are sourced from charge, current, and their time derivatives on the past lightcone, in manner such the time derivative of one is the curl of the other. In this view, an EM wave is not a self sustaining propagation (which leads the incorrect view posted above: that E and B swap energy out of phase….they are ofc in phase in the far field), rather it’s just fields at a point in space time cause by sources on the past light cone, and that cause propagates away from the source at c. I recently adopted this (classical) view after seeing too many comments about photons experiencing no time and questions about how they know to oscillate if they don’t have time. Ug. Not to mention all the misconceptions about the speed of propagation in media: the nonzero fields are caused by q, j, and their dots on the past light one, end of story. Don’t even get me started on virtual photons and their pop sci description has confused many a layman
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  4.  @drslump9314  well, if you start with coloumbs law, you need a magnetic field to be Lorentz covariant. Gravity has a similar situation. I think it’s a fine way to teach beginners about the covariant nature of maxwells eqs. There’s still a long way to go get to the the fact that EM is just an unintegratable phase on the affine connection of a tangent fiber bundle
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  5. Because charges in one frame are currents in another. The laws aren’t invariant, they a covariant
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  6.  @ismailhaggag957  you're welcome. What covariant means is the the E and B fields, charges and currents, time and space, and energy and momentum change (in different inertial frames) in such a way that the laws of physics don't change. It requires a high degree of symmetry.
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  7. no, there are fewer electrons because they are dilated. Length is contracted because you have to measure the end points at the same time. that's not the case with the electrons.
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  8. Length contraction is real. It is not a trick of perspective, and many ppl get confused thinking it is. Rather, it has to do with how spacetime is split into space and time in different reference frames. This starts at the nuclear level, where an ultra-relativistic proton (say, in the DESY beam pipe) is flattened by 1000x, and the partons are effectively non-interacting and frozen in time during an interaction. This is an experimentally observed fact.
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  9.  @drslump9314  Jefimenko is right: E is a caused by charge, changing charge and changing current on the past lightcone. B is caused by current and changing current on the past lightcone. That's it. E doesn't cause B, B doesn't cause E. The stationary cat and the moving cat at the same event have the same past llightcone, but see different charge/currents on it, and thus see different E/B configurations in the present. Nevertheless, the video is correct.
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  10.  @drslump9314  because if he said different frames of reference project the same electromagnetic 4-tensor onto different hyperplanes of simultaneity and thus resolve into different 3-fields, respectively, no would know what he's talking about.
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  11.  @taufeeqsunny6235  Negative. The proton lattice is a single physical object that, when view from a moving frame, is length contracted. The electrons are all different, on separate trajectories, that by definition have the same spacing in the frame of the protons, no matter how fast they move. Hence they spread out in their local rest frames as they accelerate to speed. If you master "Bell's Spaceship Paradox", it will all make sense, but that one has stumped many students and professionals alike. (Hint: The relativity of simultaneity matters).
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  12. then it wouldn't be a cat!
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  13. where does this video say the magnetic field is the same as an electric field?
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  14.  @creativenametxt2960  electrons don't orbit, but the probability current, [psi^* x grad(psi) - psi x grad(psi^*)], does....at least in states with L > 0.
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  15.  @marcopilati7464  since a conducting wire is neutral, the electron spacing does not change when they start moving, by definition. They are independent objects are have no need to Lorentz contract. See: Bell's Spaceship paradox, where the spaceships are stipulated to not change spacing.
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  16. no. The moving electrons have the same density as the stationary electrons, in Derek's frame. This is both an experimental fact (current carrying wires are neutral), and an a priori specification of the thought experiment.
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  17. not really.
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  18. the electron problem that fills the comments is Bell's Space Ship paradox, but instead of 2 ships remaining a fixed distance apart in the initial reference frame: it's a bunch of electrons. Of course, this means in their rest frame, the electrons, as the space ships do, spread out dilated by 1/gamma.
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  19. Because that is the set up of the problem: the current carrying wire remains neutral, so that the electron spacing, by definition, doesn't change.
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  20. This is not a reasonable way to address the problem. It's a thought experiment, and does not rely on the quantum nature of conduction; rather, it's a solid lattice 1D lattice of protons, with equally space (in the lab frame) electrons moving independently (but correlated). Just do the Lorentz transform.
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  21.  @ikhlasamin007  an SR thought experiment has nothing to do with hbar and quantum mechanics.
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  22. Permanent magnets have magnetic dipoles, so you generalize is for a moving magnet, but it’s not elucidating, unless you like tensor algebra
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  23. the electrons are defined to move such that their spacing in the lab doesn't change. They're all independent and have no obligation to act like parts of a macroscopic object.
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  24. Well, from out Galilean lives (E3 + universal time), we see Coulomb's & Gauss's Laws don't transform right, and the former can never work without the latter, so the original statement is acceptable. Of course, in Minkowski Space time (M4), there is no such cause an effect, but also in M4: there are no paradoxes (Twin, Space-Ship, Pole/Barn.because it's as trivial as pythagorous in a plane--- and what's the fun in that?).
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  25.  @drslump9314  jefimenkos eq are illuminatin, but a current is just a charge viewed from a moving frame
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  26.  @crusaderACR  there is a difference. One is parity odd and time even, while the other is parity even and time odd
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  27. Yes, you are wrong. See: Bell's Spaceship Paradox. Replace the 2 space ships with two electrons, et voilá. (The string is the length of the proton lattice spacing).
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  28. wires w/ current are neutral: therefore the electron and proton density are the same.
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  29.  @mariom5307  no, they are independent particles traveling on parallel world-lines. The don't even know about each other. Apply Lorentz contraction to their spacing would be all wrong. Of course, they are dilated in their rest frames, which is shown in the video.
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  30. They don’t need to
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  31. the electrons are contracted relative to their rest frame.
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  32. The calculation of the cats trajectory is covariant using the same laws of physics.
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  33. why a particle with spin is way beyond the scope of this video. But it accounts for it b/c: "Representation Theory of The Lorentz Group".
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  34. but the problem is stipulated by definition so that they all move w/o changing spacing, so some thing else is a foot paw. The electrons are not one thing, each is on its own path, unlike the wire.
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  35. The 4-dimensional vector field is a potential field, not a force field. The EM field in 4-dimensions in an antisymmetric tensor with (4^2-4)/2 = 6 components that become a 3-component vector and an antisymmetric tensor (3 components) when a frame is chosen. Here we start with a frame where E=0, so that's what is missing..there is only B field in Derek's frame. The reason it works out is because charge and current form a 4-vector in 4 dimensions, so any transformation is manifestly covariant.
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  36. why are the moving electrons denser, when it says they are not?
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  37. You would think it's parity, but really it's time reversal symmetry.
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  38. Why would the electrons be more densely packed than the protons? The wire is neutral, so the positive and negative charge densities are by definition: equal.
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  39. because they move with uniform spacing in Derek's frame. It's a priori specified in the problem. That's why Henry sees them dilated.
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  40. this is the opposite of the truth. Non-relativistic spin and relativistic spin are remarkably similar.
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  41. There are two effects (the Lorentz transform is linear and has a slope and an intercept). The intercept controls the relativity of simultaneity, which makes the proton lattice denser by g^2, which is too dense, Lorentz dilation of the coordinates beings in a 1/g, meanwhile the electrons are dilated by 1/g for a total charge density scaling of (g-1/g) = g*(v**2). It's best just to do the Lorentz transform yourself, otherwise it sounds like a bunch of gibberish.
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  42. In theory E field disturbances move at c, so that's always way faster than anything...by an amount equal to the speed of light, in the things rest frame. Nevertheless, this is a thought experiment, and we can imagine the electrons going 0.9999999999c, which is not way slower than c in the wire frame.
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  43. if the protons have relative motion, what do you mean "the rest frame of the protons"?
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  44.  @IdeasAboveStation  duh. Your problem description wasn't clear, but if you're talking about transforming coulombs law (F=q^2k/r^2) into a moving frame, with v perpendicular to "r", then yes, (qv X B) is attractive, but the transformed (repulsive) electric field is also stronger (since E^2-B^2 is a Lorentz scalar), so it all works out.
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  45.  @IdeasAboveStation  Just look up "Lorentz transformation of EM field". The Lorentz scalars are the invariants of the electromagnetic 4-tensor: (F_ab)(F_ ab)= -2(E^2-B^2) (e_abcd)(F_ab)(F_cd) = -4E.B The EM field strength tensor is: F_ab = d_aA_b - d_bA_a where the indices run over (t, x, y, z). d = (d/dt, d/dx, d/dy, d/dz) is the covariant 4-derivate and A=(phi, A_x, A_y, A_z) is the 4-vector potential. Phi is electric scalar potential and A_i (i=x,y,z) is the magnetic vector potential. In general, it's called "The covariant formulation of Maxwell's Equations". The last ingredient is the 4-vector current density j_a = (rho, j_x, j_y, j_z), so it's charge density (rho) and standard current density (j). Since it transforms under Lorentz transformations, and so does "A", you are guaranteed to always satisfy Maxwell equation in any frame.
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  46. A current carrying wire is neutral, so the electron spacing is the same as the positive ion lattice spacing in the lattice frame, no matter how fast they move.
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  47.  @dhruvshukla5591  the wire is always neutral in its restframe regardless of current
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  48.  @dhruvshukla5591  it’s not neutral in a moving frame because the ions and electron transform differently . If you want to understand it: do the Lorentz transform, after understanding bells spaceship paradox
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  49. Derek's electrons are tight packed than the cat's electrons.
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  50.  @Kanzu999  WHen you say "and therefore the electrons are pushed closer together" you are wrong, and all analysis after that is suspect. The current carrying wire is defined to be neutral in the problem, and there is no reason the electrons' worldlines can't make that happen.
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  51.  @Kanzu999  just do the Lorentz transformation on a series of equal spaced stationary +'s and moving -'s with neutral spacing, and all will be revealed.
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  52.  @Kanzu999  no, the opposite charge is spread out. See Bell's spaceship paradox
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  53. Why "must" the spacing of the electron contract when they start to move?
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  54. the electron spacing doesn't change when the current turns on, by definition in the thought experiment, and as an experimental fact: current carrying wires are neutral.
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  55. contracted relative to what?
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  56.  @mond2440  no, it's a completely correct representation of how the 4-current vector (rho, j) transforms in the two frames. The complaint that everyone has is misguided...the electrons don't contract in the wire frame because the wire is neutral, it's a stipulated fact of the thought experiment (and a real fact w/ wires), Henry explains the resulting dilation in the current frame at 2:08, and if you don't get it: the please review Bell's Spaceship Paradox and treat the electrons as a long line of spaceships. It is identical regarding the transformation of linear densities.
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  57.  @milap8989  please don't agree. Derek is correct. Learn some special relativity, it's totally consistent when formulated in 4D Minkowski spacetime (M4); however, when that is split into Euclidean 3d space (E3) and time (~R)...you get counter intuitive results in different reference frames; however, when one considers the relativity of simultaneity, such paradoxical results are always resolved.
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  58. the space dilates, as does time.
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  59.  @LGlink-rz2xc  see bells space ship paradox, or do the LT yourself There is no other way.
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  60.  @SK-ow4vw  This is a thought experiment, not a description of holes in a semiconductor. That adds needless complexity. It's best imagined as a linear 1D 'solid' lattice of N protons and N independent electrons with equal lab spacing at all times. It then becomes Bell's Spaceship Paradox with N spaceships. The only way to understand it is to do the Lorentz transform, the results which I posted above. (It can be done, with plots, in 100 lines of python). You can then use the E, B transformation rules, and verify it all works out, as it always does, b/c SR is internally consistent. But the electron spacing must be dilated in the cat frame relative to the lab frame, a la Bell's Spaceship Paradox where the string does indeed break. In conclusion: do the Lorentz transform, it is of the form y = mx + b, a line: it's not as intimidating as it appears.
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  61.  @somshekharrakhe6224  they’re not. In 4 vector form, maxwells eq and conservation of charge are manifestly covariant, so they transform by definition. It’s neither circular nor or in doubt once you assign space time a (1, -1, -1, -1) metric
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  62.  @jvdh4627  are you talking about holes as positive charge? That is the anti-intuitive way to look at it. If you're moving relative to the wire's rest frame: the ion lattice contracts. Meanwhile, the electrons have their widest separation in the frame where their velocity is zero. They do not contract in the lab frame when moving, because they're not physically linked together. If they were, the wire would not be neutral in the lab frame, which is a stipulated fact. btw: the reason my intuition is so good, is because, wait for it: I did the Lorentz Transformation(s).
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  63. so? That's not a static problem anymore, which makes it's it crap for pedagogy.
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  64. The reason ppl aren't talking about this more is because it's basic special relativity, and in the more sophisticated formulations of Maxwell's equations (dF=J, dJ=0), it's straightforward.
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  65. you are making it too complicated. Why bring ferromagnets and linear media into it? Focus on a proton lattice of uniformly spaced charges, and an equal number of electrons moving.
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  66.  @EgzoDiuse  no, the object is shorter. It is not an illusion.
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  67. That is totally irrelevant for the thought experiment.
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  68. No
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  69. The actual nature of conduction only obscures this thought experiment. Here, electrons move on trajectories such that their spacing is unchanged, by definition.
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  70. because they remain a fixed distance in the wire frame, as stipulated. Understand "Bell's spaceship paradox" and you won't ask the question.
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  71. why should the electrons be closer together? Who says they're moving uniformity in their instantaneous rest frame?
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  72.  @Kanzu999  drift velocity is irrelevant, as this is a thought experiment about current, not a course on the quantum mechanics of conduction. The complaint about low speed (hence small lorentz factor) misses the point that the electron density can change without it because of the relativity of simultaneity. In the wire's frame, the electrons don't change density because the wire is neutral: there is no electric field, by definition. If you don't understand: do the Lorentz transformation. SR is always right.
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  73.  @Kanzu999  because the wire is stipulated to be neutral, which means the electron-spacing can't contract, it needs to stay instep with the size of the wire. So it's defined to be not contracted. For this to be so, they need to spread out in their result frame (2:07). Note that the wire is a single object, while each electrons each move onithere own path in a manner that keeps the wire is neutral. It's the same phenomenon as Bell Space Ship Paradox, which addresses the nuances more directly, as ppl here get hung up on quantum drift and atoms (irrelevant stuff). Now in BSSP, ppl get hung up on the strength of the string...don't do that. The string is an abstraction so we can thingk about: do the spaceships contract, or do they spread apart?
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  74. fact.
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  75. no. the electrons move with the same density as when they were stationary. It is specified in the problem. Why should the protons expand?
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  76. because current has polarity?
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  77. just do the Lorentz transformation,
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  78. Bell's Spaceship Paradox, that's why.
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  79. Gravity is the minimal rank 2 interaction, while EM is the minimal rank 1 force. But that’s it
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  80. take up less space relative to what?
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  81. A terrible example, because protons make up the solid lattice of the wire. It's the electrons that move. Independently, which means Lorentz contraction doesn't apply.
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  82. NO one cares about quantum. This is a classical thought experiment.
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  83. the E field is radial, and so is the force: F = q(E + v X B) in both frames.
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  84. why would the electrons length contract?
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  85.  @kiranestake2155  I know you meant that. So: why would the electron spacing change? (Keep in mind that the wire remains neutral when conducting).
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  86.  @kiranestake2155  the positive ions don't move, so they don't contract. The electrons move in a manner that retains their at-rest spacing, so the wire is neutral. Thus in the frame moving with the current, the positive ion lattice is contracted, and the electron spacing is dilated...which is exactly how Bell's Spaceship paradox works.
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  87.  @kiranestake2155  How? They have the same acceleration (simultaneously) in the wire's rest frame. Now law against that. Again: understand Bell's Spaceship Paradox and your doubts will be quelled.
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  88. force is zero, therefore the electron spacing doesn't contract. Spacing is the key, electron themselves don't contract.
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  89. No. The electrons don’t contract, but definition
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  90. that is what the Lorentz Force Law says. Magnetic Force on a charge is proportional to the charge, the magnetic field, and the velocity component perpendicular to the field....and in a direction perpendicular to both the total velocity and the field.
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  91. Jefimenko is correct that a changing E (B) field does not cause a B (E) field, contrary to what we are taught. E & B fields are caused by charges, currents, and their time derivatives on the past light cone. His complaint about saying Lorentz contacted/dilated static/moving charge distributions "cause" a magnetic field is that that is a frame dependent thing.
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  92. holes? who needs holes. that just adds confusion. moreover: this is a thought experiment, so redo with a linear lattice of positive charges, and a line of moving negative charges. then all your concerns vanish.
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  93. W and Z boson want to know your location.
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  94. the electrons move independently. The positive lattice does not.
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  95. because it's stipulated that they don't.
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  96. contracted relative to what?
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  97. don't let reality ruin a THOUGHT experiment. Really, it's something a lowly engineer would do.
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  98. that's why Lady deuteron left our diatomic molecule. Now she's hydrogen three oh four.
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  99.  @frigneutron  take a look at "Bell's Spaceship Paradox", and then imagine the spaceships are electrons accelerating from 0-current to their final constant velocity. (And don't worry about drift-velocity, or the actual physics of conduction: that is not relevant).
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  100. But there is a reference frame in which the magnetic field is zero, yet the cat still feels a force. If B=0, how can the force be from qV x B?
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  101. charge is conserved but charge is not a Lorentz scalar, it's the time component of a 4-vector called the 4-current j = (qc, qv) and satisfies the manifestly covariant continuity eq: dj = 0 where d is the 4-nabla: d = ([d/dt]/c, d/dx)
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  102. They are length contracted relative to their rest frame.
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  103. the electrons ARE moving, and the proton lattice IS stationary. There are more than 2 objects here, one of which is positive.
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  104. No. Then there is a huge electric field in the lab that ruins everything.
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  105. Because it is stipulated not to
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  106.  @a.kzestos2085  the wire is stipulated to be neutral (because conducting wires are but that reality is not relevant to a thought experiment), nevertheless: the wire neutral, therefor the electron density is the same as the proton density, therefore the electron density isn't increases in at rest frame (which is what I think OP is asking).
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  107. obviously wires are neutral, so length contraction plays no roll. Why should it? See Bell's Spaceship Paradox.
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  108. I don't think they're related, other than: Maxwell's Eq.
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  109. but this is a special case, where Derek has F_0j = F_j0 = 0, where F_ij = -F_ji is non zero, and a four current with J_0 = 0 and J_z non-zero, then he transforms it to Henry frame where everything is nonzero, except the electron's 3-current vanishes. The most sensible way to say it is that Henry's electric field is a transform of Derek's magnetic field (because Henry's positive charge density is a transformation of Derek's two canceling J_0's that only cancel in Dereks frame). fwiw.
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  110. How does SR violate GR when SR is zero acceleration limit of GR?
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  111. Yes. It's like 2 cars driving on opposite sides of the I5. The northbound traveler says, "The southbound traveler is further left than I am", and the southbound traveler says, "The northbound traveler is further left than I am".....how can they both see the other person to their left...is there not a universal "left"?
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  112. in my experience, Miracles gets no respect in these kinds of videos.
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  113. pls don't use AI for physics. it cant do it.
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  114.  @franktank3956  so why were you stuck? What was the hang up?
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  115.  @franktank3956  it didn't say they are the frame dependent space-time and space-space components of a covariant antisymmetric 4-tensor field? That's why I said don't use AI.
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  116. charge is conserved but charge is not a Lorentz scalar, it's the time component of a 4-vector called the 4-current j = (qc, qv) and satisfies the manifestly covariant continuity eq: dj = 0 where d is the 4-nabla: d = ([d/dt]/c, d/dx)
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  117.  @XraynPR  dielectrics are materials that are polarized in an electric field. If that effect is linear, you get "Maxwell's equations in linear media" which involves both E and D fields on the electric side, and B and H fields on the magnetic side. If it non-linear, polarization (P) is described by tensors (X) as a function of electric field (E) e.g. P_i = X_ij*E_j + X'_ijk*E_j*E_k + X"_ijkl*E_j*E_k*E_l +..... usually all as a function of frequency, and that leads to all kinds of whacky phenomenon that are the domain of non-linear optics.
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  118. it's completely flawed in that it contradicts the initial stipulated conditions: when the electrons move as a current, the wire remains neutral (in its rest frame), hence they do not dilate in the wire's rest frame. Stipulated. Period. Full stop. Fuggetaboutit. If you understand Bell's spaceship paradox, you'll know this means they dilate by 1/gamma in their rest frame.
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  119. they are contracted, so that the wire is neutral
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  120. nope.
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  121. It’s not the same intensity. E2 - B2 is a Lorentz invariant
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  122. totally irrelevant when conducting (no pun intended) thought experiments.
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  123. the electrons move as fast as you want them to, as long as that is less than c.
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  124. Because you’ve left out the relativity of simultaneity in your process
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  125.  @aliengrey1708  for the electron spacing, see bells space ship paradox. If you imagine a moving lattice of normally spaced electrons in the lab frame, they all pass a stationary proton simultaneously. Call it an overlap. In a frame moving in the electron direction, those overlaps are no longer simultaneous. You just have to do the Lorentz transform and plot it on a Minkowski diagram. It’s like 50 lines of python, or less.
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  126. there is some garbage on YouTube.
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  127. You are wrong when you say moving electrons should be contracted (i.e., they should be closer together than the proton lattice spacing). Why should be closer together? The problem specifies that the electrons move without changing their density, it is specified in the thought experiment. Moreover, (not that it matters), it's an experimentally observed fact that current carrying wires are neutral.
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  128.  @lorenzomadasi4454  The positive lattice is one solid object, so it contracts when seen from a moving frame. The electrons are all on separate trajectories that by definition do not spread out in Derek's frame, hence they spread out in any one of their instantaneous rest frames. (Each electron has a different frame as they accelerate to become "current").
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  129. magnetic field lines want to be in the (permeable) metal, it lowers the field energy the closer the metal gets to the magnetic. Energy changing with position is a force.
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  130. No, the wire is neutral
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  131.  @TheRetsehc  there is a logical flaw: the wire remains neutral, therefore the electron trajectories are such that it is always neutral, and your description of them must be wrong. Hint: there is not one electron, there are many, and they move independently (but correlated). See: Bells Spaceship paradox. It is the same thing.
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  132.  @TheRetsehc  Understand Bell's Spaceship paradox (where the space ships are two electrons), and all questions will be answer. Now, it did confuse professionals for a number of years. The electrons all accelerate to "cat speed" simultaneously in the lab (wire) frame, so their lab spacing never changes and the wire is always neutral--by definition. In any other frame, "simultaneous" is different. In the cat frame, the leading electrons accelerate 1st, and the lagging one last: the cat see them dilated by gamma (g). The proton lattice is one physical object, so the cat sees it contracted by gamma (g) (see: Born Rigidity). If the lab charge density is +q and -q, the total is q+(-q)=0, while the ` cat sees [+gq - q/g] = q(g-1/g) = qg(1-1/g2) = qg(1 - (1-b2)) = qgb2 where b2 is b^2, and b is beta is v/c. With c=1, v=b. The lab has E=0 (neutral) , and B=qv (moving charges is current), the transformation of those fields to the cat frame goes E' = g(E + v X B) -> g(0+v(qv)) = qgb2....the exact same factor. It always works out.
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  133. this cat is classical. And he's got 9 lives.
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  134. So do the math for any direction. Hint: it’s harder, but it works
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  135. name the biggest flaw in logic: ____________
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  136. by what logic? the wire is a magnet, the magnet is magnet. Ergo: force.
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  137. actually, the relativity of simultaneity is bigger effect than Lorentz contraction, and it's linear at low velocities, not that the problem specifies low velocities at any time. When you start moving in the direction of current, simultaneity moves into the former future (past) ahead of (behind) you.
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  138. F = q(E + v X B)...so for the lab-cat, E=0 and v=0, so F=0. B is not zero.
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  139. 1) spin matters 2) "mu": magnetic materials are magnetized. You can look at it as generating magnetic poles on the surface, or as an energy problem. Energy density goes as BH = B^2/mu, so the material is attracted to the electromagnetic in order to lower the field energy (mu > 1).
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  140. but then the wire would not be neutral, and it's neutral. therefore: no. see 2:07
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  141. what about it? Magnets are magnetic, static charges aren't. This is about static charges being moving charges in other reference frames.
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  142. no. Only a magnetic dipole in a field gradient feels a force, and none of that applies here.
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  143. a moving charge is a current. Currents are the source of magnetic field.
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  144.  @starless7972  yes it will. This problem was solved in 1898 (Liénard-Wiechert potential). The point of Derek's set up is so that there is a frame with no electric field from which to start.
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  145. See dipole dipole interaction
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  146. a static needle is a magnetic dipole, a charged cat is not (it's an electric monopole).
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  147. too sexy, right?
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  148. totally irrelevant when conducting (no pun intended) thought experiments.
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  149. see 2:08
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  150.  @robertkesselring  I agree, you cannot move relative to space. At 1:28 the electron density is same density as the protons (call it "1") by definition. A 1:56 the lattice of protons are length contracted by gamma, so density is "g", while the electrons are dilated by gamma (-1/g). Hence the total charge density is. (g-1/g) = g*(v^2), while the current density increases by gamma. So the cat sees a stronger magnetic field and an electric field such that (E^2-(cB)^2) is preserved.
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  151. they're still magnets
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  152. One important thing about doing SR paradoxes is clarity, so when you say "the cat isnt moving" already implies an absolute rest frame, which puts you in the wrong mindset-- but that's partially Dereck's fault for setting it up. It should be the "wire" frame, and the "current frame" cat and electrons sharing the same rest frame-- or two different cats so we could say "black cat frame" "white cat frame". But the reason you and everyone else is having trouble is the length contraction is 1/2 the problem, as with Bell's Space Ship Paradox (the string breaks: electrons get further apart in orange cat frame), is the relativity of simultaneity:let's say each time a e- passes a + in the lab frame, there is a "tic" recoded. In the lab, they all "tic" at the same time from each lattice position. Now when you're moving with the current, all the ticks are asynchronous, with the lower voltage (down stream) ticks occurring before the one behind you. That means the electron density is spread out and you see a + charge on the wire....even without Lorentz contraction.
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  153.  @Kanzu999  on spreading: understand bell space ship paradox first. If you can’t master that, this one won’t make sense. It’s the same problem. The cat is repelled by the static positive charge on the wire, which agrees with the magnetic field doing it in the lab frame. If your really want to understand it. You have to do the Lorentz transformations. Once.
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  154.  @ikhlasamin007  F = v x B does not conserve angular momentum, in fact, it violates it maximally.
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  155.  @ikhlasamin007  bro: no. The Riemann Hypothesis is about prime numbers and the zeta function. Maybe study more or and comment less?
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  156. Surely? What makes you so sure?
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  157. It's a paradox. see: Bell's Spaceship Paradox for the resolution.
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  158. why would they be denser? It's is specified in the video (and true in real life) that conducting wires are neutral. See "Bell's Spaceship Paradox" to understand it. and the prior reply is garbage.
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  159. yes. Loads.
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  160. Nope. Not a thing
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  161. the relativity of simultaneity plays a huge roll in this problem, and it is not addressed.
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  162. Because t(e electrons are dilated in their restframes
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  163. no. why would they be dense?
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  164. The electrons all move on separate trajectories such that their spacing is unchanged . They do not constitute a solid object subject to relativistic stresses
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  165. name one contradiction
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  166.  @pelasgeuspelasgeus4634  what's wrong with them?
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  167. you have 2 problems with your analysis: 1) irl, a current carrying wire is neutral 2) in the thought experiment, it is stipulated that the wire is neutral, so the electron density is by definition, the same as the proton density, in the wire's rest frame.
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  168. no, the wire is neutral, so they retain their 'rest' spacing, by definition.
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  169. The idea that spins can align along an electric field (or a current, or a velocity) is a maximal violation of parity conservation, so anything after that suggestion is REJECTED!!!!!!!!. See Mdm. Wu's famous parity violation experiment in the weak interaction, in which electron velocities aligned with nuclear spin. To think that Maxwell's equations (or the quantized version called QED) could do this is manifestly symmetry violating, and offensive to all things beautiful.
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  170.  @fjarran4782  Neither. The quantum origins of electromagnetism is local gauge invariance. In this picture, the invariance of physics under a local phase change of the wavefunction of a charged (e) particle (A so-called U(1) gauge symmetry) is restored by replacing the derivative (read: kinetic momentum, p) with the covariant derivative (p-ieA)...aka the canonical momentum. A is then identified as (electric potential, magnetic vector potential). Math ppl say "A" is a connection on the manifold, and the gauge symmetry leads to conservation of charge. The power of this way of thinking becomes evident when considering quantum chromodynamics, where the gauge symmetry is SU(3), and 'charge' now becomes a fundamental representation with 3 types of charges: red, green, blue (and their anti-charges). The single photon is replaced with 3^2-1=8 color/anti-color charged gluons. Likewise for the SU(2) symmetry of the weak interaction and the 2^2-1 = 3 vector boson, W+, W-, W0...but there are some Higgs shenanigans that mix the W0 with a photon-like B, leading to two states: the massless photon of electromagnetism and the heavier Z0. It's pretty wild stuff.
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  171. think again.
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  172. why would moving electrons be more densely packed than the protons in the metal lattice?
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  173.  @barbarossa11  but the electron density (in the wire frame) is unchanged, by definition. Therefore: the density is unchanged. See: Bell's Spaceship Paradox to understand the implications of that fact.
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  174.  @barbarossa11  it does. He shows it in the video. watch the electrons closely.
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  175.  @barbarossa11  but the electron are independent, unlike a lattice of protons, which are part of a large scale structure. Look at Bell's paradox.
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  176.  @anubhabsarkar6204  In lab frame, the electrons and ions have the same density, by definition. It's defined that way in the thought experiment, and it's an experimental fact (but that's irrelevant to a thought experiment). Of course, when the current is turned on, the fact that all the electrons accelerate with the same acceleration in the lab frame, means they must spread out in their instantaneous rest-frame. This quirk of relativity is the subject of Bell's Spaceship Paradox. If you actually do the Lorentz transform, in the cat-frame, the proton density increase by gamma (g), and the electron density decreases by gamma (1/g). Note that g-1/g = g(v/c)^2 so the electric field exactly matches the rules from Lorentz transforming E and B fields.
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  177. name the most egregious:
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  178. it's because in a static world, there is only charge and electricity. When you start moving, magnetism happens (spin notwithstanding), and relativity becomes mandatory.
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  179. yes. Any motion w.r.t to the proton lattice will Lorentz contract the density, as it is longest in its rest frame. The electrons are different, as they are all separate objects, and move on separate trajectories, however those trajectories are furthest apart in their rest frame. To understand why the electrons dilate in Henry's frame relative to Derek's: see Bell's Spaceship Paradox.
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  180. no monopoles required. Magnetic fields are source from current and changing current, while electric fields are source by charge, changing charge, and changing current. That is all.
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  181. In the wire's rest frame, the cat is moving, and it's exactly as you say: it's kinetic energy does not change as the only force is F = qv X B. Meanwhile, in the current's rest frame, F' = q(E' + v' x B')....there is an electric field b/c the wire is no longer neutral, and a B field from the moving positive charges, but v= 0, so it starts out F' = qE', and accelerates.
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  182. In the stationary-cat frame the electrons aren't moving, so their spacing is the proper lattice spacing times the Lorentz factor, they are dilated relative to the wire frame.
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