Excellent! I can only echo the other comments. You are an excellent teacher! More lectures please!

The Barn Door Paradox The setting out of the barn door paradox (14:40) would be a lot simpler starting with the back doors of the barns on the right and left halves of the diagram closed at the start, as in the previous hand drawn sequence, and remaining closed until the front of the ladder gets there. At this point the back door snaps open. At that same time the front door on the left half of the diagram snaps shut. The one on the right half has to wait until the ladder has cleared before shutting. Each door then only undergoes one event (opening for the back door and shutting for the front one). At 19:00 you clearly explain that the fallacy in the apparent paradox is the assumption that the two barn doors both move in tandem in the two frames. In fact, an observer on the ladder does not see the two barn door moves as simultaneous. The back door move is first and the front door follows. However, at 26:00 you don't close the loop by spelling out that in the primed (ladder) frame of reference the two door events occur at different times. You focus instead on the length of the ladder, which is the source of people's confusion. In the ladder frame the back door move is the rightmost red dot. The front door move is an event at the intersection of the left blue vertical with the x'=0 axis, which is some time later (if I understand this correctly, which is by no means a given). This is why the ladder gets through without mishap. A couple of other points on this sequence: 1. It is not clear why the black x=ct line is there. Presumably it is explained in an earlier lecture, and might have something to do with how the x' (i.e. ct'= 0 line) is drawn. 2. At 24:05, it is not obvious why B is shorter than Bo as it is clearly longer on the diagram. Presumably, the length units of x and x' must be different. i.e. 1 metre on the x' axis is not the same length on this diagram as 1 metre on x. Thanks for the video. It certainly got me thinking. Whether along the right lines or not I will leave to others.

In the first example, I don't understand how that is the only curve that satisfies the boundary conditions... wouldn't the ball also be at O and T if it didn't move, just sat there for the time it would take to go up and come back down? I am confused because (I think?) the derivation explicitly left out the starting force. I understand why if it is moving it has to follow that curve in order to land precisely at time T given the constant g. I don't understand how we derive from just the boundary conditions + Newton's laws that any movement took place....

This is the best you can get, really enjoy all your lectures

I’ve been loving your channel since I came across it recently. Keep up the good work. One note: The armchair physicists in the comments of your videos are almost as entertaining as the videos. They are theoretical physicists, because their physics degrees are theoretical 😂

Phenomenal lecture, if there was just one change I would have loved you to have explained where the minus sign came from in the four vector

Could anyone shed some light on how to prove [H, S^2tot] = 0 and [H, S^ztot] = 0 at the end of the video? We can see it is indeed this case in the 2 spin system, because we can express H in terms of S^2tot. And We know [S^ztot, S^2tot] = 0, so they all commute. But here we cannot explicitly express the Hamiltonian, how can I see it? Thanks for your help in advance.

Thank you!!

Brilliant.

Excellent and ground up explanation of Feynman path integral. Thank you.

Dude gets more jacked with each video!

Dear Dr. Mitchell, I solved the Q 2.1Charged planes problem using images method. Calculating the electric field from two pontual charges (the real one and its image) in a generic point on the conductor plane and then obtaining the electrical densitiy vector is possible to get the expression for the surface charge distribution directly without any derivatives. But by using this method I got a slightly different result from yours ( my denominator is 2 pi instead of only pi). Would you mind to check if something is wrong? By the way your classes are excelent and I would like to ask you for a good reference to perform computational physics (I intend to make animations of electrical charge moving under different electric/magnetic field)? Thanks in advance, Marcio.

Brilliant explanation! Thank you!

Great video! Very well explained thanks Dr Mitchell!

Brilliant stuff thumbs up

Gravity doesnt exist just lies. Its all about mass and fall of bodies..

In the two pulleys example, it seems like the second pulley (the lower one) becomes an accelerated frame of reference when the mass m1 is accelerating. Do we need to account for that by changing the value of g for the second pulley to g plus the second time derivative of q1?

Does finding U matrices mean we are actually figuring out clebsch gordan coefficients?

14:10 Principle of Least Action

So good!!!

Love from turkeyy

Very good, very useful, very clear. I love it. Thank you so much

Best course ever! Thank you!

Great video! Probably the best explanation I have ever seen of these ideas. I have one (perhaps stupid) question: If the paths around the path of least action creates constructive interference, why can't paths around (very near) other paths do the same? In your example you drew 3 vectors whose sum was nearly zero, and therefore had destructive interference, but would one not see constructive interference for vectors near (similar) any of the individual paths in that example? So I guess I don't understand why the sum of these vectors _around_ the path of least action is so special, given the argument about the sum of the vectors in your example.

This lecture would improve a lot IMHO if the speaker focused on the concept of "action" before stating the Lagrangian. Explain what is going on with all the trajectories, what is the problem mathematically. As it is action remains something arbitrary and mystical, while the Lagrangian pops up "deos ex machina" of sorts.

Absolutely great work sir

The paradoxes are actual contradictions that indicate that the principle of relativity is false. The Einstein mathematics is faulty and produces mathematical contradictions that can not be removed. So his theory is actually invalid as shown by these real unresolvable paradoxes.

Thats great prof....you are a real teacher...❤❤❤❤

At around 8.40 you draw the Density of states of an uniform 1D chain. Is it correct ??? I say this because for an infinite 1D lattice you get Van Hove singularity at the band edges, which I believe in 1D is non-integrable. If I take a tight-binding 1D lattice with nearest neighbour hopping, these singularities will occur at -2t and 2t, where t is the hopping parameter.

Really nice video! Thank you very much. But what I'm missing and what I initially searched for, is an intuitive explanation, on WHY the Lagrangian is T-V. Maybe I'm missing something, but it's not clear for me, what the difference in the Energies has to do with the Action of the Path. Does anyone have a link to an explanation?

best bro best

Thanks for the lectures. I have a question regarding to last part about antiferromagnets. "We have to do all the calculation asuming broken symmetry situation, this is the way we divide the lattice into two sublattice". Could you explain this a bit? How should i relate symmetry breaking with sublattices. I know that deviding into two sublattices is good technic in antiferromagnets. But are we doing this because of symmetry breaking? Thanks

Hello, these lectures have helped so much. I had a question on how one would solve a 1d 2-site unit cell using the same fourier transform process that that you performed in the video. Do you know any resources where I could find this?

Hi, is there similar Dyson equation for the lesser Green's function?

47:11 can somebody plz explain me how r*(deltar) vanish ?

12:25 why did you consider at=0 when t=T?

@ 32:00 THE YELLOW PATH ISN'T PART OF THE PATH-INTEGRAL.

Thank you for this! Your explanation is super clear. I have the following problem. When you derive the electric force field, with the force increased perpendicular to velocity, I notice that Wikipedia gets a very different result. en.wikipedia.org/wiki/Li%C3%A9nard%E2%80%93Wiechert_potential#Field_computation With theirs, at high velocities the force is greatly increased in the direction of the velocity, and reduced to (c^2-v^2)/(c+v)^2 in the opposite direction. This makes intuitive sense to me -- in the direction of velocity the field lines are squeezed together and trailing behind they're spread apart. But your way makes intuitive sense too. Is Wikipedia wrong? Or are they somehow both right?

Why aren't we considering ∂L/∂t*dt in the differential of L at 17:26 ?

Ref 1:32 min, we see that the E field from a moving charge is calculated using Coulomb law, not at the retarded time, but at the actual time. The same is true for the magnetic field. Ref 1:40 min, we see that the magnetic field can be calculated using the Biot-Savart law calculated at the actual time. not the retarded time. These calculations show that, even though the fields are calculated from retarded potentials (ref 1:03 min), the Electric and Magnetic fields are instantaneous for a moving charge, which is the nearfield. Of course in the farfield the fields propagate at the speed of light. A similar phenomena is seen in Gravity. It has been known since the late 1700s by Simone LaPlace that nearfield Gravity is instantaneous by analyzing the stability of the orbits of the planets about the sun. Of course General Relativity predicts that in the farfield Gravity propagates at the speed of light, which was recently confirmed by LIGO. Recently it has been shown that light behaves in the same way by using Maxwell's equations to analyze the propagating fields generated by an oscillating charge. For more information search: William Walker Superluminal. This was experimentally confirmed by measuring radio waves propagating between 2 antennas and separating the antennas from the nearfield to the farfield, which occurs about 1 wavelength from the source. This behavior of gravity and light occurs not only for the phase and group speed, but also the information speed. This instantaneous nature of light and gravity near the source has been kept from the public and is not commonly known. The reason is that it shows that both Special Relativity and General Relativity are wrong! It can be easily shown that Instantaneous nearfield light yields Galilean Relativity and farfield light yields Einstein Relativity. This is because in the nearfield, gamma=1since c= infinity, and in the farfield, gamma= the Relativistic gamma since c= farfield speed of light. Since time and space are real, they can not depend on the frequency of light used. This is because c=wavelength x frequency, and 1 wavelength = c/frequency defines the nearfield from the farfield. Consequently Relativity is an optical illusion. Objects moving near the speed of light appear to contract in length and time appears to slow down, but it is just what you see using farfield light. Using nearfield light you will see that the object has not contracted and time has not changed. For more information: Search William Walker Relativity. Since General Relativity is based on Special Relativity, General Relativity must also be an optical illusion. Spacetime is flat and gravity must be a propagating field. Researchers have shown that in the weak field limit, which is what we only observe, General Relativity reduces to Gravitoelectromagnetism, which shows gravity can be modeled as 4 Maxwell equations similar in form to those for electromagnetic fields, yielding Electric and Magnetic components of gravity. This theory explains all gravitational effects as well as the instantaneous nearfield and speed of light farfield propagating fields. So gravity is a propagating field that can finally be quantized enabling the unification of gravity and quantum mechanics. The current interpretation of quantum mechanics makes no sense, involving particles that are not real until measured, and in a fuzzy superposition of states. On the other hand, the Pilot Wave interpretation of Quantum Mechanics makes makes much more sense, which says particles are always real with real positions and velocities. The particles also interact with an energetic quantum field that permeates all of space, forming a pilot wave that guides the particle. This simpler deterministic explanation explains all known quantum phenomena. The only problem is that the Pilot Wave is known to interact instantaneously with all other particles, and this is completely incompatible with Relativity, but is compatible with Galilean Relativity. But because of the evidence presented here, this is no longer a problem, and elevates the Pilot Interpretation to our best explanation of Quantum Mechanics. *KZfaq presentation of above argument: kzfaq.info/get/bejne/qcuAl61o27m1poU.html *Paper it is based on: William D. Walker and Dag Stranneby, A New Interpretation of Relativity, 2023: vixra.org/abs/2309.0145

Such good presentation

Thank you so much for these!! At min 7.51 shouldn't there be a minus from x_2 dot = -x dot? Therefore should the two terms of the kinetic energy have a minus in between? My result has (m_1-m_2) in the denominator.

Kudos to you Professor!

why we got the block diagonal matrix form

A heartfelt thank you from moroco

Thanku Sir ........ 😊

A marvelous pedagogical 1:57:34 Lec. delivered with proper scope and depth in content, easy to listen and clear level of English language. An informative and well explained Lec. indeed. Thanks a lot Dr. Mitchell.

Hello Dr. I would like to show you some of the things I am working on. Your guidance will be appreciated. Please let me know how I can contact you

Love the content, most of it is great, honestly my only critique is mentioning philosophies of String “Theory®” as though they were axioms of some sort. Otherwise, love it

This is an excellent tutorial, very clear and readily understandable. I cannot understand why there are only 124 likes to date. Thank you Dr. Mitchell. Looking forward to viewing your other videos.