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Electromagnetic waves are only created by sources. So it is not valid to set the sources to zero. When the source is included, this results in the wave equation equal to a source. Solving this inhomogeneous PDE yields a nonlinear phase vs distance dispersion curve. Apply phase speed and group speed operators on this curve shows that the both the phase speed and group speed are instantaneous in the nearfield and reduces to the speed c in the farfield, starting at about 1 wavelength from the source. After that the speed decays asymptotically toward speed c, but never becomes exactly c, even at astronomical distances from the source. So the speed of light is not a constant as once thought, and this has now been proved by Electrodynamic theory and by Experiments done by many independent researchers. The results clearly show that light propagates instantaneously when it is created by a source, and reduces to approximately the speed of light in the farfield, about one wavelength from the source, and never becomes equal to exactly c. This corresponds the phase speed, group speed, and information speed. Any theory assuming the speed of light is a constant, such as Special Relativity and General Relativity are wrong, and it has implications to Quantum theories as well. So this fact about the speed of light affects all of Modern Physics. Often it is stated that Relativity has been verified by so many experiments, how can it be wrong. Well no experiment can prove a theory, and can only provide evidence that a theory is correct. But one experiment can absolutely disprove a theory, and the new speed of light experiments proving the speed of light is not a constant is such a proof. So what does it mean? Well a derivation of Relativity using instantaneous nearfield light yields Galilean Relativity. This can easily seen by inserting c=infinity into the Lorentz Transform, yielding the GalileanTransform, where time is the same in all inertial frames. So a moving object observed with instantaneous nearfield light will yield no Relativistic effects, whereas by changing the frequency of the light such that farfield light is used will observe Relativistic effects. But since time and space are real and independent of the frequency of light used to measure its effects, then one must conclude the effects of Relativity are just an optical illusion. Since General Relativity is based on Special Relativity, then it has the same problem. A better theory of Gravity is Gravitoelectromagnetism which assumes gravity can be mathematically described by 4 Maxwell equations, similar to to those of electromagnetic theory. It is well known that General Relativity reduces to Gravitoelectromagnetism for weak fields, which is all that we observe. Using this theory, analysis of an oscillating mass yields a wave equation set equal to a source term. Analysis of this equation shows that the phase speed, group speed, and information speed are instantaneous in the nearfield and reduce to the speed of light in the farfield. This theory then accounts for all the observed gravitational effects including instantaneous nearfield and the speed of light farfield. The main difference is that this theory is a field theory, and not a geometrical theory like General Relativity. Because it is a field theory, Gravity can be then be quantized as the Graviton. Lastly it should be mentioned that this research shows that the Pilot Wave interpretation of Quantum Mechanics can no longer be criticized for requiring instantaneous interaction of the pilot wave, thereby violating Relativity. It should also be noted that nearfield electromagnetic fields can be explained by quantum mechanics using the Pilot Wave interpretation of quantum mechanics and the Heisenberg uncertainty principle (HUP), where Δx and Δp are interpreted as averages, and not the uncertainty in the values as in other interpretations of quantum mechanics. So in HUP: Δx Δp = h, where Δp=mΔv, and m is an effective mass due to momentum, thus HUP becomes: Δx Δv = h/m. In the nearfield where the field is created, Δx=0, therefore Δv=infinity. In the farfield, HUP: Δx Δp = h, where p = h/λ. HUP then becomes: Δx h/λ = h, or Δx=λ. Also in the farfield HUP becomes: λmΔv=h, thus Δv=h/(mλ). Since p=h/λ, then Δv=p/m. Also since p=mc, then Δv=c. So in summary, in the nearfield Δv=infinity, and in the farfield Δv=c, where Δv is the average velocity of the photon according to Pilot Wave theory. Consequently the Pilot wave interpretation should become the preferred interpretation of Quantum Mechanics. It should also be noted that this argument can be applied to all fields, including the graviton. Hence all fields should exhibit instantaneous nearfield and speed c farfield behavior, and this can explain the non-local effects observed in quantum entangled particles. *CZcams presentation of above arguments: czcams.com/video/sePdJ7vSQvQ/video.html *More extensive paper for the above arguments: William D. Walker and Dag Stranneby, A New Interpretation of Relativity, 2023: vixra.org/abs/2309.0145 *Electromagnetic pulse experiment paper: www.techrxiv.org/doi/full/10.36227/techrxiv.170862178.82175798/v1 Dr. William Walker - PhD in physics from ETH Zurich, 1997

This is one of the best explanations I encountered so far. Thank you.

thank you very much

Beautiful. λ is one of my favorite variables.

In which book one can study the formula for photon lifetime (05:09)

Beautiful

❤❤

thanks a thousand times!

wow

How to calculate Beam waist from the z scan data?

He speaks 70's.

Fantastic video, thank you for making these concepts intuitive. Your teaching in conjunction with the applets makes it very clear.

Wrong information provided.

How an electric field can pass a material?

I want to ask one question .If the phase angle is 180 degree this waves must be linear polarization ?

you think the robots are going to be racist?

A detailed discussion of polarizability is found in "Dielectric Matter", Ch. 6 of "Modern Electrodynamics" by Andrew Zangwill.

Very well taught Professor. I am glad to find this online. Thanks a lot.

5:46 But I didn't get it. There's still a non-symmetry on the sides of the material, but now vertically. The positive layer will appear on top and the negative at the bottom. And then apparently at 9:05 the incident and absorbed components would become collinear according to this. Doesn't make sense. I mean if we would only focus on mathematical aspects, then circle integral is 0, hence then incident tangential field = tangential absorbed, while normal components are scaled by epsilon from each side and due to that difference in scalars we have a "bending" of the absorbed field inside the material. Idk, however, what happens at the atomic level of things, but in a way it's presented at 5:46, the top and bottom layer of material will be out of pair to be cancelled, hence would induce some vertical field inside the material which would compensate incident field thus cancelling a "bending" of the field inside a material. Its something wrong about the diagram.

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Key idea(s): 1) Line Shape g(ν) = Convolution of Probability Density Function (PDF) of Electron State 0 and 1, P₀ * P₁ = P(E₀) * P(E₁). 2) Diagonal State Transitions - These are not possible in semiconductors because of the Heisenberg Uncertainty Principle: - An electron being in either state with a defined energy (i.e., E₀ or E₁) means that there is a definite position (i.e., it's confined in space, maybe to an associated atom and/or because of the forces of other electrons/charges, etc.). In order for a wave (i.e., our electron) to be confined in space (i.e., position), you need an infinite number of waves, each with different frequencies ν, to superpose into the resultant wave function that places your electron at a specific location/position - think of the Fourier transform of the wave in the time domain, i.e., the frequency domain graph/function of the electron's wave function. - The momentum of an electron is given by p = hk = 2πh/λ = 2πνh/c (the de Broglie relation). So, if we require an infinite number of frequencies to confine our electron, we don't have just one value of k; we have an entire (infinite) range of k values. That is, k --> Δk = ∞. This gives us Δp = h Δk = h * ∞ = ∞, which is non-physical, i.e., unrealistic/impossible.

clearly. thank you

great intro to the MTF, thank you for a great explanation!.

Thank you very much !

Goid job using technical jargon without ever divulging further explanations to ensure only the prior educated can reap the tiniest benefit from this drivel

Can you explain ground loops?

Mathematical masterbation... That was funny😂

9:18 wish to see E and B plane waves both are present with any imagination, ok to plot them in extra boxes without overlapping, hope to see vectors in them

Thanks a lot

Muito bom

Physicist guess more often than you think. We even have a name for it: Ansatz :) Nice vid

amazing video thank you

🙏💐💐

thanks

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Thanks a lot for the explenation, I was reading my notes without understanding anything and you saved me ☺

great video

I’ve been trying to get an intuition for this since I learned acoustics 2 years ago and I finally got it thank you bro

thanks for sharing

thanks for sharing

My Hero. Thank you!

omg, never thought that 4piR^2 associate with area of sphere. thanks shareing.

Clap your hand anytime he say “field”

Hmmm, circular electric field exists. Its called EMF and it appears in coild when magnetic field is changing. So, your explanation of "electric fields never swirling" might be in jeopardy?

What is the textbook you are using?

what is the name of that great professor?

GREAT VIDEO !!!!!!!!!!!!!!

thanks for helping me I'm from Morocco it take me time to understand how waves to be plane

SAME wonder that we make in >>>>how votage can be buildt across a coil it is just a wire then we learn that voltage is not because the resistevity of the wrie rather it is due to current struglle to build the megnatic field in the cam the same wonder bulit again how should current cross the cap while its an open circuit same solution the ekectric field is the media by which the current travels this is the most intuitive thing if you get the coil you get the cap

Thank you so much. I wish everyone teach this topic could teach like you. In your voice and explanation, one can really tell that you are passionate about teaching your students. This attitude is missing in a lot of professors today, especially here in America and yet students pay a lot tuition and other fees for University. But thank so much for passing on this wonderful knowledge. God bless you.