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$ASTS AST SpaceMobile full USASAT-NGSO-20 visualisation The animation doesn’t include J-LEO if seperate nor D-BLUEBIRD german filing and its arctic shell but it shows full SPACEMOBILE constellation currently registered by US i.e filed by FCC Brendan Carr HT: Carlos Placido
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![Quantum Mechanics Series Lecture 4 Lecture 1 established that ρ(x,t) = |ψ(x,t)|² behaves like a conserved probability density. Lecture 2 showed what drives that flow. We also saw that writing ψ = r exp(iθ) makes the probability current proportional to the phase gradient, making it clear that phase geometry literally steers the motion. Lecture 3 then showed that the centroid of that flow can move almost classically when the packet is tight and the external potential is smooth. However, that raises yet another question. If the centroid can look classical, why does the full wave still spread, bend, split, and interfere in ways no classical particle cloud would? This is because the wave is not driven only by the external potential. It is also driven by its own curvature. Write ψ(x,t) = r(x,t) exp(iθ(x,t)) with ρ = r². Then Schrödinger’s equation gives two coupled real equations. One is the continuity equation you already know. The other looks like a Hamilton-Jacobi equation, but with one extra term: Q = −(1/2m) ∇²r / r This is the so-called Quantum Potential. It depends entirely on how the amplitude bends across space. So, the wave is being shaped not only by V(x,t), but also by the geometry of its own envelope. In the animation, the upper surface is still |ψ| and its skin is still colored by arg(ψ). The glowing threads still trace the probability current. But now a second membrane hangs underneath. That lower membrane encodes the quantum potential Q itself. The porcelain bead marks the quantum centroid. The amber bead follows a classical centroid under the same external V. When those paths separate, the lower membrane tells you why. The difference is not magic but the extra term classical mechanics does not have. The math breakdown: Start from Schrödinger evolution in units with ħ = 1: i ∂ψ/∂t = [ −(1/2m) ∇² + V(x,t) ] ψ Write the state in polar form: ψ = r exp(iθ) Then ρ = |ψ|² = r² From the imaginary part, you recover probability conservation: ∂ρ/∂t + ∇·j = 0 with j = (1/m) Im(ψ* ∇ψ) = (ρ/m) ∇θ So the local velocity field is v = j / ρ = ∇θ / m Now take the real part of Schrödinger’s equation. That gives ∂θ/∂t + |∇θ|² / (2m) + V + Q = 0 where Q = −(1/2m) ∇²r / r This is the classical Hamilton-Jacobi equation with one extra term. That extra term is what makes quantum motion locally different from classical motion. Take a gradient of that phase equation and use v = ∇θ / m. Then the flow obeys an Euler-like equation: ∂v/∂t + (v·∇)v = −(1/m) ∇(V + Q) In other words, there are really two forces in the problem. One comes from the external potential V. The other comes from the wave’s own curvature through Q. That is why Ehrenfest is only approximate. The centroid can still satisfy d⟨x⟩/dt = ⟨p⟩/m d⟨p⟩/dt = −⟨∇V⟩ but the internal shape of the packet evolves under the combined influence of V and Q. When the packet stays broad and smooth, Q is gentle and the motion looks more classical. When the packet develops sharp curvature or interference structure, Q becomes strong and the classical picture breaks down. That is what this scene is designed to show live. #QuantumMechanics #Wavefunction #SchrodingerEquation #BornRule #ProbabilityCurrent #ContinuityEquation #Phase #EhrenfestTheorem #QuantumPotential #Madelung #HamiltonJacobi #MathematicalPhysics #Mathematics #Physics](https://image.24vids.com/tw-2044118124148973661/amplify_video_thumb/2044117901251072000/img/IXBMEKzfYfpY_xGi.jpg)
![The Trump administration is attacking free speech, say the media and Democrats. On Monday, Attorney General Pam Bondi said, “There’s free speech and then there’s hate speech. And there’s no place [for it], especially now, especially after what happened to Charlie.” Fear of the Trump administration led ABC to abandon late-night comedian Jimmy Kimmel yesterday, said progressives. Kimmel had claimed the man who assassinated conservative leader Charlie Kirk was “MAGA.” Brendan Carr, chair of the Federal Communications Commission (FCC), which regulates broadcast networks, said, in response, “This is a very, very serious issue right now for Disney [ABC’s owner]. We can do this the easy way or the hard way. These companies can find ways to take action on Kimmel, or there is going to be additional work for the FCC ahead.” However, prominent Trump supporters condemned Bondi’s remarks en masse, near-instantaneously, and she backtracked the next day, saying, “If you want to be a hateful person and simply say hateful things, that is your right to do so.” As for Carr, he dismissed the idea that his words played a significant role in ABC’s decision, telling Public, “the reporting is that Disney itself had their own concerns about the programming. A lot of folks want to point fingers here at convenient targets because they don’t want to see or deal with the broader market trends. Late night ratings are way down.” And yet it is difficult to believe that Carr’s remarks had no influence. It is reasonable to think that Nexstar may have feared that the FCC wouldn’t approve its acquisition of Tegna, which operates 64 stations in 51 markets, if it had allowed Kimmel’s show to continue. That purchase requires the FCC to allow Nexstar to go beyond current limits on broadcast station ownership. And, notes the Journal, Carr’s remarks may have indirectly impacted Disney: “Executives also discussed staff safety, including threatening emails staff on Kimmel’s show had received after Carr’s remarks and the posting of some of their personal information online, the people said.” The FCC repealed the “fairness doctrine” in 1987, since it required too much government regulation of content, and the FCC’s “public interest” power is not a license to police programs like Kimmel. Indeed, the FCC’s mandate today is largely structural with narrow content exceptions (e.g., indecency, children’s programming, and political advertising). As such, Carr’s remarks were “jawboning,” a term that refers to speech or implied threats by government officials to pressure private parties into actions that officials cannot legally mandate. Such jawboning can be a form of indirect censorship. President Biden engaged in similar pressure tactics when he publicly said social media companies were “killing people” by not removing Covid “misinformation.” Biden officials also invoked Section 230 to coerce platforms into greater censorship, and internal Facebook emails revealed that the company was worried about failing to secure a data deal with Europe if it did not comply with the administration’s censorship demands. The Left’s complaints about censorship are made in particularly bad faith, given its role in defending the Biden administration’s coercive jawboning and the resulting mass censorship during Covid. The Left also normalized “cancellations,” calling for countless public figures and private individuals to be deplatformed and fired for causing offense. In 2018, Kimmel mocked Roseanne Barr after ABC canceled her show after she posted an offensive tweet about a black former Obama administration official. The people decrying what Bondi and Carr said are the same ones who demanded sweeping government censorship of social media platforms in the guise of combating “misinformation” and “hate speech” in 2020 and 2021. Consider Barack Obama, who criticized Carr’s remarks. It was Obama’s people at the Department of Homeland Security, FBI, National Science Foundation, DOD, and CIA who put in place the Censorship Industrial Complex between 2016 and 2024. And it was Obama who gave a 2022 speech at Stanford laying out a vision for government “regulation” of social media platforms one week before DHS launched its “Disinformation Governance Board.” The Democrat-supported Censorship Industrial Complex was and remains, in Europe and elsewhere, a far greater threat to free speech than the angry remarks of Trump and Carr, as inappropriate and as unhelpful as they were. The Complex was embedded in the government, including the Intelligence Community, and operated secretly to manipulate information, public opinion, and “whole narratives.” New York Times columnist David French, who criticized the Trump administration for censorship, defended government censorship in the past as “correcting misinformation” and pointed to the First Amendment rights of government employees. It’s important to remember the context we are in. A little over one week has passed since an individual, who appears to be a Left-wing romantic partner of a trans-identified male, assassinated a major conservative leader, Charlie Kirk. Assassination is the ultimate form of censorship. And Kirk was a communications and organizing prodigy who many on the Right viewed as future Republican presidential material. Kirk’s killing comes after 10 years of the Left, broadly defined to include the media, Democrats, and the progressive NGO industry, dehumanizing Republicans. As such, many, if not most, on the Right hold the Left responsible for the killing of one of its most promising leaders, who also happened to be a family man and Christian. When it comes to public opinion, five times more people on the Left justify violence than those on the Right. A YouGov survey conducted after Kirk’s assassination found that 25% of people who describe themselves as “very liberal” and 17% who describe themselves as “liberal” say that it is sometimes justified to resort to violence to achieve political goals. Only 3% of people who describe themselves as “very conservative” and 6% of people who describe themselves as “conservative” said the same thing. A separate poll earlier this year found that 55% of people who identify as left of center say that it would be at least somewhat justified to murder Trump. But it is short-sighted for the Trump administration to do and say things that undermine its ability to demand free speech abroad, and hold the Left accountable at home. The Trump administration has rightly raised the alarm about censorship in Europe and Brazil of American social media platforms, and often of Americans. Carr’s remarks about the “easy way or the hard way” undercut the administration’s free speech diplomacy.... Please subscribe now to support Public's defense of free speech, read the rest of the article, and watch the full video!](https://image.24vids.com/tw-1969405155906109688/amplify_video_thumb/1969402761495396353/img/L0qXIX_dWFDlzl06.jpg)
