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.BAE Systems Maritime released CGI showing new shipbuilding hall at Govan currently under construction. 170m x 80m - capacity for 2 Type 26 frigates to be constructed side-by-side 2 x 100 and 2 x 20-tonne gantry cranes + can accommodate up to 500 workers per shift. HMS Birmingham will...

47,115 просмотров • 2 лет назад •via X (Twitter)

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Quantum mechanics has a reputation for being mystical mainly because people skip the rules and jump to interpretations. In this lecture series, we’re doing the opposite. We start from the rules, follow the algebra, and let the picture be the calculation. Classical Probability Theory combines alternatives by adding their probabilities. Quantum Theory combines them one step earlier…add complex amplitudes first, then square at the end. That swap in order is everything. Expand |a₁ + a₂|² and you don’t just get |a₁|² + |a₂|²…you get a cross-term, 2 Re(a₁ a₂*). Its sign is set by phase, so the same two contributions can reinforce or cancel. Interference is just the algebra of squaring a sum. In the 3D render, the surface height is proportional to |a(x)| (so peaks become bright bands after squaring), while the surface skin is colored by the local phase arg(a(x)). As the phase knob φ(t) is swept on path 2, the cross-term oscillates, and you literally watch the interference ridges slide across the screen. We model a detector screen with coordinates x in R² (think x = (x,y)). A quantum state assigns a complex amplitude a(x). The rule for outcomes is p(x) = |a(x)|² Now the key situation: two coherent alternatives contribute to the same outcome x. Let their amplitudes be a₁(x) and a₂(x). Quantum says a(x) = a₁(x) + a₂(x) So the probability density becomes p(x) = |a₁(x) + a₂(x)|² Expand it (this is the whole episode): p(x) = (a₁ + a₂)(a₁* + a₂*) = |a₁|² + |a₂|² + a₁ a₂* + a₁* a₂ = |a₁|² + |a₂|² + 2 Re(a₁ a₂*) That last term is the interference term. It can be positive or negative. To see phase explicitly, write each contribution in polar form: a₁(x) = r₁(x) exp(i θ₁(x)) a₂(x) = r₂(x) exp(i θ₂(x)) Then a₁ a₂* = r₁ r₂ exp(i(θ₁ − θ₂)) So the cross-term is 2 Re(a₁ a₂*) = 2 r₁ r₂ cos(θ₁(x) − θ₂(x)) That’s the fringe engine: p(x) = r₁² + r₂² + 2 r₁ r₂ cos(Δθ(x)) Now the phase knob we animate: Add a controllable phase shift φ to path 2: a₂(x) → a₂(x) exp(i φ) Then Δθ(x) → Δθ(x) − φ, so p(x; φ) = r₁² + r₂² + 2 r₁ r₂ cos(Δθ(x) − φ) As φ changes smoothly, the bright/dark pattern slides continuously. Same setup, same geometry, same magnitudes r₁,r₂, only phase changed. #QuantumMechanics #WaveInterference #ComplexAmplitudes #DoubleSlit #Physics #Mathematics

Mathelirium

81,599 просмотров • 7 месяцев назад

🎄🦞 THE LAIRY LOBSTER CHRISTMAS PLATTERS ARE HERE! 🦞🎄 Fresh from Billingsgate and cooked on the morning of your collection, these beauties are the ultimate Christmas treat! Pre-order NOW to guarantee yours — once they’re gone, they’re gone! ⸻ 🦞 THE GUVNOR! – £80 An absolute showstopper packed with luxury: • 1 x Caviar • 1 x Cockles • 1 x Crayfish tails • 1 x Shell of prawns • 2 x Dressed crabs • 1 x Full cooked Large Alaskan lobster • Large portion of extra large cooked shell-on prawns • 1 x Tin of chilli sardines • 1 x Smoked salmon • Large portion of crab sticks ⸻ 🎁 THE BABY PLATTER – £45 Perfect size, perfect flavour: • 2 x Dressed crabs • 1 x Cockles • 1 x Shell of f prawns • Large portion of cooked shell-on prawns • 1 x Caviar • 1 x Smoked salmon • Large portion of crab sticks ⸻ ✨ Collection Details ✨ 📍 Collect from The Lairy Lobster, CM13 3HU 📅 Pick-up on Christmas Eve or the weekend before ⏰ Platters need to be pre-ordered so we can prepare them fresh — please get your orders in ASAP! All platters are freshly prepared on the morning of collection and have a shelf life of around 4–5 days. These platters are examples only — actual presentation will be even better on the day! These will not be re sold, just put together for the video. 🎅🎄 DM ME to order! Merry Christmas — get ya seafood… BOSH! ❤️🦞

Thomas Skinner ⚒

280,661 просмотров • 8 месяцев назад