Beam

A breakdown of the Aharonov-Bohm (AB) effect— including the phase shift formula and the analogy to differential "speeds" in phase evolution. The diagram perfectly captures the setup: an electron beam split into two paths that encircle a solenoid (carrying current to produce magnetic field confined inside), then recombined to show interference. The key quantum weirdness is that the electrons experience no classical force (since outside the solenoid), yet the nonzero vector potential imprints a topological phase difference, shifting the interference pattern. To build on your points: Phase Shift Mechanics The wavefunction of the electron acquires a phase along each path due to the Aharonov-Bohm term in the Schrödinger equation, where the momentum operator includes (in cgs units; adjust for SI). For the two paths, the total phase difference is indeed: \Delta \phi = \frac{e}{\hbar} \oint \mathbf{A} \cdot d\mathbf{l} = \frac{e \Phi_B}{\hbar} In terms of "one side faster, one slower" intuition: it's a great way to visualize it. The phase accumulation rate acts like a effective "winding" of the wavefunction's complex argument. If you think of the de Broglie wavelength, the path with positive phase advance behaves as if the local wavenumber increased (shorter effective wavelength, "faster" propagation in phase space), and vice versa. But crucially, the particle's kinetic energy and speed remain unchanged—no Lorentz force involved. Experimental Ties This has been verified in labs since the 1960s (e.g., using superconducting solenoids to quantize flux in units of for electron pairs, but for single electrons). The interference fringes shift periodically with , with observable effects down to atomic scales in modern setups like electron holography or mesoscopic rings. Link to Broader Ideas AB underscores potentials over fields as fundamental in quantum mechanics (echoing ideas from Wheeler-Feynman or even modern gauge theories in particle physics). Classically, we can always gauge away where , but quantum paths "feel" the global topology. As for tying this into a fractal-time/phase-field cosmology: that's an intriguing angle! In standard physics, AB hints at how spacetime might have hidden structures (like in quantum gravity proposals where topology affects phases, or in condensed matter analogs like anyons in 2D systems). If your model posits time as fractal or density-varying, with phase entrainment across scales, AB could serve as a microcosm: the solenoid's flux creates a "phase gradient" in the vacuum, akin to a local distortion in a background field. Electrons navigating the paths experience differential "time flow" in their internal clocks (wavefunction oscillation), revealing emergent structure without direct interaction. This resonates with ideas in loop quantum gravity or holographic principles, where geometry encodes phases fractally.

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Our kindergarteners had the BEST time on their field trip to the @ICSVVSD! 💛 They explored, asked big questions, and even got to sign a beam that will be part of our new expanded building! @SVVSDSupt @SVVSD @BuchlerStVrain #StVrainAdvantage #PublicSchoolAdvantage #StVrainStorm https://t.co/QteOCYLrNA

イルザ、早く来てくれ

@NedNarlington @QtPossiblyLucky @WhiteHouse Thou hypocrite, first cast out the beam out of thine own eye; and then shalt thou see clearly to cast out the mote out of thy brother’s eye.

久しぶりにスト6のランクマしたらおもっくそ台パンしてもうた 1マス戻る

@nekoneroVT It’s ok I’ll save a snowball to beam you in the face with when you get back

i also like to think in the meta of Solar Actually Existing hypothetical. That she would be the first to be hit with the Softification Beam just because of Gendered shapes. Once shes solidifed as The Girl shes more visibly soft & round as opposed to the others

@tmanzii_ My goodness. In the Netherlands we just switch of the red enlighted cross above the road. Or open a beam like on a railroad. Way easier.

@driftingeyes DUDE . TWITTER DOESNT GIVE ME ANY NOTIFS ITS NOT EVEN FUNNY . i call them! fruit bros 🍓🍊 bc they are fruit . their interactions remind me of my own little brother and i so !!! found family beam attack

@CyreneAI @GiantAI_agent @CyreneAIFlows Is it real

Introducing my survival tool for @DataHaven_xyz & Camp Haven a robust flashlight with an integrated compass! Its bright beam cuts through darkness while the compass guides you through trails or emergencies. Built for adventurers! 🧭💡 #CampHaven #SurvivalTool https://t.co/8sTq1xy9Q3

Just had the misfortune to drive through Blackburn and back out and through again. What an absolute mess and the standard of driving is appalling! On coming traffic with full beam and fog lights on, blocking off junctions while in traffic queues, cutting across oncoming traffic