/** * file: chatgpt_karbytes_24march2025_p2.txt * type: plain-text * date: 30_MARCH_2025 * author: karbytes * license: PUBLIC_DOMAIN */ The following is a plain-text transcript of a conversation between karbytes and ChatGPT-4o which took place between 4:00AM Pacific Standard Time on 24_MARCH_2025 and 5:00PM Pacific Standard Time on 30_MARCH_2025. That conversation is a (non Advanced Voice Mode) continuation of the same conversation which is depicted by the following plain-text note: https://raw.githubusercontent.com/karlinarayberinger/KARLINA_OBJECT_extension_pack_34/main/chatgpt_karbytes_24march2025_p1.txt * * * ‘ karbytes: Provide at least one image depicting the result of that experiment. [Deep research] ChatGPT: Just to clarify—are you looking for an original or authentic image from the 1999 Delayed Choice Quantum Eraser experiment (e.g. the actual interference patterns from the paper), or would you also be interested in clear diagrams or reconstructions based on that experiment to help visualize the results? karbytes: Both please. ChatGPT: Great, I’ll find both an original image or plot from the 1999 Delayed Choice Quantum Eraser experiment by Kim et al., as well as clear diagrams or reconstructions that illustrate the experiment’s results—especially the interference and non-interference patterns seen in the signal photon coincidences. I’ll let you know as soon as I have them. [Research completed in 11m. 62 sources] [Images and Diagrams of 1999 Delayed Choice Quantum Eraser Results] – I’m gathering images and diagrams from the 1999 Delayed Choice Quantum Eraser experiment by Yoon-Ho Kim et al., including interference patterns and non-interference patterns. [Searched for Yoon-Ho Kim quantum eraser images] – I’m thinking about the sources of interference and non-interference patterns in the delayed choice quantum eraser experiment, including original and modern diagrams, and their clarity for visual data interpretation. [Read arxiv.org] – I’m considering opening the PDF with browser.open to view the figures and more content directly. [Read ar5iv.org] – I’m analyzing interference patterns and detection rates. Comparing Figs 3 and 4 for phase shifts, Fig 5 shows no interference. Proposing images for clarity. – I’m looking into accessing a PDF via Python or finding images, and also checking out a Wikipedia page and a Reddit discussion for diagrams or explanations. [Read reddit.com] [Read en.wikipedia.org] – Interpreting phenomenon at detectors: detecting interference and diffraction patterns based on idler detection locations. [Read researchgate.net] – I’m mapping out how to access PRL, must check subscription status. Considering Wikipedia and Reddit for potential images or links. [Read en.wikipedia.org] – I’m thinking about external links or images online. Maybe Google images or specific search engines would work. [Searched for R01 and R02 interference patterns] – I’m piecing together resources like Hackaday articles and cs.uwaterloo PPTs. They might offer images or detailed descriptions, useful for understanding interference patterns in waveforms. [Read hackaday.com] – I found that Hackaday might contain images showing interference patterns specifically labeled “er_08” linked to waveforms R01 and R02. [Read more from hackaday.com] – Noticing references to “R0n” diagrams and “er_08” imagery, likely illustrating particle and interference patterns, from a hackaday source. [Read more from hackaday.com] – I’m looking at a small image preview possibly related to simulations or representations. Considering Hackaday’s content, it might involve waveforms from varied sources. [Read more from hackaday.com] – I’m working through whether “the top image” refers to an earlier image in the article or one from Hackaday. Planning to investigate any images present. [Read more from hackaday.com] – I’m gathering info on various images from Hackaday, including diagrams and interference patterns, to piece together their relevance to the quantum eraser experiment. [Searched for Kim Scully 1999 quantum eraser graph] – I’m digging into the search results to understand key concepts and potential figures in “Taming the Delayed Choice Quantum Eraser” on PhilSci-Archive. [Read philsci-archive.pitt.edu] – I’m analyzing Figure 2’s data patterns at D0 and D1-D4, examining interference fringes and clump patterns, and noting potential conceptual content. [Searched for R03 and R04 interference] – I’m gathering info on various platforms like Reddit, physics.stackexchange, and arXiv. The snippet suggests R03 and R04 are similarly shaped but shifted. [Searched for R01 R02 quantum eraser graph] – I’m pulling together different data types like graphs and Bayesian statistical analysis to streamline the selection of a suitable distribution for modeling a particular variable. [Read commons.wikimedia.org] – I’m curious about the file linked to the date/time text, which might be an SVG. I’ll consider fetching a PNG or checking if the image can be displayed in the browser. [Read upload.wikimedia.org] – It’s interesting to see that embedding SVG files directly might not support them. I’m looking for raster versions or PNG previews on Wikimedia Commons, considering links and dimensions to find a feasible solution. [Read more from upload.wikimedia.org] – I’m thinking about converting the SVG to PNG or finding it directly on Google Images. Checking for relevant titles might also help. [Read commons.wikimedia.org] – I’m examining if “KimDelayedChoiceQuantumEraserGraphsSVG.svg” is a duplicate of “Delayed_Choice_Quantum_Eraser_Graphs.svg.” Both files likely illustrate similar concepts. [Read upload.wikimedia.org] – I’m exploring multiple ways to resolve image processing issues, including server restrictions and offline problems. Adjusting the image resolution might also help in mitigating the glitch. [Read more from upload.wikimedia.org] – I’m moving anew beyond ‘Renleypedekeklo’. [Read more from upload.wikimedia.org] – I’m digging into the pattern on a black background with a possibly incomplete red line labeled “supplied.” The image’s resolution of 666×800 might need enhancement for more details. [Read more from upload.wikimedia.org] – I’m re-evaluating how to view the image, considering smaller sizes or scrolling to capture the entire content accurately. [Read more from upload.wikimedia.org] – I’m working through the problem of a duplicate image, considering higher resolutions or different aspect ratios to improve quality. [Read more from upload.wikimedia.org] – OK, I’m working through the ‘Delayed Choice’ image issue. The ‘KimDelayedChoiceQuantumEraserGraphsSVG.svg’ file is small but seems promising. Progressing through image choices, I aim to find a suitable candidate. [Read more from upload.wikimedia.org] – Trying different image resolutions and height parameters to match the graph dimensions from the file. Searching for specific graphs to ensure the correct model and version. [Searched for Kim 1999 quantum eraser interference images] – Considering stopping by the StrangePaths blog for the quantum eraser experiment, possibly in Spanish or French. [Read strangepaths.com] – OK, let me see. I’m checking the StrangePaths blog to see if there’s an image at line 19, titled “patterns-01.jpg”. [Read more from strangepaths.com] – Interestingly enough, this excerpt explores how interference patterns emerge when adding fringe distributions. Adding two patterns forms a single distribution, canceling out the interference. Antifringing manages anti-interference patterns effectively. [Read more from strangepaths.com] – The image is small, possibly a preview. It might be scaled down, and the actual file could be larger. [Read more from strangepaths.com] – I’m analyzing a conceptual diagram with D0 correlated with D1 and D2, showing interference and anti-fringes. This progression helps to visualize these quantum mechanics experiments effectively. [Searched for D0 D1 correlation image] – I’m examining websites for PhilSci and StrangePaths. Their content and credibility are top priorities. [Searched for delayed choice quantum eraser Kim graph] – I’m thinking through possible graphs to use, considering the original data’s vectors or reproductions like the wiki vector or StrangePaths colored demonstration. The wiki vector seems ideal due to its probable creation from the actual data. [Read en.wikipedia.org] – I’m examining the “PNG preview” sizes, including 600 x 600, 768 x 768, 1024 x 1024, 2048 x 2048, and 635 x 635 pixels. [Read upload.wikimedia.org] – I’m looking into the ongoing problem with the “Delayed Choice…” file. It seems to be a recurring error. [Read more from upload.wikimedia.org] – I’m exploring reasons for preview issues, considering false positives or image triggers. The “Delayed_Choice_Quantum_Eraser_Graphs.svg” might have small graphs or partial views affecting it. [Read more from upload.wikimedia.org] – I’m piecing together different images, including “er_08.gif” from Hackaday, “patterns-01.jpg” from StrangePaths, and figures from the arXiv paper. [Searched for joint detection rate interference Kim 1999 figure] – I’m examining options like using an open method on ResearchGate or converting PDFs to text or images via Python. The accessibility of images from arXiv PDFs is also being considered. [Searched for Kim quantum eraser interference fringe graph] – Considering ResearchGate for a snippet or R01 and R02 graphs. SCIRP might offer “The Delayed Quantum Eraser Experiment Explained Classically” with possibly similar graphs. [Read scirp.org] – Mapping out Figure 1 as the experimental setup and Figure 2 with unspecified attribution, possibly Wikipedia or StrangePaths. [Read more from scirp.org] – OK, let’s confirm that SCIRP’s Figure 2 is the “Delayed Choice Quantum Eraser Graphs.svg” from Wikimedia, credited to Stigmatella. Now, I’ll check SCIRP’s HTML or PDF for images. [Read more from scirp.org] – I’m figuring out why the HTML isn’t showing or why images might be background. Considering a PDF as an alternative. [Read more from scirp.org] – I’m mapping out the idea of searching for images encoded in the PDF or revisiting the directly accessible wiki file’s version. [Read crossmark-cdn.crossref.org] – OK, let me see. The information is related to Crossmark, but not relevant for this context. [Read scirp.org] – I’m exploring browser debug or image address copying methods due to the absence of an interactive UI. [Read more from scirp.org] – Piecing together the visual elements, I’m working through the PDF content to confirm the image’s placement near its attribution note. [Read more from scirp.org] – I’m thinking about various images like the wiki figure, StrangePaths diagram, or SCIRP figure to illustrate interference patterns. Diagramming apparatus and detectors might clearly highlight results based on idler detector triggers. [Read upload.wikimedia.org] – I’m noting that adjusting the image dimensions to match the file’s original spec (535×445) is essential. Using width=923 might inadvertently set the height to 768, which seems incorrect. [Read commons.wikimedia.org] – I’m considering whether option [108], a thumbnail from “commons.wikimedia.org,” suffices, or if we should directly search for “Kim Delayed Choice quantum eraser graphs” on Google Images for a better match. [Searched for Delayed Choice Quantum Eraser Graphs.svg image] [Read more from commons.wikimedia.org] – I’m noting the image title and file details. It seems to be a standard image without interactivity. [Read more from commons.wikimedia.org] – The text refers to an image and potentially linking it to a specific source, possibly a direct URL or a citation [584]. [Read upload.wikimedia.org] – I’m working through the file paths and their contents, considering their relevance and potential mismatches to ensure the accurate image link is identified. [Read more from upload.wikimedia.org] – I’m working through the image’s black background and potential white lines. Red lines, likely interference patterns, are visible. [Read hackaday.com] – I’m working to find appropriate diagrams and interference patterns, considering background color effects, and ensuring visibility of key elements. [Read strangepaths.com] – Considering StrangePaths image for low resolution, leaning towards SCIRP figure or a clear apparatus diagram to illustrate interference patterns triggered by various detectors. [Read en.wikipedia.org] – I’m looking into StrangePaths’ quantum eraser scheme using a Mach-Zehnder interferometer. Considering a more direct approach for Kim. The Wikipedia article possibly had an explanatory figure, possibly from Commons. The DCQE setup by Kim with SPDC seems relevant. [Searched for D1 D2 D3 D4 quantum eraser diagram] [Searched for delayed choice quantum eraser apparatus diagram D1 D2 D3 D4 D0] – I’m figuring out that the Wikipedia article has an apparatus diagram, likely with an image and a caption describing it, given the mention of a “vertical black line in the upper left corner.” [Read more from en.wikipedia.org] – Pulling together the experiment setup, I identified [407] as the setup diagram and [408] as the graph with R04 supplied. [Read upload.wikimedia.org] – I’m examining the figure’s layout and identifying potential mappings for each curve, particularly focusing on the (supplied) red hump likely representing R04, while R03 might be in black or grey. [Read more from upload.wikimedia.org] – It’s worth noting any GIFs like [409] could possibly be animations, simulations, or straightforward .gif files. [Read more from upload.wikimedia.org] – Thinking through the possibility of a gif being restricted due to moderation rules. [Read more from upload.wikimedia.org] – Identifying core figures** – I’m pulling together L493’s fixed figure and L497’s animated one, with a GIF likely toggling elements. [Read more from upload.wikimedia.org] – Die aktuelle Größe der Abbildungsdatei “Kim_EtAl_Quantum_Eraser.svg” ist zu niedrig, vermutlich bei 401 px. Eine größere Version könnte die Klarheit und Auswirkung verbessern. [Read more from upload.wikimedia.org] – Interestingly enough, I’m verifying how interference patterns shift depending on path detectors, while acknowledging a need to clarify unclear points. [Read more from upload.wikimedia.org] – I’m examining links and images, considering file pages and Wikipedia references. Progress is being made through these evaluations. [Read more from upload.wikimedia.org] – I’m gathering apparatus diagrams and interference patterns from various sources, like SCIRP, philsci, and the S&N blog, to support the analysis. [Read backreaction.blogspot.com] – I’m considering the use of [67] to illustrate a basic concept, while noting its limitations and suggesting alternative approaches to depict interference fringes effectively. [Searched for quantum eraser interference R01 R02 image] – This seems to indicate a need for verification in consulting guidelines. [Read cs.uwaterloo.ca] – I’m pulling together interference patterns and apparatus images. Trying different sources and adjusting contrast for clarity. Progress is steady and intriguing! [Read philsci-archive.pitt.edu] – The PDF evolves from illustrations to pictures, likely due to alignment and word constraints. Progress is steady, akin to a hydraulic lift. [Read upload.wikimedia.org] – Scribing the analysis involves labeling curves, citing sources like Wikipedia for interference patterns, and noting phase shifts in signals detected at various paths. Delayed Choice Quantum Eraser (Kim et al. 1999) – Experiment and Results Experiment Setup (Kim et al., 1999) In 1999, Yoon-Ho Kim and colleagues performed a “delayed-choice quantum eraser” experiment to test how quantum interference can appear or disappear depending on whether which-path information is retained or “erased.” The setup (schematically illustrated below) involved a double-slit illuminated by an argon laser, producing single photons (351 nm) that pass through either slit A or slit B. After the slits, a nonlinear BBO crystal induces spontaneous parametric down-conversion (SPDC), splitting each photon into a pair of entangled photons – one signal photon and one idler photoninterference setup). The idler photon takes a longer path through a system of prisms (PS), beam splitters (BSₐ, BS_b, BS_c), and mirrors (Mₐ, M_b), leading to four possible detectors D₁, D₂, D₃, D₄ on the idler side. Importantly: D₃ or D₄ (“which-path” detectors): If an idler clicks at D₃, it could only have come from slit B; if it clicks at D₄, it could only have come from slit A. Thus D₃ and D₄ provide which-path information about the signal photon. D₁ or D₂ (“eraser” detectors): Idlers arriving at D₁ or D₂ have been recombined at BS_c such that their origin is indistinguishable – these detectors erase the which-path information. No single idler at D₁ or D₂ reveals which slit was taken. The signal detector D₀ is triggered ~8 ns before its entangled idler partner reaches D₁–D₄ (due to shorter path length). A coincidence circuit pairs each D₀ detection with the corresponding idler detection (D₁–D₄). By examining coincident counts (joint detection events), one can post-select subsets of D₀ hits corresponding to a given idler detector. This allows the experimenters to see how the D₀ pattern changes depending on where the idler went, even though D₀ itself, considered alone, shows no clear interference. Figure 1. Delayed-Choice Quantum Eraser Setup (Kim et al. 1999). Simplified diagram of the experiment. A photon passes through a double slit (left), then is split into an entangled signal-idler pair by a BBO crystal. The signal (red or light-blue path) goes to detector D₀. The idler (colored paths going downward) encounters prisms (PS), beam splitters (green) and mirrors (gray), and is ultimately detected at D₁, D₂, D₃ or D₄. Detectors D₃ and D₄ mark the photon’s origin (slit B or A respectively), while D₁ and D₂ erase the which-path information by mixing the paths. A coincidence counter (blue circuits, right) correlates D₀’s signal with each idler detector’s events. [https://raw.githubusercontent.com/karlinarayberinger/KARLINA_OBJECT_extension_pack_34/main/chatgpt_provided_image_28march2025_p0.png] Interference vs. No-Interference in Coincidence Counts Kim et al. recorded the coincidence count distributions at D₀ conditioned on each idler detector. Strikingly, they found that interference fringes appear or vanish depending on which D detector is heralding the idler: Interference Patterns (Fringes) – Eraser Conditions: When considering only those D₀ detections whose idler went to D₁ or D₂, an interference pattern emerges in the joint detection rates. In other words, R₀₁ (coincidences D₀&D₁) and R₀₂ (D₀&D₂) each show a wavy, oscillatory distribution as D₀ is scanned. These fringes are analogous to a Young’s double-slit pattern. However, the two patterns are out of phase by π (peaks of R₀₁ align with troughs of R₀₂). This phase shift is due to the differing path lengths/reflections for D₁ vs. D₂ (the beam splitter BS_c causes one subset of coincidences to interfere with a relative phase). Notably, if you sum R₀₁ + R₀₂, the fringes cancel out, yielding a flat distribution. (This combined sum corresponds to ignoring which idler detector clicked – i.e. the total D₀ pattern, which shows no interference, consistent with complementarity.) No Interference (Clumping) – Which-Path Conditions: In contrast, the subsets of D₀ hits whose idlers went to D₃ or D₄ show no interference pattern. These joint counts – R₀₃ (D₀&D₃) and R₀₄ (D₀&D₄) – exhibit a single broad diffraction envelope (a “blob” distribution) rather than multiple fringes. This is expected because D₃ and D₄ each provide definite which-slit knowledge for every photon, enforcing particle-like behavior with no two-slit interference. In fact, Kim et al. reported “an absence of interference” in R₀₃ (and similarly R₀₄). R₀₃ and R₀₄ were nearly identical apart from a slight shift in the peak position. Crucially, all four coincidence distributions R₀₁, R₀₂, R₀₃, R₀₄ are recorded simultaneously during one scan of D₀. Only when the data is partitioned by idler outcome do the contrasting patterns emerge – even though every signal photon hit D₀ long before its idler’s detection was registered. This demonstrates the “quantum eraser” idea: whether an interference pattern is present in the signal depends on how the entangled idler is measured later. Yet no information or causation actually travels backward in time; the interference is only visible in the subset selection (after correlating with D₁/D₂), and the total D₀ counts (all idlers combined) show no interference at all. Figure 2. Joint-Detection Result – No Interference vs Interference. Example of a coincidence count distribution from Kim et al.’s experiment. Shown here is the R₀₄ subset (signal coincidences when the idler went to D₄), displaying a single broad peak – i.e. no interference fringes. In the actual data, the R₀₁ and R₀₂ subsets each showed interference fringes (peaks and troughs) which were phase-shifted relative to each other. By contrast, R₀₃ and R₀₄ yielded only a smooth diffraction profile. (R₀₄ was not explicitly plotted in the original paper; it is assumed to mirror R₀₃.) [https://raw.githubusercontent.com/karlinarayberinger/KARLINA_OBJECT_extension_pack_34/main/chatgpt_provided_image_28march2025_p1.png] Published Figures and Follow-ups Kim et al.’s original Phys. Rev. Lett. (2000) article included graphs of the coincidence rates: interference fringes for R₀₁ and R₀₂ (Fig. 3 and 4) and a flat distribution for R₀₃ (Fig. 5). The key findings are often depicted in summaries and textbooks. For example, the Wikimedia Commons graphic based on Kim’s data explicitly labels the fringe patterns (R₀₁, R₀₂) versus the “clump” patterns (R₀₃, R₀₄). Many reproductions illustrate that R₀₁ and R₀₂ are complementary interference patterns whose sum recreates the single broad curve of R₀₃/R₀₄. In essence, the interference is there in the conditional data, but hidden in the aggregate. Modern discussions (and even classroom demonstrations) emphasize that selecting subsets by the idler detector is like “filtering” the D₀ hits to reveal interference that is otherwise washed out. Several follow-up studies and explanations have included helpful diagrams of this effect. One visual approach is to color-code the signal hits by the corresponding idler detector. If one plots D₀’s hits tagged by D₁ (say, red) versus those tagged by D₂ (blue), each forms a fringe pattern shifted relative to the other; but when overlaid they sum to a uniform distribution. Conversely, hits tagged by D₃ or D₄ each just form a single hump (no fringes). This reinforces the idea that interference appears only when which-path information is truly unavailable – even though the “choice” to erase or not erase is made after the signal has hit D₀. The Delayed Choice Quantum Eraser experiment thus elegantly demonstrates how entanglement and measurement selection can recover interference from an entangled particle without violating causality. Sources: Kim et al. (1999/2000) original report [ar5iv.org]; Wikipedia summary of Kim’s experiment [en.wikipedia.org]; Hackaday tutorial (2016) [hackaday.com]; StrangePaths explainer (2007) [strangepaths.com]. karbytes: In a different conversation you explained how photons can be made to travel significantly slower than the speed of light. Can the speed of electrons also be manipulated in a laboratory? ChatGPT: Yes, absolutely — the speed of electrons can be and routinely is manipulated in laboratory settings. In fact, electron velocity control is central to fields like electron microscopy, particle accelerators, semiconductor physics, and quantum optics. Let’s walk through some core ideas: 🔋 1. Electron Speed Depends on Energy Unlike photons (which always move at the speed of light in vacuum), electrons have mass, so their speed depends on their kinetic energy. In the lab, we usually control an electron’s speed by applying an electric potential (voltage): The electron gains kinetic energy E_k = q * V, where: q = charge of the electron (~1.6×10⁻¹⁹ C), V = voltage. The classical speed (non-relativistic) is: v = square_root((2 * q * V) / m_e) where m_e is the electron’s mass (~9.11×10⁻³¹ kg). For example: 1 electron-volt → ~593 km/s 10 keV → ~59,300 km/s 1 MeV → ~94% of light speed (requires relativity) ⚙️ 2. Practical Ways to Slow or Control Electrons 🧲 Electric & Magnetic Fields – Electrons can be accelerated or decelerated using fields in cathode ray tubes, electron beams, linear accelerators, and RF cavities. – Magnetic fields don’t change speed directly (they deflect direction), but magnetic lenses are used in electron microscopes to focus and guide electrons. 🧊 Cryogenic Semiconductors – In semiconductors (especially at cryogenic temperatures), electron drift velocity is reduced due to reduced kinetic energy and lattice interactions. – Electrons can be trapped or guided through quantum dots, quantum wells, and 2D materials at controlled speeds. 🧬 Cold Electron Sources – Techniques like photoemission from cooled cathodes produce electrons with very low thermal energy → slower starting speeds. – Useful in ultrafast electron diffraction and quantum optics. 🌪 Slowing via Matter Waves – In electron interferometry, electrons are guided slowly enough to exhibit clear wave-like behavior over large scales (think: de Broglie wavelength increases as velocity decreases). 🧪 Advanced: Ultra-Slow Electron Experiments There are even niche setups (e.g. Rydberg atoms or Penning traps) where electrons are almost motionless, orbiting at large distances or held in magnetic/ionic cages. – Penning traps: electrons (or ions) are held in place and manipulated using combined static magnetic and electric fields. – Motional ground state: used in quantum computing with trapped ions or electrons. Summary Table [preformatted text] Techniques | Electron Speed Effect Voltage acceleration | Increases speed (classic method) Retarding fields | Slows electrons (filters out high energy) Magnetic confinement | Controls direction; stabilizes path Cryogenic environments | Slows electron drift Trapping (e.g., Penning traps) | Can hold electrons nearly motionless Semiconductor nanostructures | Guides electrons at very slow velocities Would you like a visual or simulation showing how voltage or traps affect electron velocity? karbytes: How fast do electrons typically orbit the nucleus of an atom? ChatGPT: Great question — and the answer gets deep fast! Let’s explore it from both classical and quantum standpoints, since atomic electrons don’t really “orbit” like planets — but we can still estimate their typical speeds in various atoms. 🧮 In the Bohr Model (Hydrogen-like atoms) In the early Bohr model, electrons are treated as orbiting the nucleus in circular orbits. While not fully quantum accurate, it gives surprisingly good estimates for hydrogen-like atoms (one electron, like H, He⁺, Li²⁺). For hydrogen (n = 1 energy level), the electron speed is: v = (Z ⋅ α ⋅ c) / n Where: Z = atomic number (1 for hydrogen), α = fine-structure constant ≈ 1/137, c = speed of light ≈ 3.00 × (10 ^ 8) m/s, n = principal quantum number. 🔢 So for hydrogen in the ground state (n=1): v ≈ (1 / 137) * (3.00 * (10 ^ 8)) ≈ 2.19 * (10 ^ 6) m/s That’s roughly 2.2 million meters per second, or about 0.0073c (less than 1% the speed of light). 🔬 In Real Quantum Mechanics In modern quantum theory, electrons exist as probability clouds — they don’t have fixed orbits, but we can still talk about average kinetic energy and thus typical speed. For the hydrogen ground state wavefunction: Average kinetic energy ⟨K⟩ = 13.6 / 2 = 6.8 eV. From this, we estimate: (1 / 2) * (m * (v ^ 2)) = 6.8 eV ⇒ v ≈ 2.19 * (10 ^ 6) m/s So quantum mechanics agrees numerically with Bohr — but interprets things differently. 🧨 For Heavier Atoms (Relativistic Speeds!) For high-Z elements like uranium (Z = 92), inner-shell (1s) electrons move much faster: v ≈ (Z ⋅ α ⋅ c) / n ⇒ v ≈ (92 / 137) ⋅ c ≈ 0.67 c That’s 67% the speed of light — so relativistic corrections are required for accuracy in heavy atoms. This speed increase also affects chemistry (e.g., the color of gold and the liquid nature of mercury at room temperature come from relativistic effects on their electrons). ⚡ Summary Table [preformatted text] Atom | Z Approx. Electron Speed (1s orbital) Hydrogen | 1 ~2.2 × 10⁶ m/s (~0.0073c) Carbon | 6 ~13 × 10⁶ m/s (~0.043c) Iron | 26 ~57 × 10⁶ m/s (~0.19c) Uranium | 92 ~2.0 × 10⁸ m/s (~0.67c) Would you like a visual of these “electron cloud speeds” or a simulation of relativistic vs non-relativistic effects in orbitals? karbytes: Do electrons typically travel around the nucleus of an atom in a random manner? ChatGPT: That’s an insightful question — and the answer gets to the heart of quantum mechanics and how we think about electrons in atoms. The short version is: – Electrons don’t “travel around” the nucleus like planets orbiting the sun. – Instead, they exist as quantum probability clouds — and their position and momentum are not simultaneously well-defined. Let’s break it down: 🔮 1. No Classical Trajectories in Quantum Mechanics In the classical picture, one might imagine an electron as a tiny ball zipping in circles around the nucleus. That’s intuitive, but not accurate in the quantum world. In quantum mechanics: – Electrons are described by wavefunctions (solutions to the Schrödinger equation). – The square of the wavefunction gives the probability density — i.e., where you’re likely to find the electron upon measurement. – Between measurements, we don’t say the electron “is” at a specific point — it’s delocalized. So: electrons don’t follow a path like an orbit; instead, they form standing wave patterns around the nucleus. ☁️ 2. Atomic Orbitals Are Not Orbits What we call “orbitals” (1s, 2p, 3d, etc.) are probability distributions. – A 1s orbital (hydrogen’s ground state) is a spherical cloud — the electron is equally likely to be found in any direction at a given distance from the nucleus. – A 2p orbital is dumbbell-shaped — showing regions where the electron is more likely to be detected. – These shapes are fixed by quantum numbers and remain stationary over time unless disturbed. So rather than moving randomly around the nucleus, the electron exists in a kind of fuzzy, standing wave that defines regions where it’s more or less likely to appear. 🌀 3. Motion Still Exists — But It’s Not Random “Traveling” Even though electrons don’t orbit in the classical sense, they still have kinetic energy and non-zero momentum — especially in excited states. – Their motion is quantum-mechanical, meaning we can’t assign them a definite trajectory. – In time-dependent interpretations (or under perturbations), the probability cloud can shift, or electron density can “slosh” — but not in a random bouncing-ball way. 🧠 So What Is “Random” About It? The position where you detect an electron is fundamentally probabilistic: – You can’t predict exactly where it will be. – But you can know the probability distribution. – Over many measurements, the detections will match the orbital shape. So the randomness is in the outcome of position measurements, not in some erratic motion. 📌 In Summary: [preformatted text] Classical Analogy | Quantum Reality Electron orbits nucleus | Electron exists as a cloud of probability Predictable trajectory | Only probabilities of where it may be Moves like a planet | Behaves like a standing wave Random bouncing | Statistically distributed over space Would you like to see animations or visualizations of atomic orbitals or time-dependent electron density? karbytes: Are electrons or photons ever motionless (i.e. traveling at zero velocity)? ChatGPT: Excellent question — and it cuts to the core of how we define motion, energy, and observables in quantum physics. Let’s tackle photons and electrons separately, since their physical properties and constraints are quite different. ⚛️ PHOTONS: Are Never Motionless Photons are massless particles, and in physics, massless particles must always travel at the speed of light in a vacuum: v_photon = c = 299,792,458 m/s So: ❌ Photons can never be at rest. ❌ There is no reference frame in which a photon is stationary. ✅ They can be slowed down in media (e.g., glass, Bose-Einstein condensates), but this is due to interactions — their fundamental speed remains c between interactions. 🧲 ELECTRONS: Can Be Motionless (in principle) Electrons have mass, so they can be at rest relative to some reference frame — though this comes with quantum caveats. 🔹 In Classical Physics: – Yes — an electron at rest has zero velocity and rest energy E=mc2E=mc2. – You can hold an electron still in, say, an electric trap or vacuum chamber. 🔹 In Quantum Mechanics: The Heisenberg uncertainty principle applies: Δx ⋅ Δp ≥ ℏ2 So: if an electron has exactly zero momentum (i.e., is truly motionless), then its position is infinitely uncertain (i.e., it could be anywhere in the universe). ➤ This makes a perfectly motionless electron unphysical. 🔹 But… electrons can be very nearly at rest: – In Penning or Paul traps, electrons can be confined and cooled to have extremely low kinetic energy. – In solid-state systems, such as quantum dots, electrons can be trapped in effectively motionless states. – In Bose-Einstein condensates, electrons within atoms can have very low momenta. So: ✅ Yes, electrons can be motionless (or nearly so) in a given frame. But: their wavefunction spreads out, so “motionless” doesn’t mean “stuck at a point.” 🧊 Real-World Example: Electrons in a Trap In a Penning trap (combining electric and magnetic fields): – Electrons can be cooled to microkelvin temperatures. – Their thermal motion is drastically reduced. – They can remain nearly stationary for seconds or more. 🚫 Final Comparison: [preformatted text] particles | Can Be at Rest? | Why / Why Not Photons | ❌ | Never Massless ⇒ must travel at c Electron | ✅ Sometimes | Has mass ⇒ can be slowed, but quantum limits apply Would you like a breakdown of trapping methods for electrons or visualizations of wavefunctions for “slow” electrons? karbytes: What happens to electrons which are trapped in specific data-representing configurations inside of USB flash drives (which are at room temperature (i.e. 20 degrees Celsius) instead of close to zero Kelvin)? ChatGPT: Ah, you’ve hit a very cool intersection of solid-state physics, quantum mechanics, and information storage. Let’s unpack what happens to electrons trapped in data-storing configurations inside a USB flash drive, especially at room temperature (around 20°C or 293K). 🧠 Summary First: – In a USB flash drive, electrons are deliberately trapped in tiny insulating regions called floating gates inside transistors. – These trapped charges represent binary data (0s and 1s) — and they stay put, even at room temperature, because the surrounding material is highly insulating and the traps are engineered to hold charge stably for years. 🔌 What is Actually Storing the Data? USB flash drives use NAND flash memory, which consists of arrays of floating-gate field-effect transistors (FGFETs). 🔹 Each memory cell stores 1 or more bits – A “1” or “0” is stored by the presence or absence of electrons in a floating gate. – The floating gate is an electrically isolated conductor (often polysilicon) surrounded by insulating oxide. – When electrons are injected into this gate (via tunneling), they get stuck — this shifts the threshold voltage of the transistor. Depending on that voltage shift, a read operation can tell whether the cell holds a 1 or 0. 🔋 How Are Electrons Trapped? ➤ Electron Injection (Write Operation): – A high voltage is applied, creating a strong electric field. – Electrons are pushed (via Fowler–Nordheim tunneling or hot-electron injection) through the insulating barrier and into the floating gate. ➤ Electron Retention (Storage): – Once in the floating gate, electrons are surrounded by insulating material (e.g., silicon dioxide). – With no conductive path out, the electrons stay trapped — like flies in a glass jar. 🌡️ What Happens at Room Temperature? At room temperature (∼20°C / 293K): – Electrons remain trapped in the floating gate. – Thermal energy (kT ≈ 25 meV) is far too low to knock electrons out of the trap by itself. – The barriers surrounding the gate are typically several electron-volts high (e.g., 3–5 eV), so spontaneous escape is extremely rare. – That’s why USB drives retain data for years, even in your pocket. 📌 Thermally activated tunneling or leakage is possible but exponentially suppressed unless: – The device is old or has seen many write/erase cycles (oxide degradation), – The temperature is extremely high (e.g. > 85°C), – Or the materials are defective. 💥 How Long Do They Last? Typical data retention specs for consumer-grade flash memory: Condition Expected Retention [preformatted text] Brand new, room temp | 10+ years After many writes | 1–3 years (degrades over time) High-temp storage | Shortened lifespan 🧠 So… Are the Electrons Moving? Not really. Once trapped: – The electrons are localized in quantum wells in the floating gate. – Their wavefunctions are spread out in a small region (~nanometers), – But they don’t travel or drift — they’re effectively stationary (within the quantum trap). They still exist as quantum objects with kinetic energy, but they’re not moving across the chip, nor “orbiting” anything. 🧬 Bonus: Quantum View From a quantum standpoint: – Electrons occupy discrete energy levels in the floating gate potential. – Tunneling back out (loss) is possible, but the probability per unit time is exponentially tiny. – The system is designed to make the lifetime of the trapped state much longer than the expected usage period. 🧊 In contrast: What if cooled close to 0 K? – Lower temperatures would make tunneling even less likely. – But room temperature is already sufficient for years of stability. – Cooling is not required — flash drives are engineered to be stable at ambient temps. 🔚 Summary: [preformatted text] Property | Electron Behavior in USB Flash Drive Trapped or Free? | Trapped in floating gate Mobile? | No – electrostatically confined Motionless? | Quantum confined; not moving across gates Room Temperature Stability | Very stable – data lasts years Escape Mechanism? | Only via tunneling, and very rare Would you like a diagram of how a floating-gate transistor works or a breakdown of what happens during a read/write/erase cycle at the electronic level? karbytes: Can electrons teleport from one location to another even from within the confines of an enclosing barrier? ChatGPT: Yes — but not in the science-fiction sense of “teleportation.” In quantum mechanics, electrons can appear to “pass through” barriers they classically shouldn’t be able to cross. This is known as quantum tunneling — and it’s very real, very well-understood, and experimentally confirmed. Let’s break it down in clear terms: ⚛️ What Is Quantum Tunneling? – Quantum tunneling is the phenomenon where a particle has a finite probability of being detected on the other side of a potential energy barrier, even though it doesn’t have enough classical energy to climb over it. This is not teleportation in the sense of instantaneous or distance-defying travel, but it does violate classical intuition. 🔹 Imagine This: – An electron is trapped in a well (like a valley) with walls on both sides. – The electron doesn’t have enough energy to climb the walls — classically, it should stay inside forever. – But quantum mechanically, the electron is described by a wavefunction that “leaks” into the walls and beyond. – There’s a non-zero probability that the electron will be found outside the well, having “tunneled” through the barrier. 🌀 It didn’t physically drill a hole, climb over, or burst through — its presence just “appears” on the other side based on quantum probabilities. 🚪 Real-World Examples of Tunneling [preformatted text] Phenomenon | Description Flash memory (USBs) | Electrons tunnel into or out of floating gates to store data. Nuclear fusion | Protons tunnel through electrostatic repulsion to fuse in stars. Alpha decay | Nuclei emit alpha particles via tunneling through the nuclear barrier. Tunnel diodes | Special electronics that exploit tunneling for fast switching. Scanning Tunneling Microscopes (STM) | Detect tunneling electrons to image atoms. 🧪 What Determines the Probability of Tunneling? – Barrier width: thinner barriers → higher tunneling chance. – Barrier height: lower energy barriers → higher tunneling chance. – Electron energy: more energetic electrons → higher tunneling chance. Mathematically, the tunneling probability TT roughly follows: T ∝ e ^ (−2 * κ * d) where κ = square_root((2 * m * (V − E)) / ℏ) d = barrier width V = barrier height E = particle energy m = particle mass ℏ = reduced Planck constant 🚫 Is This Teleportation? Not in the Star Trek sense: ✅ The electron moves according to its quantum wavefunction. ❌ It does not vanish in one spot and reappear instantly somewhere else. ✅ But it violates classical confinement — it can exist in places with “forbidden” energy. That’s why quantum tunneling is sometimes described metaphorically as “quantum teleportation,” but it’s fundamentally just wavefunction evolution under the rules of quantum physics. 🧠 Bonus: Does It Violate Causality? Nope. Tunneling still respects relativistic causality and local conservation laws — but it plays by the probabilistic rules of quantum theory. 📌 Summary: [preformatted text] Concept | Quantum Tunneling Occurs through barriers? | ✅ Yes — even with insufficient classical energy Instantaneous jump? | ❌ No — it follows quantum evolution, not magic Real or theoretical? | ✅ Real — used in devices and observed in nature Like sci-fi teleportation? | ❌ Not quite — but weird and non-classical Would you like to see a simple simulation or diagram showing how an electron wavefunction tunnels through a potential barrier? karbytes: Does the electron have to be able to have an unobstructed pathway around a barrier in order to move from one side of that barrier to the other side? ChatGPT: No — the electron does not need an unobstructed pathway around a barrier to move from one side to the other. That’s the weird and fascinating nature of quantum tunneling: – An electron can cross a barrier without physically going around it — even if the barrier completely encloses the region like a sealed box. Let’s explore why that’s possible. 🔮 Quantum Perspective: It’s About the Wavefunction In quantum mechanics, an electron is not a little ball that travels in a single trajectory — it’s described by a wavefunction that assigns a probability amplitude to every location in space. When that wavefunction encounters a barrier (say, a region of high potential energy): – It doesn’t stop abruptly. – Instead, it extends into the barrier and decays exponentially inside it. – If the barrier is thin enough, that wavefunction can “leak through” to the other side. This allows for a non-zero probability that a measurement will find the electron on the far side, even if it couldn’t classically climb over or go around. 🧱 Think of This Analogy – Classical world: A marble in a box can’t escape unless there’s a hole. – Quantum world: An electron “feels” the other side of the wall through its wavefunction. If the wall is thin enough (on the quantum scale), it can be detected outside, even though it didn’t go around or over. No opening is required. No slits, no tunnels, no gaps — just a thin enough energy barrier, and quantum mechanics takes care of the rest. 🧪 Real Example: Alpha Decay in Nuclei In radioactive decay: – An alpha particle is trapped inside a nucleus by a high potential energy wall. – It tunnels through the nuclear barrier and escapes — even though there’s no pathway out in the classical sense. – This is observed and measured regularly in nuclear physics. ⚠️ So What’s the Limitation? The barrier must not be infinitely thick or infinitely high. If the barrier is: – Too wide → tunneling probability drops exponentially. – Too high in potential energy → same effect. But: If the barrier is finite (even completely enclosing the electron), there’s always some tunneling probability, though it might be vanishingly small. 🚫 Important Clarification ✅ Tunneling is a genuine quantum phenomenon — it’s not about finding secret gaps. ❌ It does not mean the electron is “squeezing through” a crack. ✅ The barrier can be solid, continuous, and sealed — and tunneling can still occur. 🧠 Summary [preformatted text] Question | Answer Must there be a path around the barrier? | No Can an electron tunnel through a sealed barrier? | Yes (if it's thin or low enough) Does this violate physics? | No — it's predicted by quantum mechanics Is there a classical analogy? | Not really — this is uniquely quantum Would you like a visual showing an electron’s wavefunction penetrating and tunneling through a barrier — even one that wraps around the region completely? karbytes: Yes please! ChatGPT: [python] import matplotlib.pyplot as plt import numpy as np # Constants for visualization x = np.linspace(-10, 10, 1000) barrier_center = 0 barrier_width = 2 barrier_height = 5 # Define potential energy barrier V = np.zeros_like(x) V[np.abs(x - barrier_center) < barrier_width / 2] = barrier_height # Define a decaying wavefunction for tunneling (qualitative) def wavefunction(x): wf = np.zeros_like(x) for i in range(len(x)): if x[i] < -1.0: wf[i] = np.cos(x[i]) * np.exp(0.1 * x[i]) elif -1.0 <= x[i] <= 1.0: wf[i] = np.exp(-2.0 * np.abs(x[i])) else: wf[i] = np.exp(-0.3 * x[i]) return wf psi = wavefunction(x) # Plotting plt.figure(figsize=(12, 6)) plt.plot(x, psi, label='Electron Wavefunction (|ψ|)', color='blue') plt.plot(x, V, label='Potential Barrier', color='red', linestyle='--') plt.axvspan(-barrier_width/2, barrier_width/2, color='red', alpha=0.1, label='Barrier Region') plt.title("Quantum Tunneling: Electron Wavefunction Through a Potential Barrier") plt.xlabel("Position (x)") plt.ylabel("Amplitude / Energy") plt.legend() plt.grid(True) plt.tight_layout() plt.show() Quantum Tunneling: Electron Wavefunction Through a Potential Barrier [https://raw.githubusercontent.com/karlinarayberinger/KARLINA_OBJECT_extension_pack_34/main/chatgpt_generated_image_28march2025_p0.png] Here’s a visual representation of quantum tunneling: – The blue curve shows the electron’s wavefunction (∣ψ∣∣ψ∣) — notice how it decays inside the red barrier region, yet still extends beyond it. – The red dashed line and shaded area represent the potential energy barrier — a region the electron shouldn't classically be able to cross. – Despite the barrier being solid and continuous, the electron's wavefunction leaks through, meaning there's a non-zero chance the electron can be found on the other side. This is a classic signature of quantum tunneling — no path around the barrier is needed, and yet the electron can still emerge on the far side. Would you like to explore how tunneling probabilities change with barrier height or width? karbytes: In order to pass through the wall of a box, does an electron have to turn into pure energy rather than remain as a mass-containing particle? ChatGPT: No — an electron does not need to turn into “pure energy” or lose its mass in order to tunnel through a wall or potential barrier. Let’s break this down clearly: 🧲 Tunneling Doesn’t Require Annihilation When an electron tunnels through a barrier, it remains an electron: – It retains its mass, charge, and identity. – It does not transform into a photon, wave of energy, or any other particle. – It simply moves from a region where it’s classically allowed to be, through a classically forbidden zone, and into another allowed region — all as a particle governed by quantum mechanics. 🔹 Its wavefunction temporarily has non-zero amplitude inside the barrier, but the electron itself is not “converted” into something else. ⚡ What About Turning Into “Pure Energy”? The phrase “pure energy” usually refers to massless particles (like photons) or energy liberated during matter-antimatter annihilation. But: – An electron doesn’t need to annihilate to move through matter. – No photon or boson conversion is necessary during tunneling. – Energy is conserved — and the electron’s total energy remains the same (even though the potential energy in the barrier is higher). It’s like this: – The electron “borrows” probability to exist in the classically forbidden zone — but not mass or identity. This is totally consistent with the uncertainty principle and the nonzero width of quantum particles. 🌀 Is There a Time or Energy Violation? Sort of — in spirit, not in math. In quantum tunneling: – The electron seems to “violate” energy conservation locally, because it’s in a region where its total energy E is less than the potential V. – But this is not a real violation — it’s a feature of the wavefunction-based model, not a breakdown of physics. There’s no need to invoke special transformations. Just standard quantum mechanics. 🧠 Analogy: Shadow on a Wall Think of an electron’s wavefunction like a shadowy blur: – Even if the wall blocks the main “body,” the blur leaks through. – If the wall is thin enough, that blur extends to the far side. – The electron doesn’t change form — it just has a small chance of “showing up” on the other side. 🧬 Quantum Particle Identity Is Preserved Electrons are fermions with: – Mass = 9.11 * (10 ^ -31) kg – Charge = −1e – Spin = 1/2 None of that changes during tunneling. It’s a quantum leap, not a transformation. ✅ Summary [preformatted text] Question | Answer Does an electron lose its mass? | ❌ No Does it become “pure energy”? | ❌ No Does it stay an electron? | ✅ Yes Is this a normal quantum process? | ✅ Yes — it's well understood and real Does it violate conservation laws? | ❌ No — energy is globally conserved Would you like to explore how this relates to phenomena like virtual particles, Hawking radiation, or quantum teleportation (in the entanglement sense)? karbytes: Yes. Describe each of those things in explicit detail. ChatGPT: [Memory updated] Awesome — let’s dive deep into each of these fascinating quantum phenomena. We'll go one at a time and build them up clearly from first principles: 🌀 1. Virtual Particles ❓ What are they? Virtual particles are temporary disturbances in a quantum field that arise during particle interactions. They’re not directly observable, but they mediate forces in quantum field theory (QFT), like the electromagnetic or strong nuclear force. – Think of them as “mathematical scaffolding” inside quantum processes — essential to the calculations but never directly measured. 🧮 Where do they appear? In Feynman diagrams, virtual particles are represented by internal lines (as opposed to external lines, which represent real particles entering/leaving a system). They appear and vanish in accordance with the uncertainty principle: ΔE ⋅ Δt ≳ ℏ This allows a particle to "borrow" energy to briefly exist as a fluctuation — but only for a short time. 📌 Key features: – Off-shell: Virtual particles do not obey the classical energy–momentum relation (E ^ 2) = ((p * c) ^ 2) + ((m * (c ^ 2)) ^ 2). – Never directly detected. – Appear in intermediate states during interactions, e.g.: + An electron emits a virtual photon, which is absorbed by another electron — this is the quantum description of electric repulsion. + Gluons exchanged between quarks are also virtual. 🧠 Why do we use them? They're tools for computing probabilities in perturbation theory (QED, QCD, etc.). They’re part of the path integral formulation where all possible interaction paths are summed over — and virtual particles fill the space between initial and final real particles. 🌌 2. Hawking Radiation ❓ What is it? Hawking radiation is a quantum process predicted by Stephen Hawking in 1974 that causes black holes to emit radiation and gradually lose mass, eventually evaporating. 🧠 The core idea: Near the event horizon of a black hole, quantum fluctuations can produce virtual particle-antiparticle pairs. Normally, such pairs annihilate almost immediately. But: – If one particle falls into the black hole while the other escapes, – The escaping particle becomes real (detectable radiation), – The one that falls in has negative energy relative to the outside, – So the black hole’s mass decreases. 🧮 This is how the mass-energy of the black hole gets converted into outgoing radiation. 🔥 Why is this wild? – Black holes glow, even though nothing can escape from inside the event horizon. – Over immense time scales, black holes can evaporate completely. – The radiation is nearly thermal — resembling blackbody radiation. 📌 Key aspects: [preformatted text] Property | Description Origin | Quantum field theory in curved spacetime Requires event horizon? | Yes Is energy conserved? | Yes — energy is drawn from the black hole Directly observed? | ❌ Not yet (but strong theoretical support) 🔗 3. Quantum Teleportation (via Entanglement) ❓ What is it? Quantum teleportation is a protocol that transfers the state of a quantum system from one location to another — using entanglement and classical communication, but not faster than light. – You're not “moving a particle” — you’re transferring its quantum state (e.g., spin, polarization) onto another particle that’s entangled with it. 🧪 How it works: Let’s say Alice and Bob each hold one half of an entangled pair of qubits. Alice has a third particle whose state she wants to teleport to Bob. – Entangle particles A (Alice) and B (Bob). – Alice performs a Bell-state measurement on her entangled particle and the third particle (the one with the unknown state). – She sends the result (2 classical bits) to Bob. – Bob uses that info to apply a specific quantum gate to his particle. – The state of the original third particle is now encoded in Bob’s qubit — even though the particle itself never traveled. 📌 What makes it cool? – It uses entanglement as a resource. – It transfers full quantum information. – But: it still requires classical communication, so it cannot violate causality or send signals faster than light. 🔒 No Cloning Allowed Teleportation destroys the original quantum state during the process. This complies with the no-cloning theorem, which forbids copying unknown quantum states. 🚀 Summary Table [preformatted text] Phenomenon | Role of Energy | What Moves or Changes? | Quantum Weirdness Level Virtual Particles | Borrowed from vacuum | Nothing real; mediates forces | 🔹 Subtle Hawking Radiation | Drawn from black hole | Mass evaporates into photons | 🔸 Wild Quantum Teleportation | Quantum state is transferred | State moves; particle stays | 🔸🔸 Deeply weird Would you like a visual diagram of one or more of these processes? Or explore how they connect to quantum computing, gravity, or time perception? karbytes: I was curious as to whether or not electrons have ever been observed to collide with each other (especially while they each are orbiting an atom's nucleus). ChatGPT: Yes — electrons can and do collide with each other, both in free space and within atoms. These collisions are well-studied in atomic physics, plasma physics, particle accelerators, and condensed matter systems. But when you bring up electrons orbiting atomic nuclei, that invites a more nuanced look, because: – In atoms, electrons aren't little balls orbiting in fixed paths — they exist as quantum clouds (orbitals). – But within that framework, electron-electron interactions and effective “collisions” absolutely occur — and they shape much of atomic behavior. Let’s unpack both ideas. ⚛️ 1. Electron Collisions in Free Space (Well-Observed) This is the most direct kind of observation: – In particle accelerators, electron–electron scattering is routinely observed and precisely measured. – These experiments test predictions from quantum electrodynamics (QED). – The scattering angle and energy distribution match theoretical predictions extremely well. These collisions show repulsion due to the Coulomb force and exchange virtual photons, as predicted. 🧲 2. Electron Collisions in Plasmas and Conductors In environments like: – Stars and fusion reactors (plasmas), – Semiconductors and metals (electron gases), Electrons are not bound to nuclei, and they frequently scatter off each other. – These are also called electron-electron interactions. – They contribute to resistance, thermal conductivity, and quantum transport effects. – In Fermi liquids (like conduction electrons in metals), collisions happen under Pauli exclusion constraints — only between electrons in distinguishable states. ☁️ 3. Inside Atoms: Do Orbiting Electrons Collide? This is trickier — because electrons in atoms are not “orbiting” like planets. Instead: – They occupy standing wave patterns (orbitals) with specific quantum numbers. – These orbitals are delocalized — meaning their exact position isn’t defined. – However: electrons interact through Coulomb repulsion and exchange interactions — even when confined to their respective orbitals. 🔹 Do They "Collide" in Atoms? Not in the classical sense. But: – There is a non-zero probability of two electron wavefunctions overlapping in space. – When that happens, the Coulomb repulsion increases — and the atom’s total energy reflects that. – This is accounted for in multi-electron atomic models, like the Hartree–Fock method and beyond. – These interactions shape the energy level structure (e.g., electron correlation, exchange energy, spin pairing effects). So: we don’t “see” two electrons bump into each other like marbles — but their quantum fields repel each other, and this has measurable consequences. 🧪 Bonus: Observing Electron–Electron Scattering – In colliding beam experiments, like SLAC or CERN, electrons are smashed into other electrons or positrons. – The results verify QED with extraordinary precision. – Elastic scattering: Electrons bounce off each other, conserving energy. Inelastic scattering: Energy is transferred; possible creation of photons or other particles. 🧬 Summary [preformatted text] Context | Do Electrons Collide? | Nature of Collision Free electrons in vacuum | ✅ Yes | Elastic/inelastic scattering Inside plasmas or conductors | ✅ Yes | Frequent scattering events Within atoms (“orbiting”) | ⚠️ Sort of | Quantum interactions, not classical hits High-energy physics experiments | ✅ Yes | Well-documented & precisely modeled Would you like to see a diagram of electron scattering (e.g., Feynman diagrams), or models of electron repulsion inside multi-electron atoms like helium or carbon? karbytes: Yes please! All the above. ChatGPT: [python] import matplotlib.pyplot as plt import matplotlib.patches as patches # Create figure fig, ax = plt.subplots(1, 3, figsize=(18, 6)) # ------------------------------ # Subplot 1: Free Electron Scattering # ------------------------------ ax[0].set_title("Free Electron Scattering (Elastic)") ax[0].set_xlim(-5, 5) ax[0].set_ylim(-3, 3) ax[0].arrow(-4, -1, 3, 1, head_width=0.2, head_length=0.3, fc='blue', ec='blue') ax[0].arrow(4, 1, -3, -1, head_width=0.2, head_length=0.3, fc='green', ec='green') ax[0].arrow(0, 0, 2, 1, head_width=0.2, head_length=0.3, fc='blue', ec='blue') ax[0].arrow(0, 0, -2, -1, head_width=0.2, head_length=0.3, fc='green', ec='green') ax[0].text(-2.5, -1.5, "Incoming e⁻", color='blue') ax[0].text(2.5, 1.5, "Incoming e⁻", color='green') ax[0].text(2.2, 1.2, "Scattered e⁻", color='blue') ax[0].text(-3.5, -2, "Scattered e⁻", color='green') ax[0].axis('off') # ------------------------------ # Subplot 2: Electron Repulsion Inside Atom # ------------------------------ ax[1].set_title("Electron-Electron Repulsion in Atom") nucleus = patches.Circle((0, 0), 0.2, color='black') orbit1 = patches.Circle((0, 0), 1.0, fill=False, linestyle='--') orbit2 = patches.Circle((0, 0), 1.5, fill=False, linestyle='--') electron1 = patches.Circle((1, 0), 0.1, color='blue') electron2 = patches.Circle((-1.5, 0), 0.1, color='green') ax[1].add_patch(nucleus) ax[1].add_patch(orbit1) ax[1].add_patch(orbit2) ax[1].add_patch(electron1) ax[1].add_patch(electron2) ax[1].arrow(1, 0, 0.3, 0.3, head_width=0.05, head_length=0.1, fc='blue', ec='blue') ax[1].arrow(-1.5, 0, -0.3, 0.3, head_width=0.05, head_length=0.1, fc='green', ec='green') ax[1].set_xlim(-2, 2) ax[1].set_ylim(-2, 2) ax[1].axis('off') # ------------------------------ # Subplot 3: Feynman Diagram # ------------------------------ ax[2].set_title("Feynman Diagram: Electron-Electron Scattering") # Draw incoming electrons ax[2].arrow(1, 1, 2, -1, head_width=0.1, head_length=0.2, fc='blue', ec='blue') ax[2].arrow(1, -1, 2, 1, head_width=0.1, head_length=0.2, fc='green', ec='green') # Draw virtual photon ax[2].plot([3, 3], [0.5, -0.5], 'k--') ax[2].text(3.1, 0, "γ*", fontsize=12) # Draw outgoing electrons ax[2].arrow(3, -0.5, 2, -1, head_width=0.1, head_length=0.2, fc='green', ec='green') ax[2].arrow(3, 0.5, 2, 1, head_width=0.1, head_length=0.2, fc='blue', ec='blue') ax[2].text(1.5, 1.1, "e⁻ in", color='blue') ax[2].text(1.5, -1.3, "e⁻ in", color='green') ax[2].text(5.2, 1.1, "e⁻ out", color='blue') ax[2].text(5.2, -1.3, "e⁻ out", color='green') ax[2].axis('off') plt.tight_layout() plt.show() Feynman Diagram: Electron-Electron Scattering [https://raw.githubusercontent.com/karlinarayberinger/KARLINA_OBJECT_extension_pack_34/main/chatgpt_generated_image_28march2025_p1.png] Here are three diagrams illustrating different forms of electron–electron interactions: 1. Free Electron Scattering (Left Panel) – Two electrons approach each other from opposite directions. – Due to their mutual Coulomb repulsion, they scatter away. – This is a classic setup in vacuum experiments or accelerator physics. – Elastic scattering: total kinetic energy is conserved. 2. Electron Repulsion in an Atom (Middle Panel) – Two electrons occupy different orbitals around a nucleus (black circle). – Even though they aren't "orbiting" like planets, their probability clouds can overlap. – When they come close, Coulomb repulsion pushes them apart. – This interaction is built into quantum mechanical models of atoms, affecting orbital shapes and energy levels. 3. Feynman Diagram (Right Panel) – This is a quantum field theory (QED) view of electron–electron scattering. – Electrons interact by exchanging a virtual photon (γ*). – These calculations precisely predict cross-sections and scattering angles. – Virtual particles exist briefly inside the diagram but are never directly observed. Would you like to simulate actual scattering angles, compare with experimental results, or see quantum wavefunction overlap animations inside atoms? karbytes: What you provided thus far in this conversation is sufficient for my purposes (of transcribing it into a karbytes blog post). Thanks for your invaluable assistance! ChatGPT: You're very welcome! I'm honored to have contributed to your exploration — and to be part of the journey that becomes a new karbytes blog post. If you ever want to expand on any of these topics (or dive into new ones), I’ll be here to assist with diagrams, clarifications, or narrative structure. Looking forward to the published piece — and thank you for such deeply thoughtful questions. 🚀🧠💫