Reformulating the Quantum Uncertainty Relation through Geometric Illustrations

<div>The geometric correlation existing within the 3-dimensional real space between the quantum state <svg height="18.6967pt" id="M62" style="vertical-align:-1.778799pt" version="1.1" viewbox="-0.0498162 -16.9179 13.3532 18.6967" width="13.3532pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0091,0,0,-0.0091,.163,-10.994)"><path d="M588 236V289H72V236H588Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,4.351,-10.994)"><path d="M935 263C895 299 821 372 745 456L719 439L824 289H72V236H823L719 87L745 70C821 154 895 227 935 263Z"></path></g><g transform="matrix(.013,0,0,-0.013,2.758,-1.651)"><path d="M570 304C570 398 525 448 414 448C385 448 343 445 312 434L329 511L321 518C297 504 262 482 244 460L233 411C195 397 159 381 128 358L135 332C160 347 189 360 224 373L111 -147C97 -210 84 -218 17 -231L13 -257L254 -247L259 -218L233 -216C183 -212 177 -202 189 -142L218 -1C238 -10 266 -12 283 -12C351 3 429 48 483 105C543 168 570 242 570 304ZM482 289C482 161 380 33 304 33C278 33 248 51 233 69L303 396C326 400 352 403 369 403C428 403 482 380 482 289Z"></path></g></svg> and various observables like <span class="nowrap"><svg height="14.9452pt" id="M63" style="vertical-align:-0.04990005pt" version="1.1" viewbox="-0.0498162 -14.8953 13.3532 14.9452" width="13.3532pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0091,0,0,-0.0091,.294,-8.971)"><path d="M588 236V289H72V236H588Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,4.482,-8.971)"><path d="M935 263C895 299 821 372 745 456L719 439L824 289H72V236H823L719 87L745 70C821 154 895 227 935 263Z"></path></g><g transform="matrix(.013,0,0,-0.013,3.325,-.45)"><path d="M483 97L471 123C436 91 401 65 392 65C388 65 384 74 390 106C414 239 444 378 457 429L455 433C444 433 429 436 416 439C392 444 368 448 344 448C281 448 204 415 152 376C71 315 23 205 23 103C23 21 57 -12 85 -12C114 -12 149 6 185 34C231 70 285 119 329 183H331L309 81C292 0 308 -12 326 -12C350 -12 421 24 483 97ZM374 387C370 363 356 291 345 261C315 193 181 50 139 50C124 50 110 71 110 118C110 224 153 331 218 379C238 394 271 402 301 402C329 402 359 394 374 387Z"></path></g></svg>,</span> <span class="nowrap"><svg height="17.979pt" id="M64" style="vertical-align:-1.419901pt" version="1.1" viewbox="-0.0498162 -16.5591 13.3532 17.979" width="13.3532pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0091,0,0,-0.0091,.555,-10.635)"><path d="M588 236V289H72V236H588Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,4.743,-10.635)"><path d="M935 263C895 299 821 372 745 456L719 439L824 289H72V236H823L719 87L745 70C821 154 895 227 935 263Z"></path></g><g transform="matrix(.013,0,0,-0.013,3.567,1.214)"><path d="M452 333C452 398 425 448 375 448C329 448 235 404 140 292H138L229 683C233 701 234 712 225 712C208 712 149 686 66 677L64 652H97C135 652 140 651 129 598L38 167C23 96 29 57 44 33C60 7 98 -12 132 -12C169 -12 232 3 290 41C383 102 452 223 452 333ZM365 316C365 199 308 87 239 49C221 39 200 35 183 35C137 35 99 70 112 163C116 191 123 215 129 233C190 316 290 392 330 392C348 392 365 372 365 316Z"></path></g></svg>,</span> and <svg height="14.9452pt" id="M65" style="vertical-align:-0.04990005pt" version="1.1" viewbox="-0.0498162 -14.8953 13.3532 14.9452" width="13.3532pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0091,0,0,-0.0091,.555,-8.971)"><path d="M588 236V289H72V236H588Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,4.743,-8.971)"><path d="M935 263C895 299 821 372 745 456L719 439L824 289H72V236H823L719 87L745 70C821 154 895 227 935 263Z"></path></g><g transform="matrix(.013,0,0,-0.013,3.978,-.45)"><path d="M383 397C383 424 344 448 299 448C244 448 172 409 132 375C66 319 23 227 23 146C23 42 74 -12 146 -12C208 -12 298 30 359 103L343 124C315 95 248 48 192 48C145 48 111 85 111 163C111 228 129 294 151 330C171 363 201 401 241 401C275 401 302 384 325 356C332 347 339 344 348 348C373 360 383 381 383 397Z"></path></g></svg> is depicted. This figure is copied from Ref. [<a href="/journals/ahep/2023/6703001/#B1">1</a>].</div>

Advances in High Energy Physics

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Figure 1

Figure 1: Reformulating the Quantum Uncertainty Relation through Geometric Illustrations 