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目录中的所有方程，每件商品一行。

  1. Null Beacon – Cosmic Event Horizon / Causal Disconnect Physics T-ShirtT-Shirt \[d_{\text{EH}}(t) = a(t)\int_{t}^{\infty} \frac{c\,dt^{\prime}}{a(t^{\prime})}\]\[d_{\text{EH}} \to \frac{c}{H_\Lambda} \quad (\text{pure de Sitter})\]
  2. Ole Rømer Sticker – Io Isn’t Late. Light Is. | Physics StickerPaper products \[\Delta t = \frac{\Delta d}{c}\]\[\begin{gathered} \frac{2\,\text{AU}}{c} \approx 998\ \text{s} \approx 16.6\ \text{min} \\ (\text{R\o mer's estimate} \approx 22\ \text{min}) \end{gathered}\]\[c = 299\,792\,458\ \text{m/s (exact)}\]
  3. Orbitick – GPS Clock Correction / Gravitational Time Dilation Physics StickerPaper products \[\frac{\Delta f}{f} \approx \frac{\Delta\Phi}{c^2} - \frac{v^2}{2c^2}\]\[\frac{\Delta f}{f} = +4.4647\times10^{-10}\]\[\begin{aligned} f_0 &= 10.23\ \text{MHz} \\ &\quad\times(1 - 4.4647\times10^{-10}) \\ &= 10.229\,999\,995\,43\ \text{MHz} \end{aligned}\]
  4. Oscillayne – The Harmonic Pulse / Waveform Resonance Physics T-ShirtT-Shirt \[\ddot x + \gamma\dot x + \omega_0^{2}x = \frac{F_0}{m}\cos\omega t\]\[A(\omega) = \frac{F_0/m}{\sqrt{(\omega_0^{2}-\omega^{2})^{2} + \gamma^{2}\omega^{2}}}\]
  5. Pendulux – Foucault Pendulum / Earth’s Rotation Physics StickerPaper products \[\omega_{\text{prec}} = \Omega_\oplus \sin\varphi\]\[\Omega_\oplus = \frac{360^\circ}{23.93\ \text{h}}\]\[\Omega_\oplus \approx 15.04^\circ\ \text{per hour}\]
  6. Plasma Drift – Ionized Gas / Plasma Physics T-ShirtT-Shirt \[\omega_p = \sqrt{\frac{n_e e^{2}}{\varepsilon_0 m_e}}\]\[\lambda_D = \sqrt{\frac{\varepsilon_0 k_B T_e}{n_e e^{2}}}\]\[\vec v_E = \frac{\vec E \times \vec B}{B^{2}}\]
  7. Primordix – Big Bang Nucleosynthesis / Primordial Helium Physics StickerPaper products \[Y_p \simeq \frac{2\,(n/p)}{1 + n/p}\]\[\begin{gathered} \frac{n}{p} \approx \frac{1}{7} \;\Rightarrow \\ Y_p \approx \frac{2/7}{8/7} = 0.25 \end{gathered}\]\[\left.\frac{n}{p}\right|_{\text{freeze}} \approx e^{-Q/k_B T_f}\]\[\begin{aligned} Q &= (m_n - m_p)\,c^2 \\ &= 1.293\ \text{MeV} \end{aligned}\]
  8. QED Vertex Tee: Alpha Near 1/137T-Shirt \[-ie\gamma^{\mu}\]\[\alpha = \frac{e^{2}}{4\pi\varepsilon_0\hbar c},\qquad \alpha^{-1} = 137.035\,999\,177(21)\ \text{(CODATA 2022)}\]\[\alpha^{-1}(m_Z) \approx 128\]
  9. Quarkbinders – Quantum Chromodynamics / Strong Nuclear Force Physics T-ShirtT-Shirt \[\lvert B\rangle \propto \varepsilon_{ijk}\,\lvert q^{i} q^{j} q^{k}\rangle\]\[\alpha_s(Q^{2}) \approx \frac{12\pi}{(33 - 2n_f)\ln\!\left(Q^{2}/\Lambda_{\text{QCD}}^{2}\right)}\]
  10. Quavo & Lia – The Entangled Twins / Quantum Connection Physics T-ShirtT-Shirt \[\lvert\Psi^{-}\rangle = \tfrac{1}{\sqrt{2}}\left(\lvert\uparrow\downarrow\rangle - \lvert\downarrow\uparrow\rangle\right)\]\[\rho_B = \operatorname{Tr}_A\lvert\Psi^{-}\rangle\langle\Psi^{-}\rvert = \tfrac{1}{2}\mathbb{1}\]
  11. Reflexia – The Nonlocal Mirror / Quantum Nonlocality Physics T-ShirtT-Shirt \[S = E(a,b) - E(a,b^{\prime}) + E(a^{\prime},b) + E(a^{\prime},b^{\prime})\]\[\lvert S\rvert \le 2 \ (\text{local}), \qquad \lvert S\rvert \le 2\sqrt{2} \ (\text{quantum})\]\[E(a,b) = -\cos(\theta_a - \theta_b) \ (\text{singlet})\]
  12. Refracta – Fermat’s Principle / Snell’s Law Physics StickerPaper products \[\frac{\sin\theta_1}{v_1} = \frac{\sin\theta_2}{v_2}\]\[n_1\sin\theta_1 = n_2\sin\theta_2,\qquad n = c/v\]\[\delta\!\int n\,ds = 0\]
  13. Relicta – Cosmic Microwave Background / Relic Blackbody Physics StickerPaper products \[T(z) = T_0\,(1+z)\]\[T_0 = 2.72548\ \text{K}\]\[B_\nu(T) = \frac{2h\nu^3}{c^2}\,\frac{1}{e^{h\nu/k_B T}-1}\]\[\nu_{\text{peak}} \approx 160\ \text{GHz}\]
  14. Revolvix – Spinor Rotation / The 720° Return Physics StickerPaper products \[\begin{aligned} R(2\pi)\,\psi &= e^{-i\,2\pi\,\hat{n}\cdot\boldsymbol{\sigma}/2}\,\psi \\ &= -\psi \end{aligned}\]\[R(4\pi)\,\psi = +\psi\]
  15. Richard Feynman Sticker – Quantum? It’s Complicated. | Physics StickerPaper products \[K(b,a) = \sum_{\text{paths}} e^{iS[x(t)]/\hbar}\]\[P = \left\lvert\sum_k \phi_k\right\rvert^{2}\]
  16. Saltara – Hydraulic Jump / Froude Number Physics StickerPaper products \[\mathrm{Fr} = \frac{v}{\sqrt{g h}}\]\[\frac{h_2}{h_1} = \frac{1}{2}\left(\sqrt{1 + 8\,\mathrm{Fr}_1^2} - 1\right)\]
  17. Satyendra Nath Bose Sticker – Particle Guy. Major Stats. | Physics StickerPaper products \[\bar n(\varepsilon) = \frac{1}{e^{(\varepsilon-\mu)/(k_B T)} - 1}\]
  18. Scatterina – Rayleigh Scattering / Why the Sky Is Blue Physics StickerPaper products \[I_s \propto \frac{1}{\lambda^4}\]\[\frac{I_s(450\,\mathrm{nm})}{I_s(700\,\mathrm{nm})} = \left(\frac{700}{450}\right)^4 \approx 5.9\]
  19. Schrödy – Schrödinger’s Cat / Quantum Superposition Physics T-ShirtT-Shirt \[\begin{aligned} \lvert\Psi\rangle = \tfrac{1}{\sqrt{2}}\bigl(&\lvert \text{undecayed}\rangle\lvert \text{alive}\rangle \\ {}+{} &\lvert \text{decayed}\rangle\lvert \text{dead}\rangle\bigr) \end{aligned}\]\[P(\text{alive}) = \left\lvert \langle \text{undecayed},\text{alive} \vert \Psi\rangle \right\rvert^{2} = \tfrac{1}{2}\]
  20. Sortex – Maxwell’s Demon / Landauer Erasure Physics StickerPaper products \[Q_{\text{erase}} \ge k_B T \ln 2\]\[k_B T \ln 2 \approx 2.87\times10^{-21}\ \text{J}\]\[(T = 300\ \text{K, per bit})\]
  21. Spaghetta – Black Hole Physics / Spaghettification Stretch Physics T-ShirtT-Shirt \[\Delta a \approx \frac{2GM\,L}{r^{3}}\]\[r_s = \frac{2GM}{c^{2}}\]
  22. Spinwell – Angular Momentum Physics StickerPaper products \[L = I\omega\]\[I_1\omega_1 = I_2\omega_2\quad(\tau=0)\]
  23. Stairohm – Quantum Hall Effect / Resistance Plateaus Physics StickerPaper products \[\begin{gathered} R_{xy} = \frac{h}{\nu e^2} = \frac{R_K}{\nu} \\ \nu = 1, 2, 3, \ldots \end{gathered}\]\[\begin{aligned} R_K &= \frac{h}{e^2} \\ &= 25\,812.807\,45\ldots\ \Omega \end{aligned}\]\[R_{xx} = 0\ \text{on a plateau}\]
  24. Stellar Core – Nuclear Fusion Physics T-ShirtT-Shirt \[4\,{}^{1}\mathrm{H} \to {}^{4}\mathrm{He} + 2e^{+} + 2\nu_e\]\[Q = \left(4m_p + 2m_e - m_\alpha\right)c^{2} \approx 26.73\ \text{MeV}\]
  25. Stephen Hawking Sticker – Black Holes? Been There, Bent That. | Physics StickerPaper products \[T_H = \frac{\hbar c^{3}}{8\pi G M k_B}\]\[S_{BH} = \frac{k_B c^{3} A}{4G\hbar}\]
  26. Subrahmanyan Chandrasekhar Sticker – No Seconds. | Physics StickerPaper products \[\begin{aligned} M_{\text{Ch}} &= \frac{\omega_3^{0}\sqrt{3\pi}}{2}\left(\frac{\hbar c}{G}\right)^{3/2} \\ &\quad\times\frac{1}{(\mu_e m_H)^{2}} \\ &\approx \frac{5.73}{\mu_e^{2}}\,M_\odot \end{aligned}\]\[\begin{gathered} \mu_e = 2\ (\text{carbon/oxygen}) \\ \Rightarrow\; M_{\text{Ch}} \approx 1.43\,M_\odot \\ (\text{usually quoted as } 1.44) \end{gathered}\]\[\begin{gathered} \mu_e = 2.5\ (\text{assumed in 1931}) \\ \Rightarrow\; M_{\text{Ch}} \approx 0.91\,M_\odot \end{gathered}\]
  27. Superfluid – Quantum Fluid at Near Absolute Zero Physics T-ShirtT-Shirt \[v_c = \min_{p}\frac{\varepsilon(p)}{p}\]\[\oint \vec v_s\cdot d\vec\ell = n\,\frac{h}{m_4}\]
  28. Terminara – Terminal Velocity Physics StickerPaper products \[m\frac{dv}{dt} = mg - \tfrac12\rho C_d A\,v^2\]\[v_t = \sqrt{\frac{2mg}{\rho C_d A}}\]\[v(t) = v_t\tanh\!\left(\frac{g t}{v_t}\right)\]
  29. The Silence Beyond – Cosmic Horizon / Observable Limit Physics T-ShirtT-Shirt \[d_{p}(t_0) = a(t_0)\int_{0}^{t_0}\frac{c\,dt}{a(t)}\]
  30. The Spark Herald – Electromagnetism / Lightning Command Physics T-ShirtT-Shirt \[\nabla\cdot\vec E = \frac{\rho}{\varepsilon_0}\]\[\nabla\cdot\vec B = 0\]\[\nabla\times\vec E = -\frac{\partial\vec B}{\partial t}\]\[\nabla\times\vec B = \mu_0\vec J + \mu_0\varepsilon_0\frac{\partial\vec E}{\partial t}\]\[c = \frac{1}{\sqrt{\mu_0\varepsilon_0}}\]\[\vec S = \frac{1}{\mu_0}\,\vec E\times\vec B\]
  31. Thermal Mirage – Heat Refraction / Optical Distortion Physics T-ShirtT-Shirt \[n\cos\alpha = \text{constant}\quad\text{(stratified air)}\]\[n - 1 = K\rho \propto \frac{p}{T},\qquad n - 1 \approx 2.9\times10^{-4}\ \text{at STP}\]\[\alpha_{\max} \approx \sqrt{2\,\Delta n} \approx 0.4^{\circ}\ \text{for}\ \Delta T \approx 30\ \mathrm{K}\]
  32. Theta Warden – Strong CP Problem Physics T-ShirtT-Shirt \[\mathcal{L}_\theta = \bar\theta\,\frac{g_s^{2}}{32\pi^{2}}\,G^{a}_{\mu\nu}\tilde G^{a\,\mu\nu}\]\[\bar\theta = \theta - \arg\det M_q\]\[d_n \sim 10^{-16}\,\bar\theta\ e\,\text{cm}\]
  33. Unruh Effect TeeT-Shirt \[T = \frac{\hbar a}{2\pi c k_B} \approx 4.06\times10^{-21}\ \mathrm{K}\times\frac{a}{1\ \mathrm{m\,s^{-2}}}\]\[x^{2} - c^{2}t^{2} = \left(\frac{c^{2}}{a}\right)^{2}\]
  34. Vera Rubin Sticker – Galaxy Rotation? She Saw the Dark Side. | Physics StickerPaper products \[v(r)^{2} = \frac{G M(r)}{r}\]\[v(r) \approx \text{const} \;\Rightarrow\; M(r) \propto r\]
  35. Vevette – Higgs Field / Vacuum Expectation Value Physics StickerPaper products \[V(\phi) = -\mu^2|\phi|^2 + \lambda|\phi|^4\]\[\begin{gathered} \langle\phi\rangle = \frac{v}{\sqrt{2}} \\ v = (\sqrt{2}\,G_F)^{-1/2} \end{gathered}\]\[v \approx 246\ \text{GeV}\]\[m_f = \frac{y_f\,v}{\sqrt{2}}\]
  36. Void Whisperer – Dark Energy Expansion Physics T-ShirtT-Shirt \[\rho_\Lambda = \frac{\Lambda c^{2}}{8\pi G} \approx 6\times10^{-27}\ \mathrm{kg\,m^{-3}} \approx (2.2\ \mathrm{meV})^{4}\quad(\hbar = c = 1)\]\[\Lambda = \frac{3\,\Omega_\Lambda H_0^{2}}{c^{2}} \approx 1.1\times10^{-52}\ \mathrm{m^{-2}},\qquad w = \frac{p}{\rho c^{2}} = -1\]\[\rho_{\mathrm{vac}}^{\mathrm{naive}} \sim \bar M_{\mathrm{Pl}}^{4} \sim 10^{73}\ \mathrm{GeV^{4}}\quad\text{vs}\quad \rho_\Lambda \sim 10^{-47}\ \mathrm{GeV^{4}}\]
  37. Vortessa – Kármán Vortex Street / Strouhal Shedding Physics StickerPaper products \[f = \mathrm{St}\,\frac{U}{D}, \qquad \mathrm{St} \approx 0.2\]\[\mathrm{Re} = \frac{U D}{\nu}\]\[\frac{h}{a} \approx 0.281\]
  38. W-ZED – Weak Nuclear Force / Boson Carrier Physics T-ShirtT-Shirt \[M_W = M_Z\cos\theta_W \quad (\text{tree level})\]\[\frac{G_F}{\sqrt{2}} = \frac{g^{2}}{8M_W^{2}} \quad (\hbar = c = 1)\]\[R \sim \frac{\hbar}{M_W c} \approx 2.5\times10^{-18}\ \text{m}\]
  39. Wolfgang Pauli Sticker – One Per State | Physics StickerPaper products \[\psi(1,2)=\frac1{\sqrt2}\bigl[\phi_a(1)\phi_b(2)-\phi_a(2)\phi_b(1)\bigr]\]\[\psi\equiv 0\quad\text{when }a=b\]
  40. Zeno – Quantum Zeno Effect / The Observer Physics T-ShirtT-Shirt \[P_{\text{stay}}(t) \approx 1 - \left(\frac{t}{\tau_Z}\right)^{2}, \qquad \tau_Z = \frac{\hbar}{\Delta H}\]\[P_{1\to 2}(n) = \tfrac{1}{2}\left[1 - \cos^{n}\!\left(\tfrac{\pi}{n}\right)\right]\]
  41. Δ-X – The Heisenberg Runner / Uncertainty Principle Physics T-ShirtT-Shirt \[\sigma_x\,\sigma_k \ge \tfrac{1}{2}, \qquad p = \hbar k \;\Rightarrow\; \sigma_x\sigma_p \ge \tfrac{\hbar}{2}\]