In physics, particularly in quantum mechanics, "delta x delta p" refers to the product of the **uncertainty in position ($\Delta x$)** and the **uncertainty in momentum ($\Delta p$)** of a particle. This product is central to the **Heisenberg Uncertainty Principle**, which states that it's impossible to simultaneously know both the exact position and the exact momentum of a particle with arbitrary precision. The more precisely you know one, the less precisely you can know the other. The mathematical formulation is: $\Delta x \cdot \Delta p \ge \frac{\hbar}{2}$ Where: * **$\Delta x$** (delta x) is the uncertainty in the particle's position. * **$\Delta p$** (delta p) is the uncertainty in the particle's momentum. * **$\hbar$** (h-bar) is the reduced Planck constant (Planck's constant divided by 2π), a very small fundamental constant of nature. **What it means:** * **It's not about measurement error:** This isn't a limitation of our measuring instruments. It's a fundamental property of the universe at the quantum level. The particle itself doesn't *have* a perfectly precise position and momentum simultaneously. * **Wave-particle duality:** One way to intuitively understand it is through wave-particle duality. If a particle is described as a wave, a very localized wave (small $\Delta x$) requires a superposition of many different wavelengths, meaning a large spread in momentum ($\Delta p$). Conversely, a wave with a very precise wavelength (small $\Delta p$) must be spread out over a large region of space (large $\Delta x$). * **Implication for the text:** In the context of the text you provided, the Heisenberg Uncertainty Principle is used to explain why the classical definition of "absolute zero" (as absolute stillness) clashes with quantum reality. Even at 0 Kelvin, particles must retain some "zero-point energy" and motion because if they were perfectly still (zero uncertainty in momentum, $\Delta p = 0$), their position would become infinitely uncertain ($\Delta x = \infty$), which is physically impossible for a confined particle.