IndexCuánticaMug

Fuzzwick

Uncertainty Principle Physics

\[\sigma_x\,\sigma_p \ge \frac{\hbar}{2}\]
$21.99 USD
$21.99 USD
Oferta Agotado
Size

Can you pin down where a particle is and how fast it moves at once? Fuzzwick says no. Heisenberg’s uncertainty principle, σxσp ≥ ħ/2, is a property of quantum states, not of clumsy instruments: squeeze the spread in position and the spread in momentum must grow. Pixel-art black ceramic mug in 11 or 15 oz; equation, symbols and sources in the physics panel below.

Shipping calculated at checkout by destinationMade to order, ships in ~10 days

Details

Size & material11oz · 15oz

Black glossy ceramic mug with a C-handle. Lead- and BPA-free.

  • 11oz: 0.33 l
  • 15oz: 0.44 l
CareDishwasher & microwave safe

Dishwasher safe (top rack) or hand wash. Microwave safe.

ShippingBy destination

Shipping calculated at checkout by destination.

Made to order: about 10 days of production and handling before it ships.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

You can't know both a particle's position and its momentum perfectly: the product of their spreads is at least ħ/2. This comes from position and momentum not commuting in quantum mechanics, not from clumsy measurement.

Fuzzwick is never quite where you left him, and never quite as fast as you thought.

The first line on this mug is the uncertainty principle for position and momentum. Prepare many copies of a particle in the same state. Measure position on some and momentum on others. The spread of the position results times the spread of the momentum results can never be smaller than half the reduced Planck constant. Earle Kennard proved this form in 1927, the same year Heisenberg published his famous thought experiment.

Heisenberg argued from disturbance: to see an electron sharply you must hit it with short-wavelength light, and the light kicks it. That picture is memorable, but the inequality is not about clumsy instruments. It is a property of the state itself. A state with a sharp position is built from many momenta, so its momentum spread is large. In 1929 Howard Percy Robertson gave the general rule, the second line, for any two quantities; the third line is the commutator that makes position and momentum the classic case.

So the line FOUND YOU. LOST YOUR SPEED. is a joke with a true core. Pin down where Fuzzwick is and his speed is not lost or zero. It is spread out: measure it and you could get a wide range of answers.

Squeeze one spread and the other must grow. Fuzzwick does not mind. Fuzzy is his natural state.

Equations

\[\sigma_x\,\sigma_p \ge \frac{\hbar}{2}\]
\[\sigma_A\,\sigma_B \ge \tfrac{1}{2}\left\lvert\langle[\hat A,\hat B]\rangle\right\rvert\]
\[[\hat x,\hat p] = i\hbar\]
SymbolMeaningUnit
\(\sigma_x\) standard deviation (spread) of position measurements on identically prepared systems \(\mathrm{m}\)
\(\sigma_p\) standard deviation of momentum measurements on identically prepared systems \(\mathrm{kg·m/s}\)
\(\hbar\) reduced Planck constant \(\mathrm{J·s}\)
\(\sigma_A, \sigma_B\) standard deviations of observables A, B (same units as A and B) \(\mathrm{[A],[B]}\)
\([\hat A,\hat B]\) commutator AB − BA (unit of A times unit of B) \(\mathrm{[A][B]}\)
\(\hat x, \hat p\) position, momentum operators \(\mathrm{m, kg·m/s}\)

Sources

  1. Robertson (1929) The Uncertainty Principle, Phys. Rev. 34, 163
  2. Heisenberg (1927) Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik, Z. Phys. 43, 172
  3. Kennard (1927) Zur Quantenmechanik einfacher Bewegungstypen, Z. Phys. 44, 326
  4. Encyclopaedia Britannica — Uncertainty principle
  5. Stanford Encyclopedia of Philosophy — The Uncertainty Principle

Source Kennard, E. H. (1927). Zur Quantenmechanik einfacher Bewegungstypen. Zeitschrift für Physik 44, 326–352.doi.org/10.1007/BF01391200

Field notes

Ver todo
1 3
Ver todo