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White · Black
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S–5XL
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Size & fitS–5XL

Unisex heavy cotton (Gildan 5000), classic fit.

Unisex tee size chart, inches
SizeWidthLengthSleeve
S182815.1
M202916.5
L223018
XL243119.5
2XL263221
3XL283322.4
4XL303423.7
5XL323525

Measurements in inches, ±1.5 in tolerance.

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The physics

Quavo and Lia never speak. Each of them, alone, is completely random. Together they always disagree, perfectly.

The first formula on this page is their state, the spin singlet: Quavo up and Lia down, minus Quavo down and Lia up, in equal amounts. Measure both spins along any common axis and the answers are always opposite. That is the correlation. In 1935 Albert Einstein, Boris Podolsky and Nathan Rosen used a state like this to argue that quantum mechanics must be incomplete: the outcomes, they reasoned, must have been fixed in advance. The same year Erwin Schrödinger gave the phenomenon its name, entanglement. Later, in a 1947 letter, Einstein called the idea spooky action at a distance.

The second formula is the part people leave out. Ask what Lia's spin looks like on its own, ignoring Quavo entirely, and the answer is the identity matrix divided by two: fifty-fifty, in every direction, with no information at all. Nothing anyone does to Quavo changes that. Measure him along x, along z, or not at all, and Lia's own results stay exactly fifty-fifty. So entanglement cannot carry a message. The correlation appears only when the two lists of results are brought together and compared, by ordinary means, no faster than light.

John Bell showed in 1964 that these correlations cannot be explained by instructions fixed in advance and carried along, if nothing travels between the two. Experiments starting in 1972 and recognised by the 2022 Nobel Prize confirmed the quantum predictions.

What that means is still debated. Some read it as nonlocality, some as a reason to rethink what a measurement outcome is. All agree on the predictions, and on the absence of any signal.

Quavo and Lia do not communicate. They were never two separate stories to begin with.

Equations

\[\lvert\Psi^{-}\rangle = \tfrac{1}{\sqrt{2}}\left(\lvert\uparrow\downarrow\rangle - \lvert\downarrow\uparrow\rangle\right)\]
\[\rho_B = \operatorname{Tr}_A\lvert\Psi^{-}\rangle\langle\Psi^{-}\rvert = \tfrac{1}{2}\mathbb{1}\]
Symbols
SymbolMeaningUnit
\(\lvert\Psi^{-}\rangle\) spin-singlet state of two particles \(\mathrm{1}\)
\(\rho_B\) reduced density matrix of particle B \(\mathrm{1}\)
\(\operatorname{Tr}_A\) partial trace over particle A —
\(\mathbb{1}\) identity \(\mathrm{1}\)
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