A small tool to view real-world ActivityPub objects as JSON! Enter a URL
or username from Mastodon or a similar service below, and we'll send a
request with
the right
Accept
header
to the server to view the underlying object.
{
"@context": [
"https://www.w3.org/ns/activitystreams",
{
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"inReplyToAtomUri": "ostatus:inReplyToAtomUri",
"conversation": "ostatus:conversation",
"sensitive": "as:sensitive",
"toot": "http://joinmastodon.org/ns#",
"votersCount": "toot:votersCount",
"blurhash": "toot:blurhash",
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}
}
],
"id": "https://mathstodon.xyz/users/gregeganSF/outbox?max_id=109282874435082188&page=true",
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"published": "2022-11-03T12:24:20Z",
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"published": "2022-11-03T12:24:20Z",
"url": "https://mathstodon.xyz/@gregeganSF/109279855268163423",
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"content": "<p>[13/13] This is a proof by Peres of the Kochen-Specker Theorem!</p><p>Think of each triad as a quantum measurement where 1 of 3 orthogonal possibilities must be observed.</p><p>Then we just exhibited a set of 16 measurements whose results can’t be pre-determined, independent of what we do.</p>",
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"en": "<p>[13/13] This is a proof by Peres of the Kochen-Specker Theorem!</p><p>Think of each triad as a quantum measurement where 1 of 3 orthogonal possibilities must be observed.</p><p>Then we just exhibited a set of 16 measurements whose results can’t be pre-determined, independent of what we do.</p>"
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"content": "<p>[12/13] And the coup-de-grace: triad 16 gets a green on the right face, reddifying an orthogonal vector in triad 5 on the top face.</p><p>Every ray has a colour now, and up to symmetry, we had no choice in what we did.</p><p>But … triad 5 now has THREE red rays.</p><p>The goal is impossible!</p>",
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"content": "<p>[11/13] Surprising absolutely no one, triad 3 gets a green on the top face, reddifying an orthogonal vector in triad 16 on the right face.</p>",
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"content": "<p>[10/13] Now triad 15 gets a green on the top face, reddifying an orthogonal vector in triad 3 on the right face.</p>",
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"content": "<p>[9/13] And the cascade continues: triad 8 falls to the inevitable, with a new green on the left face, reddifying a ray orthogonal to it in triad 15, on the top face.</p>",
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"content": "<p>[8/13] And now that means two reds in triad 12, so the third ray, also on the left face, must turn green.</p><p>This in turn reddifies a ray orthogonal to it in triad 8, on the top face.</p>",
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"content": "<p>What this means, though, is that given a pair of spins, you can’t say that the result you get for one of these measurements “would have been the same” if you’d done it as part of a different set of measurements: as part of the row it belongs to, rather than as part of its column. Because if you try to write a fixed 1 or –1 in each of the 9 squares, telling you the values for those measurements, it is impossible to make the products of all rows equal 1, but the products of all columns –1.</p>",
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"content": "<p>David Mermin came up with these matrices in 1990, in the form of measurements on a pair of quantum spins, as shown below.</p><p>Every measurement in this grid will give 1 or –1, and if you perform the three measurements in one row, or one column, at the same time, the product of the three results you get will always be 1 for a row, and –1 for a column. This follows from our original statements about the grid of matrices.</p>",
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"content": "<p>If you take the three matrices in one row or one column of this 3×3 grid, they will all commute with each other, and the result of multiplying all three together will be the identity matrix for rows, but minus the identity matrix for columns.</p>",
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