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(Pseudo-)Riemannian Geometry: Difference between revisions
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|timestamp=6:11 PM · Jul 9, 2021 | |timestamp=6:11 PM · Jul 9, 2021 | ||
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=== 2024 === | |||
{{Tweet | |||
|image=Eric profile picture.jpg | |||
|nameurl=https://x.com/EricRWeinstein/status/1862659585863193057 | |||
|name=Eric Weinstein | |||
|usernameurl=https://x.com/EricRWeinstein | |||
|username=EricRWeinstein | |||
|content=Q: Is a “Harald trumpet” expanding while resting on a shelf? | |||
A: No. It just sorta sits there. Neither growing nor shrinking. | |||
Q: Well then, is the cross-sectional circumference of its surface expanding as you travel down its tubing length from mouthpiece to bell? | |||
A: Yes. | |||
Q: Do mathematicians have an intrinsic way to describe this without having to artificially locate the trumpet in any particular place, or do they have to have it sit in a three dimensional space? | |||
A: They use something called a Riemannian metric (or [[(Pseudo-)Riemannian Geometry|Pseudo-Riemannian metric]]) so they can study the trumpet as having a curved 2 dimensional surface without having to stick the trumpet artificially in a three dimensional space as in the picture. | |||
Q: So is that the confusion? It’s just bad language? | |||
A: Yes. The Universe is not expanding. The size of its cross-sections as measured by the intrinsic Riemannian volume, is what is expanding as you travel down its tube from the Big Bang (mouthpiece) towards the present (the bell). | |||
Q: How can that be?? I was just watching Professor X and he said “The universe…” | |||
A: I don’t know what to tell you. Sorry. | |||
|quote= | |||
{{Tweet | |||
|image=PhysInHistory-profile-oPMz8-kf.jpg | |||
|nameurl=https://x.com/PhysInHistory/status/1862542311785140563 | |||
|name=Physics In History | |||
|usernameurl=https://x.com/PhysInHistory | |||
|username=PhysInHistory | |||
|content=If the Universe is Expanding, What is it Expanding Into? ✍️ | |||
|media1=PhysInHistory-X-post-1862542311785140563-GdkUV55XkAETBZa.jpg | |||
|timestamp=5:01 PM · Nov 29, 2024 | |||
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|timestamp=12:47 AM · Nov 30, 2024 | |||
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== Related Pages == | == Related Pages == | ||