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July 18

Identify some more trees?

Scene in Laramie, Wyoming, USA. I'd like to put it into Commons categories for the trees along the street — particularly the big prominent one near the centre — but I don't know anything about this kind of thing. Nyttend (talk) 08:04, 18 July 2024 (UTC) PS, I was guessing blue spruce for the big one at the centre, but the shape is quite different from those of the trees pictured in that article. Nyttend (talk) 08:20, 18 July 2024 (UTC)[reply]

A zoom-in on the image shows some distinctive spruce cones, and it is certainly blue-ish (Caveat: the blue spruce is an uncommon specimen tree in the UK and I'm not sure that I've ever seen one in person). Alansplodge (talk) 10:53, 18 July 2024 (UTC)[reply]

Speaking as a regular WP:Wikiproject Plants contributor, I would prefer that users didn't assign species categories to images such as this unless they were absolutely certain of the identification. Ideally, the image would include the label from the arboretum or botanical garden. Abductive (reasoning) 21:11, 20 July 2024 (UTC)[reply]

Lorentz transformations.

For deriving the Lorentz transformations, our article Derivations of the Lorentz transformations relies on their linearity. How do we know they must be linear? Our article answers: Since space is assumed to be homogeneous, the transformation[s] must be linear. I wonder, how their linearity is deduced from the homogeneity of space, before we've found how they will look like...

For the time being, I'm adding an Einsteinian source for this claim in the article, even though I don't know how Einstein derived this claim. HOTmag (talk) 23:41, 18 July 2024 (UTC)[reply]

The Lorentz transformations are linear transformations by definition. The linearity comes from their domain being a linear "Newtonian" spacetime isomorphic to the product of Euclidean 3-space and a linear time axis. --Lambiam 09:48, 19 July 2024 (UTC)[reply]

Thanks. However, rather than assuming linearity - from the very beginning (as you do), Einstein's claim I've quoted from our article - derives linearity - from the homogeneity of spacetime. My question was: how can the quote be justified. HOTmag (talk) 10:02, 19 July 2024 (UTC)[reply]

This is the article in which Einstein introduced the special theory of relativity. His spacetime is flat, and the reference frame of a stationary observer is basically the same as for Lorentz, so space is an Euclidean 3-space. The "homogeneity" is that the laws of physics are invariant under an isometric transformation of space. Just homogeneity is not enough; to reach the conclusion, the flatness is essential. --Lambiam 00:19, 20 July 2024 (UTC)[reply]

Let's assume that the space is flat, and that the laws of physics are invariant under an isometric transformation of space. How do you infer from these assumptions, that the Lorentz transformations (which are actually not isometric) are linear? This is what I can't understand yet... HOTmag (talk) 18:35, 20 July 2024 (UTC)[reply]