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mel knipsenhello underground <a href="https://pixelfed.social/discover/tags/melknipsen?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#melknipsen</a> <a href="https://pixelfed.social/discover/tags/buörnz?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#buörnz</a> <a href="https://pixelfed.social/discover/tags/sweden?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#sweden</a> <a href="https://pixelfed.social/discover/tags/stockholm?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#stockholm</a> <a href="https://pixelfed.social/discover/tags/metrostation?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#metrostation</a> <a href="https://pixelfed.social/discover/tags/street?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#street</a> <a href="https://pixelfed.social/discover/tags/streetphotography?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#streetphotography</a> <a href="https://pixelfed.social/discover/tags/symmetries?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#symmetries</a> <a href="https://pixelfed.social/discover/tags/escalator?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#escalator</a>

The Krononaut Moon Project 🌑  How Noether’s Theorem Revolutionized Physics❛❛ Emmy <a href="https://me.dm/tags/Noether" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Noether</a> showed that <a href="https://me.dm/tags/fundamental" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#fundamental</a> <a href="https://me.dm/tags/physical" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#physical</a> <a href="https://me.dm/tags/laws" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#laws</a> are just a consequence of simple <a href="https://me.dm/tags/symmetries" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#symmetries</a>. A <a href="https://me.dm/tags/century" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#century</a> later, <a href="https://me.dm/tags/her" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#her</a> insights continue to shape <a href="https://me.dm/tags/physics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#physics</a>. ❜❜ 🔗 <a href="https://www.QuantaMagazine.org/how-noethers-theorem-revolutionized-physics-20250207/" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://www.QuantaMagazine.org/how-noethers-theorem-revolutionized-physics-20250207/</a> 2025 Feb 07 🔗 <a href="https://Wikipedia.org/wiki/Emmy_Noether" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://Wikipedia.org/wiki/Emmy_Noether</a> … <a href="https://me.dm/tags/EmmyNoether" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#EmmyNoether</a> <a href="https://me.dm/tags/Community" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Community</a> <a href="https://me.dm/tags/TimeTravel" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TimeTravel</a> <a href="https://me.dm/tags/Research" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Research</a> <a href="https://me.dm/tags/theorem" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#theorem</a> <a href="https://me.dm/tags/theoretical" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#theoretical</a> <a href="https://me.dm/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#math</a> <a href="https://me.dm/tags/science" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#science</a> <a href="https://me.dm/tags/conservation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#conservation</a> <a href="https://me.dm/tags/laws" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#laws</a> <a href="https://me.dm/tags/woman" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#woman</a> <a href="https://me.dm/tags/physicist" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#physicist</a> <a href="https://me.dm/tags/Kronodon" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Kronodon</a>

JMLR'Invariant Physics-Informed Neural Networks for Ordinary Differential Equations', by Shivam Arora, Alex Bihlo, Francis Valiquette.<a href="http://jmlr.org/papers/v25/23-1511.html" rel="nofollow noopener noreferrer" translate="no" target="_blank">http://jmlr.org/papers/v25/23-1511.html</a> <a href="https://sigmoid.social/tags/invariantized" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#invariantized</a> <a href="https://sigmoid.social/tags/invariants" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#invariants</a> <a href="https://sigmoid.social/tags/symmetries" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#symmetries</a>

CorradoExploring the possibility of probing fundamental <a href="https://astrodon.social/tags/spacetime" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#spacetime</a> <a href="https://astrodon.social/tags/symmetries" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#symmetries</a> via <a href="https://astrodon.social/tags/gravitationalwave" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#gravitationalwave</a> <a href="https://astrodon.social/tags/memory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#memory</a><a href="https://phys.org/news/2024-07-exploring-possibility-probing-fundamental-spacetime.html?utm_source=nwletter&utm_medium=email&utm_campaign=daily-nwletter" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://phys.org/news/2024-07-exploring-possibility-probing-fundamental-spacetime.html?utm_source=nwletter&utm_medium=email&utm_campaign=daily-nwletter</a>

New Submissions to TMLRTowards fully covariant machine learning<a href="https://openreview.net/forum?id=gllUnpYuXg" rel="nofollow noopener noreferrer" target="_blank">https://openreview.net/forum?id=gllUnpYuXg</a><a href="https://sigmoid.social/tags/symmetries" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#symmetries</a> <a href="https://sigmoid.social/tags/symmetry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#symmetry</a> <a href="https://sigmoid.social/tags/covariance" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#covariance</a>

Published papers at TMLREquivariant Mesh Attention NetworksSourya Basu, Jose Gallego-Posada, Francesco Viganò, James Rowbottom, Taco Cohen<a href="https://openreview.net/forum?id=3IqqJh2Ycy" rel="nofollow noopener noreferrer" target="_blank">https://openreview.net/forum?id=3IqqJh2Ycy</a><a href="https://sigmoid.social/tags/attention" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#attention</a> <a href="https://sigmoid.social/tags/features" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#features</a> <a href="https://sigmoid.social/tags/symmetries" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#symmetries</a>

mj<a href="https://mastodon.sdf.org/@defrisselle" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@defrisselle</a> <a href="https://fribygda.no/@Mizmar" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@Mizmar</a> Yeah, if we were only talking about the theory of <a href="https://c.im/tags/GR" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#GR</a>, then we'd have an open & shut case against my vague use of "dimensions in quotation marks".Since reality is only poked at with <a href="https://c.im/tags/models" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#models</a> we know to be inconsistent (big picture) and incomplete (like all), I think there's nothing but room to wonder what a better theory would look like. One thing we do know, it will require a different approach to <a href="https://c.im/tags/time" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#time</a> & dynamics, for at least one of the discrepant models on the table. Regardless of whether or not any of us have a better solution, GR's combining of space & time plus use of curvature of 4D is putting time on each spatial dimension. Are they independent? It depends. For what reason would they be included, if not to have specific instances where they were needed to be calculated separately? There's a lot of translation/transforming between "every day physics" and GR; momentum & stress tensors, etc. Other work has shown that the curvature is not required in the way postulated by GR. There are also other geometries, <a href="https://c.im/tags/symmetries" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#symmetries</a>, manifolds, etc. In SR, there's a 10D Poincare group, which includes 4 spacetime translations. The reality is, that physicists jump back & forth between models based on context & convenience. Euclidean 4D (3+1) is not the same as Minkowski 4D.There are different types of mass, from context, and I'd argue the same holds for Time. (I'm happy to expound..)At any rate, time dilation & length contraction work together in all directions, to satisfy the conflict between individual perception (I'd argue that conscious observers anthropocentrically use a Cartesian coordinate system centered on themselves) and a consistency of explanatory power of the model, for all frames of reference. There would be fewer problems if we only had to contend with mass & gravity, but <a href="https://c.im/tags/SR" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#SR</a> is based around light, so conflicts with <a href="https://c.im/tags/QM" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#QM</a> cannot be avoided.The velocity 4 vector in GR uses dt for dx, dy, and dz. In SR, this 4-velocity cannot be defined, as the 'proper time' between events (d\_tau) is zero. QM has to input time to 3D, and doesn't even have a position operator for the photon. The list of differences goes on, of course, but I think this is enough to resolve the disagreement at hand. All of these things are just ways we try to measurably explain events/interactions between objects/observers.

mj<a href="https://mastodon.online/@jcastroarnaud" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@jcastroarnaud@mastodon.online</a> <a href="https://mathstodon.xyz/@jcastroarnaud" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@jcastroarnaud@mathstodon.xyz</a> Thank you so much for the extended response, it helps to get a quick orientation, and draw out some clarity in the terms used. The reason I started from numbers as <a href="https://c.im/tags/systems" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#systems</a> is that they do have their own natural structures & <a href="https://c.im/tags/symmetries" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#symmetries</a> when applied to certain sets or topologies.Specifically, I'm generally looking at the differences between <a href="https://c.im/tags/Time" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Time</a> and <a href="https://c.im/tags/Space" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Space</a>, their metrics, and their many relations that form fundamental parts of models, which we already know require alternative <a href="https://c.im/tags/methods" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#methods</a> to transform.There seems to be some promise in using different metrics for them at the start, rather than as an additional <a href="https://c.im/tags/abstraction" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#abstraction</a> layer, added to the system. I'll be checking the leads you gave, in order to better frame this idea. Thanks again!

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