hello underground
#melknipsen #buörnz #sweden #stockholm #metrostation #street #streetphotography #symmetries #escalator
#symmetries
How Noether’s Theorem Revolutionized Physics
❛❛ Emmy #Noether showed that #fundamental #physical #laws are just a consequence of simple #symmetries. A #century later, #her insights continue to shape #physics. ❜❜
🔗 https://www.QuantaMagazine.org/how-noethers-theorem-revolutionized-physics-20250207/ 2025 Feb 07
🔗 https://Wikipedia.org/wiki/Emmy_Noether … #EmmyNoether
#Community #TimeTravel #Research #theorem #theoretical #math #science #conservation #laws #woman #physicist #Kronodon
'Invariant Physics-Informed Neural Networks for Ordinary Differential Equations', by Shivam Arora, Alex Bihlo, Francis Valiquette.
http://jmlr.org/papers/v25/23-1511.html
#invariantized #invariants #symmetries
Exploring the possibility of probing fundamental #spacetime #symmetries via #gravitationalwave #memory
Towards fully covariant machine learning
Probing fundamental #symmetries of #nature with the #Higgsboson
https://phys.org/news/2023-04-probing-fundamental-symmetries-nature-higgs.html
Equivariant Mesh Attention Networks
Sourya Basu, Jose Gallego-Posada, Francesco Viganò, James Rowbottom, Taco Cohen
Yeah, if we were only talking about the theory of #GR, then we'd have an open & shut case against my vague use of "dimensions in quotation marks".
Since reality is only poked at with #models 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 #time & 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, #symmetries, 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 #SR is based around light, so conflicts with #QM 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.
@cy
One of the great #symmetries in the problem of one-person-hoarding-them-all, is they will quickly have to reduce their prices, or start giving stuff away, lest ppl come with pitchforks.
Or start a new #money.
Bitcoin was a response to one type of #monopoly of money, #CentralBanking and so we can reasonably expect that if #BTC ever gets monopolised that ppl will democratically jump ship to another. We estimate bitcoin entropy will set in in about 200 years (ceterisParibus).
same #symmetries can be mathematically implemented in different ways, depending on the procedure of random selection that one uses
Alon drory
Bertrand #paradox
same #symmetries can be mathematically implemented in different ways, depending on the procedure of random selection that one uses
Alon drory
Bertrand #paradox
continuous #symmetries cannot be spontaneously broken at finite temperature in systems with sufficiently short-range interactions in dimensions d ≤ 2
continuous #symmetries cannot be spontaneously broken at finite temperature in systems with sufficiently short-range interactions in dimensions d ≤ 2
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