Read the actual actual article: https://arxiv.org/abs/2502.14367
The authors prove that given any sequence of rotations W “almost always” there is a sequence of rotations W’ formed by scaling every rotation angle in W by the same positive factor, such that the sequence W’W’ is the identity (that is, apply all the rotations in W’ and then apply all of them again).
The issue isn’t the result, it’s popsci writing.
No, the original paper is saying something like: given the sequence say 12 -> 3 -> 7, there is a sequence 12 -> 3x -> 7x -> 7x + 3x -> 7x + 3x + 4x where 7x+3x+4x = 12. Obviously here x=6/7, but doing something like this with arbitrary rotations in 3D isn’t so simple.
If you’re referring to doing moves on a Rubik’s cube, no that’s irrelevant to the theorem. If you’re referring to applying a sequence of rotations to a whole solid cube, then yes.
The example given in the OP is incorrect. /u/gameryamen is implying something like: given a sequence of rotations W there is a scale factor a>0 such that W(a)W(a)W = 1, with W(a) the same sequence of rotations as W but with all rotation angles scaled by a.
This is not what the paper does. The paper finds an a such that W(a)W(a) = 1.
His whole post seems bunk, honestly. Example:
Having one more shot in your follow up acts as kind of a hinge, opening up more possibilities.
This seems completely irrelevant. It seems that maybe they’re referring to the probabilistic argument the authors give to justify why their theorem should be true (before giving a complete proof), but this argument involves repeating the same exact rotation two times, not two different rotations in sequence.
They use continuity and the fact that F(0) = 1 to conclude that, since it also takes on a negative value (what they put effort into arguing), it must also attain 0. So no, they don’t find it directly, but it is technically possible to express F explicitly and then numerically find a root.
Yes, “quantum teleportation” just means transfering a quantum state from one location to another without knowing what that state is, in the same sense that you can copy a file from one place to another without knowing its contents. So it’s just a particular kind of information being transfered, not anything about how quickly it’s transfered. There is a lot of awful terminology in quantum mechanics.
This sentence is shit, but I want to point out at least that “magic” is jargon for “well-behaved” or “particularly well-suited (for our application)”. It’s essentially “magic” like in the phrase “it works like magic”.
All the successful theories were developed from experimental results
The more I think about this, the more I’m not sure I 100% agree… For example, special relativity essentially came from the observation that Maxwell’s equations were not Galilean invariant, and instead invariant under this weird other group (what we now call the Lorentz group); and QED essentially came from Dirac wanting to take a “square root” of the Klein-Gordan equation.
(Of course, real history is more intricate than this.)
This is not about the same article nor the same authors.
The authors of the original article cited by this news outlet did not measure any time on Mars in any way. They did a theoretical calculation of the time difference with Earth based on astronomical data about Mars like mass, orbit, etc.