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by MajimasEyepatch 111 days ago
According to the post, this result was first derived for gluons in a previous paper. That paper was provided to the model as context, and then the model was asked to derive an analogous result for gravitons, which presumably has not been done before. The authors claim it would have taken "considerable time" for human experts to derive the graviton result.

I don't see any reason to believe that this exact problem was solved before in the training data, but it's definitely an incremental result based on a very similar problem that the model had seen before.
1 comments
gus_massa 110 days ago
Gluons have spin 1 and Gravitons [1] have spin 2. This adds a lot of subtle difference in the calculations. Some are obvious like replacing a 1 with a 2 (or a 1^2 with a 2^2). Some are super tricky:

For example if you have two gluons, you apply the rules of sum of spin and get

  1 × 1 = 2 + 1 + 0
(They can be coupled in the same direction and get 2, or the oposite direction and get 0, or something in between and get 1.)

But for gravitons, the rules are

  2 × 2 = 4 + 3 + 2 + 1 + 0
(They can be coupled in the same direction and get 4, or the oposite direction and get 0, or something in between and get more cases in between like 2, but also 1 or 3.)

If you want to make give physicist nightmares and make mathematician cry, a tiny part of the details are in https://en.wikipedia.org/wiki/Table_of_Clebsch%E2%80%93Gorda... and https://en.wikipedia.org/wiki/Table_of_Clebsch%E2%80%93Gorda...

In conclusion, I'm not sure how difficult is to do the conversion from gluons to gravitons, but I'd recommend to run away.

[1] Assuming they exist.

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