I'm very glad now that I didn't go down the "comment" route. Let's look at someone who did!

First there was this:

A proposal to measure photon-photon scattering

which contains equations in the abstract and was therefore never going to be a fun read. The paper opens with a reference to an unpublished paper by the same author which apparently shows that the calculation of light by light scattering from Euler-Heisenberg is wrong. That's quite a claim.

The gist of the paper is that a bog-standard perturbative calculation gives the correct answer, as you'd expect. There is also a reference to an old, independent, perturbative calculation which reproduced E&H's result, but seemingly can't be trusted as it was fudged in order to agree with E&H.

Interesting so far!

The paper ends though with some dodgy comments on both gauge and Lorentz invariance: for example, they claim that the QED polarisation tensor isn't transverse... I'm pretty sure it is, you know. There's a reference to one of their own papers where they show this. Note that they're using a UV cutoff which doesn't preserve gauge invariance, so it seems to me that they've broken gauge invariance and found that... oh... gauge invariance is broken. Check.

So this morning comes the comment:

Comment on : A Proposal to Measure Photon-Photon Scattering

which, somewhat disappointingly, open with neither a disgruntled "this contradicts my fabulous result" nor a direct "this is HORSESHIT" slap-down. Instead, it rather mildly points out that the "new" result gives a cross section 40 orders of magnitude larger than the old, and that this violates known _experimental_ bounds on the cross-section.

Pretty slap-downy, at a medium pace.

But today also sees the full calculation of the new result! It's here:

Light-Light Scattering

and lays the blame at the foot of an "unphysical gauge condition" which I can't see discussed explicitly. They say that the box diagram is finite in QED... really?! Can an expert on this confirm or deny it? I could get up and open a textbook but, you know, sleepy...

Personally, I'd love it if Euler-Heisenberg was wrong. It would be tremendous fun. I think it's more likely that these trailblazing chaps have just screwed their calculation, either because they've shagged gauge invariance or ... ah, they add three box diagrams together, say "each is divergent but the sum is not and therefore we don't need to regularise." Hunggg. This could be where they dropped the ball. If I have an expression which is finite then clearly no regularisation is needed. However, if I have three dodgy expressions then I can't just add them up and claim the whole thing will be fine. So I guess they've dropped an "infinity - infinity = 0 ball.

Still! Let's hope it doesn't end here. There's plenty of scope for more comments with ever increasing irritation. Physicists -- I know you won't let me down!

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