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Lafiel said:

the important thing here is, that they showed through maths (based on todays understandings) that their proposed setup has a good chance of detecting photon-photon reactions

there isn't enough money and resources to just build every setup people come up with, so it's very important to be able to proof mathematically, that in theory this should work

and if it doesn't that's an exciting result aswell, as it could indicate our models can be further tweaked or unknown effects/interactions still linger out there waiting to be found

I highly doubt this experiment would've changed anything about the validity of special relativity ... 

If it was consistent from the cosmos to the high energy particle world then what would going the other way change ?