The noncommutative QED (NCQED) has a non-Abelian nature due to the presence of 3- and 4-photon vertices in the lagrangian. Thus, NCQED predicts a new physics contribution to the $$\gamma \gamma \rightarrow \gamma \gamma $$
γ
γ
→
γ
γ
scattering already at the tree level. We have examined NCQED by studying the light-by-light process at the 14 TeV LHC with intact protons. Our results show that the NC scale up to $$\Lambda _{\mathrm {NC}} = 1.64(1.35)$$
Λ
NC
=
1.64
(
1.35
)
TeV can be probed in the $$pp\rightarrow p(\gamma \gamma )p \rightarrow p'(\gamma \gamma )p'$$
p
p
→
p
(
γ
γ
)
p
→
p
′
(
γ
γ
)
p
′
collision for the time-space (space-space) NC parameters. These bounds are stronger than the limits that can be obtained in the light-by-light scattering at high energy linear colliders.