Are long gamma-ray bursts standard candles?

Gamma-ray bursts (GRBs) are widely proposed as an effective probe to trace the Hubble diagram of the Universe in high redshift range. However, the calibration of GRBs is not as easy as that of type-Ia supernovae (SNe Ia). Most calibrating methods at present make use one or some of the empirical luminosity correlations, e.g., Amati relation. One of the underlying assumptions of these calibrating methods is that the empirical correlation is universal over all redshifts. In this paper, we check to what extent this assumption holds. Assuming that SNe Ia exactly trace the Hubble diagram of the Universe, we re-investigate the Amati relation for low redshift ($z<1.4$) and high redshift ($z>1.4$) GRBs, respectively. It is found that the Amati relation of low-$z$ GRBs differs from that of high-$z$ GRBs at more than $3\sigma$ confidence level. This result is insensitive to cosmological models. We should be cautious when using Amati relation to reconstruct the Hubble diagram of the Universe.