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While the width-luminosity relation (WLR) among type Ia supernovae (slower isbrighter) has been extensively studied, its physical basis has not beenconvincingly identified. In particular, the 'width' has not been quantitativelylinked yet to a physical time scale. We demonstrate that there are two robustfundamental time scales that 1. can be calculated based on integral quantitiesof the ejecta, with little dependence on radiation transfer modeling and 2. canbe inferred from observations. The first is the gamma-ray escape time $t_0$,which determines the long-term evolution of the bolometric light curve and isstudied in this Paper I. The second is the recombination time of $^{56}$Fe and$^{56}$Co, which sets the long-term color evolution of the emitted light and isstudied in Paper II. Here we show that the gamma-ray escape time $t_0$ can bederived with $\sim 15\%$ accuracy from bolometric observations based on firstprinciples. When applied to a sample of supernovae, the observed values of$t_0$ span a narrow range of $30-45$ days for the wide range of observed$^{56}\rm Ni$ masses $0.1M_{\odot}\lesssim M_{^{56}\rm Ni}\lesssim 1M_{\odot}$. %This (trivial) bolometric WLR This narrow range of the gamma-rayescape time across the range of luminosities (a trivial WLR) is consistent withcentral detonations and direct collisions of sub-Chandrasekhar mass whitedwarfs (WDs) but not with delayed detonation models for explosions ofChandrasekhar mass WDs, which are therefore disfavored as the primary channelfor the population of type Ia supernovae. Computer codes for extracting $t_0$from observations and models and for calculating gamma-ray transfer in 1D-3Dare provided.

Type Ia supernovae have two physical width-luminosity relations and they favor sub-Chandrasekhar and direct collision models. I. Bolometric