Dark matter is currently one of the main mysteries of the Universe. There is much strong indirect evidence that supports its existence, but there is yet no sign of a direct detection^{, –}. Moreover, at the scale of galaxies, there is tension between the theoretically expected dark matter distribution and its indirectly observed distribution^{, , –}. Therefore, phenomena associated with dark matter have a chance of serving as a window towards new physics. The radial acceleration relation^, confirms that a non-trivial acceleration scale a₀ can be found from the internal dynamics of several galaxies. The existence of such a scale is not obvious as far as the standard cosmological model is concerned^,, and it has been interpreted as a possible sign of modified gravity^,. Here, we consider 193 high-quality disk galaxies and, using Bayesian inference, show that the probability of existence of a fundamental acceleration is essentially 0: the null hypothesis is rejected at more than 10σ. We conclude that a₀ is of emergent nature. In particular, the modified Newtonian dynamics theory^{, , –}—a well-known alternative to dark matter based on the existence of a fundamental acceleration scale—or any other theory that behaves like it at galactic scales, is ruled out as a fundamental theory for galaxies at more than 10σ.