We are so accustomed to the time-bandwidth limit that we often take it to be a fundamental relation that cannot be overcome. Contrary to this belief we here propose that the storage/delay time of a system can in fact be decoupled from the operating bandwidth, by breaking Lorentz reciprocity. We discuss two different mechanisms for breaking Lorentz reciprocity and show that-in the correct system layout-both can result in systems that exceed the conventional time bandwidth limit by orders of magnitude.