de Broglie Wavelength For the Proton at a Very Low Velocity

In modern physics, the de Broglie wavelength is considered to be the matter wave. However, the de Broglie wave has a series of strange properties. It is not mathematically defined for a rest-mass particle, when v=0. However, one can claim a particle never stands still and that the de Broglie wavelength only converges towards infinite when v converges to zero. An infinite matter wavelength would also be strange. We have good reasons to think that the de Broglie wavelength only is a mathematical derivative of the true matter wavelength, which we believe is the Compton wavelength. Although noted briefly here, this has already been described by Haug \cite{Hau20UnifiedA} and is a topic for another article. What we will focus on here is that the length of the de Broglie wavelength, if we use an observational window of one second and the minimum observable velocity, is the Planck length per second. Then the de Broglie wavelength for a proton actually has a length very close to the assumed radius of the observable universe. We think most likely this is a coincidence, particularly since one second is an arbitrarily chosen time unit, and not a fundamental time unit such as the Compton time, or the Planck time, for example. Still, we think this finding is worth mentioning and could be the basis for further discussion.