I have recently begun using diatomaceous earth to brush my teeth and they have never felt cleaner.
DE has a negative charge and all the bad stuff (plaque, tartar, and bad bacteria) has a positive charge. The bad stuff is attracted to the DE and gets whisked right off the teeth and tongue.
Also my teeth are as white or maybe more than the commercial teeth bleach gets them. Same principle--the DE just pulls the stains right off. I have also filled a bleaching tray or tooth guard with mud made with DE and water and worn it while I showered. It pulls the bacteria from under the gum line and leaves your gums so healthy without the abrasive brushing.