Can remaindermen of a life estate physically and personally inspect the property during the life of the Life Tenant?

This is one of the MANY reasons why people shouldn't leave life estates to people without a lengthy document specifying rights and obligations. If the will did not specify, generally the life tenant is responsible for taxes, insurance and routine maintenance. But if no rights of inspection were spelled out in the will, you are pretty much on your own. The life tenant has the right to the full use and enjoyment of the property. Unless a separate writing gave you the right, you have no right to enter onto the property. Certainly I would recommend checking regularly on the status of property taxes, to be sure the property doesn't end up in a tax sale. You could also drive by periodically. But if you want to do an inspection, and if the life tenant doesn't voluntarily allow it, you would have to go to court to try to force the inspection.