It is forbidden for a person eating meat and a person eating dairy food to eat at the same table if they are acquainted with one other. The Sages enacted this prohibition out of the concern that as acquaintances, they might share their food with one another, forgetting the prohibition against eating meat with dairy food.
The way to avoid this prohibition is to place a "Heker," or a reminder, in between them on the table, which will remind them not to share each other’s food. The "Heker" must be an extraneous object that does not otherwise naturally belong on the table. For example, if neither of them plans to eat bread at the meal, then they may place a loaf of bread on the table as a "Heker." Similarly, a vase that is not normally on the table can serve as a valid "Heker." However, a bottle of soda that is used as part of the meal cannot serve as a "Heker," since it belongs on the table as part of the meal.
Can two people avoid this prohibition by appointing a third part to act as a "Shomer" (literally, "watchman") to watch them and ensure that they do not share each other’s food?
There is an opinion among the Halachic authorities allowing two people to eat meat and dairy at the same table and rely on a third party "Shomer." Proponents of this view draw proof from the story of Abraham’s guests, to whom he served milk and butter, as well as meat (see Bereshit 18:8). Presumably, the meat and dairy foods were served to different guests, and they ate together because, as the Torah says, Abraham stood over them as they eat ("Ve’hu Omed Alehem Tahat Ha’etz Vayochelu"). If so, then this story provides a basis for allowing milk and meat to be eaten at the same table if a "Shomer" is designated to watch and ensure that the food is not shared.
The accepted Halacha, however, does not follow this opinion. Taking food from somebody else’s plate is something that happens too quickly for a "Shomer" to prevent. According to the accepted view, therefore, assigning a "Shomer" is not an effective means of avoiding the prohibition against eating milk and meat at the same table.
Summary: It is forbidden for a person eating meat and a person eating dairy food to eat at the same table if they are acquainted with one another, unless they place something on the table that is not needed for the meal and is not normally on the table.