If it were truly synthesized from scratch -- individual atoms plucked one by one from the air -- the answer to the question of whether or not it is kosher is mu (http://www.catb.org/jargon/html/M/mu.html) as kosher is inapplicable to non-food items.
Even if the donor cells are from non-kosher animals, there is a modest body of responsa (case law) that seems to permit it. Some authorities permit the use of gelatin made from non-kosher animal bones, claiming that the end product is totally different in nature than the starting (non-kosher animal) product; and that creating the gelatin required putting the animal product into a state of total inedibility, thus removing it from the domain of kosher/non-kosher, notwithstanding its subsequent reconstitution into edible food. Vat-grown meat is supposed to be very similar if not identical to bio-meat, so it's unclear if these authorities would rule the same way for vat-grown pork as they do for pork-derived gelatin.
Even amongst sources who do not abide by the above ruling (and it appears a majority do not), there may yet be hope for the kosher cheeseburger. If the donor cells which are vat-cultured are from a kosher cow, the resulting food may not be considered meat (with respect to the prohibition of mixing meat and milk). Again, based on responsa regarding the gelatin question, gelatin made from kosher bones and hides is parve (neither meat nor dairy). However, these responsa seem to agree that one of the main arguments that this is so is because one stage of gelatin creation is processing the raw material into what is essentially non-food, thus eradicating its inherent "meatness" (but nothing can remove its applicability to the question of kosher). This may or may not be applicable to the case of vat-grown meat; however, if the process entails some cells being stripped away from the meat and/or pulverized into something inedible for a period of time, the resulting product may well be kosher but not considered meat. The only question left would be: american cheese or whiz?
Even if the donor cells are from non-kosher animals, there is a modest body of responsa (case law) that seems to permit it. Some authorities permit the use of gelatin made from non-kosher animal bones, claiming that the end product is totally different in nature than the starting (non-kosher animal) product; and that creating the gelatin required putting the animal product into a state of total inedibility, thus removing it from the domain of kosher/non-kosher, notwithstanding its subsequent reconstitution into edible food. Vat-grown meat is supposed to be very similar if not identical to bio-meat, so it's unclear if these authorities would rule the same way for vat-grown pork as they do for pork-derived gelatin.
Even amongst sources who do not abide by the above ruling (and it appears a majority do not), there may yet be hope for the kosher cheeseburger. If the donor cells which are vat-cultured are from a kosher cow, the resulting food may not be considered meat (with respect to the prohibition of mixing meat and milk). Again, based on responsa regarding the gelatin question, gelatin made from kosher bones and hides is parve (neither meat nor dairy). However, these responsa seem to agree that one of the main arguments that this is so is because one stage of gelatin creation is processing the raw material into what is essentially non-food, thus eradicating its inherent "meatness" (but nothing can remove its applicability to the question of kosher). This may or may not be applicable to the case of vat-grown meat; however, if the process entails some cells being stripped away from the meat and/or pulverized into something inedible for a period of time, the resulting product may well be kosher but not considered meat. The only question left would be: american cheese or whiz?