It might be a good idea to explain why I think carrying in one's pocket on the Sabbath Day is OK. To do that in a structured way.
The basic idea comes from the gemaras [Bava Batra 85] about acquisition. The question is if an object in the vessel of a person is thought to be in the domain of the person or the larger domain. There are differences if the vessel belongs to the seller or the buyer or to a third party. But the fact remains that the major question is if the object is considered to be in the larger domain or the bag. That is how the Rashbam explains it. Then the connection with Shabat comes from the Gemara that equates the two issues in Bava Batra 86.
The reason this is important is that a public domain does not seem to need 600,000. Even though Rashi and Tosphot both say that it does still it is hard to see how this could have been fulfilled in ancient Persia and the Gemaras in Shabat seem to treat the streets there as public domains.
The basic idea comes from the gemaras [Bava Batra 85] about acquisition. The question is if an object in the vessel of a person is thought to be in the domain of the person or the larger domain. There are differences if the vessel belongs to the seller or the buyer or to a third party. But the fact remains that the major question is if the object is considered to be in the larger domain or the bag. That is how the Rashbam explains it. Then the connection with Shabat comes from the Gemara that equates the two issues in Bava Batra 86.
The reason this is important is that a public domain does not seem to need 600,000. Even though Rashi and Tosphot both say that it does still it is hard to see how this could have been fulfilled in ancient Persia and the Gemaras in Shabat seem to treat the streets there as public domains.
