Comment: "Since our minds are not

"Since our minds are not connected together as in a matrix hive, their idea belongs to them alone."

its correct that our minds are not connected together (some would argue this) in a matrix, but people's ideas reside with them alone. introducing the word 'belongs' implies ownership, but that is what you are trying to prove! and simply making a declaration is not a proof!

If they freely choose to share it with the world, that is their right to do so. But if they desire to keep the idea secret onto themselves until such time in the future, that is their right as well.
yes. it is a person's right to keep whatever ideas they have in their head to themselves.

Now along comes a second person and by whatever means, becomes aware of the engineer’s idea. The question becomes, does this person have the right to copy the engineer’s cumulative work, create a variation of it and benefit from that modification?
why are you dismissing the means by which someone becomes aware of the 'engineer's idea'? is there not a difference between someone breaking into your office, thus violating your property rights, and stealing schematics and someone independantly thinking of the idea? any system of thought that cannot draw a distinction is fundamentally flawed.