The idea is that you can't do that because the conditions necessary for you to be at the entrance of the time travel working prevent you from being at the exit of the wormhole at the same time.
To get to the entrance, you must leave the Earth (with the entrance) at time X. After you've left, you can enter the wormhole and emerge from the Earth side at time X+e.
You leave Earth in 2020. You leave one end of the wormhole here, and take the other with you on a near-light-speed journey 40 light years away. One year goes by for you due to relativity, you pick up a burger from alien McDonald's, then step into your wormhole- which exits in 2021, not 2040.
Edit: no wait, I can't be understanding this right. You could just journey back home with your wormhole and give it to someone else.
To get to the entrance, you must leave the Earth (with the entrance) at time X. After you've left, you can enter the wormhole and emerge from the Earth side at time X+e.
You leave Earth in 2020. You leave one end of the wormhole here, and take the other with you on a near-light-speed journey 40 light years away. One year goes by for you due to relativity, you pick up a burger from alien McDonald's, then step into your wormhole- which exits in 2021, not 2040.
Edit: no wait, I can't be understanding this right. You could just journey back home with your wormhole and give it to someone else.