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Ethereal Jaunt says: "An ethereal creature is invisible, insubstantial, and capable of moving in any direction, even up or down, albeit at half normal speed. As an insubstantial creature, you can move through solid objects, including living creatures."
Can a PC run or double move? If so, does this reduce each type by half as well?
Yes, they can double move and run, and yes, since both double move and run are based on your speed, which is halved, the maximum movement for either method will also be halved.