I like to know do vacuum space have momentum due to quantum fluctuations?
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No. There would be no direction for the vacuum expectation value of the momentum since all directions in a vacuum are equivalent.
G. Smith
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The total momentum at any point will be zero but as there are minute fluctuations in electric and magnetic fields, it can be stated that vacuum has momentum.
Do check out the existence of virtual particles. This might help you understand deeper about properties of vacuum