yes, but nearly unmeassureable, because E=mc^2, adding energy increases mass

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Here’s an un-old-ified link: https://reddit.com/r/NoStupidQuestions/comments/1voz7kz/if_i...

How Much Does the Internet Weigh? https://youtu.be/WaUzu-iksi8?si=T4x1M45i-p4y4A_r

Check the dooblydoo for a bibliography of links!

Measurement scale matters.