This was the key question in Watergate scandal.
But, this post is actually about what a Ph.D student should know and when they should know it. Here are a few different answers I have heard:
When the student knows more about the topic than their advisor/supervisor they are ready to submit their thesis.
At the end of your Ph.D you should know more about the topic than anyone else in the world.
The student should know more about the project than their advisor by the time they do their comprehensive exam (a few years into a US Ph.D).
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