Why can't we see the light before we turn on the bulb?

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Pardon me if there is an obvious answer, I have not spent too much time thinking about it.

Having stumbled upon the "light cone." (Just the spacetime diagram centered around the event of turning on a light source.) I have the following question:

I am not going to be too detailed, but why can't see the light from a light bulb we switched on before we switched it on, if the light emits in the past direction as well as the future direction?
 
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It does not emit in the past direction.

Only events within the past light cone can affect the light. Anything outside the light cone is causally unconnected to the light bulb.
 
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