Fix any words that may be used incorrectly: the physics professor asked the class "does time proceed/precede from past to present, and on into the future, or is the concept of time simply an illusion/allusion? "

The physics professor asked the class, "Does time proceed from past to present, and on into the future, or is the concept of time simply an illusion?".

The definition of the first two is on the other question. 

Illusion: a thing that is or is likely to be wrongly perceived or interpreted by the senses.
Allusion: an expression designed to call something to mind without mentioning it explicitly; an indirect or passing reference.

The last definition of the word is a bit confusing so I'll give you an example.
Ex: Emma dramatically raised her hand, "Romeo, oh Romeo, where art thou?" 
The line "Romeo" is an allusion to Shakespeare's Romeo and Juliet, even though it doesn't mention it specifically.