We know that Romeo's feelings are more akin to infatuation due to the intensity of his feelings plus the suddenness with which he switched from loving Rosaline to Juliet. His feelings for Rosaline and his hurt over her rejection were so intense and all-consuming that he worried his father due to the fact that he had been seen staying out all night, night after night, and been seen crying each morning at dawn. This all-consuming intensity alone and any rejection of reasonable advice is evidence alone that Romeo feels infatuation rather than real love. In addition, Romeo confesses to confusing real love with mere physical attraction, another symptom of infatuation, when he first sees Juliet in his lines, "Did my heart love till now? Forswear it, sight! / For I ne'er saw true beauty till this night" (I.v.54-55). Even Friar Laurence believes Romeo has confused real love with infatuation, as shown when he declares that "young men's love then lies / Not truly in their hearts, but in their eyes" (II.iii.68-69). Even just before he marries them, Friar Laurence expresses the belief that all they feel for each other is mere infatuation by warning their love is likely to die just as soon as it has begun, "like fire and powder" (II.vi.10).
While Juliet's love at first is also all about physical attraction, the moment Romeo kills her cousin Tybalt gives her a chance to make choices and for her love to mature. At first, she feels she has been deceived by Romeo and that his beautiful exterior really houses a devilish soul. But then she decides that she should not speak dishonorably of her husband, simply because he is her husband. She then makes the reasoned conclusion that Romeo must have killed Tybalt out of self-defense and further decides to continue loving and trusting Romeo. This one moment of choice is real love, but Romeo never has a moment to make a similar choice. Therefore, only Juliet's love for Romeo is mature enough to be considered real love rather than infatuation.
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The word "absolutely" means something complete that is presented in its entirety in an integral way. Another meaning that this word has is the sense of independence. Something absolute is something that does not need to relate to anything, nor depend on anything for what it is.