Quantum Mechanics: Unfamiliar Arena of Before & After

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In the Elegant Universe, on page 129, first paragraph, it says

""...ultramircoscopic examination of space (and time)---it describes an unfamiliar arena of the universe in which the conventional notions of left and right, back and forth (and even of before and after) lose their meaning."

of course, this is illustrating quantum foam.
When Greene says that the meaning of "before and after lose their meaning", does he mean that before and after occur at different times, so to speak? Like, after would happen before before? Of course, that doesn't make any sense at all...but this is quantum mechanics. It doesn't make any [common] sense.
I am sure my understanding of it is incorrect( because it violates laws stated in thermodynamics; Entropy is only in one direction). I would like some clarification please.
 
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On first note, I'd would like to say that it is a great book and I hope you have fun with it.

On second not, I think you answered your own question. When you said "space (and time)" I think what you should have said was spacetimeThis is because, while your space is warping heavily (which would explain why the definitions of front, back, and side to side don't apply) so is your time dimension. Time would be warped along with space, both skewing the defintions.

Paden Roder
 
But what did Greene mean when he said that notions such as before and after loose their meaning?
 
He means that when events occur within a Planck scale time period there is no meanigful way of putting them in chronological order.
 
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