I keep hearing that infinity is only a mathematical concept and not a physical possibility. Therefore, is there an opposite of Planck Length, the LONGEST possible lenght something can be?
Well, I suppose you could say that the longest possible length something could be is the size of the universe, although since that’s always changing, I’m not sure how helpful that is. On the other hand, there’s not really a shortest possible length either (at least that we know of); the Planck length is just a length scale at which the effects of relativity and quantum mechanics are both important (crudely speaking). It DOESN’T mean that the Planck length is the minimum possible length, so I don’t see why there should be a maximum possible length, either.
I mean, say you have a really really really long rope, say, 10 billion light years (I have to wonder why you’d want it, but that’s beside the point). Tie a 4 foot rope to one end. Now you have a very slightly longer rope. Keep on doing it. Assuming you have an infinite supply of material from which to make your ropes to begin with, you can make it as long as you want, but you’ll always have a rope of finite size, right? That doesn’t mean you can’t add to it.
What g8rguy said…the length of the universe (which may be infinite).
But, FWIW, the Planck Length is not the smallest possible length…it’s just the smallest length that modern physics can describe/understand.