Einstein এর সমীকরণগুলো কেন black –hole এর বেলায় কিম্বা Big Bang এর শুরুতে ভেঙে পরে, তার একটি খুব সহজ ব্যাখ্যা দিয়েছেন David Simmons-Duffin নামের একজন পদার্থবিদ।ব্যাখ্যাটি নিম্নরূপঃ
We know :
1/(1–x) = 1 + x + x^2 + x^3 + ……… (*)
Here's the analogy:
• The left hand side is like the exact answer (what the correct theory of everything would predict)
• The right hand side is the kind of answer we get from current theories -- a series expansion (and we actually don't know all the coefficients)
• Small x is like low energies (most of observed physics)
• Large x is like high energies (relevant to black holes and the Big Bang)
Use small values, like 0.1, 0.0345, etc for x . You'll find that the formula works very well. Now try some bigger numbers like 1 or 1000. Not only does the equation not work, but the right hand side doesn't even make sense. This is what we mean by an equation "breaking down at high energies."
Then where is the discrepancy ?
Because the equation ( * ) makes sense only in the radius of convergence , which is 1 here. and thus the equality doesn't hold for x>1. That is the whole point of my answer. The energy expansion in effective field theory also has a finite radius of convergence and thus can't be used at high energies.
