3 ms·

Please help me understand the logic of naturalness. Suppose we have one constant, alpha, approx= 1.425, and another (beta) approx=2.157 - such setup is deemed n

Please help me understand the logic of naturalness. Suppose we have one constant, alpha, approx= 1.425, and another (beta) approx=2.157 - such setup is deemed natural. And if the other constant is approx 2.157 times 10^40, it's not natural. and needs fine-tuning, right? The underlying assumption is that fine-tuning is not needed for a former setup, that is, if beta was about 0.5%, or 0.05% different from where it sits at 2.157, then we would be totally fine, Universe would look the same for all intents and purposes. I fail to see how this follows. Maybe the difference by 10^(-40) would make life impossible? how can we possibly know this?

blablabla123 9y ago
It's not really about the values of constants but about where they appear and about their size. So imagine we have some Physics setup were certain laws should hold. There is some magical formula called Lagrangian L = stuff. When you construct this L from scratch, you add everything you have. That is some e for the Electron field function, some phi for the Higgs, some m for its mass etc etc. At first this sounds like an insanely long and random equation. But because of all the constraints in your setup its 'only' one page long for the Standard Model case. Oh yes and then there are some stupid terms which must be really small to only _softly_ violate the constraints. E.g. CP-symmetry for strong interactions - violation of this symmetry hasn't been observed in nature "Strong CP problem". That's where fine-tuning has to happen at the moment...
- resource0x 9y ago
  Please confirm that my understanding is correct. You have a number of "stupid" terms in Lagrangian, whose cumulative effect must be small in order for the whole theory to make sense at all. This small cumulative effect can be achieved in 2 ways: 1) each term is small 2) terms more or less cancel out. When each term is small, we call it naturalness, otherwise it's fine-tuning. If this is correct, then... say you have N random varaibles, and you know that the sum is small. What is more likely: that each of N variables is small, or that the sum is small because it just happens to be small? :)
  - blablabla123 9y ago
    Fortunately there are not so many terms of this kind in the Standard Model case. :) However terms don't really cancel each other out. (I'm sure you could construct a scenario where that happens but that doesn't generalize.) It's part of the construction manual if you will to have only independent constants and terms.

blablabla123 9y ago

It's not really about the values of constants but about where they appear and about their size. So imagine we have some Physics setup were certain laws should hold. There is some magical formula called Lagrangian L = stuff. When you construct this L from scratch, you add everything you have. That is some e for the Electron field function, some phi for the Higgs, some m for its mass etc etc. At first this sounds like an insanely long and random equation. But because of all the constraints in your setup its 'only' one page long for the Standard Model case. Oh yes and then there are some stupid terms which must be really small to only _softly_ violate the constraints. E.g. CP-symmetry for strong interactions - violation of this symmetry hasn't been observed in nature "Strong CP problem". That's where fine-tuning has to happen at the moment...

resource0x 9y ago
Please confirm that my understanding is correct. You have a number of "stupid" terms in Lagrangian, whose cumulative effect must be small in order for the whole theory to make sense at all. This small cumulative effect can be achieved in 2 ways: 1) each term is small 2) terms more or less cancel out. When each term is small, we call it naturalness, otherwise it's fine-tuning. If this is correct, then... say you have N random varaibles, and you know that the sum is small. What is more likely: that each of N variables is small, or that the sum is small because it just happens to be small? :)
- blablabla123 9y ago
  Fortunately there are not so many terms of this kind in the Standard Model case. :) However terms don't really cancel each other out. (I'm sure you could construct a scenario where that happens but that doesn't generalize.) It's part of the construction manual if you will to have only independent constants and terms.