Is the Neutron Lifetime a Surprising Result of 'Unnatural' Numbers in Physics?

[tzimie]

Neutron lifetime is approx. 880s, or 1.6 * 10^46 planks times.

Also, in a "naive" model quarks fly back and forth at almost light speed, bouncing back and forth, and only a single bounce per 3.3*10^26 times is fatal to the existence of a neutron. Even this model is wrong, it shows to what extent neutron is "almost" stable.

Are these numbers surprising to the same extent as other "unnatural" numbers in physics?

 

[DrChinese]

Neutron lifetime is approx. 880s, or 1.6 * 10^46 planks times.

Also, in a "naive" model quarks fly back and forth at almost light speed, bouncing back and forth, and only a single bounce per 3.3*10^26 times is fatal to the existence of a neutron. Even this model is wrong, it shows to what extent neutron is "almost" stable.

Are these numbers surprising to the same extent as other "unnatural" numbers in physics?

Surprising in what way? In the order of magnitude of the small cross-section?

By "unnatural", do you mean that in the way of a "magic" number (one that cannot be independently derived)?

 

[tzimie]

Surprising in what way? In the order of magnitude of the small cross-section?

By "unnatural", do you mean that in the way of a "magic" number (one that cannot be independently derived)?

Just the magnitude of the dimensionless numbers in my first post.
We know that huge dimensionless numbers can be easily provided comparing the weakness of gravity vs QM interactions, but in the case of neutron no gravity is involved.

 

[DrChinese]

Just the magnitude of the dimensionless numbers in my first post.
We know that huge dimensionless numbers can be easily provided comparing the weakness of gravity vs QM interactions, but in the case of neutron no gravity is involved.

I guess you could make that statement about anything with a long half-life. In fact, if the proton has a half-life, it would be >50 orders of magnitude greater. There are a number of large ratios at the 120 orders of magnitude level too.

So I guess "surprise" is in the eye of the beholder.

 

[PeterDonis]

in a "naive" model quarks fly back and forth at almost light speed, bouncing back and forth, and only a single bounce per 3.3*10^26 times is fatal to the existence of a neutron

Where are you getting this "naive" model from? If you just made it up yourself, please review the PF rules on speculative/personal theory posts.

The neutron decays through the weak interaction, which (for this particular case) involves an up quark changing into a down quark. It has nothing to do with quarks "bouncing". The lifetime of the neutron is due to the large mass of the W particle (roughly 80 GeV) which mediates the weak interaction involved.

 

[tzimie]

The neutron decays through the weak interaction, which (for this particular case) involves an up quark changing into a down quark. The lifetime of the neutron is due to the large mass of the W particle (roughly 80 GeV) which mediates the weak interaction involved.

I understand that the lifetime of neutron is sensitive to mass of W particle, but how exactly sensitive is it?
What if W was 100 or 160 GeV, how long would be the lifetime?

 

[PeterDonis]

how exactly sensitive is it?

Roughly speaking (there are a lot of complications in the detailed calculation), the lifetime goes like the fourth power of the W boson mass, so doubling the mass would make the lifetime 16 times as long; halving the mass would make the lifetime 1/16 as long; etc.