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

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In summary, the neutron has a lifetime of approximately 880 seconds or 1.6 * 10^46 plank times. In a "naive" model, it was thought that 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. However, this model is incorrect and the actual reason for the neutron's almost stability is due to the weak interaction, specifically the large mass of the W particle. The lifetime of the neutron is sensitive to the mass of the W particle, with the lifetime going like the fourth power of the W boson mass.
  • #1
tzimie
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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?
 
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  • #2
tzimie said:
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)?
 
  • #3
DrChinese said:
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.
 
  • #4
tzimie said:
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.
 
  • #5
tzimie said:
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.
 
  • #6
PeterDonis said:
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?
 
  • #7
tzimie said:
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.
 

1. What is the "Unnaturalness of Neutron"?

The "Unnaturalness of Neutron" refers to the fact that the neutron, one of the three fundamental particles that make up an atom, is an unstable particle. This means that it has a relatively short lifespan and will eventually decay into a proton, an electron, and a neutrino.

2. Why is the unnaturalness of neutron significant?

The unnaturalness of neutron is significant because it raises questions about the stability and balance of the universe. If the neutron was perfectly stable, it would be the only particle needed to make up all the elements in the universe. However, its instability leads to the creation of new particles, which affects the overall composition of the universe.

3. How is the unnaturalness of neutron related to nuclear reactions?

The unnaturalness of neutron plays a critical role in nuclear reactions. In nuclear fission, for example, a neutron is absorbed by a heavy nucleus, causing it to become unstable and split into smaller nuclei. This process releases a tremendous amount of energy and is the basis for nuclear power plants and nuclear weapons.

4. Can the unnaturalness of neutron be observed in everyday life?

Although the unnaturalness of neutron is not directly observable in everyday life, its effects can be seen in various technologies and processes. For example, medical imaging techniques such as PET scans rely on the unstable nature of neutrons to create images of the body's tissues and organs.

5. Can the unnaturalness of neutron be explained by current theories?

While there are several theories that attempt to explain the unnaturalness of neutron, it remains an unsolved mystery in physics. Some theories propose the existence of new particles that could explain the neutron's instability, while others suggest that it is a fundamental property of the universe that we have yet to fully understand.

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