✎ Hierarchy Puzzle [The Physics Travel Guide]

You've loaded an old revision of the document! If you save it, you will create a new version with this data.

====== Hierarchy Problem ======

<blockquote>
According to the Higgs mechanism, space is filled with a uniform density of Higgs substance. But because of the complexity of the quantum vacuum, the calm sea of Higgs substance is continually disturbed by the rapid production and annihilation of all sorts of virtual particles. The constant buzz of virtual particles affects the density of the space-filling Higgs substance. Just as ghosts flickering in and out of the netherworld leave vivid memories in the minds of impressionable indi- viduals, so virtual particles leave their indelible imprint in the Higgs substance. The swirling of virtual particles effectively gives a gigantic contribution to the density of the Higgs substance, which becomes extremely thick.
Theoretical calculations show that this contribution to the density of the Higgs substance is proportional to the maximum energy carried by virtual particles. Since virtual particles can carry huge amounts of energy, the molasses-like Higgs substance becomes thicker than mud or even as hard as rock when quantum-mechanical effects are taken into account. Ordinary particles moving inside this medium should feel a tremendous resistance or, in more precise physical terms, should acquire enormous masses. Calculations based on a simple extrapolation of the Standard Model all the way down to the Planck length yield the result that electrons should be one million billion times more massive than what we observe – as heavy as prokaryote bacteria. But since electrons are obviously not as heavy as bacteria, we are confronted with a puzzle: why is the Higgs substance so dilute in spite of the natural tendency of virtual particles to make it grow thicker?
This dilemma is usually referred to as the naturalness problem. The density of the Higgs substance determines how far the W and Z particles can propagate the weak force; in other words, it determines the weak length. Therefore, when virtual particles make the Higgs substance thicker, they effectively make the weak length shorter. The naturalness problem then refers to the conflict between, on one side, the tendency of virtual particles to make the weak length as small as the Planck length and, on the other side, the observation that the two length scales differ by the enormous factor of 1017. Let us rephrase the problem with an analogy.
Suppose that you insert a piece of ice into a hot oven. After waiting for a while, you open the oven and you discover that the ice is perfectly solid and hasn’t melted at all. Isn’t it puzzling? The air molecules inside the hot oven should have conveyed their thermal energy to the piece of ice, quickly raising its temperature and melting it. But they did not.
The naturalness problem is equally puzzling. The energetic virtual particles are like the hot air molecules of the oven analogy, and the Higgs substance is like the piece of ice. The frenzied motion of virtual particles is communicated to the Higgs substance, which should become as hard as rock. And yet, it remains very dilute. The weak length should become as small as the Planck length. And yet, the two lengths differ by a factor of 1017.
Just as in the inside of a hot oven nothing can remain much cooler than the ambient temperature, so in the quantum vacuum virtual particles do not tolerate that the weak length remain much larger than the Planck length. Thus, the real puzzle is that no hierarchy between weak and gravitational force should exist at all, let alone there being a differ- ence by a factor of 1017. The essence of the naturalness problem is that the anarchic behaviour of virtual particles does not tolerate hierarchies.
At this point, a very important warning should be issued. The naturalness problem is not a question of logical consistency. As the word says, it is only a problem of naturalness. Virtual particles provide one part of the energy stored in the Higgs substance. Nothing forbids the possibility of nature carefully choosing the initial density of the Higgs substance in such a way as to nearly compensate the effect from virtual particles. Under these circumstances, the enormous disparity between the weak and Planck lengths could be just the result of a precise compensation among various effects. Although this possibility cannot be logically excluded, it seems very contrived. Most physicists have difficulties accepting such accurate compensations between unrelated effects, and regard them as extremely unnatural.

<cite>"A Zeptospace Odyssey" by Guidice</cite></blockquote>
<tabbox Student>

* [[https://arxiv.org/abs/0801.2562|Naturally Speaking: The Naturalness Criterion and Physics at the LHC]] by G.F. Giudice
  * http://syymmetries.blogspot.de/2017/06/naturalness-pragmatists-guide.html
 
<tabbox Researcher> 
[[https://inspirehep.net/record/189504/|Fine Tuning Problem and the Renormalization Group
C. Wetterich]]
<tabbox Examples>

--> Example1#

<--

--> Example2:#

<--
  
<tabbox History>

</tabbox>

Please solve the following equation to prove you're human. 207 +4 = Please keep this field empty:

Edit summary

Note: By editing this page you agree to license your content under the following license: CC Attribution-Share Alike 4.0 International

User Tools

Site Tools

Page Tools