Explaining the Hierarchy problem for beginners

[eiyaz]

https://en.wikipedia.org/wiki/Hierarchy_problem

I understand that hierarchy problem is the large discrepancy between aspects of the weak force and gravity. But why? Why is the explanation, that gravity is simply a much weaker force not acceptable? Is it possible that gravity is just an exponentially weaker force?

Every explanation says the hierarchy problem is looking for the reason why gravity is so much weaker than other force without explaining why this is a problem in the first place (for non-physics and mathematicians.)

 

[mfb]

There are two things called hierarchy problem.

The first question is simply the interaction strength. We can express all those as dimensionless values. The interaction strength of the strong interaction is about 0.5, the weak interaction strength is about 0.03, and the electromagnetic interaction strength is about 0.01. The strength of gravity is about 0.0000000000000000000000000000000000001. Possible? Sure. But it looks very odd.

The second point is the Higgs mass. The Standard Model tells us that the Higgs mass is the sum of two independent components: its bare mass and quantum corrections. While we cannot calculate the quantum corrections exactly, they should be about 10¹⁹ GeV (roughly the Planck mass). We also know the sum of the two components: 125 GeV - the two summands cancel each other nearly perfectly. What are the odds that two unrelated numbers agree in the first 16 decimal places?

The two questions are connected: The Higgs mass puzzle comes from the large Planck scale compared to particle masses, which is equivalent to the tiny coupling strength of gravity.

 

[eiyaz]

There are two things called hierarchy problem.

The first question is simply the interaction strength. We can express all those as dimensionless values. The interaction strength of the strong interaction is about 0.5, the weak interaction strength is about 0.03, and the electromagnetic interaction strength is about 0.01. The strength of gravity is about 0.0000000000000000000000000000000000001. Possible? Sure. But it looks very odd.

The second point is the Higgs mass. The Standard Model tells us that the Higgs mass is the sum of two independent components: its bare mass and quantum corrections. While we cannot calculate the quantum corrections exactly, they should be about 10¹⁹ GeV (roughly the Planck mass). We also know the sum of the two components: 125 GeV - the two summands cancel each other nearly perfectly. What are the odds that two unrelated numbers agree in the first 16 decimal places?

The two questions are connected: The Higgs mass puzzle comes from the large Planck scale compared to particle masses, which is equivalent to the tiny coupling strength of gravity.

It feels like something is wrong because we think the discrepancy too large and unnatural to the human mind? Or is something mathematics and scientifically wrong?

 

[mfb]

It looks unnatural. The mathematics is fine, but it looks very odd.

There are other issues with the standard model that lead to mathematical problems, but the hierarchy problem could be "just" a ridiculous amount of fine-tuning.

 

[DennisN]

The two questions are connected: The Higgs mass puzzle comes from the large Planck scale compared to particle masses, which is equivalent to the tiny coupling strength of gravity.

Thanks a lot, mfb, I did not know about that. Very interesting! I'd like to know more about this, so I will look on the net for more info. If you happen to have any suggestions of good links/sources regarding this (i.e Higgs mass/particle masses versus gravity coupling), I would be very interested.

 

[eiyaz]

It looks unnatural. The mathematics is fine, but it looks very odd.

There are other issues with the standard model that lead to mathematical problems, but the hierarchy problem could be "just" a ridiculous amount of fine-tuning.

So is it safe to say there is no hierarchy problem, other than the human mind's feelings of unnaturalness?

 

[eiyaz]

I know this is a little late, but I just found out marcus died, when I tried to PM him for a clearer answer. Probably the among greatest loss to this forums. May your spirit travel with the neutrinos for all of time.

 

[mfb]

The human minds' feelings of unnaturalness are the hierarchy problem.

Note that we had similar instances in the past where an unnatural value or small deviations from expectations lead to a deeper insight. As an example, the electron g-value shows a small deviation from Dirac's prediction of 2, which was later explained by QFT. Same for the Lamb shift, which helped developing QFT. The proton has a g-value that doesn't have such an explanation - an early hint that it is a composite particle.

 

[zito1]

So is it safe to say there is no hierarchy problem, other than the human mind's feelings of unnaturalness?

All the science we have comes from the human mind. If it looks unnatural to the human mind, that may be a sign that it really doesn't fit all the other science.

Maybe everything we know is wrong. Or maybe we can never know anything. I'm sure not going with either of those without double checking...I think it's safe to say that we should take such conundrums seriously unless we want to give up the entire enterprise.

 

[weirdoguy]

Maybe everything we know is wrong.

Not wrong - incomplete.

 

[mfb]

Maybe everything we know is wrong.

All our technology is based on things we know. I don't think it's pure coincidence that it works. If you randomly combine different rocks you don't produce a working computer.

 

[Vanadium 50]

Maybe everything we know is wrong

Maybe it is. But this no-nothing position is intellectually sterile. It says we can never know anything, so we might as well go back to living in caves and hunting with clubs.

I think it's safe to say that we should take such conundrums seriously

What conundrums are not being taken seriously?