Why is the hierarchy problem a problem?

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  • #26
Vanadium 50
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Michael gave it in a talk somewhere. I copied it down there. But the idea is that the first term is the Higgs bare mass and the second term is the radiative corrections to the mass. Neither is calculable today, all we know is the rough size and the difference between those numbers.
 
  • #27
Buzz Bloom
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Neither is calculable today
Hi Vanadium:

Does this mean that the values were once calculable, but now they aren't? If so, can you explain why that might be so? If not, please clarify?

Regards,
Buzz
 
  • #28
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A new (yet unformulated) theory might allow to calculate them in the future. That is the "today" aspect.
 
  • #29
Buzz Bloom
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A new (yet unformulated) theory might allow to calculate them in the future. That is the "today" aspect.
Hi mfb:

If that is the case, where did Michael Dine get his numbers? Were they just made up to make a point about how the Higgs mass seems to have a "magical" quality?

Regards,
Buzz
 
  • #30
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All those digits? Sure. We know the magnitude of the number, but not the precise value.
Googling the number directly leads to Michael's talk.
 
  • #31
Buzz Bloom
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All those digits? Sure. We know the magnitude of the number, but not the precise value.
Googling the number directly leads to Michael's talk
Hi mfb:

Thanks for the link and the Google hint. Both PDF files look both interesting and difficult. It will no doubt take me a while to digest whatever I can get out of them.

Regards,
Buzz
 
  • #32
haushofer
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Does anybody know a reference where a list is given with finetuning-examples in science in general? :)
 
  • #33
atyy
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The hierarchy problem is a fine-tuning problem within the Wilsonian framework that the QFTs we use are effective field theories. If they are not effective field theories, but correct and complete quantum field theories, then there is no hierarchy problem.

http://quantumfrontiers.com/2013/06/18/we-are-all-wilsonians-now/

"Wilson’s mastery of quantum field theory led him to another crucial insight in the 1970s which has profoundly influenced physics in the decades since — he denigrated elementary scalar fields as unnatural. I learned about this powerful idea from an inspiring 1979 paper not by Wilson, but by Lenny Susskind. That paper includes a telltale acknowledgment: “I would like to thank K. Wilson for explaining the reasons why scalar fields require unnatural adjustments of bare constants.”

Susskind, channeling Wilson, clearly explains a glaring flaw in the standard model of particle physics — ensuring that the Higgs boson mass is much lighter than the Planck (i.e., cutoff) scale requires an exquisitely careful tuning of the theory’s bare parameters. Susskind proposed to banish the Higgs boson in favor of Technicolor, a new strong interaction responsible for breaking the electroweak gauge symmetry, an idea I found compelling at the time. Technicolor fell into disfavor because it turned out to be hard to build fully realistic models, but Wilson’s complaint about elementary scalars continued to drive the quest for new physics beyond the standard model, and in particular bolstered the hope that low-energy supersymmetry (which eases the fine tuning problem) will be discovered at the Large Hadron Collider. Both dark energy (another fine tuning problem) and the absence so far of new physics beyond the HIggs boson at the LHC are prompting some soul searching about whether naturalness is really a reliable criterion for evaluating success in physical theories. Could Wilson have steered us wrong?"
 
  • #35
atyy
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A handwavy way to think about it is that if the theories we have are not the final theory, then fine tuning of our crummy wrong theory is indicating something about the high energy theory that is peeping through to the low energy. This is why fine tuning is often argued to indicate new physics.
 
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Both dark energy (another fine tuning problem) and the absence so far of new physics beyond the HIggs boson at the LHC are prompting some soul searching about whether naturalness is really a reliable criterion for evaluating success in physical theories. Could Wilson have steered us wrong?"
Is naturalness anything else than a pure aesthetic argument? Why should we expect nature to be elegant?
 
  • #37
Is naturalness anything else than a pure aesthetic argument?
No, it is not. We have examples of theories with fine tuning being superseded by theories without one.
Give me a case where the opposite happened, if you know one.
 
  • #38
atyy
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Well, we know that the Standard Model is not complete. It does not include gravity, its options to account for dark matter are at best questionable, it tells us nothing about dark energy or inflation, and even if we ignore gravity we would have the Landau pole as problem at even higher energies.
 
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  • #40
ohwilleke
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One example of concerns about fine tuning leading to fruitful scientific theories would be the anomalous magnetic dipole moment of the electron aka "g-2" (i.e. why is the magnetic dipole moment of the electron, "g", not exactly 2, but instead, some tiny but very exactly measured small amount greater than two).

It turns out that this slight discrepancy arises in QED from interactions with virtual photons, and that if your theory doesn't allow for virtual photons (and other odd assumptions of path integrals like inclusion of photon paths at slightly more and slight less than the speed of light "c" even though those paths are highly suppressed) that you get an answer different from the physical one. The notion would be that fine tuning if it is observed must exist because we are missing something of the same sort of mathematical character as the inclusion of virtual photons in our theory which is why our expectations are so off. The search for why g-2 was fine tuned produced theoretical progress. Now, I can't say that the intellectual history of that discovery really establishes that fine tuning was the insight that really made the difference in figuring out that virtual loops needed to be considered in QED (and the rest of the Standard Model as well), but it is a historical example that captures the notion.
 
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  • #41
Anomalous magnetic moment in QED is not an example of fine tuning.

An example of fine tuning would be a theory where two large free parameters interact (subtracted, divided, etc) to give a vastly smaller number.

Before QED, no theory at all explained electron's anomalous magnetic moment. (I'm not sure we even had a theory or any kind which was predicting the value of electron's magnetic moment, anomalous or not).
 
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  • #42
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Dirac's relativistic quantum mechanics "predicted" a value of exactly 2. If you modify the theory to get a free parameter, this parameter seems to be fine-tuned to nearly agree with Dirac's prediction.
 
  • #43
Vanadium 50
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I don't think the magnetic moment is a good example of fine tuning. As said above, it does not arise by a near cancellation. The "if you replace it with a free parameter" argument can be applied to absolutely every constant and every measurement, so it provides no real insight.
 
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  • #44
Haelfix
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A classic example would be the self energy of the electron in classical EM.
$$M_{observed}=M_{bare}+\frac{e^{2}}{4\pi \epsilon r_{e}}$$
Experiment sets a limit on the the size r so that the self energy was greater than 10 GeV and thus the first bare term must be chosen to cancel the second self energy term with a finetuning at about the O(.001) level
.511Mev=-9999.489+10000.000 Mev
Of course quantum mechanics comes to the rescue to 'explain' this finetuning, by adding the positron and the related quantum electrodynamic symmetry. This sort of picture is sort of the conceptual equivalent to explaining the Higgs mass by something like Technicolor.
 
  • #45
king vitamin
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I don't think the magnetic moment is a good example of fine tuning. As said above, it does not arise by a near cancellation. The "if you replace it with a free parameter" argument can be applied to absolutely every constant and every measurement, so it provides no real insight.
It actually is a good example of fine tuning, because Dirac left out a term for "simplicity." The so-called "Pauli term"
[tex]
\kappa [\gamma_{\mu},\gamma_{\nu}]F^{\mu \nu} \psi
[/tex]
can be added to the Dirac equation for arbitrary [itex]\kappa[/itex], which makes the magnetic moment an adjustable parameter while satisfying all necessary symmetries. It's actually Wilson who saves us here: this term is non-renormalizable, so it's irrelevant at low energies, giving us Dirac's universal result. It's not a near-cancellation scenario like the cosmological constant or Higgs mass, but Dirac did "fine-tune" [itex]\kappa[/itex] to zero.
 

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