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In String Theory In A Nutshell by Elias Kiritsis,

Standard Model is unstable as we increase the energy (hierarchy problem of mass scales) and the theory loses predictivity as one starts moving far from current accelerator energies and closer to the Planck scale.

How is predictivity related to instability of higgs vacuum? Is this about QFT predictions done perturbatively, such that we cannot describe particles in middle of transition? Or something else?

In any case my question was confusing: it is just asking why we have predictivity problems when we have an unstable model.

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  • $\begingroup$ Theories are attempts to describe the reality within their limits of applicability. Any theory taken to the extreme eventually breaks down. Our universe doesn't live in the "false vacuum" and is not about to jump to the "true vacuum". These concepts are just abstractions made up by scientists in an attempt to describe what they don't know. To get to the Plank scale you need to convert 2000 galaxies of the Virgo cluster to the energy of one proton. No one is or will be moving "closer to the Plank scale" ever. No need to worry about it. It's not falsifiable, thus cannot be scientifically tested. $\endgroup$ – safesphere Jun 7 '18 at 23:53
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    $\begingroup$ @safesphere - false vacuum is a well-defined and legitimate concept, that may or may not apply to reality. If we are living in a false vacuum, presumably the time to decay is enormous, or the universe would already have transitioned. You can't test it directly, but you can still reason about whether or not it is implied by a given theory of physics. Hopefully the question will receive a technically informed answer. $\endgroup$ – Mitchell Porter Jun 8 '18 at 0:48
  • $\begingroup$ Oh and btw - inflationary models involve the transition out of a false vacuum - so in that case, the consequences of the alleged false vacuum are entirely testable. $\endgroup$ – Mitchell Porter Jun 8 '18 at 1:11
  • $\begingroup$ @MitchellPorter Thanks for jumping in to defend false vacuum! And also for bringing in the "inflationary models", another great example of an enormous success the modern science has become. $\endgroup$ – safesphere Jun 8 '18 at 3:53
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    $\begingroup$ Is Kiritsis talking about vacuum decay? It sounds like he's talking about taking the SM cutoff to higher energies. $\endgroup$ – Mitchell Porter Jun 17 '18 at 14:15
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When you have an unstable equilibrium , even in classical mechanics, these predictions can be random. Which way will this rock fall in a small earthquake?

unstable

The angle cannot be predicted, because it depends on many factors, from the direction of the quake to the localized strength of frictional forces holding the rock in the unstable equilibrium.

it is just asking why we have predictivity problems when we have an unstable model.

In the classical case, it is too many variables needed for a safe prediction.

Quantum mechanics is inherently probabilistic, and this means that factors influencing stability will enter with a probability . In the simple case of crossing an energy threshold, as with the Higgs mechanism, there are quantum mechanical probabilities of how this threshold is crossed, which , by construction of quantum mechanics can only predict probability distributions. In the case of a universe, as we live in one universe we just get one throw of the dice, and calculations may not give predictable angular or mass or energy distributions, quantum mechanically.

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  • $\begingroup$ Oh. So we can predict probability of any event using standard model - forget about deficiencies such as neutrino mass issues - but this is not meaningful because we can only have limited information about our world? So we cannot really predict (probability of) our universe fate, because other unaccounted factors can change the outcome significantly due to instability? If this is what the author meant, it looks like this concern is more of a beauty issue (we really want to have stable predictions) than a serious reality issue. $\endgroup$ – Lucia Guzheim Jun 17 '18 at 17:25
  • $\begingroup$ It is not a beauty issue,it is a fundamental reality issue as physicists understand it now, fundamental reality is quantum mechanical. In the classical case above if you had the information of all the inputs , theoretically you would be able to calculate the angle of fall. In the quantum mechanical case the specific observable will have a probability for a single measurement, only probability distributions are deterministic, measurements are one instance of a probability distribution. $\endgroup$ – anna v Jun 17 '18 at 18:24

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