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This explanation needs a couple of major caveats: The Standard Model does predict unification at ~250 GeV, but it does NOT predict unification at either 10^16

This explanation needs a couple of major caveats: The Standard Model does predict unification at ~250 GeV, but it does NOT predict unification at either 10^16 GeV or 10^19 GeV. Those predictions come from particular extensions of the Standard Model (grand unified theories or various quantum gravity models, respectively) which have been studied by particle theorists for their simplicity. Which is to say: Those unification scales come from speculative models, not from tested physical law. We do not know with any certainty what lies beyond the energy scales we've tested. You should take with a generous grain of salt any claims that we have physical models that work across an additional 14 orders of magnitude. Consider the range of phenomena that we've discovered in moving from the ~1 cm scale of a glass of water to the 10^-14 cm scale where quantum chromodynamics kicks in.

Iwan-Zotow 8y ago
Mmm... Particulars of unification depends on how you extend SM, but general idea about unification at 10^16 GeV based upon EM/Weak and QCD coupling constants energy dependence taken directly from SM. Basically, if you plot those coupling constants vs log(E), you'll get their merge at circa 10^16 GeV. That's baseline and it is pretty much pure SM, details are filled differently from different GU theories.
- auntienomen 8y ago
  Yes, but you need to assume there's a desert to get that result. Otherwise the renormalization flow is different.
  - Iwan-Zotow 8y ago
    Yes, I stand corrected, thanks
cft 8y ago
The Plank scale (Grand Unification scale) comes from the simple dimensional analysis, that combines the gravitational constant with the Plank constant (and the speed of light). It doesn't not really depend on the details of a grand unified theory. It was fist calculated to be 10^19GeV in 1899 by Max Plank, well before any quantum field theory (well before quantum mechanics for that matter). Because it combines the Plank constant with the Gravitational constant, we know that it corresponds to the energy scale at which quantum phenomena unify with the gravitational phenomena. Currently the only theory that describes this unification is String theory, but as the op correctly noticed, it's far from any possible experimental confirmation. I was at a seminar of Alexander Polyakov, one of the founders of string theory, who compared the string theory to the knowledge of Democritus about atoms. He said that even though the atomic theory of Democritus was essentially correct, it was about 2,000 years ahead of any possible experimental verification. In his opinion this is how long it will take us to verify our Grand unified theory experimentally.
- auntienomen 8y ago
  I've never quite believed this argument. It's worked in a lot of circumstances, I agree, but it requires the dimensionless constants to be of order 1. This is usually a reasonable assumption, but it's known to be false in gravity! The cosmological constant ought to be the leading order term in the EH action, but it's too small by ~100 orders of magnitude.
  - cft 8y ago
    The argument that dimensionless constants are of the order 1 works well for the theories that have been tested experimentally so far. We don't know the value of the cosmological constant. I am not even certain that it is not exactly zero. But it's not dimensionless, it has dimension length^-2, and is usually expressed in the units of Planck's length (currently thought to be 10^-122 I think). If it indeed turns out to be not zero, it is a new fundamental constant, much like the gravitational constant or the speed of light. I didn't not understand your statement about EH action: the cosmological term there has a dimensionless coefficient of the order 1. Are you talking about some effective action, arising from a string theory model?

Iwan-Zotow 8y ago

Mmm... Particulars of unification depends on how you extend SM, but general idea about unification at 10^16 GeV based upon EM/Weak and QCD coupling constants energy dependence taken directly from SM. Basically, if you plot those coupling constants vs log(E), you'll get their merge at circa 10^16 GeV. That's baseline and it is pretty much pure SM, details are filled differently from different GU theories.

auntienomen 8y ago
Yes, but you need to assume there's a desert to get that result. Otherwise the renormalization flow is different.
- Iwan-Zotow 8y ago
  Yes, I stand corrected, thanks

cft 8y ago

The Plank scale (Grand Unification scale) comes from the simple dimensional analysis, that combines the gravitational constant with the Plank constant (and the speed of light). It doesn't not really depend on the details of a grand unified theory. It was fist calculated to be 10^19GeV in 1899 by Max Plank, well before any quantum field theory (well before quantum mechanics for that matter). Because it combines the Plank constant with the Gravitational constant, we know that it corresponds to the energy scale at which quantum phenomena unify with the gravitational phenomena. Currently the only theory that describes this unification is String theory, but as the op correctly noticed, it's far from any possible experimental confirmation. I was at a seminar of Alexander Polyakov, one of the founders of string theory, who compared the string theory to the knowledge of Democritus about atoms. He said that even though the atomic theory of Democritus was essentially correct, it was about 2,000 years ahead of any possible experimental verification. In his opinion this is how long it will take us to verify our Grand unified theory experimentally.

auntienomen 8y ago
I've never quite believed this argument. It's worked in a lot of circumstances, I agree, but it requires the dimensionless constants to be of order 1. This is usually a reasonable assumption, but it's known to be false in gravity! The cosmological constant ought to be the leading order term in the EH action, but it's too small by ~100 orders of magnitude.
- cft 8y ago
  The argument that dimensionless constants are of the order 1 works well for the theories that have been tested experimentally so far. We don't know the value of the cosmological constant. I am not even certain that it is not exactly zero. But it's not dimensionless, it has dimension length^-2, and is usually expressed in the units of Planck's length (currently thought to be 10^-122 I think). If it indeed turns out to be not zero, it is a new fundamental constant, much like the gravitational constant or the speed of light. I didn't not understand your statement about EH action: the cosmological term there has a dimensionless coefficient of the order 1. Are you talking about some effective action, arising from a string theory model?