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The Plank scale (Grand Unification scale) comes from the simple dimensional analysis, that combines the gravitational constant with the Plank constant (and the

by 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?

by cft 8y ago

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?