© Matt Strassler [March 19, 2014]
Particle physicists describe the amoung of energy in an object or process in terms of eV (electron-volts) or GeV (1,000,000,000 electron-volts).
The mass M of a proton (which is about the same as the mass of a hydrogen atom) is about 1 GeV/c², where c is the universal speed-limit [the “speed of light”]; thus it’s mass-energy Mc² is about 1 GeV. [Actually the number is about 0.938 GeV/c².]
The Large Hadron Collider [LHC] makes protons collide with energy of a few TeV (and 1 TeV = 1000 GeV).
Roughly speaking, the energy required to make the lightest possible black hole is called the [“reduced”] Planck energy, a million million million GeV (i.e., 1,000,000,000,000,000,000 GeV.) For particle collisions at this energy, in contrast to collisions at lower energy, gravity is as important a force in determining how the collision plays out as are any of the other forces.
The Planck mass is the Planck energy divided by c², the Planck time is Planck’s constant h divided by the Planck energy, and the Planck length is the Planck time times c. Quantum gravity — where space and time themselves become subject to quantum jitter (“quantum fluctuations“) — becomes important when an amount of energy comparable to the Planck energy is compressed into a ball with a radius of the Planck length.
The Energy Scale of “Dark `Energy’ “
The amount of “dark `energy’ ” or “cosmological `constant’ ” Λ (which is neither energy nor necessarily constant in time — it is really an amount of energy density [energy per unit volume] along with negative pressure of exactly the right amount) is measured as an energy per unit volume, i.e., energy/length3.
By multiplying by (hc)3, where h is Planck’s constant and c is the universal speed limit (“the speed of light”), physicists form a quantity which is an energy to the fourth power. Taking the square root of the square root of that quantity [i.e., the “fourth root”] gives them an energy. So the “energy scale” of the “dark `energy’ ” is
- [(hc)3 Λ]1/4
Important: remember this is the overall scale associated with the dark energy, NOT the amount of dark energy per unit volume. If I increase the energy scale by a factor of 10, I increase the amount of dark energy per unit volume by a factor or 104 = 10,000 !
The maximum energy scale that dark energy could possibly have during inflation is the Planck scale. The dark energy in the universe today has a scale about a million million million million million times smaller than that! [i.e. 1030 = 1,000,000,000,000,000,000,000,000,000,000 times smaller!]