I thought that Klein-Gordon's describes bosons, while Dirac's describes fermions.

11 minutes ago, StringJunky said:

Is that because ZPE is sub-quantum in value? Nothing in the sub-quantum domain can normally affect the quantum domain.

I'm not sure what you mean by "sub-quantum". The ground state is just the bottom rung of the energy ladder for every quantised system. For instance the electron in the 1s orbital of the H atom is in the ground state, with a residual kinetic and potential energy that cannot be reduced. The ground vibrational state of a diatomic molecule still has residual kinetic and potential energy that cannot be reduced. And so on.

There is sometimes a misconception that ZPE applies only to the vacuum. Vacuum ZPE is indeed a somewhat mysterious feature of quantum field theory. However ZPE itself is far more general and applies to everything quantised, in principle. (Though as it happens the ground rotational state of a diatomic molecule has no zero point energy, because of how the maths works out for quantised rotation).

A few notes about the overcolourfull but untenable Heat Death.

First and foremost it comes from the realms of classical thermodynamics, and preceded both Einstinian relativity and QM.

Second it assumes the universe may be regarded as an isolated system.

In this model there are two extremal 'drivers' to processes

The Principle of Maximum Entropy

The Principle of Minimum Energy.

Both are system properties and since one represents a min and the other a max they often compete or work in opposite directions.

But because they are independent it is also possible for one or the other to be inactive.

There are oscillatory systems for which the entropy remains constant and thus are driven by the energy principle and are independent of entropy.

Also since the models are of isolated systems energy remains constant.

It should also be noted that energy is not a substance but a thernmodynamic accounting of energy that passes into or out of the system.

Cosmologically this means that models that allow energy to leak or disappear or appear are not handled or included.

QM complicates this by allowing energy to be temporarily 'borrowed' from somewhere else so long as the energy of the final system is lower than before.

Cooper pairs and Higgs bosons provide good examples here.

Not quite accurate any solution to the Dirac equation is a solution of the Klein Gordon equation. It is treated as a foundation equation of QFT. Though today it's main use is bosons such as Higgs.(scalar) Once you involve spin (under Dirac use of spinors) then the Dirac equations are used.

For other readers

Edited January 12Jan 12 by Mordred

3 hours ago, exchemist said:

I'm not sure what you mean by "sub-quantum". The ground state is just the bottom rung of the energy ladder for every quantised system. For instance the electron in the 1s orbital of the H atom is in the ground state, with a residual kinetic and potential energy that cannot be reduced. The ground vibrational state of a diatomic molecule still has residual kinetic and potential energy that cannot be reduced. And so on.

There is sometimes a misconception that ZPE applies only to the vacuum. Vacuum ZPE is indeed a somewhat mysterious feature of quantum field theory. However ZPE itself is far more general and applies to everything quantised, in principle. (Though as it happens the ground rotational state of a diatomic molecule has no zero point energy, because of how the maths works out for quantised rotation).

I understood, maybe wrongly, that everything that can be measured has a quantum value, and stuff like individual virtual particles have energy values much lower, such that they cant be measured i.e. sub-quantum. I thought the ZPE was the lowest energy anything can happen, but it doesn't mean the point of no energy at all.

E2A

Edited January 12Jan 12 by StringJunky

57 minutes ago, StringJunky said:

I understood, maybe wrongly, that everything that can be measured has a quantum value, and stuff like individual virtual particles have energy values much lower, such that they cant be measured i.e. sub-quantum. I thought the ZPE was the lowest energy anything can happen, but it doesn't mean the point of no energy at all.

E2A

This is not about virtual particles though. It is standard undergraduate level chemical QM, involving bog-standard quantum systems, like vibrating chemical bonds or electronic states in atoms and molecules. As I said previously, although the idea of zero point energy often gets popularly associated with the energy of the vacuum, virtual particles popping in and out of existence and that weird QFT stuff, it is actually quite general to all kinds of mundane quantum system. Here's a simplified diagram of the energy well of a chemical bond between 2 atoms. The vibrational energy this system can have is restricted to certain quantised values, E₀ , E₁, E₂ etc. Notice that E₀ is not at the bottom of the well. That means there is still some kinetic energy left in the ground state - it is still vibrating a bit, in effect. You can't get that bit of energy out because it is already in the lowest allowed state. That is zero point energy, which the molecule will still have even at absolute zero.

(The animation about the photon is just to point out if it doesn't have the correct energy it can't excite the vibration to the next level up. This is not important for the present discussion, it was just on the first decent diagram I found to copy.)

5 minutes ago, exchemist said:

This is not about virtual particles though. It is standard undergraduate level chemical QM, involving bog-standard quantum systems, like vibrating chemical bonds or electronic states in atoms and molecules. As I said previously, although the idea of zero point energy often gets popularly associated with the energy of the vacuum, virtual particles popping in and out of existence and that weird QFT stuff, it is actually quite general to all kinds of mundane quantum system. Here's a simplified diagram of the energy well of a chemical bond between 2 atoms. The vibrational energy this system can have is restricted to certain quantised values, E₀ , E₁, E₂ etc. Notice that E₀ is not at the bottom of the well. That means there is still some kinetic energy left in the ground state - it is still vibrating a bit, in effect. You can't get that bit of energy out because it is already in the lowest allowed state. That is zero point energy, which the molecule will still have even at absolute zero.

(The animation about the photon is just to point out if it doesn't have the correct energy it can't excite the vibration to the next level up. This is not important for the present discussion, it was just on the first decent diagram I found to copy.)

Ok. Right. corrected.

8 hours ago, exchemist said:

While this diagram is up, I'd like to mention something interesting about zero-point energy. If one considers a chemical bond to hydrogen and the corresponding chemical bond to deuterium, then because the mass of a deuterium atom is greater than the mass of a hydrogen atom, the zero-point energy of the deuterium atom is lower than the zero-point energy of the hydrogen atom. That is, in the diagram above, E₀ for deuterium is lower than E₀ for hydrogen. But the classical energy curve for the different hydrogen isotopes is the same, so that the top of the curve which corresponds to bond breakage will be same for both isotopes. However, because the zero-point energy for deuterium is lower than the zero-point energy for hydrogen, it takes more energy to break a bond to deuterium than to break a bond to hydrogen. Thus, chemical reactions for which breaking the bond to hydrogen or deuterium is the rate-determining step will be slower for deuterium than for hydrogen. This makes "heavy water" (deuterium oxide) somewhat toxic to most lifeforms.

19 hours ago, exchemist said:

This is not about virtual particles though. It is standard undergraduate level chemical QM, involving bog-standard quantum systems, like vibrating chemical bonds or electronic states in atoms and molecules. As I said previously, although the idea of zero point energy often gets popularly associated with the energy of the vacuum, virtual particles popping in and out of existence and that weird QFT stuff, it is actually quite general to all kinds of mundane quantum system. Here's a simplified diagram of the energy well of a chemical bond between 2 atoms. The vibrational energy this system can have is restricted to certain quantised values, E₀ , E₁, E₂ etc. Notice that E₀ is not at the bottom of the well. That means there is still some kinetic energy left in the ground state - it is still vibrating a bit, in effect. You can't get that bit of energy out because it is already in the lowest allowed state. That is zero point energy, which the molecule will still have even at absolute zero.

(The animation about the photon is just to point out if it doesn't have the correct energy it can't excite the vibration to the next level up. This is not important for the present discussion, it was just on the first decent diagram I found to copy.)

Thanks @exchemist That diagram was really interesting & useful. +1