# An equilibrium equation

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#### jeffreyH

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##### An equilibrium equation
« on: 07/06/2016 22:01:28 »
Where x = 1 to n, A1 to An are system components an equilibrium equation can be defined in the following way.

$$A_e\,=\,\frac{A_1+A_2+...A_n}{n}\,=\,A_x$$
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#### chiralSPO

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##### Re: An equilibrium equation
« Reply #1 on: 07/06/2016 23:26:38 »
I'm not sure what you mean by equilibrium. This looks to me like a formula to calculate an average value. What do you means by system components?

I am probably biased because my understanding of equilibrium is mostly as a concept in chemistry, which this equation does not fit...

#### jeffreyH

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##### Re: An equilibrium equation
« Reply #2 on: 08/06/2016 08:11:40 »
This is simply an abstract equation. The components are each An. You are right in that it is an average but the point being each Ax equals Ae so that all components are of equal value. The average Ae is then an equilibrium value as well as an average. The components could represent mass, velocity, energy, temperature or the number of apples in a fruit pickers basket. I want to explore the introduction of fluctuations. It may or may not be interesting.
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#### jeffreyH

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##### Re: An equilibrium equation
« Reply #3 on: 09/06/2016 22:33:40 »
We could start by setting all Ax equal to 1/2 hf so that we then have the zero point energy of the electromagnetic field at all points in the set.
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#### jeffreyH

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##### Re: An equilibrium equation
« Reply #4 on: 10/06/2016 20:33:30 »
In fact this should really be

$$\frac{h\nu}{2}+\frac{h\nu}{e^{{h\nu}/{kT}}-1}$$
« Last Edit: 10/06/2016 20:36:40 by jeffreyH »
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#### jeffreyH

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##### Re: An equilibrium equation
« Reply #5 on: 10/06/2016 21:09:48 »
Now we can consider a universe where the only particles are electrons and each has exactly the same kinetic energy and the density of the electron gas is uniform everywhere. How can useful work be done in such a universe? Can the vacuum create the conditions necessary? Can spontaneous fluctuations be enough? Surely they would have to be unevenly distributed and not simply random? Otherwise wouldn't they just even out to an average everywhere? Is it differences in the masses of particles that matter? Is this what causes the uneven distribution? Does this imply a role for the Higgs field in initiating the big bang?
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#### jeffreyH

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##### Re: An equilibrium equation
« Reply #6 on: 11/06/2016 11:47:51 »
Gluons and quarks add mass via kinetic and binding energies but again if we had a universe with only protons with identical kinetic energy then nothing would really change. If we simply had one dense object consisting of quarks and gluons then we do not have the required particles or momenta to initiate a change. If the Higgs promoted an incerease in local densities this could help.

If we go back to the electron only universe then density variations would increase local gravitation which would in turn deflect the direction of the path of particles. This would then causes changes in momentum that were not conserved overall. So that if the force of gravity had not separated out first after the big bang then there may never have been a universe as we know it.
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#### jeffreyH

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##### Re: An equilibrium equation
« Reply #7 on: 15/06/2016 22:35:50 »
If we set P = einπ then P assumes a value of either -1 or +1 based on n being odd or even. As discussed in the thread on the Euler Identity this can represent handedness or polarity or both. Then we can formulate the equation Pe = {P1+P2+...+Pn}/n. Then the absolute value of |Pe| is the probability of polarity with the sign of the result defining the direction. In a situation where polarity is 50/50 then the result is a probability of zero. In situations where an equilibrium exists these types of random fluctuations may well have a dramatic effect if the balance is shifted heavily in one direction. Especially with respect to the handedness of particles where charge disparity could well come into play.
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#### jeffreyH

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##### Re: An equilibrium equation
« Reply #8 on: 15/06/2016 23:45:20 »
For anyone wanting to understand what on earth I am talking about might find it informative to read the following page.

http://www.quantumdiaries.org/2011/06/19/helicity-chirality-mass-and-the-higgs/
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#### jeffreyH

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##### Re: An equilibrium equation
« Reply #9 on: 17/06/2016 08:23:48 »
With changes in velocity come changes in the dimensions of space and time. If this effects does not apply to the background Higgs field then its density will undergo an apparent change with change of velocity. So that the rate at which particle mixing occurs is a function of velocity. Hence time dilation with increaing velocity. At this moment in time I wouldn't even know how to begin to formulate the mathematics of this hypothesis.
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