Let’s get started on the math In quantum mechanics, a group of particles known as fermions (for example, electrons, protons and neutrons) obey the Pauli exclusion principle. This states that two fermions cannot occupy the same (one-particle) quantum state. The states are labeled by a set of quantum numbers. In a system containing many fermions (like electrons in a metal), each fermion will have a different set of quantum numbers. To determine the lowest energy a system of fermions can have, we first group the states into sets with equal energy, and order these sets by increasing energy. Starting with an empty system, we then add particles one at a time, consecutively filling up the unoccupied quantum states with the lowest energy. When all the particles have been put in, the Fermi energy is the energy of the highest occupied state. What this means is that even if we have extracted all possible energy from a metal by cooling it to near absolute zero temperature (0 kelvin), the electrons in the metal are still moving around. The fastest ones are moving at a velocity corresponding to a kinetic energy equal to the Fermi energy. This is the Fermi velocity. The Fermi energy is one of the important concepts of condensed matter physics. It is used, for example, to describe metals, insulators, and semiconductors. It is a very important quantity in the physics of superconductors, in the physics of quantum liquids like low temperature helium (both normal and superfluid 3He), and it is quite important to nuclear physics and to understand the stability of white dwarf stars against gravitational collapse.
The Fermi energy goes as the 2/3 power of the number of protons or neutrons. This energy is very high for a “zillion” neutrons. The Fermi temperature is the temperature at which the typical electron has a thermal energy equal to the Fermi energy, meaning that the typical neutron is reasonably likely to be excited above the Fermi level. see http://scienceworld.wolfram.com/physics/FermiTemperature.html For more info see http://www.youtube.com/watch?v=knVD1AfiozA On Wed, Mar 27, 2013 at 2:37 AM, Axil Axil <[email protected]> wrote: > *You can pack a "zillion" protons into a tiny space.* > > No, protons need to pair with neutrons to get close; that is how they form > nuclei. > > Hydrogen will form metal hybrid chemically. But then they are not mobile > anymore. > > All the above does not apply to neutrons. Neutrons cannot be packed by the > zillions into a tiny space. > > > > > On Wed, Mar 27, 2013 at 1:20 AM, David Roberson <[email protected]>wrote: > >> If you are dealing with hydrogen in an NAE, is it necessary to consider >> it as being the size of a hydrogen atom in free space or can you treat it >> as a far smaller proton? You can pack a "zillion" protons into a tiny >> space. >> >> I would expect hydrogen to be different than any other element when >> contained within a metal matrix. It only has one electron in orbit and it >> just seems likely that this single electron could be "lost" within the >> metal atoms surrounding the nucleus. It is not hard to imagine that the >> proton charge would be neutralized or shielded by the activity of many >> electrons from the adjacent metal atoms. If this happens, then why not >> expect more protons to be able to occupy a region closer than normal to >> each other when so confined and shielded. I guess the trick would be >> associated with the interaction of the metal electrons. >> >> Dave >> >> >> -----Original Message----- >> From: Axil Axil <[email protected]> >> To: vortex-l <[email protected]> >> Sent: Tue, Mar 26, 2013 10:08 pm >> Subject: Re: [Vo]: Low Energy Neutrons and Local Temperature >> >> There is a basic falsity in the LENR+ particle argument be it neutron >> or protons. >> You cannot pack the volume of particles needed to produce the energy >> demonstrated in the LENR+ systems into those small NAE cavities at the >> volumes needed because of the Pauli Exclusion Principle. >> It is like packing 10 lbs. of crap into a one oz. bag. >> LENR cannot be based on particles entering into a nucleus. >> For those who want to play with numbers, run a calculation that >> determines the maximum density of protons or neutron that are allowed by >> the PEP into the NAE and then determine the number of NAE that are required >> to produce 10 kilowatts per second. >> You will find that the numbers just don’t add up. >> >> Cheers: Axil >> >> On Tue, Mar 26, 2013 at 9:26 PM, David Roberson <[email protected]>wrote: >> >>> I agree with the first order of business you state. >>> >>> The second one could depend upon how quickly a reaction takes place >>> since the vibration is a mechanical response to the temperature of the >>> metal. The kinetic energy of a nucleus should be something that can be >>> calculated and I would suspect that its rate of movement is determined by >>> the forcing function which is a relatively slow process. I believe that a >>> quantum mechanical action occurs so fast that the slow motion vibration of >>> the nucleus is not important. I compare this to taking a snap shot of the >>> instantaneous position and velocity of the nucleus. >>> >>> My visualization is that the quantum mechanical formula defining the >>> behavior takes a quick look at the nucleus and nearby neutron and acts when >>> they are in the best proper condition relative to each other. Of course if >>> this process is slow, then my concept would not be valid and something in >>> line with your second order would be appropriate. Has the time frame for >>> quantum mechanical activities of this nature been determined? Another >>> question: has the time frame for any quantum mechanical coupling been >>> measured? That is the first question. I have read that entangled >>> particles react at speeds in excess of light or considered instantaneous at >>> great distances. Would this behavior be considered typical? >>> >>> Dave >>> >>> >>> -----Original Message----- >>> From: James Bowery <[email protected]> >>> To: vortex-l <[email protected]> >>> Sent: Tue, Mar 26, 2013 7:55 pm >>> Subject: Re: [Vo]: Low Energy Neutrons and Local Temperature >>> >>> >>> >>> On Tue, Mar 26, 2013 at 5:29 PM, David Roberson <[email protected]>wrote: >>> >>>> I have to question how one is able to have stationary neutrons. I >>>> assume that you refer to neutrons that are stationary relative to our frame >>>> of observation. >>> >>> >>> Relative to the statistical position of the mass of which they are a >>> part. >>> >>> >>>> One question that I keep asking is how quickly does a quantum >>>> mechanical effect take place? >>>> >>> >>> The first order of business is: What is the formula for the nuclear >>> strong force vs distance between a nickel nucleus and a neutron? >>> >>> The second order of business is: When a nickel nucleus is vibrating in >>> solid nickel, what is its spatial probability density function? >>> >> >> >
