To quote Wikipedia,
*The Pauli Exclusion Principle is the quantum mechanical principle that no two identical fermions (particles with half-integer spin) may occupy the same quantum state simultaneously. A more rigorous statement is that the total wave function for two identical fermions is anti-symmetric with respect to exchange of the particles.* Does this mean that two identical electrons in identical states have wave functions that cancel each other out? If this is the case, why do we have the Pauli Exclusion Principle? It seems that getting two electrons too close should annihilate both of them (or cancel them out, or however you want to say it), but instead we have the Pauli Exclusion Principle, where somehow the electrons remain separate. Why? Feynman in multiple writings suggested thinking about "exchanging particles" in terms of exchanging them as they move through time. That is, they can either move in two parallel paths as they move forward, or they can cross paths (exchange roles). The antisymmetric cancellation applies to the latter, but not to the former. Now if you think that through, it means that the parallel path remains strong even as the crossover paths cancel out, resulting in the two particles avoiding each other and maintaining unique paths (wave functions). The net result is not full cancellation, but cancellation at the edges, where the particles would cross. (Feynman goes into a lot more detail about rotations, but frankly that part can get you sidetracked a bit; it's the "anti-crossover" part that counts in terms of actual outcomes.) Another consequence of identical fermions cancelling each other out is that packing more fermions into a tight space forces their space-filling wavelengths to become shorter also. Since in quantum mechanics the spatial wavelength of a particle defines its momentum, particles that are squeezed in this fashion also get very, very hot. A neutron star is a good example. Pauli exclusion -- the "constriction of space because crossover cancels but parallel does not" -- allows neutrons to pack together very densely indeed and get very hot. There are limits, however. When gravity gets too monumental, even Pauli exclusion is unable to keep up with the pace, and the entire star collapses, very quickly. Thus is born a stellar-sized black hole, or at least this is one example of how one can form. Cheers: Axil On Tue, Mar 26, 2013 at 2:21 PM, Axil Axil <[email protected]> wrote: > Electrons and protons can affect neutrons because they are all fermions. > Neutrons are used as probes to see what protons are doing. > > Asymmetry energy (also called Pauli Energy). An energy associated with the > Pauli exclusion principle. If it wasn't for the Coulomb energy, the most > stable form of nuclear matter would have the same number of neutrons as > protons, since unequal numbers of neutrons and protons imply filling higher > energy levels for one type of particle, while leaving lower energy levels > vacant for the other type. > > Pairing energy. An energy which is a correction term that arises from the > tendency of proton pairs and neutron pairs to occur. An even number of > particles is more stable than an odd number. > > This Paring energy is why atoms with double magic numbers are the most > stable nuclei. > > Fission occurs in very heavy atoms with mismatched proton neutron pairing: > U235, Pu239. > > Neutrons repel each other. This fact will increase the average energy of a > large pack of neutrons that concentrate near the NAE. > > This is why I think that producing an ultra-low energy neutron in a NAE is > not possible. > > The W&L theory is simplistic in this regard. > > Cheers: Axil > > On Tue, Mar 26, 2013 at 12:15 PM, David Roberson <[email protected]>wrote: > >> I was considering the behavior of ultra low momentum neutrons within a >> metallic structure and a question arose. Why would the local temperature >> of the nickel atoms not completely dominate the activity of the low >> momentum neutrons? >> >> As we all are aware, temperature of operation for LENR devices is >> typically around 1000 K or more which is far beyond that associated with >> the ULM neutrons of the W&L theory. This elevated temperature of the >> metal atoms reflects rapid movement of the nuclei as they bound back and >> forth within their electron cloud inside metal matrix. One would expect >> the relative motion of the two bodies (nucleus and neutron) involved in the >> reaction to be the key determining factor in the net interaction and not >> the motion of just one. For this reason, I find it perplexing to discuss >> just the neutron energy when we consider these interactions. >> >> The other possibility to consider is that higher energy neutrons might >> have an advantage in many situations as they pass through the metal volume. >> Each metal nuclei must undergo many accelerations as it trades momentum >> and energy with its brother atoms. This would appear as a continuous range >> of velocities with time. An elevated temperature for these atoms would >> suggest that they change direction more times per second as it rises. >> During the brief period of time that the neutrons are nearby, perhaps a >> match in velocity occurs which allows the neutron to be exposed to the >> large capture cross section associated with the near zero relative velocity. >> >> For a reaction such as that hypothesized above to be important the >> interaction time frame must be very short. The temperature caused >> movements are mechanical in nature and should be slow as compared to >> quantum mechanical reactions such as the absorption of a neutron by a >> nearby nucleus. Does information exist which can confirm that the quantum >> mechanical effects are of short duration in such a case? Also, how far can >> the quantum mechanical interaction reach away from the nucleus if the >> relative velocity of the pair is actually zero at a finite point in time? >> >> Dave >> > >
