quark rest mass equation
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alistair - 17 Oct 2004 11:05 GMT for quarks of electric charge -1/3 rest mass = rest mass of down quark x n^2 where n = 1,3,5,7
for quarks of electric charge +2/3 rest mass = rest mass of down quark x n^2 x 2^N where N = -1,1,3,5
The values of n^2 represent a circular area of magnetic charges (rest mass is proportional to number of magnetic charges per quark) on the circumference of which a single electrical charge orbits an electrically neutral 3-charge nucleus.At n = 5 the density of magnetic charges becomes so great that the Pauli exclusion principle is overcome by gravity and the circular area can contain ten times more magnetic charges than the equation says it should at n=5.This is why the top quark and bottom quark have such large masses.
The values of n^2 in the Bohr equation for the energy levels of atomic hydrogen are also areas containing magnetic charges.The values of N probably have their origin in the quantisation of angular momentum of the orbiting charge or the quantisation of the magnetic moment.
alistair - 17 Oct 2004 23:26 GMT If n = radius of orbiting charge and the orbited charges have a net electric charge and doubling the charge of the orbited particles gives a doubling of radius then the following force laws arise:
when n=1 force = k1 x 1/r^3 n=3 force = k2 x 1/r^7 n=5 force = k3 x 1/r^11 n=7 force = k4 x 1/r^15
As the force decreases - on doubling the charge and the radius - the velocity and magnetic moment of the orbiting charge decreases and the rest mass increases.
This was deduced using rest mass = constant x electric charge/current x Area and noting, from experimental data for quark rest masses, that on doubling the quark charge magnitude:
for n =1 rest mass halves for n=3 rest mass doubles for n=5 rest mass increases eight times for n=7 rest mass increases 32 times*****
*****this is the rest mass increase at n=7 before the Pauli exclusion principle is overcome by the gravity? of magnetic charges inside the circle, which give an observed rest mass increase of 10 x 32 = 320 times.
alistair - 18 Oct 2004 19:07 GMT For the relativistic doppler shift:
change in wavelength = (c - Vs) To / (1 - Vs ^2 /c^2)^1/2
where Vs is emitter velocity, c is speed of light and To is time.
Suppose change in wavelength was equal to just 1 / (1 - Vs ^2 / c^2)^1/2
then (c - Vs) To = 1 c -Vs = 1 / To
c = Vs + 1 / To c = Vs + frequency of emitted wave
I now suggest that for M = Mo / (1 - v^2 /c^2) ^ 1/2
that this relation is actually
M = Mo x (c - Vs) To / (1 - Vs ^2 /c^2)^1/2
when (c - Vs) To = 1 and c = Vs + frequency of emitted wave [SI units are correct because a frequency = a velocity when wavelength is fixed at 1 metre: v = lambda x f becomes v = f)
In other words a mass emits a wave as it travels through space at constant velocity.The slower the mass travels , the greater the frequency of the emitted wave.A mass at rest would emit the highest frequency. Because of this inverse doppler relation for a rest mass,a rest mass moving through a sea of magnetic charges would keep moving at the same speed - Newton's first law!!
alistair - 18 Oct 2004 23:04 GMT We can form a neutron from each of the quark families: The quarks in a proton made of up and down quarks have a total rest mass (experimental) of 0.02 Gev. The quarks in a proton made of charm and strange quarks would have a mass of about 4 Gev.This means that the quarks of a proton made from charm and strange quarks are about 200 times (4/0.02) more massive than a standard proton's quarks.And this is about the ratio of the mass of a muon to an electron. The quarks in a "proton" made of four top quarks and one bottom quark (top,antitop,top,top,bottom)- a kind of pentaquark - would have a total rest mass of,say,4x, where x is the mass of one top quark (assuming bottom quark has a relatively small mass compared to top).The ratio of a tau's mass to that of an electron is about 3200:1.Comparing the "proton" containing 3 antitop quarks and one top quark to the standard proton of mass 0.02: 4x/0.02 = 3200 x = 16 Gev
using rest mass of a quark = n^2 x rest mass of down quark x 2^N and N = 5 and rest mass of down quark = 0.01 Gev : 49 x 0.01 x 2^5 = 16
It seems that the rest mass of the top quark should be at least ten times smaller than is experimentally observed (174 Gev).
This gives support to the idea that the top quark has a very large mass because the Pauli exclusion principle is being overcome.Otherwise its mass would be 16 Gev as the lepton mass ratios suggest.
A. Larcinese - 20 Oct 2004 16:38 GMT With regards to your last/second-to-last post, I think your logic is fine. I am not learned enough to critique it, but the question comes to my mind is where does all of this additional mass come from?
You express that theoretically the top quark should be isolated at 16 or 17 GeVs, but you also state that in the labs they have been unable to do so at any power below 174 GeV. Could this have anything to do with a change in energy level while in motion relative to the change in energy generated by, say, the bottom quark in motion? I mean, technically there should be some exponential difference in that relationship if you are examining a 'pentaquark.'
Maybe I didn't make any sense, but I am interested in this logic that you have brought to my attention. What do you think accounts for this additional experimental mass?
alistair - 21 Oct 2004 16:55 GMT > With regards to your last/second-to-last post, I think your logic is > fine. I am not learned enough to critique it, but the question comes [quoted text clipped - 11 lines] > you have brought to my attention. What do you think accounts for this > additional experimental mass? The additional mass comes from the space around the quark - it is in the form of mass-causing particles which are real (not virtual vacuum particles). In the top quark and bottom quark there is just more mass squeezed into a given area -raising the density of space.I think this density increase happens because spin 1/2 fermions team up into spin 1 bosons which can live in the same space at the same time.Thus the rest mass around a quark's electric charge could show superfluid behaviour (zero viscosity) and this would be reflected perhaps in the scattering of photons electrons etc. off the bottom and top quarks.
alistair - 20 Oct 2004 23:38 GMT To overcome the Pauli exclusion principle, mass-causing fermionic particles, inside a circlular area surrounding a nucleus of electric charges, must become highly ordered and form one big boson like a superfluid.Because a superfluid is non-viscous we would expect photons and electrons to scatter off a top quark and bottom quark differently to how they scatter off the other quarks. Why does the density of mass-causing fermions increase ten times for the bottom and top quarks? This must be the limit at which the superfluidity can survive.We know that the bottom quark has a rest mass of about 5 Gev and that current particle accelerators could take the mass up as much as 200 times, to about 1 Tev. But this doesn't happen, so the density increase of ten times seems to be the limit.We can speculate that particles in the space around the top and bottom quarks make superfluidity untenable above a certain density because the particles have a small enough wavelength to be absorbed by the mass-causing fermions, and to split the fermions up.
alistair - 21 Oct 2004 10:42 GMT The next quark in the series will be at n = 9 and it will have a rest mass of 2 x 9^2 x 2^7 x 10 x 0.02 Gev = 4150 Gev = 4.1 Tev (if it is part of a three-quark "proton")or 2.05 Tev (if it is part of a five quark "proton"). The quarks at n =3 have not been detected.This could be because they are sometimes mistaken for the strange quark and charm quark but there is also the possibility that at n= 3 an electrically neutral "neutron" forms but no "proton" (an uncharged "neutron" at n=9 would be undetected in accelerator experiments).The decay rate of the Zo is not affected by new quark families (the decay rate depends on the number of different types of neutrino). This could be because the non-existence of a "proton" at n=3 or n=9 would suggest neutrinos and antineutrinos do not exist for processes of the type: "neutron" -> "proton" + "electron" + antineutrino.
alistair - 21 Oct 2004 17:14 GMT CORRECTION: At n =11 the quark of charge +2/3 will have a rest mass of 6.2 Tev (five-quark) or 4.1 Tev (7-quark) or 12.4 Tev (3-quark).These values will come from an energy of 24.8 Gev - just out of the range of the next generation of accelerators!The quark, at n =11, of charge -1/3 would already have been detected if it could live in isolation from the quark of charge +2/3 because its rest mass is only about 24.2 Gev.
alistair - 21 Oct 2004 17:52 GMT Do the leptons overcome the exclusion principle and increase their rest mass beyond what is expected from the equation?If they do so by a factor of about ten then we can expect to see them at 2.2 Tev or 4.4 Tev or 13.6 Tev (using proportionality relationships e.g 2 x rest mass of quark (+2/3) + 1 x rest mass of quark(-1/3)from one quark family divided by 2 x rest mass of quark (+2/3)+ 1 x rest mass of quark(-1/3)from another quark family = rest mass of lepton from family 1/rest mass of lepton from family 2. This might explain why we haven't seen them so far.
alistair - 21 Oct 2004 14:38 GMT At n =11 we would expect a quark of charge + 2/3 with a rest mass of 12.4 Tev (5-quark) or 24.8 Tev (3 quark).A 7-quark would give a rest mass of about 37.2 Tev.
alistair - 18 Oct 2004 23:08 GMT CORRECTION to my previous post: Comparing the "proton" containing 3 antitop quarks and one top quark
SHOULD READ: Comparing the "proton" containing 3 top and one antitop quark..
alistair - 21 Oct 2004 23:30 GMT A neutrino made from an up quark and an anti-up quark would have a rest mass half as great as an antineutrino made from a down quark and an anti-down quark. The quarks of opposite electric charge would become so close together that the mass-causing particles which surround the charges would be squeezed to such an extent that many of the mass-causing particles would be shed.This is probably why the neutrino and antineutrino have such low masses compared to another particle that is electrically neutral overall - the neutron.In the neutron there are two electric charges of the same sign that repel one another and so do not get close enough to squeeze their mass-causing particles. Muon neutrinos and electron neutrinos and tau neutrinos are each distinguishable from one another because n will have a different integer value for the quark pairs in each neutrino - in other words the neutrinos all have different rest masses.Why does an electron have such a small mass compared to a proton? An electron is made from three quarks -2/3,-2/3 and +1/3 (the electron is an antiproton!!).There are two charges of -2/3 in the electron and two charges of +2/3 in the proton.The quarks of charge -2/3 in the electron may be getting pushed together by the repulsion of negative charges in the vacuum - this would decrease the colour force between them and the total rest mass of the electron.At the same time the charges of +2/3 in the proton may be getting pulled apart by the attraction of negative charges in the vacuum giving the proton a higher rest mass than it would otherwise have.Negative charges in the vacuum must be smaller in size than positive charges, enabling them to get closer to the quarks of the proton and electron. The decay rate of the Zo boson could be unaffected by new quark families if the new quarks make new z bosons - in other words an electrically neutral Zo could be made of three quarks +2/3,-1/3,-1/3.
alistair - 21 Oct 2004 23:48 GMT Neutrino oscillations could occur when mass-causing fermions associated with one electric charge ( a neutrino is made from two charges : +1/3 and -1/3) move over to the other electric charge and then back again.So n=5 for one charge can become n=3 while n=3 for the other charge can become n=5 and vice-versa. An electron neutrino with n=1 for both electric charges, would not be able to oscillate,because there is no excited state which can lose energy.
alistair - 22 Oct 2004 19:35 GMT The following relates to the magnetic moment associated with the rest mass of a quark, and makes the idea seem more plausible because the origin of relativistic spin can be linked to one charge orbiting another: If I have two negative electric charges, one of them with a far larger magnitude than the other, orbiting a positive charge,this system of charges could represent a rotating electric field vector and a rotating magnetic field vector( since magnetism is a form of electric energy).The ratio of the angular velocity, mvr, for one negative charge compared to the other could be a unitless quantity of magnitude 1/2 - the same magnitude as quantum relativistic spin for a fermion.By increasing the radius of the orbit of one negative charge I could change this ratio to 1/1 = 1 and create a spin 1 particle (a photon perhaps)or I could change the ratio to 2/1 (a graviton perhaps). In addition, by changing the magnitude of the charges I could change the ratio of electric field/magnetic field (which gives a speed).
alistair - 22 Oct 2004 21:43 GMT The general wavefunction for a free particle is:
Y (x,t) = A cos( kx - wt) + iA sin (kx - wt)
and the complex conjugate is:
Y*(x,t) = A cos( kx - wt) - iA sin (kx - wt)
These are multiplied together to give,along with a proportionality constant, the probability of finding a particle at a particular place at a particular time.It is not known why this should be so.Here is a suggestion:
If the wavefunction already represents a probability before it is squared, then multiplying it by another wavefunction - the complex conjugate - suggests that we are dealing with the probability of two events occurring simultaneously.This could be the probability of one charge being in a particular place at a particular time, and another charge being at that place at the same time.
alistair - 22 Oct 2004 22:50 GMT There are six electric charges in a photon in two groups of three - one group with a charge of -1 and one group with a charge of +1. When the polarization of a photon is changed,the groups flip over (like a drumstick with one group on each end) in the direction in which the photon is travelling.This is an acceleration of charges and results in the generation of another photon, with a speed greater than light.Why does the second photon have a speed greater than light? Because when particles are emitted they travel faster than the emitter.Charges in a photon moving through a sea of mass-causing particles have mass by virtue of colliding with the mass-causing particles (but no permanently attached particles causing rest mass),so by the law of conservation of momentum,when something with a big mass emits something with a smaller mass,the smaller mass moves faster than the slowly recoiling bigger mass.Accelerated fermions with rest mass can emit photons travelling at the speed of light and photons travelling greater than the speed of light.Photons moving faster than the speed of light are the particles that cause correlations in Einstein-Podolsky-Rosen paradoxes.
alistair - 01 Nov 2004 01:02 GMT At n = 5 the density of magnetic
> charges becomes so great that > the Pauli exclusion principle is overcome by gravity and the circular > area can contain ten times more magnetic charges than the equation > says it should at n=5.This is why the top quark and bottom quark have > such large masses. Another possibility is this: The Pauli exclusion principle is not overcome. The particles that cause mass exist with a wavelength given by the Planck length. The Planck length of 1.6 x 10^-35 metres should actually be about 9 x 10^-35 metres ( using [Gh/c^3]^1/2). So the speed of a photon with a wavelength close to the Planck length is 0.3 times smaller than we normally measure it.Therefore E=mc^2 becomes ten times smaller due to the c^2 term and so the mass must become ten times greater to compensate and keep the energy at the expected value. Can a photon have such a small wavelength and therefore such a colossal energy which corresponds to 10^114 Joules per cubic metre.Perhaps so, if the well-known vacuum calculation of quantum mechanics of 10^120 Joules/m^3 is anything to go by.But the force of gravity would also have to be inhibited or else space-time would be curved to an unimaginable degree- these photons could not be allowed to curve space-time and so cannot emit or absorb gravitons.
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