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Protons repel protons, and electrons repel electrons supposedly by the momentum of emitted photons. So how do photons attract, for example, protons to electrons?
I believe I already answered this exact question a few weeks ago. I hate to disagree with Dr Muller, but in this case, in my opinion, the uncertainty of the proton’s position is not an answer, sorry Dr Muller. Uncertainty is a black box that ‘in my opinion,’ is used to explain off too many phenomenon that no one wants to give thought to.The Heisenberg Uncertainty Principle gives us the minimum constraint on a wave function’s position, not how BIG it can be. That is, The HUP is given byThe 4 pi in the denominator is the result of usually seeing Planck’s constant written in ‘reduced form,’ represented by h-bar. There are a few things to know here. First, Planck’s constant, by definition is indivisible, as it represents the smallest slice of energy possible in normal space-time. You therefore do not divide the indivisible h by 4 pi (I see this in doctoral level lectures, and it is the second most stupid thing I have ever seen; I’ll save the first most stupid for some other post). Second: pi is not even a rational number. Dividing the indivisible h by an irrational number that has no discrete value in itself is - absurd. Third, h-bar was written by Dirac because he recognized that since h only deals with wave functions, it must have a value fundamentally related to a wave cycle, which is 2-pi. This is why h-bar is h/2pi. Four: 4-pi represents two full wave cycles, the minimum number to describe a wave function as being in one of two possible positions. Thus, the 4-pi in the denominator purely represents the smallest amount of energy possible in normal space-time, spread over the minimum requirement for a wave cycle to be considered as being in more than one position.Five, sigma-x represents the distribution of possible locations of the wave function, sigma-p represents the distribution of velocities (and hence momenta) that got the wave function to those superpositions distributed over sigma-x. The equation ONLY STATES THAT THIS DISTRIBUTION MUST BE GREATER THAN THE MINIMUM SLICE OF ENERGY POSSIBLE IN NORMAL SPACE-TIME SPREAD OVER TWO WAVE CYCLES. THERE IS NO PROVISION FOR ALLOWING A PROTON TO INFLATE TO 10,000 TIMES ITS SIZE.SIX: I don’t know how many times I have had to repeat this, the HUP only refers to wave functions, not ‘particles.’ Once a wave function is detected, it is no longer a wave function, and the HUP is non-sequitur. The proton is not a wave function. According to the Standard Model (We’ll go with that for a moment) it is a composite of we don’t know what. It has taken ‘particle physicists’ half a century of smashing them with a giant hammer to figure out that they don’t know what it is made of by looking at the broken pieces. The pieces, so far, weigh 100 times more than the thing before they smashed it with a hammer. So, they invoke the HUP to (Uncertainty Principle) claim the excess mass comes from the Uncertainty Principle, with a certainty out to about 15 decimal places… The spin of these invoked contents account for 2% of the proton’s spin. (Referred to a the ‘spin catastrophe.’)Now, we have someone claiming this composite region inflates to 10,000 to a million times it size, consistently, to explain the position of the electron; as absurd as the answer is, doesn’t answer the question, ‘why do electromagnetic things attract?’If we use the spin angular momentum of the electron, and the proton or positron, whatever, and think of it as a boomerang, I use this analogy:In Feynman terms, imagine a man in one boat and a woman in another. They have no means of propelling their boats, but happen they are supplied with boomerangs. How can they get their boats together? By throwing a boomerang away from the man, the woman would experience a reaction force from the boomerang towards the man. The boomerang could then circle round and approach the man from behind, and on reaching him, could exert a force on him towards the woman.In this diagram, the woman throws the boomerang (virtual photon, spin 1), which has spin +1/2, producing force Fv, the momentum of the throw also producing force F1. The man catches the boomerang, producing force F2. In this instance, there is an ‘attractive’ force, likened to the man being an electron and the woman being a positron. But why does the ‘force’ obey the inverse square law?We can generalize the electromagnetic force in terms of any constant, represented by k, two charges, and distance:And again, Heisenberg’s uncertainty principle, purely in terms of delta-E:In this case, delta-t is purely mediated by r^2, the distance.That is as close to a Feynman explanation as one would get, perhaps.A virtual photon is not massless, but is off mass shell, that is, possess mass. This is where we come to chirality and helicity. Helicity is a spinning massive particle, we’ll say counter clockwise. Because it has mass, it cannot go as fast as light, meaning thqat you can get in front of it and see it apparently spinning the opposite way, clockwise. Chirality refers to massless photons, which you cannot get in front of because you cannot exceed v=c to do so, so they only ‘spin’ in two polarization states, clockwise or counterclockwise.Because a virtual photon has mass, it is helic, not chiral, giving it 3 polarization states. The 3rd polarization state is observed by passing the slow moving virtual photon and watching it ‘spin’ apparently in the opposite direction.Its mass and 3rd polarization state account for the boomerang effect shown above. Note that in order for the boomerang argument to work, the arrow goes around and points the opposite way, as seen coming at you as opposed to the helic spin of when it was launched.I hope this over simplified explanation helps. As for the proton’s uncertain position as a wave function, you will note that the delta-t in the HUP equation above simply will not allow for a proton to extend as far as a valence electron. So, that is just wrong.In fact, as I look at this a few months later, I can tell you exactly how wrong it is. A virtual photon mediating a magnetic field can live exactly 3 wavelengths. That is a certainty; exactly three. This is referred to as a Near Field Effect. Radio antennas, for instance, produce a powerful magnetic field that does not drop off with the square of the distance. For instance, if your transmission is at 300 megahertz, then your wavelength is 1 meter. The magnetic field produced by the Near Field Photons is exactly uniform throughout a 3 meter domain from the antenna; then comes to a dead stop, like a brick wall.A proton has a diameter of 1 femtometer, 10^-15 meters. The first electron orbital is out at 10^-10 meters. That means Muller’s Uncertainty Principle explanation has to extend the proton diameter 5 orders of magnitude greater than it normal cross section. In order for that to happen, the delta-t has to decrease by 5 orders of magnitude, spontaneously. In this amount of time, if you do the algebra, you find that the massive virtual photon actually has to exceed the speed of light in order for there to be any prayer of that answer being in any way possible.The proton has a diameter of 10E-15 meters, a hydrogen atoms valence electron is 10E-10 meters, meaning the uncertainty principle would have to allow the photon to inflate to 10,000 times its diameter, for just the lowest ground state of hydrogen. When you take the virtual photon mass and spin angular momentum, that is impossible. The HUP will work no magic here. The argument via HUP might hold some, but very little, water if the virtual photon had no mass, but this is not the case.The uncertainty of the photon’s position is also equally outward as it is inward, that is, of what little uncertainty there is in a virtual photon’s position (because of its mass, reduces the uncertainty, such as the uncertainty of a battle ship’s position) it is not emitted unidirectionally away from the proton from the electron. This exacting vector must be exactly 180 degrees opposite the proton’s position to be true. Since it is the electron’s position that is uniquely uncertain, this requires the electron to have 1) a certain position and 2) foreknowledge of its vector toward the proton from where it will be when it emits the virtual photon, exactly 180 degrees away from the proton’s position and 3) a reason for emitting only photons 180 degrees away from the proton.Thinking inside the box and staying there because it feels safe when people agree with you is why we are living in the Holocene Extinction. If we thought for ourselves, the world would change; would already have done so.I’d like to thank Dmitry Popov for catching my typos, I was writing proton when I was thinking photon.I answered a similar question at When we say that spin-1/2 fermions must go through 720 degrees to equal the 360 degrees required by spin-1 bosons, what exactly is being measured?I found this in an old text I wrote some years ago:It is not possible to ignore the relativistic effect of velocity of recession. 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