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New Theories / Re: What is a photon ?
« on: 13/07/2020 17:04:58 »What physical experiment could be performed to demonstrate that particles are Riemann spheres?
Orientate an Electron such that it's axis (pointing from the point 0 to the point ∞) points in the "up" direction. Then it will not emit a photon in the "down" direction.
Also: particles seen from their northern hemispheres will look different as seen from their southern hemispheres.
Wrong. The direction of photon emission when an electron drops from excited state to ground state is random with respect to the electron's spin state, which is the only way of talking about an electron’s axis. The direction of photon emission is determined in a probabilistic manner by multiple factors including the prevailing magnetic field, of which the nearby nucleus is a major component, and preserving energy momentum conservation over event accumulation.
In addition, electron spin is a matter of angular momentum, in effect spinning clockwise or counterclockwise. It is not a matter of which way a pole is pointing. Electrons with opposing spin values are not ‘upside down’ with respect to each other. They are spinning in opposite directions. To drive that home, the only formulation for spin states that matches measurements is the formalism of angular momentum. For that to be the case, the clockwise or counterclockwise spin must be with respect to a fixed axis. That is, your hypothetical 0 and ∞ axis must always point in the same direction, negating your argument.
Now explain what differences there may be between the two hemispheres of an electron. Oceans, continents, ice caps? Your insistence that the metrics of a Riemann sphere are those of an ordinary sphere and not the varying metrics of a complex plane mapping argues against any difference.
Also, since the question Kryptid asked is about a physical experiment, how would you determine which photon came from which electron and how to determine the axis orientation of the individual electrons?
So what does “communicated between fields (plural)” mean?
Think of the Feynman diagram of an electron scattering off an electron. What happens is: one electron must tell the electromagnetic field that it wants to scatter of another electron following a path λ, and it must specify its momentum. This must be read off the electron field interacting with spacetime. Then the electron must specify it's expected momentum change. Then the electromagnetic field must compute the virtual photon direction and wavelength and the positions for invoking the creation and annihilation operators, then the virtual photon must communicate the change of direction of momentum to the other electron. Only then can the virtual photon be emitted.
Wow, where do I start?
To begin with, you are using two different meanings of the term ‘field’. Originally you used the term with respect to a particle being a ‘vibration’ in a field, which would imply field theory, a field being a mathematical apparatus for determining the properties at any given point. Now you are using the term to refer to the electromagnetic fields of electrons. Same word, different meanings.
The term λ (lambda) does not appear in Feynman diagrams. That term is used in General Relativity for the Cosmological Constant. What does appear in Feynman diagrams is the term γ (gamma), which is the symbol for the photon. In Feynman diagrams, it is the label applied to the wavy line that indicates the exchange of virtual photons. This diagram show electron-electron scattering.
In Quantum ElectroDynamics (QED) for which Feynman diagrams were first invented, the path is not first chosen. In theory, any path at all might be used, each having its own probability amplitude. This is a wavelike entity. As such, probability amplitudes constructively and destructively interfere with each other. The effective path is the one with the greatest surviving probability amplitude, and usually the only survivor with a resulting probability (square modulus of amplitude) of unity. Paths happen. They are not chosen. There are experiments demonstrating multiple paths being used such as the famous double-slit example.
There are people here who are familiar with deep Physics and deep Mathematics. You cannot make it up as you go along and not get called out.
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