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mysearch
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Hi,
I am trying to get a better understanding of what aspects of an electron-positron collision can be physically observed as opposed to mathematically inferred. In part, my confusion is based on a number of different sources, e.g. see links below, which seem to adopt different approaches to describing the same thing, i.e.
Graphically, we appear to have an electron [e-] and positron [e+] colliding and annihilating at [t1,x], which results in a photon being created, which then ‘transmutes’ back into an electron and positron at [t2,x]. As such, the photon seems to exists for [t2-t1] but travels no distance.
We appears to have a positron [e+] scattering at a point [x1,t], while the electron scatters at a point [x2,t]. Based on a left-to-right timescale, it seems to suggest zero time, but a separation [x2-x1].
Thanks
I am trying to get a better understanding of what aspects of an electron-positron collision can be physically observed as opposed to mathematically inferred. In part, my confusion is based on a number of different sources, e.g. see links below, which seem to adopt different approaches to describing the same thing, i.e.
- Scattering or annihilation: Collision cross-section
- Feynman diagrams: probability amplitude and rules
- Dirac notation: transition amplitudes, creation/destruction operators
- Are (p1+p2)=(p3+p4) representative of initial and final observable states, such that the conservation of momentum and charge have to be maintained?
- Does the probability of any final observable outcome depend on the energy of the initial state, e.g. does the probability of collision also have to account for the collision cross-section, if defined as a function of energy?
- Is it is true say that annihilation and scattering reflect only the main possibilities of many other potential permutations; although other permutations may have diminishing probability amplitudes associated with each additional vertex coupling, which are not observable?
Graphically, we appear to have an electron [e-] and positron [e+] colliding and annihilating at [t1,x], which results in a photon being created, which then ‘transmutes’ back into an electron and positron at [t2,x]. As such, the photon seems to exists for [t2-t1] but travels no distance.
- In the specific case of electron-positron annihilation, can the photon continue to exist as it doesn’t seem to violate any obvious conservation laws and would appear to have one less coupling factor? – see question regarding whether this is a virtual photon below.
- What quantum process describes a photon of energy changing back to an electron-positron pair, i.e. it doesn’t appear to result in a lower energy state?
We appears to have a positron [e+] scattering at a point [x1,t], while the electron scatters at a point [x2,t]. Based on a left-to-right timescale, it seems to suggest zero time, but a separation [x2-x1].
- Is this sort of physical interpretation simply inappropriate, if so, what are these diagrams actually trying to convey by alluding to time-distance axes?
- Does the photon in either diagram have any observable existence, i.e. does it have to be described as a virtual photon and does it have to comply with all conservation laws?
- Is there any physical evidence that the virtual photon is ‘really’ created or is this simply an inference of the maths?
- In terms of the scattering process, does the physical separation [x2-x1] essentially correspond to the dynamic energy cross section of the collision?
- Does scattering require more initial state energy than annihilation?
Thanks