Discussion Overview
The discussion centers around the theoretical implications of an electron that instantaneously stops moving, particularly focusing on the resulting electromagnetic (EM) radiation and the waveform produced by the collapse of its magnetic field. Participants explore various models and equations, including the Lienard-Wiechert potentials, to understand the nature of the radiation emitted during this abrupt change in motion.
Discussion Character
- Exploratory
- Technical explanation
- Debate/contested
- Mathematical reasoning
Main Points Raised
- Some participants propose that the instantaneous stop of the electron leads to infinite acceleration, suggesting that the emitted EM wave would also have infinite frequency and amplitude.
- Others argue that the acceleration can be modeled as a delta distribution in time, questioning whether this simplification yields a finite result for the bremsstrahlung electromagnetic field.
- A few participants suggest that using the Lienard-Wiechert potentials is necessary to accurately describe the situation, while others believe a simpler approach comparing the fields of a moving and stationary charge suffices.
- There is a discussion about the presence of a radiation field that must exist due to the acceleration, with some expressing uncertainty about how to define it in the context of a delta-function singularity in acceleration.
- One participant notes that during the deceleration, energy is radiated, and the spectrum of this radiation may correspond to the Fourier analysis of the deceleration curve.
- Concerns are raised about the implications of infinities in the problem, with some questioning why such infinities in the solution would be surprising given the problem's setup.
- Participants discuss the behavior of the electric field after sudden deceleration, noting the presence of a "kink" in the field and its implications for radiation.
- There is a mention of the need for balanced EM radiation, suggesting that other accelerations may need to occur to achieve this balance.
- Some participants emphasize that the curl of the electric field is indicative of radiation, while others clarify that the appearance of circular field lines occurs only when the charge's electric field becomes negligible.
Areas of Agreement / Disagreement
The discussion remains unresolved, with multiple competing views on the nature of the radiation produced by the electron's instantaneous stop and the appropriate models to describe it. Participants express differing opinions on the necessity of complex equations versus simpler models, as well as the implications of infinities in the problem.
Contextual Notes
Participants acknowledge limitations in their assumptions, particularly regarding the treatment of infinite acceleration and the definition of fields on the future lightcone. There is also uncertainty about the mathematical treatment of singularities in acceleration and their physical implications.
)? The red line is the worldline of the charge, and at ##t' = 0##, its 4-velocity is parallel to the ##t'## axis, so the charge is instantaneously at rest at this time in ##S'##. Also, the vector ##R## joining this event to ##E## is null, and thus parallel to the yellow lightcones.