There is a contradiction between the natural width of the energy transition, which is determined by the lifetime at the corresponding energy level and the spectral line width of the radiation line, which is determined by the duration of the wave train.
For example: For the Mössbauer transition, whose lifetime is of the order of 2 years, while the interaction time at the receiving end is about 10^(-10) sec.
Mathematically, this interaction is expressed by the Feynman diagram of the electron - electron interaction, which integrates over the internal photon line, which, together with the delta functions of the vertex parts, limits the photon spectrum.
By the way, the same paradox applies to any other type of collision.
So, is exist (really) the electromagnetic field?
@Mark L.Gurari
It exists . Mathematics is to simply the understanding .
BR, it's not resolution of the paradox. Try to consider it in gist. As a forming the coherent states from short wave trains (on transmitting ends), and expansion of the coherent states on the stationary ones on receiving ends. May be these ideas can resolve the paradox. By the way, it can have a practical sense.
sir,
considering human brain to be nothing more than a computing machine that perform a lot of algorithms using unseemingly complex methods like analogy,feelings,intuitions,mathematics,learned experiences through experimentation etc. which are better not to be considered as philosophical methods and mindly processes ..............because of the fact " physical information".
real world information has to embodied in some physical system.......and is carried by light ,electricity or any other medium......
but once we would know the answer of the question.....
"how human brain can create abstract informations like ideal circle,ideal resistor and inductor etc...with the researches in information theory.....
specifically AEP,information thermodynamics And quantum information theory ...."
you would know your answer....
you can,,,for now ,,,,assume that,,,,everything whether physical or philosophical
is not abstract or real,,,,,,it's information.............
information is energy...
and energy is matter...
and matter is information...
MORE SPECIFICALLY "PHYSICAL INFORMATION"....
HOPE YOU WUD GET MY IDEAS.............
Dear PT
I disagree with you, but it's interesting point of view. So, no difference between physical reality and any abstract images - they all are information. No difference between a fake and the truth.
As an analogy of the question I can mention the 18 century theory of phlogiston - theory of heat or temperature propagation. The equations of heat (temperature) conductivity precisely described these processes, but nothing explained about their physical nature, before Joule and Boltzmann. The same way it is with Maxwell's equations.
Concept of electric field had been introduced by Gauss as a convenient way for expression of Coulomb's Law. Maxwell's equations precisely describe the processes of EM fields propagation but nothing explain about their physics nature.
sir,
with this kind of thinking ......"whether abstract concepts like fields refer to reality or not?" ...........i had been for most of the time..........like the most other people
wondering,"how mathematics and other abstractness r unreasonably effective"..
but what i realize is ,,,universe has certain definite properties ,no matter how you describe it ;it would in reality would remain the same,,irrespective of your description or perception.our technologies r just the fusion of few of them,known through experiments.
now my point is,,it doesn't matter whether electromagnetic field is real or mathematical abstraction ,,,
only that,there is a distribution of force for a test charge in space(which we can call an experiment) ,which we can describe by considering some vectors arranged in a way ....which we would call
"a vector field" or field lines for a charge or magnet.
you see we humans ,are limited by infrastructure and abilities of our brains;
so we can just build up our knowledge in our mind itself to design ,build and perform better experiments and nothing else we can do. we even do not know whether we r real or not.
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