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We know that an electromagnetic wave is produced by periodically changing electric field (by an accelerating charged particle). We know that the electric field of a point charge varies inversely with square of distance from the charge. Therefore the amplitude of the electromagnetic wave such as light must go on decreasing and practically vanish on covering a finite distance. But , as we know, it doesn't happen and we see the light waves coming from stars very far away. Then what's happening there? Or am I wrong? Please explain.

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  • $\begingroup$ In photon terms, sure for a single photon, maybe only a frog would see it, but obviously a star emits a large amount of photons. If no interaction occurs along the way, the wave/photon will keep going. van.physics.illinois.edu/qa/listing.php?id=84900 $\endgroup$
    – user167453
    Oct 9, 2017 at 13:18
  • $\begingroup$ But why the amplitude doesn't decrease with time? $\endgroup$ Oct 9, 2017 at 13:21
  • $\begingroup$ Why should it? This is why we have the wave/photon duality, some things are easier to calculate or think about in momentum conservation terms. (Like a photon...tiny bullet), The energy density drops as the sphere expands, but the total flux remains constant. If the amplitude diminished, the total flux would also, but it doesn't. $\endgroup$
    – user167453
    Oct 9, 2017 at 13:37
  • $\begingroup$ So it can't be explained by wave nature? $\endgroup$ Oct 9, 2017 at 16:35
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    $\begingroup$ It's (much) easier to use photons, at least for me it is. In the same way, explaining diffraction or interference using photons will give you a headache. But my argument is possibly wrong, if you take into account the fact that photons lose energy emerging from a large mass, such a neutron star. I need to look that up, (or rather, you do, sorry :). The model of an EM wave that the pictures show is not to be taken too far, it's the start of using math seriously, and forgetting about mental pictures, which are confusing. In other words, it's real physics...+1 $\endgroup$
    – user167453
    Oct 9, 2017 at 16:57

2 Answers 2

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The reason we can see stars from far away is because those stars are unimaginably bright up close. Stars do vary in brightness depending on the star type and distance, and there are certainly stars whose light we cannot see. Read about apparent magnitude and absolute magnitude.

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We know that an electromagnetic wave is produced by periodically changing electric field (by an accelerating charged particle).

Photons are emitted by accelerated charges. The energy of the photons depends on the strength of the acceleration, e.g. small accelerations of electrons lead to infrared radiation and braking radiation Bremsstrahlung to X-rays or gamma radiation. mostly The electric field you mentioned is needed, for example, in an antenna rod for the forward and backward acceleration of electrons. As a result, the electrons emit polarized photons and one is able to identify a common oscillating electric and a common oscillating magnetic field from all these photons. Such radiation has the properties of an electromagnetic wave.

The light or electromagnetic radiation from the sun is mostly the result of the chaotic acceleration of charges and the flow of the emitted photons does not have the properties of a wave.

... the amplitude of the electromagnetic wave such as light must go on decreasing and practically vanish on covering a finite distance. But , as we know, it doesn't happen and we see the light waves coming from stars very far away.

The amplitude of EM radiation has to do with the intensity of the light. The intensity of a monochromatic radiation - all photons of the same wavelength - has to do with the number of photons through a given area in a given time.

The potential decrease of intensity is only correct if there is an indistinguishable number of photons. But there are stars so far away that their observation is only possible by collecting single photons. Thus the potential decrease is right only other a long time of observation and the energy packages which arrive the earth are discrete one.

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