In his 1905 paper on emission and transformation of light, Einstein says, quanta are localized points in space. Did he mean that there are space gaps between quant in space and there is a time lag between the emission of quanta by the source?
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2$\begingroup$ Are you asking what photons are, or are you asking what Einstein thought they were? Note that photons require quantum field theory to fully describe them and that did not exist in 1905. For what photons are see this old answer of mine. $\endgroup$– John RennieCommented Jun 10 at 16:05
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$\begingroup$ The latter. What Einstein thought they were. From the wording of his 1905 paper it appears that he is saying that quanta/photons are indeed energy localized in certain points in space as opposed to being a continuous spacial function. $\endgroup$– LearnerCommented Jun 10 at 17:32
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$\begingroup$ Yes. He supported quanta. But in the em field quanta can overlap if there is enough of them. $\endgroup$– PhysicsDaveCommented Jun 10 at 21:41
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$\begingroup$ Physics and chemistry teachers and textbooks often say that electromagnetic energy is emitted discontinuously. But this leads to an impression in the mind of the learner that they are talking about spatial and temporal discontinuities. The wording of this paper from 1905 may be lending support to such a description. But I believe the word discontinuous is used more in a mathematical sense (discontinuous variable) than about the physical appearance or aspects of the emission or propagation of electro magnetic energy. But I could be totally wrong. $\endgroup$– LearnerCommented Jun 11 at 4:05
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If the photon is a freely propagating photon that has some momentum uncertainty, then it is indeed somewhat localized in real space (think of Heisenberg's uncertainty principle). Have a look at Gaussian wave packets for example.
You could also consider photons in some finite square box. Then if you would know the photon's momentum precisely, then it is maximally delocalized as its spatial wave function would extend throughout the whole box.
The reason why photons (and other quantum mechanical particles) are often thought of as being trapped in this box, is because their wave functions are then normalizable. As the size of the box were to go to infinity, then the wave function's amplitude would go to zero.
