There are no particles, there are only fields (2012)
From the paper, at the top of page 10 of the PDF, at the end of section A:<p>&quot;Some authors conclude, incorrectly, that the countability of quanta implies a
particle interpretation of the quantized system. Discreteness is a necessary but
not sufficient condition for particles. Quanta are countable, but they are spatially
extended and certainly not particles. Eq. (3) implies that a single mode&#x27;s spatial
dependence is sinusoidal and fills all space, so that adding a monochromatic
quantum to a field uniformly increases the entire field&#x27;s energy (uniformly
distributed throughout all space!) by hf. This is nothing like adding a particle.
Quanta that are superpositions of different frequencies can be more spatially
bunched and in this sense more localized, but they are always of infinite extent. So
it&#x27;s hard to see how photons could be particles.&quot;<p>As mentioned above, you can take linear combinations of these different single particle states at different energies and come up with various energy&#x2F;location spreads. Doesn&#x27;t one such combination  have a spatial spread of zero? This would correspond to a single quanta at a single location in space.<p>My physics may be a bit rusty since I have been out for a while. Combining the different frequency components from the different field configurations is not _exactly_ the same as simple Fourier analysis, on the face of it. However, the individual contribution from a given field configuration (meaning a single frequency) is very small since there are so many different field configurations contributing (an infinite number). I believe the Fourier result does apply to the expectation value of the particles location here.<p>If I am thinking correctly this seems to be a very critical error in the paper. Someone correct me if I am wrong.<p>* * *<p>EDIT: I believe I said something incorrectly. Where I said &quot;I believe the Fourier result does apply to the expectation value of the particle&#x27;s location here.&quot; I meant to make a stronger statement, &quot;I believe the Fourier result does apply to the effective value of the particles wave function in this location in this case.&quot; (The expectation value being zero would not bean the field does not extend to that location.)