What causes the electric field in a Daniell Cell? I would like to know what causes the e-field in a Daniell cell.
From a chemistry point of view, I do understand that this is initiated by a redox reaction in which Gibbs free energy is decreased.  The elemental zinc anode (in aqueous zinc sulfate) becomes oxidized by losing two electrons.  The copper(II) ions (from the aqueous copper sulfate) become reduced by gaining two electrons, thus causing the elemental copper cathode to accumulate in size.  The circuit is completed by the addition of a salt bridge that helps balance out the charge of the electrolyte in each of the half cells as the reaction occurs.
However, I have difficulty understanding the process from an electronic point of view --specifically concerning the e-field.  I realize that the valence electrons of the elemental zinc (in the 4s orbital) want to be at a lower energy level, and they find that in the 3d10 and 4s1 orbitals of copper. This difference in electric potential gives the cell its voltage.
But how does this potential difference cause an e-field to arise?  I suppose it could begin with the spontaneous reaction of elemental zinc to Zn2+ (aq) and two electrons.  This would explain the negative pole of the field.  But what is drawing the electrons over to the other cell?  Is it the positive charge of the Cu2+ in the copper(II) sulfate electrolyte which surrounds the elemental copper cathode?  I don't suspect the flow could just be from electron diffusion.
There was a similar question to mine asked a few weeks ago, but the discussion there was a bit fruitless.
 A: I am not a native English speaker, so my English, far from perfect, sorry.
IMHO, the cause of EMF (electromotive force) of chemical battery is not clarified within the present human knowledge.
According to electrochemistry books, the EMF originates from Gibbs energy. Yes this must be true, but we notice that the thermodynamics (Gibbs energy) is a kind of result of some averaging procedures for extremely large number of particles close to Avogadro number ($\sim 6\times 10^{23}$), the present thermodynamics based discussion does not give the cause of EMF of chemical battery from some fundamental physics/chemistry processes composed of few particles.
Electric scalar potential ($\phi$) is a scalar potential and at the same time, it is important to note that  the electric scalar potential is a single valued quantity. There is some places of high potential values and some places of low potential values. A positive charge particle can gain some kinetic energy if the particle starts from high potential place, but continuous gain of kinetic energy is impossible only from electric scalar potentials.This resembles accelerator physics, only big scalar potential difference does not accelerate charged particle continuously; it needs external high frequency electric fields, not only from electric scalar potentials, of some specific configurations of equipment.
You wrote:

I suppose it could begin with the spontaneous reaction of elemental zinc to Zn2+ (aq) and two electrons.

I agree with what you wrote. I suppose that EMF of chemical battery comes from some decaying process of excited state. For describing EMF of chemical battery, I suspect that incorporating the vector potential ($\bf{A}$) together with the scalar potential ($\phi$) is essential.
But I am sorry I do not have well described theory at the moment.
