Electronics > Beginners
Isolation transformer and electrons
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Gregg:
The following is an attempt to provide the OP with another viewpoint toward understanding the question posted; it may not be 100% correct due to simplification. 

nForce,
It may help to let go of thinking of electrons actually flowing like so many basic explanations comparing electricity to water suggest.  It may be closer to reality to consider the electrons more like the balls of a Newton’s cradle where a force on one end of the set causes an almost equal reaction on the far end.  Electrons are not free to flow like water in a hose; a good conductor just has the electrons not as tightly attracted to the nucleus as an insulator.  From the electron’s perspective, it gets kicked from one nucleus to the next and thereby kicking another electron on down the line.  If the potential continues or reverses, it may be a different electron that gets kicked away, but none of them go very far of and by themselves.   
If a force is applied to an isolated wire to cause electrical potentials like shown in the graphic posted by Shock with neither end connected to make a circuit, the electrons don’t jump off the ends of the wire; the wire in this instance acts like a capacitor, the charge potential varies from end to end but there is no circuit.  The graphic probably would be closer to reality if it showed the blue dots being packed tighter at one end and farther apart at the other rather than disappearing from the ends.
To get back to the transformer: the secondary is an isolated wire with potential(s) being induced by the magnetic fields created by the primary.  Even if the primary has a connection somewhere in its circuit connected to ground, from the perspective of the electrons in the secondary they are like stars in the night sky; they may have potential energy but no measurable interaction.  To put the transformer question into a very basic scenario: take two batteries (your choice) and connect a terminal of one to the earth ground; try measuring any potential to ground from the second battery and because there is no circuit there is no potential from either terminal of the second battery to ground even though each battery has its own potential.
In other words potential is just potential, nothing happens unless there is a circuit.  Most electrical parameters need to be considered as circuits first and what is happening in the circuit all the way from the source back to the source.  The secondary of a transformer is considered to be an isolated source.  Potential is how far you need to keep your fingers away.  Amperage is the damage it can do if the circuit resistance or impedance is lower than needed to keep it under control. 
Old school AC welding machines are an example of transformers similar to the posted question.  These  devices were merely a transformer with a few taps on the primary that stepped the voltage (potential) down to a level less than lethal while stepping the amperage (ability to melt metal welding rods and add heat to the substrate) up with a core that easily saturated before drawing more current than the input could provide. One arbitrary output terminal was connected to the metal being welded, usually considered “earth”.  Several of these welders could be connected to the same potential steel via the building structure, ship hull etc. but the different welders wouldn’t swap electrons and interact because they were different circuits and the potential only existed for each individual circuit.  More modern welding machines are usually SMPS DC but the output still has to be isolated.
Then there are autotransformers.  Transformers with isolated secondaries can be used as autotransformers such that the secondary potential can be either added or subtracted from the primary; however caution needs to be exercised as to the connections.  Then there are autotransformers that have only one winding a configuration most Variacs utilize.  Look it up for further details.
Shock:

--- Quote from: nForce on December 11, 2018, 07:24:41 pm ---Yes, so the electrons are switching between earth and the wire, and between earth and the transformer. But my point was about the earth (planet).

--- End quote ---

The earth as a whole is considered neutral. It has the ability to conduct (and alternate) electricity in a completed circuit. Though not the most reliable conductor of electricity which is why ground/earth rods are sunk into favorable conditions depending on the soil type, moisture, depth.

There is actually a high voltage transmission line system called "Single Wire Earth Return" which just uses one conductor and the earth to complete the circuit over long distances.

As mentioned, the Neutral side of the mains is connected to Earth throughout the distribution network at various points (at least here it is). Because the mains is now Earth referenced (not floating) making a connection between Live and Earth to complete a circuit will cause electrons to move back and forth like I showed in the previous image.

How far do the individual electrons travel in a Live to Earth circuit? Not very far at all, they would alternate similar as with wires given the same propensity to conduct. Do they still alternate in the ground, earth, soil? Yes where it's conducting and not 100% insulating.

What path do they take to complete the circuit? The majority would be "shared paths" of least resistance to the nearest neutral line I would imagine. Perhaps there is also some capacitive effect as well, I'm not sure. But we know electrons alternate through conductors, even poor ones. They tell us this at school :).
SG-1:
nForce, I think you would find the electricity articles here very interesting:

http://amasci.com/elect/elefaq.html
wbeaty:

--- Quote from: Gregg on December 12, 2018, 02:52:49 am ---It may help to let go of thinking of electrons actually flowing like so many basic explanations comparing electricity to water suggest.  It may be closer to reality to consider the electrons more like the balls of a Newton’s cradle where a force on one end of the set causes an almost equal reaction on the far end. 

--- End quote ---

OK, but electrons also flow too.  An electric circuit is like a flywheel made of electrons, where if you push on one part, the whole thing turns as a unit.  (So, it's like a circular Newton's cradle!  Or like a loop of hose that's completely full of metal spheres, all lined up.  Jerk one sphere, and fast waves fly all around the loop, but also, all the spheres move ahead, like a turning wheel.)


--- Quote from: Gregg on December 12, 2018, 02:52:49 am ---Electrons are not free to flow like water in a hose; a good conductor just has the electrons not as tightly attracted to the nucleus as an insulator. 

--- End quote ---

Not true.  Electrons in metals are free to flow, very much like water in a hose.  They flow slowly as a group, while the waves (the energy) zoom fast.  The "flywheel" turns slowly, but the whole thing turns as one, so energy can flow almost instantly to every part of the "wheel."   

In a good conductor, the electrons have left their original atoms, and are orbiting around all through the metal.  In other words, they're jumping between atoms all the time, inside all metals everywhere.  This is more like a vibration than like a flow.   An "electric current" is when they jump slightly more in one direction.  They all move along in one direction, while also jumping/vibrating.  (Air and wind is similar, where individual air molecules are always wiggling, even when the "air" is still, with zero wind.  The energy in wires is like sound waves.  The electric current is like slow wind.) 

But inside an insulator, the electrons don't do this, but instead stay in their individual atoms.    If metals are full of "electron liquid," then insulators are choked with solid "electron ice."
wbeaty:

--- Quote from: nForce on December 02, 2018, 05:45:22 pm ---But how do electrons know on the other side of an isolation transformer that we don't have a current loop?

--- End quote ---

Simple:  in circiutry, electrons flow in loops only.   

But don't just accept this answer; instead ask why.

Why do electrons only flow in loops?   It's because if we wanted them to flow in a one-way direction, we'd need kilovolts, megavolts, to apply enough force.   Electrons are actively held inside of wires by their enormous attraction to the positive charges of atom nuclei.  The electrons of the metal can flow in a loop, but can't leave the metal circuit.

If electrons in a circuit are like a flywheel, then it's very easy to spin the flywheel, but very hard to pull chunks out of it.    That's why electrons stay inside the isolated circuit: an immense voltage-force would be needed if you wanted to push any of them out of the loop and into the Earth.   

Why?  It's because metals are half electrons, half protons, all in balance and strongly attracting.  If we make electrons flow in a circle, then they always stay near some protons.  But if we try to make them flow in one direction, then we're fighting against an immense-but-unnoticed attraction-force.  We're pulling them away from the enormous positive charge inside the copper.

---

Also, always remain aware that one wire doesn't "have a voltage."

Instead, each wire has many voltages at the same time (voltage WRT the ground is usually kilovolts, voltage WRT the sky is megavolts, WRT the sun or moon is even higher.)     In other words, voltage is like altitude, and your body doesn't "have altitude."  The altitude of a single point is meaningless.   Altitude is always measured between two points.  So, your body has many altitudes at the same time: altitude above the floor, altitude above the dirt, altitude above the average local landscape, altitude above sea-level, altitude above the center of the earth...  and voltage behaves like that.

The Earth isn't actually at zero volts.   Instead, we'll find several megavolts between Earth and sky (ionosphere.)    We could say that the sky is at +1.5MV and the Earth is at -1.5MV.   Or say that the sky is at zero volts and the Earth is at -3MV.  Both are true at the same time, because Earth's surface has many voltages all at the same time  ...because voltage is always measured between two points.   

The word "electric potential" means something like length-in-an-E-field.    And length only has meaning when it's measured between two points.

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